'~SUBSURFACE ELECTROMAGNETIC TARGET CHARACTERIZATIONAND IDENTIFICATION

Luen Charm Chan

CQ The Ohio state University

0 ~ElectroScience LaboratoryDopttorn~t of Electrical engIneednaI Coluntbus, Ohio 43212

Techr~ical Report 784722-3 4 -p

Contract DAAK7O-77-C-0114 IiAU , I1Jujne 1979

C.) A PPROVED) F0R pw iLI RELE:AS1-EwsI) RTHWiT oN UN~IA ITED.

U.S. ArmyMobiityDepartment of the Army

U.S.ArmyMobiityEquipment Research and Development CommnandFort Belvoir, Virginia 22060

S79 8--0 9 032

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I1. SUPPLEMENTARY NOTES

The material contained in this report is also used as a dissertation submitted1. to the Department of Electrical Engineering, The Ohio State University aspartial fulfillment for the degree Doctor of Philosophy.

19. KEY WOROS (Confinriu on reverse side Of necoffiery and Identify by block number)

Subsuwrface radar Prony's methodImpulse source Predictor-correlator

N Crossed-dipole antenna Digital processorI \ Mine-like target Microcomputer

Complex natural resonances _______

~ 12 - s I RACT (*.,,JInua. mi re.'erxp oli. II ti.v.s.ity end Identif~y hv block nu.b,n' )v

A method for subsurfdLu radar targiet chdracterization and identification isde-scribed. This method characterizes subsurface radar targets by their complexnatural resonances which are extracted directly from their backscattered time -t domain waveforms, The differencen eqtiatinn rnpffirients; arnciated with the com-piex resooidiices dre Lhten ustd in the predictor-correlator for tdryet identitica-tion. Both the characterization and identification processes are extensivelytested with real radar measurements and found to yield practical target identi-fication performance. The target identification p~rocess is simple and involves4

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"only simple algebraic operations. Based on the identification process, a?'first-generation 4&A microcomputer identification radar system is implementedfor target identification in real time. This radar system is found to yieldpractical identification performance.

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ACKNOWLEDGMENTS

The author wishes to express his appreciation to his graudateadviser Professor D.L. Moffatt, and former graudate adviser ProfessorL. Peters, Jr. for their guidance duri,;q the course c-f this work andfor their thorough reading of the original draft of the dissertation.A debt of gratitude is owed to the other member of the reading com-mittee, Professor A.A. Ksienski, for his critical review of the text.Special thanks are also due the author's colleagues, Mr. C.W. Davis,

III for his consultations and helpful suggestions; Mr. R. Gaglianellofor his help in the implementation of the microcomputer target identi-tication system. Above all, the author wants to express his deepestappreciations to his wife Shu Mee whose seemingly endless patience,understanding and help made this experience of disseration writingmuch easier.

The material contained in this report is also used as a disserta-tion submitted to the Department of Electrical Engineering, The OhioState University as partial fulfillment for the degree Doctor ofPhilosophy.

...

TABLE OF CONTENTS

Chapter Page

I INTRODUCTION ............ .................... 1

A. Research Goals 1B. Related Research in Subsurface Target

Characterization and Identification 2C. Structure of This Report 4

II MEASURED AND PROCESSED WAVEFORMS FROM THE

SUBSURFACE TARGETS .......... ................. 5

At. Objectives 5

B. Subsurface Electromagnetic VideoPulse Radar System 5

C. The Subsurface Targets 11D. Raw Measured Waveforms 14E. Processed Waveforms 15

III CHARACTERIZATION OF SUBSURFACE TARGETS BYTHEIR COMPLEX NATURAL RESONANCES ...... .......... 26

A. Objectives 26B. Complex Natural Resonances 26C. Derivation of Prony's Method 28D. Clutter and/or Noise in Prony's Method 32E. Applying Prony's Method to the Processed

Measured Backscattered Waveforms 33F. The Extracted Resonances of the

Subsurface Targets 36

IV THE PREDICTOR-CORRELATOR iDENTIFIER ........... 47

A. Objectives 47B. The Predictor 49C. The Correlator 50SD. The Predictor-Correlator aS d Filter 51E. The Identification Algorithm 62F. Performance of the Predictor-Correlator

Identifier 64

iv

i." •,

Chapter Page

V EFFECTS OF RADAR BANDWIDTH ON THE CHARACTER-IZATION AND IDENTIFICATION OF SUBSURFACETARGETS . . . . . . . . . . . . . . . . . . . .. . . 77

A. Introduction 77B. Processed Waveforms Obtained With

the Long-Cable System 77C. Extracted Resonances 77D. Target Identification Performance 81

VI EFFECTS OF TARGET DEPTH AND SIZE ON THECHARACTERIZATION AND IDENTIFICATION OFSUBSURFACE TARGETS .......... .............. 83

A. Introduction 83B. Processed Waveforms 83C. The Extracted Resonances 89D. Target Identification 94

VII ELECTROMAGNETIC MINE DETECTION AND IDENTIFICATION. 95

A. Objectives 95B. A Second Model of the Mine-Like Target 95C. False Target Measurements in the

Rough Road 98D. Mine Identification 98E. A Small Antenna for Improved Performance

in Mine Identification 102

VIII A MICROCOMPUTER SYSTEM FOR REAL-TIME ON-LOCATIONSUBSURFACE TARGET IDENTIFICATION ..... .......... 114

A. Objectives 114B. Structure of the Microcomputer Target

Identification System 114C. Implementation of the Microcomputer System

for Subsurface Target Identification 116D. Calibration of the Microcomputer Target

Identification System i27E. Real-Time Identification Performance of the

Microcomputer Target Identification System 129F. Possible Future Improvements on the

Microcomputer System 130

v

Chapter Page

IX A METHOD FOR REAL-TIME ON-LOCATION TUNING OFTHE IDENTIFICATION RADAR TO THE GROUNDCONDITION ......... ...................... 133

A. Objectives 133B. The Use of Backscattered Waveforms

From Thin Wires to Estimate TheGround Parameter 133

C. Automatic Tuning of the IdentificationRadar to the Ground Condition 135

X SUMMARY, CONCLUSIONS AND RECOMMENDATIONS .... ...... 139

A. Summary 139B. Conclusions 142C. Recommendations for Future Work 142

REFERENCES 143

APPENDIX

A DERIVATION OF PRONY'S METHOD FOR TRANSIENTWAVEFORMS WITH MULTIPLE-ORDER POLES ............. 150

B DERIVATION OF PRONY'S METHOD AND ITS VARIATIONS. . 156

C 185

D 189

E 190

F 206

G 209

H 210

1 214

A. The APU and Its InterfaceWith the SDK-80 214

B. The Microprogram for theMicrocomputer System 218

C. Details in Obtaining the SecondSet of Identification Data Withthe Microcomputer System 255

J 258

vi

- ~trt------.. -. -

"LIST OF TABLES

-Table Page

1 Average Lxtracted Resonances of the 'iinc-Like

T rarget in Different Ground Conditions ..... ....... 45

2 Avurage Lxtracted Resonances of the nrassCylinder in Difft-rent Ground Coiiditions .......... 46

3 Average Extracted Rusonances of the AluminumSph•re, Copper Sheet and the Wood Board ...... ... 46

4 Summary of Single-Look IdentificationPerformance of the Short-Cable System.PI=1O0% For All Cases ........ ..... ....... 71

5 Determining tihe Detection Parameters ForIdLntification of the 1iiie-Like TargetIn A Wet Ground Condition. RID=30 cm ....... ... 72

6 Average Extracted RLSonanCUS of thu Mine-LikeTarget in a Wet Ground Condition ......... .... 73

7 determining the Identification Thresholds forthe 11irne-Liku Target in a Wet GroundConuitioni. RID=30 cm .... ............... .... 74

8 Summary of Sing le1-Look Iduntification Performinceof the Short-Cable SysLem Based on AdditionalPreprocessing and :lultiple-Threshold Algori thni.PI= 100'.% For All Cases ........ ............... 75

Average Extracted Rusonances of the Mine-LikeTarget and thu Brass Cylinder in the Long-Cable System ....... ................... .t

10 Average Exlracted Resonances of the AluminumSphere, Copper Sheet and the Wood Bnard in0te Long-Cable System.. .......... ..... ..... 80

vii

Tab le Page

11 Summary of Single-Look Identification Performanceof the Long-Cable System. Additional CableLengthm200m. PI=lO0% For All Cases ........... .... 81

12 Summary of Single-Look Identification Performancefor the brass Cylinders of rlifferent SizesPi=1 O0% For All Cases ..... ................ ... 94

13 Single-Lock Identification Statistics: The Firstand Second Model of the Mine-Like Target vs theFalse Targets in the Rough Road-Bed. PI-1 00%... 101

14 Single-Look Identification Performance forIdentification of the Mine-Like Target Withthe Small-Antenna System. PI=100% ........... .... 112

I', Computation Time Required by the .ýPtl to, Performthe Floating-Point Arithmetic Operations ...... 123

16 'lumber oil Arithmetic Operations Required toEvaluate ,(T) of Equation (56) at a Valueof T=T 0 i . . . . . . . . . . . . . . . . . . . . . . 124

17 Extracted Resonances of the Mine-Like Targetat Various Antenna Locations in Icy Ground. ..... 186

18 Avurage Extrdcted Resonances of the ,i~ne-LikeTarget Waveforms Obtained Using the 12mLong1 Antenna .......... .................... 189

19 Values of the Correlation Coefficient for theIdentification of the Mine-Like Target inWet Ground .......... ..................... 200

20 ValuL.s of the Correlation Coefficient for theIdentification of the Mine-Like Target inDry Ground ...... ..................... .... 201

21 Values of t6e Correlation Coefficients for thcIdentification of the Mine-Like Target and theBrass Cylinder in Dry Ground ................ ... 202

22 lOeternmining the Detection dnd IdentificationThresholds for the Identification of theMine-Like Target. R10=30 cm .... ............ ... 203

viii

Ta ' 1) pa(2 A

23 Determining the Detection and IdentificationThresholds for the Identification of theBrass Cylinder. RID=30 cm ................ ..... 204

24 Determining tie Detection and IdentificationThresholds for the Identification of theAluminum Sphere. RID = 37 cm .............. .... 205

25 Average Extracted Resonance of the Different-Size Different-Depth Cylinders ...... ........... 207

26 Average Extracted Resonances of the 5cm DeepDifferent-Length Thin Wires .... ............ .... 208

27 Average Extracted Resonances of the Mine-LikeTarget ........ ....................... ..... 209

28 Determining the Detection and the IdentificationThresholds for the Identification of the Mine-Like Target with the Small-Antenna System.RID=45 cm ....... ..................... ..... 211

29 FIR Filter Coefficients Used in the Preprocessorof the Microcomputer Identification System ..... ... 212

30 Determining the Identification Thresholds for theIdentification of the Mine-Like Target in theSmall-Antenna System Based on FIR Filtering . . . . 213

31 APU Command Suimmary ........... ....... ....... 217

32 Table of Conwuands Implemented in the Micro-co,,mpu ter Sys tem ............. .................. 218

33 Difference Equation Coefficients Used in theMicrocomputer System for Identification ofthe Mine-Like Target ..... ................ .... 256

34 Identification Thresholds for the Identificationof the Mine-Like Target With the MicrocomputerSystem ........ ....................... ..... 257

35 Extracted Resonances from the 3 0cw Long, 5cmDeep Thin Wire.Antenna Location = Centerof Wire ........... ..... ...................... 258

ix

Table Page

36 Extracted Resonances from the On-SurfaceThin Wire (30cm Long). Antenna Location-Center of Wire ..... .................. ..... 259

r

i.

I .. . . .... .. . . . . .;. . . . .. .. o _ • v . . • • • -• -. . .. -"... .. .

II

IILIST OF FIGURES

Figure Page

1 The subsurface pulse radar and its blockdiagram .......... ..... ...................... 6

2 Characteristics of the impulse source intime and frequency domain .................. .... 7

3 Typical raw waveform received by the pulseradar system ..... ................... .i..... 9

4 Physical characteristics of the subsurfacetargets ....... ...................... ..... 12

5 Measurement locations and antenna orientation. 13..3

6 Typical average raw waveforms from the sub-surface targets ............ ................. 16

7 Processed waveforms from the mine-like targetat different antenna locations in wet ground . . . 18

8 FFT of the processed waveforms from the mine-like target ..... ................... ....... 19

9 Processed wavefonns from the other subsurface

targets ....... ...................... ..... 20

10 FFT of the processed waveforms from the othersubsurface targets ..... ................ ..... 21

11 Signal-to-clutter ratio estimates of the wave-forms from the subsurface targets at differentantenna locations .......... ................. 24

12 Processed waveforms from the brass cylinder indry and icy ground ........... ................ 25

13 Location of the extracted resonances of themine-like target at different antennalocations in icy ground ........ .............. 37

xi

L ..-

14 Locations of the average extracted resonances ofthe mine-like target in different groundconditions ....... ....... ..................... 41

15 A typical backscattered waveform received bythu 12m long antenna from the mine-liketarget ....... ....................... ..... 42

16 Avwrage extractPH resonances from the mine-like

target waveforms received by the 12m longantenna ...... ... ...................... ..... 43

17 Locations of the extracted resonances of thebrass cylinder in different ground conditions . . . 44

18 Transfer function of the preprocessor filter usedin the 0.6m long antenna system for targetidentification ...... ................... ..... 48

19 Bounds of the iean-square error L ........... .... 54

20 The decision-making process for the multiple-threshold identification alqorithm ........... ... 63

21 Typical I(T) curves for the identification ofthe mine-like target in wet ground ..... ......... 65

22 Typical :(T) curves for the identifiL.ation of

the mine-like target in dry ground ........... .... 67

23 Typical ,(r) curves for the identificatio:i ofthe brass cylinder in dry ground ............ .... 68

24 Wi ;trriut.i(Jrl of comrrelation coefticie ent- for theidentLification of the mine-like target in wetground. R,11 730 cm ..... ................. ..... 70

25 Typical long-cable processed waveforns from themine-like target and the wood boara ........ ... 78

26 Extrd(:Led rUsonances from the long and short-cable mine-like target waveforms ............ .... 79

27 Layout of the buried cylinders ...... ........... 84

28 Layout of the buried thin wires ...... .......... 85

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/I

Figure Page

29 Processed waveforms from the different-sizecylinders at 30 cm depth ....... .............. 86

30 Processed waveforms from the 300cm long cylindersat different depths ..... ............... .... 87

31 Processed waveforms from the different-size thinwires at 5 cm depth ......... ................ 88

32 Average extracted resonances of the 30cm longcylinders at different depths ............. .g.o.. 90

33 Averaged extracted resonances of the different-size thin wires at 5 cm depth .... .......... .... 92

34 Averaged extracted resonances of the different-size cylinders at 30 cm depth ............. ..... 93

35 Processed waveforms from the two models of themine-like target ........ .................. 96

36 Averaged extracted resonances of the two mine-like targets .......... .................... 97

37 The rough road for false-target measurements .... 99

38 Processed waveform from a typical false targetin the rough road ....... ................. . 100

39 The small crossed-dipole antenna for improvedmine identification performance ...... .......... 103

40 Processed small-antenna waveforms from the 5cmdeep subsurface targets ....... .............. 104

41 Processed waveforms from 5cm deep targetsmeasured using the 0.6cm long antenna .... ....... 105

42 Additional processed small-antenna waveformsfrom the 5cm deep targets ....... ............. 106

43 FFT of the small-antenna waveforms shown inFigure 40 ....... ... ..................... 107

44 FFT of the small-antenna waveforms shown inFigure 42 ....... ... ..................... 108

xiii

I iqu r! PPage

45 Extracted resonances from the mine-like target.Waveforms taken using the 0.15m and the O.6mlong antenna in similar ground conditions ......... 09

46 Average extracted resonances from the waveformsof the 5cm deeo targets obtained with thesmall antenna ........ ... .................... ill

47 Typical I,(T) curves for the identification ofthe mine-like target using the small-antennasystem ......... ..... ....................... 113

48 Transfer function of the preprocessor filterused in the small-antenna system for targetidentification ........... ................... 113

49 Block diagram of the microcomputer system for on-location subsurface target identification in realtime ......... ..... ........................ 115

50 Picture of the microcomputer target Identificationsys tem ......... ................... ...... 117

51 Tile microcomputer and its components ........ 118

52 The identification process implemented in the Imicrocomputer system . . . . . . . . . . . . . . . . 120

53 Design of the precprocessor FIR filter for target4identification with the small-antenna micro-computer system ..... ................... ..... 126

54 Typical processed mine-like target waveformreceived by the microcomputer system .......... .... 128

55 Processed mine-like target wavefonrs receivedby the microcomputer and the fast samplingsystem ......... ..... ....................... 131

56 A waveform from a buried thin wire for calibrationof the ground parame-ter... .................. .... 136

57 Waveforms from an on-surface thiin wire (30cmlong) for automatic tuning of the subsurfaceradar to ground condition .................. .... 138

58 Connection diagram for the APU .............. .... 214

xiv

--.... "" i . ~

Figure Page

59 The chip-select (CS) signal for the APU ..... .... 215

60 The ROM-inhibit (El) and RAM-inhibit (E2)signals ....... ........... ............ 216

12

xv

I- , tr r

CHAPTER IINTRODUCTION

A. Research Goals

Subsurface radar detection and identification of geological andman-made structures is an area of current importance. Examples are:location of utility pipes such as plastic and metallic gas pipes andwater pipes[l,2,3], location of voids and tunnels[4], anthropologymapping[5], and possible exploration of energy sources such as oil,gas and coal. Yet, almost all of the work done in this area wasdirected toward target detection, rew attempted the problem of tar-get identification. Subsurface target identification is a problemfar more severe than the identification of aerospace targets by con-ventional radars where the target can literally be seen and the classof false targets is limited in scope. Underground there are varitiesof unknown false or undesired targets to complicate the task. Further-more, the medium Involved, i.e., the ground, is usually lossy, inhomo-geneous and, most of all, electrically weather-dependent. These pro-blems, together with the presence of the air-ground interface makesthe task of subsurface target identification truly formidable. It isfor these reasons that, to date, there is no single technique orsystem capable of identifying subsurface targets in real time.

In this study, a technique for subsurface target identificationis developed and extensively tested with real radar measurements col-lected using a video pulse radar[l-4] under different conditions (i.e.,different ground conditions, different antennas, etc.). This techni-que is implemented with a "first-generation" microcomputer system todemonstrate the feasibility of real-time subsurface target identifica-tion.

The technique used in this study characterizes subsurface targetsby their complex natural resonances[7-11], which are extracted directlyfrom the processed time domain waveforms via Prony's MethodEl2-15].A predictor-correlator[40] useq the difference equation coefficientsassociated with these complex resonances as discriminants to generatea correlation coefficient for target identification. This characturi-zation and identification method is attractive for it characterizes theresponse of a target by a set of complex numbers which is independentof the pulse radar location. Furthermore, the complex resonances andthe difference equation coefficients are pre-determined, thus, only sim-ple algebraic operations are involved in calculating the correlationcoefficient for a real-time identification decision.

2

[B. Related Research in Subsurface_Tarqet Characterization andIdentification

Electromagnetic techniques have been used successfully formany years for probing the earth. Keller and Freschnecht[25] givean excellent summary of these procedures. A recent summary of sub-surface probing techniques is given in a report by D.C. Gates, eta 1.[26]

Perhaps the earliest documentation of a subsurface electro-nagnetic radar system is contained in a patent issued in 1937 inwhich an electrical analog of seismic systems is described[16].There is, however, no mention of successful implementation of sucha radar. There have been attempts to use bistatic radar configura-tions of this type but the results have generally not been highlysuccessful[17,18], The reason, recognized by Horton[19], is thatthe tail of the pulse coupled directly from the transmit to the re-ceive antenna occurs "just at the time when the maximum of the re-flected pulse (from a buried target) must be accurately timed.This coincidence tends to ruin the measurement".

, ,A significant result in video pulse technology Is described ina patent by Lerner in which a video pulse system is used for more

moderate depths[20]. Lerner's scheme differed from the earlier patentin that the same antenna was used for both transmitting and receiving.Lerner introduced a combination of TR, ATR and Hybrids to separatethe transmitted pulse and the received target signal.

In this study, a crossed-dipole antenna system is used to in-corporate this function into the antenna itself, ie., transmit-receive isolation is achieved by isolating the antennas themselves,The crossed dipole is an orthogonal dipole pair, one horizontal dipolefor transmission arid another orthogonal horizontal dipole for recep-tion, which provides substartial reduction of the primary (directlycoupled) signal on the receiving antenna. Many measurements havebeen ,nade on a variety of shallow targets (less than 15 m) using theseconcepts[1-4,21,22]. Targets include geological structures such asfaults, joints, sink holes and man-made structures such as pipes. Acommercial unit for pipe detection based upon the research and designwork at the ElectroScience Laboratory, and designated as Terrascan,is being produced by Microwave Associates Inc.[6]. The pulse radarused ir, this study for subsurface target identification -is a Terra-scan-like radar system.

A major reason for the success of the characterization and identi-fication procedures discussed in this dissertation lies in the improve-ments In the antenna system. The original cross-type antenna struc-ture developed at the ElectroScience Laboratory for subsurface radarapplications was basically a crossed bowtie geometry wrapped arounga sphere[21], but this was subject to noise. The crossed bowtie

•j

3

evolved into various planar crossed-dipole arrangements as used byMoffatt[4]. These arrangements were, however, too awkward for usein real-time on-location target identification. Later, Young[l,3]introduced the loaded folded dipole geometry of the Terrascan system.Tribuzi[66] improved this by introducing the loaded folded bowtieconfiguration. Wald[59] further improved the electrical character-istics of this structure by eliminating part of the supporting struc-ture. He also constructed the small antenna used in a later part ofthis aissertation for identification of mines. The design of thesmaller antenna was dictated by the results obtained in this dis-sertation since its purpose was to shift the antenna resonance tomore nearly coincide with those of the mine-like target.

One of the first studies initiated in the development of thepulse radar system with the crossed-dipole antenna for subsurfacetarget detection and identification was the detection and identifi-cation of TDMB mines[28-35]. This study included efforts in thedevelopment of antenna systems and techniques to extract the char-acteristic spectra of the electromagnetic fields scattered by theTDMB mine. In 1970, Sullivan[21] Investigated the feasibility ofusing the characteristic real-frequency resonances of subsurfacetargets in the identification of simple buried objects. The systemused in Sullivan's study was a video pulse radar with a crossed-polarized antenna system. A similar system using crossed dipoleswas later used by Moffatt, et al.[4] in the probing of man-made andgeological subsurface targets. The subsurface video pulse radarsystem was then modified and developed to be the existing Terrascansystem in a study to detect gas 1mipes[l-3]. To automate the Terra-scan system for automatic target *identification, Chan[22] investi-gated a matched filter technique for automatic identification ofplastic pipes using a Terrdscan-like radar system.

Other methods have been employed in the detection and identi-fication of subsurface targets., In particular, various techniquesof Pattern recognition[37-39] were used by Echard, et al. for thedetection and identifivation of buried mines[36].

This study investigated the possibility of using in situ targetcomplex natural resonances to characterize and identify subsurfacetargets. The basic method was first introduced by Hill[40] in thedetection of targets near the surface of the earth, and later usedby Chan, et a1.[23,48-50] in the characterization and identificationof subsurface targets.

4

C. Structure of This Report

The structure of this report is as follows:

Jn chapter II, the basic radar measurement procedure is per-sented. In addition, preliminary signal processing is discussedsince certain preprocessing does improve the target identificationresults.

In Chapter III, we present a method for extracting from responsedata records (I.e., the time-domain waveforms) the complex naturalresonaitces associated with the targets. This method, known as Prony'smethod, is outlined and applied to extract target resonances from t ebackscattcred waveforms in the time domain.

In Chapter IV, the predictor-correlator method for targetidertification is discussed and applied to the waveforms collectedin this study. Detail identification statistics are given.

In Chapter V, the effects of radar bandwidth on the character-ization and identification method are studied.

In Chapter VI, the effects of target size and depth on thecharacterization and identification method are discussed.

in Chapter VII, we direct attention to the detecion and identi-fication of mine-like targets in practical situations. Improvementson the pulse radar system are made for the implementation of a port-able, real-time on-location subsurface target identification radar.

In Chapter VIII, we discuss the implementation of the sub-surface identification radar as a microcomputer system. Detailedprodecures of the implementation aru presented. Real-time targetidentification results using the microcomputer system are given.

In Chapter IX, a method for automatic tuning of the identi-fication radar to the ground condition in real time is discussed.This method is simple and can be easily incorporated into the micro-computer system for real-time subsurface target identification.

In Chapter X, major achievements accomplished in this work aresuninarized. Conclusions and recommendations are made.

I

CHAPTER II

MEASURED AND PROCESSED WAVEFORMSFROM THE SUBSURFACE TARGETS

A. Objectives

The objectives of this chapter are the following:

1. To give a description of the subsurface pulse radarand the subsurface targets selected for this ,tudy andto summarize the procedures taken to measure the back-scattered waveforms from these targets. Raw (unpro-cessed) waveforms from the targets are shown.

2. To summarize the signal-procpvs-ing techniques usedto partially suppress noise and clutter in the raw

wavefonis. Processed waveforms are given.

B. Subsurface Electromagnetic VideoPulse Radar System

The video pulse radar system used to collect measurements forthis study basically consists of three components: the energy source,the antenna system for signal transmitting and receiving and thereceiver for signal processing. The design of these components isdictated by the electrical properties of the ground, the depth ofthe target of interest as well as the target, clutter and noisecharacteristics. A picture of the Terrascan-like subsurface pulseradar used in this study together with a basic block diagram isshown in Figure 1. The basic components are: the impulse generator,the crossed-dipole antenna system and the receiver. Basic operationis as follows. The impulse generator transmits short pulses of energythrough the transmit antenna into the ground. The presence of atarget scatters the incident energy toward the receive antenna. Thisscattered energy is received as a sampled time-domain waveform fortarget characterization and identification.

Tn the current study a short video pulse of aoiproximately 150ps duration (at 3 dB points) and a nominal IQOOV peak amplitudewas used (see Figure 2). This pulse duration is much shorter thanthose used in conventional radar practice. Furthermore, a con-ventional radar has a few percent bandwidth about its carrier

5

6

CONTRCLLED

CROSSED DIPOLE

'101" -A,

1000-

500-0J

0

0 1 2 3 4

0 (a)

-20-

-40

0 1 2 3 4 5 6 7 8 9 10FREQUENCY (GHz)

(b)

Figure 2. Characteristics of the impulse source in time~and frequency domlain.

frequency whereas this video pulse output spectrum spreads fromessentially dc (repetition rate = 256 Hz) to beyond 3 GHz. It isthis broad band of frequencies inherent in this narrow pulse thatmakes target identification a possibility, i.e., the scattered fieldsfrom the targets can be sampled over a very broad frequency band andeach sample contains information about the targets. The use of sucha narrow pulse also has a second substantial advantage for the de-tection and identification of shallow targets, in that the transmit-ted pulse magnitude has fallen to a low value before the pulse re-flected from the target returns to the antenna. This "time isola-tion" effectively minimizes the width of the radar "dead zone" andenables the scattered pulse to be observed over a wide time span.A second fonri of isolation exists in the choice of the antenna system.The pulse radar uses a pair, of crossed, loaded, folded dipoles withO.6m (2 feet) long arms lying flush with the ground surface (seeFigure 1). The crossed-dipole antenna system achieves substantialisolation between transmit and receive antennas. For a perfectlyorthogonal pair and no target perturbation, the transmitted pulsewould not be observed on the receive antenna. In practice, antennaisolation on the order of 60 dB below the nominal pulser voltage isachieved routinely. Such isolation further minimizes the width ofthe "dead zone" and is essential for shdllow-depth target identifica-tion. The dipoles are heavily loaded, with both resistors andincorporated absorber in the antenna to reduce mulitiple reflectionsand consequently reduce pulse distortion caused by the antenna. Thecrossed-dipule antenna system has two additional advantages for theidentification of subsurface targets. First, being a cross-polarizedsystem it is insensitive to reflections from layers which are parallelto the antenna irms. An important example is the ground surfacewhose reflection of the incident pulse energy would produce extraneouss ignals in other nutn-orthogonal systems. Second, received waveformsobtained from objects which have no symmetry with respect to theantenna arms go through a polarity revwrsal as the crossed-dipoleantenna system is rotated (about its vertical axis) by 90". Thisfeature represents a valid method by which a target can be separatedfrom an extended rio-tarqet echo which is introducwed by multiple re-flectiuns on the antenna structuref3].

Typical raw time-domain waveforms received with the antennaoriented at 0" and at 90' over the center of o plastic mine-liketarget are shown in Figure 3. Several waveform features can bedescribed. The iirst sharp impulsive-type portion of the waveformis due to direct coupling between the transmit and receive antennas.From the amplitude of the coupling signal and the pulser output, it

*A smaller anternna (0.15 in) is later used for a more specific purpose

of mine identification.

'-I-

w W%

4-3

004-

0 0

00

00

LL.

10

is seen that about 60 db isolation is achieved. Note that this sig-nal does not change significantly with antenna orientation and thuscan be removed by forming the difference of the two wavefonris. Thecoupling signal is a source of clutter but it is also useful as atime reference for target depth and range, since it occurs at essenti-ally the time the source impulse is radiated from the feed terminalsof the transmit antenna. The next feature of the waveform beyondthe impulse is the random clutter due to the ground surface irregu-larities directly beneath the antenna. Because of the short durationof the impulse arid good antenna design, this clutter feature dies outin a few nanoseconds. Thus, only a small portion of the clutter over-laps the return from the mine-like target. The signal from the mine-like target appears to be rather strong. Furthermore, it reversespolarity when the antenna is rotated by 90". thus, its amplitude willdouble in the difference wavefonn. The mine-like target signal ex-tends through a time window of approximately 30 ns and falls toa negligible level at the time the balun reflection occurs. The balunis necessary for connecting the unbalanced impulse generator to thebalanced dipole antenna. Thu impedance mismatch at this connectionis the source of the balun reflection. The balun reflection limitsthe width of the reflectionless time window of the system. In thepresent system, the width of the reflectionless time window is 36.5ns, which turned out to be wide enough for the identification of theshallow subsurface targets considered in this study. For a widerwindow, one can lengthen the delay cable at the balun-antenna con-nection. One can also greatly suppress the effects of the balun re-flection by shortening the length of the delay cable at the balun-antenna connection. In this case, the balun reflection would occurin the time region where the target signal is much higher in amplitude.In a later section, we describe a smaller antenna which was used forimproved target identification performance. This small antenna masbuilt with the delay cable shortened and the balun structure placedalmost at the antenna feed points. The balun reflection can be com-pletely elimin,ited if a balanced pulser is made available in thefuture. . limination of the balun would also yield a narrower trans-inlitted pulse due to less cable loss and dispersion.

An unproces sed time-domain waveform is present in the receiverfor target characterization and identification. The structure of thereceiver basically consists of J sampling oscilloscope for signalreception. a signal-processing unit for clutter and noise reductionand I unit for i ,- rjet ciharacterization and identification. In thisstudy, because of the flexibility it offered, a general-purpose digi-ta l compu ter was first used to control the sampl ing oscilloscope andto implement the processing, characterizati on avid identification units.After all of the target characterizati n and identification procedureshad been established, much of the flexibility was discarded and a re-latively Simple systelli designed for tdrij;t. detection anid identifica-tion. "ilci I s ystem1 wa, impl 1emented with ! ,i,;irocomputer for targetidentification in real time. Discussion of the microcomputer systemis presented in Chapter VIII.

I*1

Il

C. The Subsurface Targets

Five targets of similar size were buried at the same depth of5 c.n (2 inches, measured from the qround surface to the nearest tar-get surface). Figure 4 shows the geometry of the targets.

All targets were buried in the backyard of the ElectroScienceLaboratory at points where the ground is known to be relatively un-disturbed (i.e., free of other objects). The average dc conductivitywithin 30 cm (12 inches) of the ground surface measured at the targetsites ranged from 30 mS/m for wet ground to about 20 mS/m for dryground and 10 mS/m for icy ground. The relative dielectric constantmeasured at approximately 100 MHz ranged from 25 for wet ground to16 for dry ground and 9 for icy ground.

Since a goal of this study was to achieve separation of a mine-like target from other (false) targets using radar data, a majoreffort was directed toward the study of the mine-like target. Themethod of identification developed here can easily be adapted tosystems in which other targets are considered as desired targets ortargets to be separated.

Backscattered waveforms were obtained using the subsurfacepulse radar system. Measurements were made at different ground loca-tions with respect to the various targets. Locations of the antennacenter for these measurements are shown as dots in Figure 5. Ateach location two backscattered waveforms were obtained using twodifferent antenna orientations, one of which was a 90' rotation witrirespect to the other. A standard antenna orientation used in obtain-ing the rieasuremenLs is shown in Figure 5. Measurements were obtainedwith the antenna center vertically above the center and edges of thetargets. Beyond the target edges, measurements were made at theregular interval of 15 cm (6 inches).

Data accumulation was started in early June 19/7 and continuedthrough early April 1979. lOuring this period the qround conditionchanged from wet to dry and to icy. Data were obtained for eachground condition to gauge the effects of the changing ground conditionon the characterization and identification of the subsurface targets.

12

0 30.5 c m

PLASTIC MINE-LIKETARGET

3,5m 14.6cm

'1 o10.2cm -/(0.5Cm WALL THICKNESS)

• ALUMINUM

BRASS CYLINDER SPHERE

.ccm

Th-.O.. c

COPPER SHEET WOOD BOARD

Figure 4. Physical characteristics of the subsurfdce targets.

..

13

NI

S W E

cm

* BRASS PLASTIC* CYLINDER MINE-LIKE

•TARGET

0 ANTENNAORIENTATION

06 ALUMINUM SPHERE

0

COPPER SHEET

• • WOOD BOARD

Figure 5. Measurement locations and antenna orientation.

0_ 0.. . . . . . ..S- - : _

.. .-0L

14

D. Raw Measured Waveforms

All waveforms collected by the Terrascan-like radar used inthis study consist of 256 samples in a time window of 50 ns. The(hardware) basic sampling period TB is 0.2 ns, giving a samplingfrequency of 5.12 GHz*.

There are three possible classes of signals present in theseraw waveforms.

1. Noise: noise refers to extraneous signals which arenot in any way related to the radar source signal.Examples are thermal noise, interference, etc.

2. Clutter: clutter refers to extraneous signals whichare related to the radar source. Examples aretransmit-receive coupling, reflection from groundsurface irregularities, and echoes from objectsother than the desired target.

3. Desired Signal: desired signal refers to echoes of theincident source energy from the desired target.

For shallow targets the desired signal may include direct reflectionsfrom the target and multiple reflections between the target and theantenna. Since the antenna is so near the target, the antenna radi-ation mechanisms and the target scattering mechanisms may not be dis-tinct.

Noise and clutter are the extraneous signals that the signal-processing unit is designed to suppress under certain conditions.

The scattered fields from the targets, both desired and un-desired, plus noise and clutter produce a signal at the terminalsof the receive antenna. In most conventional receivers noise isreduced by the introduction of filters. For broad-band signals thisis not possible but noise is reduced substantially by averaging anumber of received waveforms. In general, however, for this antennasystem even in our local urban environment where many strong inter-fering signals exist, the voltage pulse caused by the scatterer isclearly visible on the oscilloscope. In the subsurface pulse radarsystem, due to the low sensitivity of the antenna system to above-

*Waveforvis collected by the microcomputer system consist of 128samples in a time window of 25 ns. The microcomputer system isdiscussed In Chapter VIII.

15

ground disturbances, the noise level is inherently low. Furthermore,it was found that a simple arithmetic averaging process is an effec-tive means for reducing noise[22,24]. This means of course that thenoise is not target-induced.

Typical averageraw waveforms are shown in Figure 6. Thesecond waveform (---) in each figure is obtained by rotating theantenna by 90'. If the observed signal is caused by direct couplingbetween the transmit and receive antenna (T-R coupling), the signalwould not be changed by this rotation. On the other hand if thesignal is caused by any external scatterer, a polarity reversalis observed. These raw waveforms illustrate the various classes ofsignals. Figure 6-a shows a no-target waveform which is a receivedwaveform with no target (desired or undesired) present within theradar range. Such a waveform, after averaging, contains clutteronly. Figure 6-b shows a waveform from the desired mine-like target.In this waveforni, the T-R coupling and the ground surface clutteroccur early in time and because of the shallow target depth a certainportion of the desired signal is overlapped by the clutter. It is

these extraneous signals that various signal-processing techniquesare designed to suppress. Figure 6-c shows a waveform from the brasscylinder.

E. Processed Waveforms

Before proceeding to the target identifiration alqorithms, acertain amount of preprocessing of the data is desirable. This isessential here since the goal is to obtain the purest scattering data

is• possible for target characterization. These steps are made possible

by the availability of a computer in the measuring system. The dataprocessing will not all be essential in a field system to detect andidentify such targets. It is envisioned that any such preprocessingthat may be required can be done in a microcomputer which will be apart of the final system. The preprocessing here included:

1. Arithmetic averaging: this process forms the arithmeticaverage of ten raw waveforms at the same antennalocation and orientation.

2. Amplitude shift: any dc drift in the waveforis iscorrected by adjusting the base line.

3. GatinA: the time regiors before the T-R antenna couplingand after the first balun reflection are replaced bva straight line at zero level. The resulting"effective" time window (same for all waveforms) is3 .5 ns wide (186 samples).

4. Time shift: the effective time window is shifted tothe same time region for all waveforms.

16

JLC 1 .-

I o 2o LA01.co

LiiuI4,-

wj /

0 40

jo o

0 71 (n00

N. 0o. 0.

woo

I0WA%

(3

r **.0 .~t91~ Pt:~W.li~t 'NfUV*.#* N&.l N ~p 4..- A~h ~ .~b N .... LA

I 17

5. 90'-rotation difference technique: this process formsthe difference between two average, shifted andgated waveforms from the same antenna location butwith different antenna orientations of which oneis 900 rotation with respect to the other.

6. Multistation avera ing: this process forms theat riltet c average of all the difference waveforms(5. above) from the antenna locations which presentidentical relative geometry between antenna and

il target.These processed waveforms are considered to be relatively

noise and clutter-free. Furthermore, they contain only the back-scattered information from the individual targets since the groundof the target sites was undisturbed (free of other objects) andrelatively smooth, These processed waveforms are to be used only toestablish the parameters of identification system. They are not usedfor the identification of an unknown target.

A set of processed waveforms and their Fast Fourier Transforms(FFT)[64] for the mine-like target at various antenna locations in awet ground is shown in Figures 7 and 8. Typical waveforms for the

other targets are shown in Figures 9 and 10.

The following important generalizations with regard to thesewaveforms are made:

1. All time-domain waveforms exhibit transient behaviorin the late-time region where only the natural responseof the target exists. This transient behavior is ofprime importance, and, as will be shown in Chapter III,dictates the characterization and identification methodfor these targets.

2. The strong peaks in the FFT's of the waveforms indicatethe possible existence of resonance behavior in the back-scattered waveforms. These peaks may be a good approxi-mate measure of the imaginary parts of the complex reson-ances of the targets in situ. Note that while the time-domain waveforms from different antenna locations overthe mine-like target change noticeably, the locations ofthe stronq peaks in their FFT's stay relatively unchanged(see the vertical dotted lines in Figure B), indicatingthe complex natural resonances of the target are excita-tion invariant. This was anticipated and is the mostattractive feature of the target characterization scheme.

.~i

Li 0 l

Li 4-IC

z c_6 La.

0 W~ r

o U 0 LL. t00

LU Mr. 0-

440 0 A

w~ U) 0

E E Ez u u

Ln W)J

LL1~

UH

T&4

19

0

Ilr. w

z LUZLU Li L

L.0 L&. Li.0 0

L)I

LU U. 39

EE E E L

z an n Il) U)

4 .4-

20

E 06 0

0 8

'4-

ui

ci. 0

I- >- C.

tc . 0Tfe0 6n

m0~

S I

X(U,03

00

L

00

W ~04

LU&

0U (nAJ0

LU 2 4-)- 4-

z 0

22

3. For the waveforms given in Figures 7 and 9 the signallevel of the cylinder is the highest while the signallevel of the sphere is the lowest. As a reasonable quanti-tative parameter for comparison of signal and clutterlevels, the following definition of signal-to-clutter ratio(S/C) was used in this study.

S A LT EM-ENT (1)

ENT 'ENT

where

ET is the energy of the target signal,

EM is the energy of the measured waveform, and

E is the statistical mean energy of the ensemble ofclutter or no-target waveforms used to estimateENT- In this study, we considered only single-target situations, hence a collection of 51 no-target measurements taken at various locations inthe vicinity of the target site was used as theensemble of clutter waveforms.

The Energy of a waveform was defined and estimated ;is follows.

te> r 2 (t)

A t=t s tA Bt T (2)

where r(t) is the waveform under consideration and tt are the starts e

and stop-flee of the interval of interest. In this stud]y ts was takento be the time at which the absolute maximum of the wavefonii occurredand t, was taken to he thu time at which the balun reflection occurred.Therdsons for these choices of ts and teargieinlercpts

The ' ae gven n lterchapters,

The ,mean clutter level was evaluated as

51 t>• ( •[ (t)l t.i I i)/T )

i:_ I t.. ts i r i i bENT ................ 51- (3)

where rNTi(t) is the ith no-target waveform in thp ensemb'le and tsi,0 Ore the stdirt and stop time, respectively of the ith no-target

waveform.

I.J

23

Using the above definitions, the signal-to-clutter ratio atvarious antenna locations over the 5cm deep targets were evaluatedand are given in Figure 11. It was found that the signal-to-clutterratio for the mine-like target ranged from 0.21 to 3.50 depending on

A the antenna location and orientation*. The brass cylinder and thewood board targets had the highest and lowest signal-to-clutterratios, respectively.

The three items mentioned above: the transient behavior, thecomplex natural resonances and the signal level of the oackscatteredwaveforms are of prime importance in subsurface target identifica-tion. Their dependence on changing groutd conuitions complicates theidentification process. Any practical subsurface target identifica-tion algorithm must be able to adapt to this changing condition andidentify the desired target in a wide range of, if not all, groundconditions. A comparison between the brass cylinder waveform in dryand icy ground Oiven in Figure 12 clearly shows thu effects of chang-ing ground condition. Althouq'h both waveforms exhibit similar trans-ient behavior, the time intervals between the zero crossings aredifferent, indicating a shift in the locations of the target reson-ances. The amplitudes of the two wavefornis are also different.

The FFT's of the backscbttered waveforms indicate that thestrongest frequency concentration is at about 70 MHz, furthermore,almost all signal energy is in the 0-500 MHz frequency band. This"system bandwidth" is of great significance in subsurface targetidentification for it dictates the number of target resonances andthe magnitude of the correspond 4 ng residues in the backscatteredwaveforms.

In the next chapter we attempt to characterize the various rub-

surface targets by approximating their processed backscattered wave-forms hlith a finite complex expunential series with the complex expon-ents being the complex natural resonances of the targets. A methodfor extrac;ting these resonances directly from the time-domain wave-forns will be presented. Results from the application of this method

A are 'livwn.

"*S/C depends also on the ground condition. The estimates given inFigure 11 was based on a set of measurements ontained in a relative-ly dry ground condition over a time period of several d ys. Further-more, S/C at syninetric locations are assumed equal. S/GV0 whenEM" NT1

. ., - ,- - r., .

24

* N

0.24, W E- E17.5 S ',5.0 0.49

27.74 •33**g 0 1

5.6 15 .cm6 0.2

i BRASS 2.73 PLASTICCYLINDER 3.50= MINE-LIKE

ti TARGET

0

>K ANTENNA

ORIENTATION

0 0 .4r•'047 01.04' ALUMINUM SPHERE

0.240

Si

00.27

*20

* 3.01 COPPER SHEETS 1,200

•0

0

. 0.39

a WOOD BOARD

0

1 ifpJrv 11. Signal -to-clutter ratio estimates of thewaveforms from the subsurface targetsat different antenna locations.

ti

--.

25

c icu0

(A

10

.00)IA

000,-

CHAPTER IIICHARACTERILATION OF SUBSURFACE TARGETS BY

THEIR COMPLEX NATURAL RESONANCES

A. Objectives

This chapter sunmmarize,' a study of the characterization of sub-surface targets by their complex natural resonances. A method for,extracting the resonances from the processed backscattered waveformsis derived for completeness. The method is known as Prony's method

[12-151 and, when applied to measured data, it is extremely sensitiveto the values of its parameters. An approach to solve certain ofthese problems will be presented. Prony's method is applied to theprocessed backscattered waveforms and an analysis of the resultingresonances Is focused on the following:

1. The excitation invariance of the complex natural

resonances of the individual targets with respect toantenna location.

2. The degree of distinction between the complex naturalresonances of the different targets.

3. The effects of changing ground condition on thelocation of the complex natural resonances.

B. Complex Natural Resonances

The concept of using complex natural resonances for targetcharacteritation is developed from the fact that all finite-sizeobjects have resonances that depend on their physical characteristicssuch as size, shape and composition as well as the medium surroundingthe object. These resonances, however, are independent of the excita-tion[40]. As a useful but inexact analogy, in circuit theory, theforti of the transient response of a lumped linear circuit may bedetermined from the knowledge of the resonances and the correspondingresidues of the response function in the complex frequency plane.The actual transient response of the circuit is then simply a sunma-tion of all the residues multiplied by the inverse transforns of theresonances. In 1965, Kennaugh and Moffatt[41] generalized the impulseresponse concept to include the distributed parameter scattering pro-blemis and suggested that a lumped circuit representation, at low

26

i

27

frequencies or long time, was possible. Later, similar and more for-mal representations have been designated as the Singularity ExpansionMethod (SEM)[7-8]. This hypothesis is generally supported by the factthat typical transient response waveforms, such as those shown inChapter II, appear to be dominated by a few exponentially damped sinu-soids. Based on this concept, a subsurface target can be character-ized by a set of complex natural resonances which is independent ofthe location and orientation of the crossed-dipole antenna. Theseresonance,: oiwever, are dependent on ground condition. Such a char-acterization is attractive for it catalogs a target by a small setof complex numbers.

The backscattered waveforms from the subsurface targets receivedby the pulse radar system are good approximatluns to the impulse re-sponses of the targets. Further.ore, they appear to be dominated bya few exponentially damped sinusoids, and thus can be represented as

N sitr(t) : ] ai e (4)

where r(t) is the received transient wavefomn, si's are the complexresonant frequencies or pole locations in the complex frequency plane.These have, by common usage in this representation, become designatedas complex resonances or more simply as resonances. These variousterms will be used for si in this document, al's are the correspond-ing residues and N is the number of complex resonances within the fre-quency band of the radar system. The corresponding expre•sion In thecomplex frequency domain is

N a,)>' (Ss_ iT (5)i.~l

where <.[ ] is the Laplace transform operator[42] and s is thecomplex frequency. Note that the resonances are not dependent onantenna location and orientation however, the residues are.

In order to exploit Equation (4), it is necessary to firstdetermine the values of the corIplex natural resonances of the targets.The method used here extracts the resonances of a target directlyfrom its transient response. This method is known as Prony's method,which was first derived by Prony in 1795[12], and was later suggestedby Van Blaricum, et al., for extracting the pole singularities oftransient waveforms in 1975[14].

1-

28

C. Derivation of Prony's Method

In discrete form, Equation (4) can be written as

N siKTBr(KTB) = ai e K ,1,2... (6)i-l

where K is the sampling index and T is the basic hardware samplingperiod of our measurement system (see Chapter II). For an exactsolution of the 2N unknowns a1 and si, we can set up 2N (nonlinear)equations by using 2N sample values of r(KTB). Prony's method uses2N uniform samples, and

N sinTr(nT) ai e ; n O,l,2 . ,M 2N-1 (7)

where T, the Prony interval, is the interval between the samples usedalong the waveform. In general, N itself also represents an unknownwhich is usually fixed by a trial and error process.* If no waveform

Ai interpolation is exercised, T is equal to integer multiples of TB.Writing out Equation (7), we have 2N equations

r° = al + a2 '" + aN 1rI = alZl + a 2 z2 + aNzN

r2 = a Z az+ 4,NZ (8)

rM zi+ a z + * + N J

where

11n r(nT)

andS TsiTe

*N represents the number of target resonances which are excited by

interrogyting frequencies within the "system bandwidth".

29

Equation (8) is a set of nonlinear equations in the zi's. Let zl,z 2

zN be the roots of the algebraic equation

(t + (izI + ,,2z2 + "" NzN = 0 (9)

so that the left hand side of Equation (9) is equal to the product

(Z-zl)(Z-z 2 ) ... (Z-ZN) 0 (10)

that is,

N N

Y (trnzil ii (z-zi) 0 (11)m=O i'l Il

Thus, if we can evaluate ,tm, then zi can be obtained by a simplefactorization of an Nth degree polynomial. To solve for CAm, weobtain from Equations (7) and (8)

N N ( i K ,IN "mrK~m N (]K alzi) , K = 0,I,2...M-N

ii.0 IliO OIII=O IelOi 0

Interchanging the order of the summation yields

N NIt L 1r41 = da1 z (till z I

m=0O i1 1 0

From Equation (11), we see that the summation inside the parenthesisof the above equation is zero, thus, we arrive at the desired linearhomogeneous difference equation

NM' K+m 0 ; K 0,1 ,2 'M-N (12)

I1 0

Thus, the sample values of r(t) satisfy an Nth order linear homogene-ous difference equation. This difference equation is commonly refer-red to as the Prony difference equation.

The Prony difference equation ts linear and homogeneous, andcan be used to solve for the N+l coefficients, i.e., ,'s. In theclassical Prony's method, these coefficients are obtained by setting

=1 and solving the resulting matrix equation by matrix inversiontiat is,

- .. _,--.-

30

whereAU-()

r, r2;.. rN -

LM-N rM-N+l -N+2 "-

r0 N

Band C - N+l

L'N - 111is readily invertable. Standard coptrroutines such as GELG[43)can be used to do the matrix Inversion. Once the tjj's are deter-mined, the next step is to solve for the N values of zi. These zi's

are-. obtained by finodinrg the roots of Equati on (11) . 'The N roots arecomplex numbers and because r( t) Is real , these complex numbers Appearin complex conjuyate pairs. The polynomial root find-Ing process canb(ý easily performed by using standard routines, such as *iull1er[44,45].

It is now trivial to obtain the palcs s* Since the roots of

LjUdLtifln (11) were defined b~y Equdtionl (8), theC Poles are simply

Si (14)

The final step in Prony's method is to determine the value of

0h0 residues .. To do this, we simply solve the maitrix equation

embodied in Lquation (8). In matrix form this set of equations iswritten as

DEr (15)

where

31

Z1 Z2 . ZN

Z2 Z2 ... 2

L1 2~ " N

D=

"1 0i! a2 rl

E and F •* I i

* I"

INrN-1

where now the only unknowns are the elements of the residue matlrx E.

The above derivation of Prony's method Is valid only when allnatural resonances present are simple poles. For multiple-orderpoles, a slight modification is necessary in solving for the residues.The derivation of Prony's method for multiple-order poles is given inAppendix A for completeness. However, in this study we have not foundit necessary to postulate multiple-order poles.

In suiimiiary, Prony's method solves for the complex natural reso-nances (poles) and the corresponding residues associated with the back-scattered time-domain waveforms from a system of nonlinear equations(Equation (8)) by breaking it down into three simple steps:

(1) Solve for the values of a m's of the linear Equation (13)by matrix inversion.

(2) Solve for the poles by factoring the polynomial ofEquation (11).

(3) Solve for the residues from the linear Equation (15)by matrix inversion.

The derivation of Prony's method is simple enough. However, itsapplication to the measured backscattered waveforms is a much morecomiplicated process. The following section outlines some of thedifficulties.

- --- -.

32

D. Clutter and/or Noise inP rony' Me tThod

Prony's method has been found to be extremely sensitive toclutter and/or noise. Its ability to extract the complex naturalresonances of a waveform accurately is severely inhibited by the pre-sence of clutter and noise[46-48]. Since Prony's method is an inter-polation process (otherwise referred to as curve fitting), in the pre-sence of clutter and/or noise, it will give a set of poles which fitthe noisy transient response but will not necessarily represent thecomplex natural resonances of the target. Various signal-processingtechniques have been applied to reduce the effect of clutter and/ornoise in Prony's method[ 46-48], with the most comronly used being theleast-square error technique. With it, Equation (13) in the previoussection 'is solved in the least-square sense. In this case M samplesare used in lieu of 2N samples where M-.2N. Thus, the matrix A becomesrectangular, and Equation (13) is solved by the pseudo-inverse techni-cl ue

ATAB ATC (16)

or

Q D (17)

where

J, A ATA

and

D jATC

Since ,in the signal covariance matrix, it is real, symmetricand positive definite, and is thus readily invertible to yield thevalue of iMlI S.

A second technique applied to reduce noise in Prony's methodwas brougnt about by the observation that, in solving for the N+l

III's in the M homogeneous Equations (13), we can, instead of setting10N=, require that the Euclidean noimi of the o vector be 1, i.e.,

N N 2 1 (lu)

Such an approach leads to the eigenvalue method[48,49,52].

i'I

33

1nstead of setti g the leading coefficient .,N=I, we can ofcourse set any of the N+l coefficients to 1 in solving for the aln'Sof Equation (10). Such a constraint leads to the interpolationversion of Prony's method[51,52].

The classical Prony's method, the eigenvalue method and theinterpolation version of Prony's method were all considered in thisstudy. For completeness, derivations of the eigenvalue method andthe interpolation version of Prony's method are given in Appendix B.

Numerous other signal-processing techniques have been applied[46-47], thus far, however, no completely satisfactory result hasbeen reported using measured data. In the following section a syste-matic procedure that is giving good results for the present data isoutlined. This procedure was used in extracting the complex naturalresonances of the processed backscattered waveforms in Chapter II andyielded our best results to date. As we will see, the procedure doesindeed provide satisfactory target separation.

The problem is really one of linear prediction and is prominantin many diverse disciplines[53]. No general solution has yet emergedand the acceptability of a given method really depends upon the appli-cation. It is interesting however that minimizing the total squarederror (actual vs estimate) in some sense is a common starting point.Yet this in no way optimizes the resonance locations. For our purposebecause the resonance locations need not be found in real time, pre-sent methods are adequate If nut completely satisfying. A real needis to compile and translate all of the various methods already beingused. Such a tutorial unified review would be invaluable but is be-yond the scope of the present effort. We can of course easily incor-porate any new techniques into the identification scheme.

E. App.ly linpProny's Method to the Processed'Mea-su-red N~ka-c-c-týtPe Y~ave~oms

In applying Prony's method, one approach is to pre-determinethe following parameters:

1. N, the number of poles to be extracted from the waveform.Van Blaricum[14,15,47] suggested a method which relies onthe fact that the (N+l)th eigenvalue of the matrix shouldequal ,(2, the variance of the additive gaussian stationaryand uncorrelated noise. Such a method does not seempractical for our measured data in which the clutter seemsto be nonstationary (transient).

2. T, the Prmony interval. Obviously, undersampling (T toolarge) will almost surely bring aliased results. It wasalso found that oversampling produces extraneous highfrequency poles.

Z'.

34

3. cts e trhe start and stop time of the fitting interval.ts must lie in the time region where the forced responseportion of the backscattered waveform has ended and temust lie in the region where clutter/noise effects arenot dominant.

4. M, the number of sample points used in the fitting process.M determines the amount of overspecification on the systemof Equations (13).

In the presence of clutter and/or noise, it was found that theaccuracy of the extracted resonances was found to be extremely sensi-tive to the values of the above five parameters[48]. For the methodto yield an accurate solution, we have to find the "right" set ofvalues for these parameters. The approach developed in this studyis to vary these parameters (over a reasonable range) and assume thatthe "right" values of the parameters corresponding to the "desired"resonances are those that allow the closest approximation to the mea-sured wavefonrm in the time domain. That is, a calculated waveform isdeveloped from the resonances and residues found, and this waveform iscompared to the original waveform point by point over the fittinginterval [t,,t ] and the iotal squared error found. The solutionwhich affords ?he smallest total squared error is considered to be the"desired" solution. This approach is used to find the coefficients of

it the difference equation but once done for a target needs not be re-peated for target-separation purposes. It is conceivable that such asearching procedure can be lengthy. Furthermore, ranges of the para-meters are dependent on the waveform being processed. However, witha little experience, one can usually minimize them. The ranges ofthese parameters in this sutdy were fixed as follows:

1. The numbor of ",;ignificant" peaks in the Fast FourierTransfonru of the waveforms is usually a good measure ofN and since the nLimber of "significant" peaks is between2 and 7 in all wavefoms considered, the range of N waschosen to be fro,'i 4 to 14 (we assumed that one peakcorresponded to it most two poles).

2. Shannon's sampling theorem constrains the maximum valueof T, while the bandwidth of the radar system (<500 MHz)constrains the minimum value of T.* The values of T werechosen to be 3T,5... IOT corresponding to minimumand maximum Nyq1ist roquenci~s of 256 MHz and 768 MHz,respectively.

*Frequencies beyond the system bandwidth conLains noise only unlesswe attempt some spectral estimation techniques. The approach maybe worthy of study when ,studying "deeper" targets.

-

35

3. The values of ts were chosen to be tmax,(tmax+ 2 TB),

(tmax+4TB) "' (tmax+8TB) where tmax is the time atwhich the absolute 'maximum of the waveform occurs. Itwas found that such a choice eisured a decaying naturein almost all the waveforms considered. t was chosen toto be the time at which the balun reflectign occurs(see Chapter I1).

4. Since a vastly oversized M would result in an unstablesolution from Prony's niethod[13,15,48], the values ofM were chosen to be 2N, 3N, 6N.

Each set of values of the five parameters (N,T,tste,M) willgive a set of complex resonances when Prony's method is applied to awaveform. This set of complex resonances maximizes the fit betweenthe approximated waveform rA(t) and the measured waveform r(t) in theInterval (ts,ts+(M-l)T] with the sampling interval of T. For allcomplex resonances resulting from all possible sets of (N,T, tte,M)in the chosen range, the "desired" set of complex resonances ýschosen to be the one which minimizes the total normalized point-bY-point squared error r over the error-calculating interval. The errovr, which will be henceforth referred to as mean-square error, is defineda .. ,s (r(t)-rA(t))2 (r2(t)+r2A(t) ; t -iTB (19)

s In this study, r(t) was taken to be the processed measured wave-

form and the approximated waveform rA(t) was generated via the methodof linear prediction[53], where

N -

rA(t+mT) ) -_.. rm(t+iliT) (20)S|m=O ۥlno

m 0

In Equation (20), rA(t) and rM(t) are the approximated and theprocessed measured waveform, respectively, the ,II's are the differenceequation coefficients obtained from the Prony's method, and mo Is anindex chosen for suppression of clutter and noise effects. In this

study, mo was chosen to be the coefficient of maximum magnitude.With Equation (20), the mean-square error r can be expressed as

. .

36

t. -NT+ili I>i --2- x iM( t+mT

t-t5+mifoT , 114I

t~te_*NT~moI. ; t 1 iT2 (21)

From Equations (12) and (21), we note that the mean-square erroris zero when the measured waveform is free of clutter/noise and isperfectly characterized by Equation (4). The error should be smallwhen rM(t) is closely approximated by Equation (4),

The choice of the above error criterion is related to the formof the correlation coefficient osen in the target identification al-gorithm of Chapter IV, in such . way that minimization of c, resultsin the maximization of the correlation coefficient.

With the above search procedure, Prony's method and its varia-tions were applied to the processed waveforms to extract their complexnatural resonances. Results are shown in the next section.

F. Thu Exr.racted Resonances ofthe Subsurface Targets

The locations of extracted resonances of the wine-like targetat different antenna locations in icy ground are plotted in Figure 13(here only poles in the upper left half s plane are shown, detailsare given in Appendix C). From Fiyure 13, we make the followingobservations:

I. The (,extracted resonances Lend to form "clusters". Sonepossible clusters are shown in Figure 13. The formationof the$L clusters are based on the obviousness of clu'ter-ing of the resonances and the known fact that the accuracyin detenining the real part of the extracted resonance isn normally poor. A cluster can contain at most one poleextracted from a waveform. Poles with residues which arethree orders down in magnitude compared to the 'laxiniumresidue are discarded. Poles which are remote from theclustered g(roups are excluded. Beyond an obvinus weighingdictated by the actual pole locations no real significanceshould be attached to the shape of the closed contoursurrounding each cluster.

2. Only a small number of clusters br resonances are present.

• ..- •',r-r~q '-- " . "-"" • • . ' "Tf•;.*-.;. '.' " "• ' •;.. ... 'I

37

0 CENTER

a 15cm EAST OF CENTER

A 15cm SOUTH OF CENTER

0 15 cm WEST OF CENTER

v 15cm NORTH OF CENTER:. - 500m 30cm EAST OF CENTER

A 30dmSOUTH OF CENTER to

"0 30cmWEST OF CENTER

Y 30cm NORTH OF CENTER 400

* AVERAGE

.i'4

200

-O0o -600 -400 -200

Q ( 106 NEPERS/S)

Figure 13. Location of the extracted resonances of thenine-like target at different antennalocations in icy ground.

38

3. The variation in the real parts of the resonances within acluster is generally greater than the variation in theirimaginary parts. There is at least one more major factor,besides the ever-present clutter/noise, that causes suchvariations, namely, the target-antenna interactions. Atthe shallow depth of 5 cm, for most antenna locationsconsidered, the targets are in the near field of theantennas for the entire bandwidth (< 500 MHz) of our radarsystem.

4. An additional-factor contributes to the variations in theextracted resonances from the mine-like target, namely,its complex structure. This target possesses the mostcomplex structure of allitargets considered.

5. The phenomenon of certain resonance(s) being weakly excitedin certain radar aspects is evident. The weakly excitedresonances were.not extracted.

6. As expected, the residues are aspect dependent Thisbecomes evident by noting the variations of .7:.gnitudeof the residues of the poles in the clusters K)eeAppendix C).

7. The mean-square error c is small (< .01, see Appendix C)in all cases considered, meaning that the finite sum ofcomplex exponentials fits the measured waveforms well.This is a necessary condition for our identificationalgorithm whose correlation coefficient is defined to beunity minus the mean-square error c.

In this study, a subsurface target was characterized by the set ofaverage extracted resonances. Averaging was performed over all theextracted resonances in each cluster. For the mine-like target, theaverage extracted resonances are shown as solid dots in Figure 13.Parameters such as the variation from the average of each pole with-in the cluster is not meaningful because of its causes which include,besides the effects of clutter and noise, the possible variations inthe pole excitation at the various antenna locations and orientations.Slight pole variations due to the variations in the antenna locationsand orientations is possible for the finite exponential sum represent-ation of the tarc'-t's transient response is only an approximation andthat the targets ... nsidered are located in the closed vicinity of theradar system.

The extracted resonances shown in Figure 13 were obtained usingclassical Prony's method (i.e., uN=l). Classical Prony's method wasfound to extract poles with tighter clusterings among the resultsgiven by other methods under the constraint am=l,m=0,l-..,N[52]. Theeigenvalue method provided results similar to those given by the

39

Classical Prony's method. Thus, no clear cut choice of method wasdiscernable. Accordingly, the extracted resonances shown in thisdissertation were the results of either of these two methods.

In order to see the effects of the changing ground condition onthe location of the extracted resonances, the average resonances ofthe mine-like target in different ground conditions are tabulated inTable 1 and are plotted in Figure 14. From Figure 14, we see thatthere were five (pairs) extracted resonances. The imaginary parts ofthe extracted resonances were relatively insensitive to changes inground condition. This seems to imply the resonances of the mine-like target are internal resonances. This also means that the 'targetidentification scheme when applied to this target will be relativelyinsensitive to ground conditions.

The implications of the fact that there were five (pairs) reson-ances extracted from the mine-like target waveforms is significant.It means that this target can now be characterized by a finite-ordersystem.

Not all the extracted resonances are related to the scattirlnqmechanisms of the mine-like target. In fact, the lowest resonaicewas found to be the antenna resonance of the system. This becomesparticularly clear when we study, the resonances extracted from themine-like target waveforms collected with a 12m long antenna. 3ygating out the late'time portion of the backscattered waveform fromthe mine-like target received by the 12m long antenna, we effectivelyeliminated the resonance of the antenna created by the finite lengthof the antenna arms. Thus, poles extracted from these waveforms areall target-related. A typical such backscattered waveform in thetime domain is shown In Figure 15, The short time window (comparedto the O.6m long antenna waveforms of Figures 7) of the waveformIndicates the absence of any low frequency content. The averageextracted resonances from the mine-like tarqet waveforms received bythe l2m long antenna at various locations aru shown in. Figure 1G.A quick comparison with the extracted resonances from the 0.6ni longantenna waveforms reveals the fact that the resonance with imaginarypart of approximately 60 MHz is the antenna resonance. Thus, for thesystem with the 0.6nm long antenna, four (pairs) target resonanceswere present in the received waveforms. The antenna resonance wasextracted from almost every waveform of all targets considered.

In contrast to the case of the plastic mine-like target, thebrass cylinder was found to possess external resonances. Table 2lists the average extracted resonances of the brass cylinder Irnvarious qround conditions. Locations of these resonances are Plsoplotted in Figure 17, From Figure 17 we see the following effectsof the changing ground condition on the extracted resonances of thebrass cylinder. rirst, the antenna resonance is insensitive to changesin the qround condition. This may be attributed to the fact that the

40

arms of the crossed-dipole antenna were not in electrical contact withthe ground surface. Second, the imaginary parts of the three higher-order* resonances increased significantly when the ground changes fromdry to icy. This is to be expected, because the resonances of thebrass cylinder are external resonances. The increase in the imaginaryparts of these external resonances indicated a decrease in the valueof the dielectric constant of the ground. Third, the real part ofthe three higher-order resonances generally decreased as the groundchanged from dry to -icy, indicating that icy ground in this case wasmore lossy. The increase in loss seemed to be the reason for theabsence of the real cylinder pole In icy ground.

The average extracted resonances of the aluminum sphere, coppersheet and wood board are tabulated In Table 3. From Table 3 we seethat the antenna resonance is present in the waveforms of all targets.Note that the extracted resonances of the five targets considered layin the same general region of the complex frequency plane and areonly marginally separated. Such is expected to some extent becauseall targets considered have (again marginally) similar sizes. Suchmarginal level of distinction in the poles is expected to presentdifficult tests for the identification algorithm. Furthermore thenumber of resonances for th" various targets are also close (4 to 5pairs); this further tests our identification method.

The location of the target resonances are related to the scat-terig mechanisms of the target. For subsurface targets, these rela-tionships are complicated by the presence of the air-ground interface,the ground condition and the characteristics of the transient antennasystem. For shallow targets the near-field effects and the target-antenna interactions further complicate the picture. In this disser-tation, we do not intend to explore these relationships. Instead, weproceed to use the extracted resonances for identification of thevarious subsurface targets. In the next chapter, a basic identifica-tion algorithm will be given and identification results using theextracted resonances as the discriminants will be presented.

*Order here denotes increasing imaqinary part.

* 1n ~ '-

41

500

o WET GROUND* DRY GROUNDA ICY GROUND

4

400

-300

200

100

-0

-800 -600 -400 -200 0

a (106 NEPERS/S)

Figure 14. Locations of the average extracted resonancesof the nine-like target in different groundcondi tions.

....

42

M -J

dl

*4 VJ

43

500

0 -400

-300o

0So

-- 200

- 100

-800 -600 -400 -200 0a 106 NEPERS/S)

Figure 16. Average extracted resonances. from themine-like target waveforms receivedby the 12m long antenna.

* -*. .*.*i

44

S.........50 0

o DRY GROUNDo ICY GROUND

0

420000 - 300 N

U __

::,,i -- 200

ANTENNA - . 100

-800 -600 -400 -200 0a (106 NEPERS/S)

Figure 17. Average extracted resonances of the brasscylinder in different ground conditions.

45

I- LhJ Wi. W~. W. LWj

C) CIQ +1r -1 +1 Ckq -7_C__In_-

H j LAJ LL.J LLJ WL00 -czW 0.W

m a

I M m T"

-J I .-)... . .

I- W LLJ LJWLUj

;i 0 . L ()P )02! ;t IC) 01. f-cOCI'llelL4.. I".. C~ ý.o Ol 0

LO Ii'I CJ W+cm-

LQW R

.. DO altLr. L 'c

LrI

0. eI)W -1, 1 4

U.1 m -1 LM Wr N m xU -C r-l% ,-d c )mrai L-HL M e.

C4 1- r In M - -)

0 l Y- CI 0 U') UWU.LL

-j -C -o%4 r, dýk- CrLL~ L

46

00co Ch m4mcnH i LJiL.WA I. bAJ juJ ww .jL

uico 4T m Cl LA.I < mV C~J r" O~l

C0 (D 0 -aV1. M%

+1 -T1 +1 +1 +1 41 +1 +1 1:

I- H LLILLLJ Wj CL LiWj L

r%.oomr% N oC . -

0r Nr- M ,NMM1

p~l.. . . . C

II L

*L. .L L L LJLju A0 e4 1% ON + OW. ko 1O:)C

M CM0 o mko-4 ~ it-_ _ --Vm Nr

I- LULLUýIJ 0.1 tJ LLU H UU0.L

0" m~"n- OH ej 0 ujCJ

II -LU N'O m0 mi. m~ Ch~~x w W L) W w 0 9j uj w

tor t0C LUUU..J I- 9 U Q.,- co 6M

Ll) ! 0` %O* '.0

II U. fm I I 1 I0A 0

I- LUS.JLUU H CULCL

LL71 LiLa W 71L "-L LJU

I c M04! !

CHAPTER IVTHE PREDICTOR-CORRELATOR IDENTIFIER

A. 0Qec tiv es

Thi:A chapter summarizes tUe targec identification procedurebased on the predictor-correltor identification method[40,.-]1].A detailed analysis on the predictor-correlator is presented.Identification performances based on real radar measurements aregiven.

Processing for target identification using the predictor-cor-relator consists of comparing a measured wavearm from an unknown" arget with a calculated waveform produced using the resonances ofa known desired target. The procedure Is as follows:

1. Preprocessing: The preprocessor attempts to suppressclutter and noise. For "single-luok"* identification,the following preprocessing steps are taken:

a. Arithmetic Averaging (see Chapter II),

b. Amplitude Shift (see Chapter II).

c. Time Shift (see Chapter II).

d. 90"-rotation Difference (see Chapter II).

e. Filtering: It was found that with the systeim underdiscussion, almost all of the target signal energyresided in the 0-500 MHz region (see Chapter II),thus, to suppress out-of-band clutter and noise alow-pass trapezodal filter with the transfer functionshown in Figure 18 was inserted into the preprocess-Ing unit. Various critical frequencies were tested,the ones shown in Figure 18 yielded the best !deritifi-cation performance.

* i.e., Identification based on a single radar observation

S.It. . .. i

48

HMf)

f M"

OT 500 2560

Figure 18. Transfer function of the pre-processor filterused in the 0.6m lonq antenna system fortarget identification.

For design flexibility, the filtering processes wereperforned in the frequency domain with the Fast Fourierfransform (FFT) package available in the digital computersystem library. The only goal of the filtering operationis to remove the out-of-band frequency contents withoutadding any extraneous frequencies to the spectrum of thetarget response. The trapezoidal filter structure is adigital filter and was used here because of its linearphase characteristics and the availability of the FFTpackage 'in the digital computer. The FFT package allowstremendous flexibilities in digital filter design. Itis important to note that the use of the trapezoidalfilter here was not meant to be "optimum". More extensivestudy may well yield a better filter structure.

2. Detection: The detector performs a screening operationfor the predictor-correlator identifier by rejecting asundesired-target waveforms those waveforms whose para-meters are not within the desired ranges. The para-meters considered in this study were:

I

I

49

a, Waveform energy (as defined in Chapter II).

b. Peak timing of the waveform.

c. Peak amplitude of the waveform

The desired ranges of the detection parameters were determineoby studying the ranges of these parameters of the desired-targetwaveforms. Examples illustrating the choosing of the detection para-meters are given in Section F of this chapter.

3. Prediction: Predict the calculated waveform using theProny dif.erpece equatign.. .

4. Correlation: Calculate the correlation coefficient forthresho dentification by comparing thE processed andthe calculated waveforms. The correlation coefficient isdefined to be unity minus the normalized total squarederror.

This approach assumes that the poles and the difference equationcoefficients for the desired target have previously been obtained.Thus, only simple algebraic operations are involved in calculating thecorrelation coefficient for an identification decision.

B. The PredictorThe predictor generates the calculated waveform. With the com-

plex natural resonances and a chosen value of T. the coefficients,,t1 's of the Prony difference equation (see Equation (12)) can bedetermined via Equation (11). Thus, for one value of T, we can gen-erate a calculated waveform by one of the following methods.

1. One- stepLjpreaiction:

N- 1rc(t+N[,T) ' -"III rM (t++mT) (22)

or

2. I1!Xte r.PPo. a-t ion:

N -

rc(t+moT,T) : *', rM(t+mT) (23)

ITI = 01I1I #1110

* 50

where

t = ts+nTB , naO,l,2...

and

ToiTB , -1,2,...

rc(t,T) and rM(tT) are the calculated and processed measured wave-form, respectively. t , is the start-time (see Chapter II and III).The parameter mo is an index chosen for suppression of clutter andnoise effects. In this study the interpolation method was used andmo was chosen to be the coefficient of maxinum magnitude. By comn-"aeaing Equtibns (.2),°(23) and (12) we note that when the measuredwaveform is from the desired target, rc(t) and ry(t) are equal andhence perfectly correlated. Note that one calcu ated waveform isconstructed at each chosen value of T and the same measured waveformis used to construct calculated wavefonrms for all chosen values of T.

The one-step prediction method was first used by Hill whoapplied it to the detection and identification of targets (aboveground) near the half space[40]. This method was then modified byMoffatt, et al.[9] to become the interpolation method for improvedperformance in clutter/noise. The predictor uses past values of themeasured waveforms only, while the interpolator uses both past andfuture values and, together with its normalization process, was foundto perform better in the presence of clutter/noise,

C. The Currelator

The correlation coefficient, formed by comparing the calculatedand the processed measured waveform, is a function of T.

te-NT+moT•. [v' (t ,T )- rM (t )]2

t=t + foTT te-NT+moT (24)

'. (r c(tT)+r 2 t)xt = s~moT c

where the start-time ts is taken to avoid the forced response of thebackscattered waveform, while the stop-time te is taken to avoid thelow-amplitude signal at the tail end of Lhe waveform. In this studyt. was taken to be the tivie the absolute maximum of the waveformoccurs, while te was taken to be the time the balun reflection occurs.

Equation (24) can be rewritten as

51

te-NT+moT

t . 2rc(tT)rM(t)p(T ) = t NT oT(2 5 )

te-NT+m0T

t=ts+mT

We note that the numerator of the quotient in Equation (25) is thecross-correlation between the calculated and processed measuredwaveforms. The nominal range of p(T) is -1 < p(T) < 1, and

(T = when rc(t) = rM(t) (26)

The quotient term in Equation (24) is identical to the mean-square error t- in Equation ',21) when the approximated waveform rA(t)in the Prony process is equal to the calculated waveform r c(t). Thus,

p(T) = 1 - (27)

The imdortatice of Equation (27) lies in the fact that it ties

the characterization and the identification processes toqethersuch a way that optimization of one process (e.g., minimum c) witilead to the optimization of the other (maximum p(T)). Therefore,the evaluation of optimum values of the parameters (N,T,tsteM) inthe characterization process leads also to optimum values in theidentification process. This is rather significant in the evaluationof ,(T).

From Equations (24) and (25), we see that the interval in theerror calculation is from t-+m0 T to te-NT+moT, givinq an errorinterval size of te-ts-NT. Thus, the size of the error intervaldecreases as T increases.

D. The Predictor-Correlator as a Filter

In order to understand the operation of' the predictor-correlatoridentifier, it is helpful to consider the identifier as a lineart 4me-invariant filter.

From Equations (21) and (24), we see that, an instantaneouserror e can be defined as

52

Ne(t+moT) = rM(ttI1oT) - r (t+moT) rM(t+mT) (28)

Thus, the instantaneous error e can be interpreted as the output ofa Finite impulse response (FIR) filter[54-56] with the filter coef-ficients &m where

•mr11M, ta (29)

•:• m0

Note that although the filtering operation is based on the samplinginterval T, the instantaneous error exists at the sampling periodof T , where T is taken to be multiples of TB. In the Z domain [54-56),the Tnstantaneous error is given by

-N+m k-iE(Z) Z 0 Z C(7)RM(Z) (30)

where

E(Z) Z transform of the instantaneous error, based on TVN ('N-m

C(Z) / I, Tm Z'm, is the Z transform of the filterm=0 Om 0 coefficient sequence.

RM(Z) = Z transform of the processed measured waveform

and

T = KTB, K= 1,2,'"

The product C(Z)R%(Z) in Equation (30) is the filtering opera-tion in the Z domain. ince the Z transform is based on the samplinginterval T, thus this product term alone results in samples only atthe sampling intervals Qf T in the tine domain. The weighed sumoperation (weighed by ZI/k) fills the time interval between thesesamples with samples at finer sampling interval of TB, and thusassures a yetter error waveform resolution. The presence of thefactor Z-"11o is to make sure that the starting point of the instan-taneous error be consistent with that stated in the definition ofthe instantaneous error for the case of the interpolation method.

Usinq Equations (11), we rewrite Equation (30) os

-N+mo k-l iN

E) mi RM(Z) IL (l-7'zj)0o j=l

jI,

S3

s .Twhere Z, z e are the locations of the desired-target resonancesin the I plane, s. are the complex resonances in the s plane and Nis the number of 2omplex resonances of the desired target. Notethat the locdtions of the complex resonances in the Z plane arefunctions of the sampling interval T.

From Equations (24-31), we make the following important observa-tions:

1. The mean-square error r is the normalized energy ofthe instantaneous error e. c is directly related toe as follows.

_e2 (t)t _(32)

e (t) + 2 )' rM(t) " 2 I rM(t)e(t)tt

where the summations in Equation (32) are taken over the errorinterval. The lower and upper bounds of the mean-square error uare given by Equation (33)

1(33)

where

2e (t)A t

rM(t)t

and the suwiiiatlons are again taken over the error interval.

The error bounds are plotted as a function of x in Figure 19.

From Figure 19, the following observations are made.

a. is bounded as follows

2 ~','.

2 when e(t) = 2rM(t) and (34)

0 when e(t) 0 .

54

2.0 UPPER BOUND

0.5

t(n

0

0

w

0'%0 4.0 8,0 12.0 16.0 20.0

x

Figure 19. Bounds of the mean-square error r

55

b. The lower bound of c increases monotonically as the energyof the instantaneous error rI'* Increases. c approaches1 as r' approaches infinity.

c. The upper bound of c increases monotonically from 0 to 2as c' increases from 0 to the value of

S4ý rM2(t)/((te- ts)/TB

At this &' value, c attains its maximum upper bound of 2.The upper bound of c decreases from 2 to 1 as c' increasesto infinity. Although the upper bound of r does not in-crease monotonically as -' increases from 0 through itsentire range, the lower bound does. Thus, it is reasonableto say that large c' generally means large c.

2. The difference between the one-step prediction and theinterpolation method lies in the filter gain normaliza-tion factor I/amo. In the one-step prediction method,

%N=l, thus, the possibility of larger-than-one filtercoefficients N exists. Such filter coefficients wouldof course amplify clutter and noise effects. In theinterpolation method, Im^ is the difference equationcoefficient of maximum magnitude. Thus, no filter coef-"ficient can have value larger than one,

3. For the desired targett, RW(t) is given by the Z transformof Equation (4) and thus Equation (30) can be written as

1 -N+mo k-1l N N Im 0 1 M 1-1Z1) ,il

0 Ill

I z-N+m 0 k-lI T Q(Z) N- Z . II (l-Z'Iz (35)

"100 N1 JulUI (l-rZ'Iz)0 11 tii Z

,A teNT+mo

L YT, e2 (t)/((te-ts )/TB)

t=t +moT

s i

56

where N, is the number of complex resonances present inthe wavdform and, N is the number of all possible complexresonances of the desired target present within the radarbandwidth and used for target identification purposes.Since certain target resonances may not be excited forsome radar locations and orientations, N1 and N are notneressarily equal. Q(Z) is a polynomial of order N1 in

From Equation (33), we see that the predictor-correlator iden-

tification process is basically a pole-removal process. Furthermore,the process of pole removal is performed by putting zero's at thelocations of the poles.

In the case of Ni=N,ki-N+mo k-y K

E(Z) . mZ Z Q(Z) (36)

Thus

e(nTB) q(nTB) 0 for nTBmoT (37)

0

whereq~T) t1 [N+mio k-I Q(t

q(nT8) Z r, Q(Z

where C 1l[ ] is the inverse Z transform operation. Since Q(Z) is apolynomial of order N in Z-l, q(nTB) is zero for nTB >.moT [54-56].Thus, the instantaneous error e(nTB) is zero for nTB moT and themean-square error would also be zero in this time region. Theabove derivation is based on the assumption that the resonance timereqion of the waveform starts at t-0. Since the resonance region ofthe waveforms considered in this study is assumed to start at tuts,the mean-square error would be zero for t " t +m T. This is thelower limit of the error-calculation Interoal as~defined in Equations"(21) and (24).

In the case of NO,

-N+mo k 1 N-N1E(Z) Z Z O(Z) ii (lI-Z' ) (38)"m i =00

57

Thus

e(nTB) = q'(nTB) (39)

whereN'(n T LZ Ok-I -Z N-N1

q(nT Q(Z) r (1-Z'IZ (40)B)0 n Jul

Since Q(Z) is of deqree N1 in Z , thus q'(nTB) is aqain zero fornTBfjmoT. Thus putting the number of all possible extracted resonances

of the desired target in the identifier assures a zero error and thusa unity correlation coefficient for the desired target waveforms fromall radar locations and orientations. If not all possible extractedresonances are used for target identification, the possibility ofN1>N exists and in this case,

"1N+mo k k Q4E(Z) Z 0 Z N .,N _. (41)

mo i-0 H (l- ZI)i-1

The instantaneous error has poles in its 7. transform, causingit to be a waveform of Infinite duration [54-56]. Thus, a large mean-square error could occur for a desired-target waveform, possibly caus-inq the correlation coefficient to be much less than one.

4. For an undesired target, the instantaneous error dependson the processed waveform rM(t) as well as the locationsof the zero's in the identifier. Small error could resultonly in the cases where the undesired-target waveform isclosely characterized by a set of complex resonances whichare approximately equal to the desired-target resonances(i.e., the zeros in the identifier). In the one-pole casewhere,

RM(7) 1 1

c(Z) (1-ZIZ2) (42)

where R (1), the Z transform of the measured waveform is assumed tohave on y one pole at Z, with residue 1. C(Z), the identificationfilter is assumed to consist of a zero at Z2. The error can beexpressed as

L .. '......... ... . .. .... i' . .. .

58

N+m zk 1 1 z=-

E(Z) Z 0'm i/. lZZ l. kl-Z- Z21 43

m 0120O ~-Z Z1) (3

-Nm k 1ii =0 Z mo

Thus,

I _2 r • /)/T (44)

where I1I11 denotes complex magnitude. Hence the total squared errorIs directly proportional to the magnitude square of the difference

beLween the locations of the pole and the zero.

In a two-pole case where

1-7 l-Z*l~(RM(Z I-'-•" l I''Iz•(45)

C(Z) - -Z' 71 (I ZZ)

where [ 1* denotes complex conjugation. The error can be expressed as

I -N+m 0k-iE(Z) - z a Z L z, +"m0~~ Z= -7 Z -Z*I

1-Z -1 (46)(

2., 20°"!

1.

59

or

E )Z z k i z j z*) + (i zz +Cm o 0 z

o101 [(ZZ2) (zl-z)z]Z"2 F-(ZI.Z )z Z * *) * ,

+ z2 " Li z' 1-1~ JJ (47)

The total square error ' is independent of the first two terms on theright hand side of Equation (47). Furthermore, the inverse Z trans-form of the last two terms are given by [54]

-1 4 z-l( zlz2 + •Z 1,2* -ZI:; 1Z 21-Z"le x

x cos [Lol C-T) + O. J (48)

and

S. ,(z -z)z + (z z ) \-1 [ Y-2 1-9 2 y 2 *

(t- (t-2T)_- i~zi-z211 117211 c x

)+01 (50)

x cos[w,-(t-2T )2)

where ol and o2 are the arguments of the complex numbers (Zl-Z2) .and

Z2, resp ectively

From Equations (47) and (48), w.e see that :'

"I(t-T) {o[qtT+l

0(t iZZ212e 10 s[(•"l~t-t-T))+ •))

ITI

.-A

60

Thus, the instantaneous error depends on the following three items:

a. The amplitude factor IIZ,'Z21 2 = e 2T + e -

-2e 12 cos(W -u2)T, where s " J+JW is thelocation of the zero of the filtgr in the s plane,

l•.; 2e'T " (ti1 "•2)Tb. The factor 2 lz211 = Te

c. The phase term ciwT+o 2=( 1l+w2 )T.

All of the above three items are dependent on the sampling inter-val T. Thus, in designing the identification radar, the value(s) ofT should be chosen to maximize -.' by considering its dependence on theabove three items. In maximizing -_'. we note the following guidelines:

a. Small values* of T result in l 1Z1 -Z ii approaching zero.This causes ' to approach zero. Thus, small T valuesoffer no identification capability.

b. Large values** of T also result in iz -z 11 approachingzero. Thus, large T values offer no identification"capability.

c. Intentediate value of T should be chosen to satisfy thefollowing conditions as closely as possible:

2•IT 2c2T (.l+i)

I. e e and e , approach 1

Sii (,l-_t2 )T approaches In

(I'll +1`i2) approaches 2 ,,

iv. To prevent severe aliasing effects, we requirethat - .m ' and ("2T

* Small T in this case means that the quantity (W•-,)T approaches 0it IT ý"2 T e "I +("2 ) T 1

and the quantities e , e and e approach 1.S2t 1IT 2<• 2 T

"**Large T in this case means that the quantities e , e

and e 1 2 approdch 0a.

,_ •,. +--: •:•:• ,-. """ " • .. r.': f"l•="% ~ ... . .. - .,- -.- ... .. ..

61

Conditions I. and ii. maximize the amplitude factorliZ1 -Z.411. Conditions I. and ill. make sure that the secondtel'm in Equation (5r0) Is maximized and has the same sign asthe first term, Conditions ii. and ill. require that2TiuT , .* Condition i. requires that T be as small aspossible. Thes, toether with condition iv indicate that areasonable compromise is to choose T Such that ,,2T=ir.

Although the above analysis is based on a two-pole system,'I for s ysLuil of iore than two poles, the above rcsults are expccted

to be reasonably valid when ol is taken to be the Imaginary part ofthe dominant pole of the measured waveforn to be identified and w2is taken to be the imaginary part of the zero of the identificationfilter which is closest to the dominant pole. In practical targetidentifications situations, the waveforms from the desired as wellas the undesired tarqets almost always contain more than two poles(see Chapter I11). Furthermore, the dominance of the resonances ofthe undesired target is generally unknown, Thus, for better identi-fication performance, it is advisable to base the identificationdecision-iiiaking process on more than one value of T. Based on theanalysis in this section, the smallest "effective" value of T Is inthe neighborh~ood of TN where

TN LIm 2. . (51)

and 11M-= 2 ,fM is the maximum imaginary part of the desired-targetresonances. In applying the criterion given by Eqý,tion (51) tochoose the values of T for target identification, t,;, word neighbor-hood should be emphasized and taken to mean that, althmugh t-l--e6ngTevalue of T for optimum target-separation performance c,,irot be foundwithouL the complete knowledge of the undesired-target wavefonii, thevalue [JTN should give reasonable, if not the optimhum performance.Furthermoore, for target identification based on more than one valueof T, the region of t values chosen ilhiuld contain TN.

The analysis presented in this qection arc generally supportedby the identification resultsi obtained in this study. Iientifica-tion results are shown in Section F of this chapter.

It is a:,S1uied thit '2"'I NOL thaOL the design of the low-pass Itiller in the preprocessor of the identification radar assures

that frequencies higher than '2 will be highly attenuated. Thus

'2 .. 1 is a valid assumption,

•LI

62

I ho I•dtliti f i cti. 0o1. Al!'jnyri thltl

In this study, a "single-look" identification algorithm was used.At identification decision was made for every measured backscatteredwaveform. The identification aIgorithmi was one of threshold identi-fication based on tIe values of p.(T) evaluated at different values ofT, and the average value of p(T) denoted by <p(T 0 )>. Thus,the decisionalgorithm was

1' 1 (T01 'H for i~1 and 2 .. and I"Desired Target" when

(To "(Toi

p .(Tr ): for ii r .. o

"TAI

"Undesired Target" when 1i(T01) '"THI for i~l or 2 oror ,p (T0 )> THA

"THi is the identification threshold for ,(T) at the T value of Toi.To is are the values of T chosen for optimum identification perform-ance A is the identification threshold for the average of 0 (T)taken ov6 all the values of TQi. Thus, for a single measured wave- 4form, we evaluate its correlation function I(T) at all chosen valuesof Thi and compare the values p(Toi) and ,(To(T> to PTHi and OTHA, 2respectively for an identification decision. Figure 20 illustrates 4.the decision-making process. In Figure 2C, the value of the p(T)curve represented by "dots" at To1 , T02 ' 'To5 as well as <'(To)> aregreater than their corresponding thresholds hence, the targets it re-presents is by decision a "desired" target. The I(T) curve represented &

by "boxes" has at least one of the values ,(Toi) or .:,)(T,)- below itsc:orr-wpond inrg t~hreshold, thus,, tLhe target it represe~nts is by decision

an "undesired" target, .

Toi's are Lhc value of T chosen for optimum identification per-fora•rice. Thie volu s of To1 are closely related to the value of theresonances of the desi red target and Equation (51). Details concern-ing tne values of Tel 's will be further discussed in the next section.In 'qua tion (52), quotation marks are used to signify a decision, i.e.,",hsired target" is by decis ion a desired target while in realit y itcould he an uidusirud target (in case of false alorm).

Thau dcntiticaLion algoriLhin given In Squat ion (52) reduces toits simplest fort when only one value of TO is considered. In thiscase, the identification aigorithini is 01

I;.

""LtM . .... ...

63

o DESIRED TARGET

03 UNDESIRED TARGET1.0 1-1-- 1.0

x THRESHOLD

0 b.. 5 I

XXw x xx V

U.

@w

0 A 0

I' I -A I A A 1 0

-93\d SAMPLING INTERVAL

LU T (0.2ns)a:'

"-J RANGE OF-05

6TiITa• B

Figure 20. lhe decision-mnakirng process for the multiple-threshold identification algorithm.

64

" D o " i re d o r q o " I .'I w h e l o ) T H ( 5 3 )

"ULndesired LaryguL" when '(Io) ' TH

In the following section, the predictor-correlator identifi-cation method is applied to the processed waveforms, Identificationperforandnce will be presented and discussed.

i F. Perfonnance of the Predictcr-

,o-r-etor IdentifierIn order to demonstrate the effectiveness of the predictor- I

correlator, a set of identification perfomlancP besed on a single I

value of ,(T) were obtained by applying the predictor-correlator"alone (i.e., without the filter and the detector) to the differ-e' nce wavefomis. Identification results based on multiple values of

,! •,(T) and with the filter and detector operations instated will be•.!presented late in this section. Identification perforinance was

i characterized by a •,(T) curve. Typical I,(T) curves are shown in

, Figure 21. In this case, the identifier was set to identify the•" mine-like target in a wet ground condition.

-•:•.From Figure 21, we find that typical I,(T) curves have the

-- • fol lowing features:

1. The value of •,(T) is approximately 1 for small valuesof T. This is true for o•(T) of both the desired andundesired targqets, This region of T has no identifi-cation capability.

2. The re~lion of T. where "optimnal" identification perform-ance occurs is in the immediate neighborhood of TNwhere tm is gjiven tLy Equation (51). In this case forjijentijf'i'cation of thle mine-like tarqlet in a qe~t groundCondition. The resonanIce'; of the mine-like target as(Jven in Table Ic was used. Thus, fMj = 420 MHz, corre-spondlinq t~o the rounded TN walle of 6 T[B (or 1.2 ns).For the ,,(T) curves 11vwen in Figure 21, the -e,.Iion ofTo is from 6 TI. to 11 TIj. This result sopported theobservatlimi, made in Section D of this chapter. Thefact. that the reqlion of , t ffvc~tive valuer, of 1' containedvalu',4 lar(W<•r t,1111 IlN indic,itrcd that., the dominant pole(s)in the colppur sheet wave I'omi had imlaginary 1,.,rts lowe•rthan 4?0 MV~z.

3. Theu vdIuO Ot i,(T) fluctuates w-hen T is much larger thanTN (T, 21). This rerion of T has no identification capa-bility, . es des the r'eason given in Section 0 of thischapter, this can also be attributed to the fullowing.

I.

it "" "" . . ." .... "' '". . "-.... . .. .. . ... . - .T "-

S... ... •:•"'•"..... i.............. ... 'nine-l •ik t ...rg ....t in : a ..... we ground j cond... i• •tion. - ,--• . -. .. . •

65

1.0

- -- MINE-LIKE TARGET

- -"- -COPPER SHEET

[.. La.

il -ig-.50 6 12 Is 24 30

p - S4MPLING INTERVAL T (O.2ne)

F i~n 'l I I 1 iT) (lurvw', frJl the identi f icat~iollSf- tfv uirne-i i ke tarjet. in wet ground.

S, .. , • , • ,.S - * S . $• • .. ,• • . .

It

66

F1irst, alidsing of the high frequency zeros in the iden-

tifier makes these zeros ineffective. Second, the sizeof the error interval of the error ý decreases as T in-creases, for the number of instantaneous error samplesused in the calculation of , decreases. Third, becauseof the large value of T, only the tail end of the mea-sured waveform is used in the calculation of f. Thisregion of the measured waveform has low signal level.

The above features of the ,(T) curves were generally observed

in dalmoSt all Cd'%eS considered. The siynificance of these features

is that optimal identification perfornuance occurs in a confined range

of T values in the immediate neighborhood of TN. Hence one knows a

priori the value or range of values of T on which to base the imple-

mentation of the radar system. These features are again demonstrated

in the ,(T) curves given in Figures 22 and 23 for the identification

of the mine-like target and the brass cylinder in dry ground, respec-

tively.

In this study, the criterion for optimum identification performi-

ance was to require perfect identification of desired-target returns,

and thus optimal performance was the one with the lowest false alarm

probability obtained by varying T. Single-look identification and

false alarm probabilities are estimated in a frequency of occurrencesense. Thus,

N2 (54)

NN4 (55)

FA N"3

where

PI Probability of identification

SPFA Probability of false alarm

all.. . ... .... . ... ..... ..

N1 Total number of desired-target waveforrms within theiduntification range.

N2 Numiner of desired-target signals which are correctlyidentified within the identification range.

N3 Total number of other- Larget waveforii-,.

67

MINE-LIKE TARGET

BRASS CYLINDER

- -- COPPER SHEET

-"----- ALUMINUM SPHERE

I-z

U,.

z 0o

0 %1 I 24 30:-.U II|SAMPLING INTERVAL T(O.2ns)w

ccI"hv

t I

* ,.

F i our'e? . Typicil c(u) urves for the identificationof thi, miem-liko tarqet in dr'y r(round.

[. - . - j ~

68

BRASS CYLINDER

MINE-LIKE TARGET

-- COPPER SHEET

-- '--- ALUMINUM SPHERE

-.... WOOD BOARD

1.0

w_ 0.5-

w0

0 6 Ila2 24 30

SSAMPLING INTERVAL T (0.2ns)

at

• -0.5 III

"-1.0

Figure 23. Typicdl (T) curves; for the identificationof the brass cylinder in dry ground.

S~i

69

N4 - Number of oLher-target uaveforins whichi are Mistakento be desired-target waveforms.

Note that N3 , N4 basically determine the accuracy or "confidence inter-val"[65] , f the above estimates of the identification statistics.

To see the degree of separation beLween the mine-like target andother subsurface targets, consider the distribution of correlation co-efficients shown in Figure 24. In this case, the system is set toidentify the mine-like target in wet ground. From Figure 24, we seethat, for P1 = I00%, and To = 9T,, the minimum separation margin be-tween the mine-like target and other targets is 0.93 in the value of

(To). In this case, for an identification performance estimate ofPI = l00%, PFA" 0% 'one can set the identification threshold eTH at avalue ranging from -0.26 to U.167. The maxiiium value of OTH s 0.167.The correlation coefficients for the mine-like target shown in Figure24 include only cases measured within the identification range RID.In this study, identification range is the radar range measured romthe center of the target. Correlation coefficients for the other tar-gets include all cases measured.

A suninary of optimal single-look identi ication) performance is

qiveti in Table 4 (for details, see Appendix E). Estimates of Pi100%, PFA - 0" identification performance were obtained for the

identiication r~ange of 30 cm measured from the center of the mine-like target and the brass cylinder.

This set of identification performance basically establishedthe fact that the predictor-correlator identification method workedin its simplest form and with a minimum amount of preprocessing.However, in a practical system, une would prefer to have the filterand detector inserted for better performance in more severe clutter/noise environment provided that the amount of time taken to performthese operations are not too large to make them non-cost-effective.Furthermore, tne multiple-threshold algorithm would also providebetter performance.

In target identification with detection and multiple-thresholdoperations, the ranges of the detection parameters, i.e., waveformienergy, peak timing and peak magnitude must be chosen. Furthenirore,the values of Toi as well as the identification thresholds r'PTHi and"TmA must be detenylined. In this study,-t ihQ.pwsaeters werew ..mentally determined via the following procedure:

1. The ranges of the detection parameters were chosen tobe the ranges of these parameters of the wavefornsmeasured from the desired target within the identifi-cation range.

2. Choose the range of To values based on the conditionsgiven in Section D of his chapter.

70

~ N 0 (O It N 0_I I

co

:0 6 4-0w 0

*C

LAJO

w 4I J

04-)EIt) 0

S 4-

0 LL N 4-E

~~~~~~r 60 - - - - _ _ 6~.~

w wi

Lu

0 0

go*0 0 Od

I- U

w LC-

A IAV IO0*-.J(3J J70

71

TABLE 4SUMMARY OF SINGLE-LOOK IDENTIFICATION PERFORMANCE

OF THE SHORT-CABLE SYSTEMPI 1 IO0% For All Cases

NUMBER OF"WAVEFORMS

:"0 LUJDESIRED TARGET T RID PFA ,

•-(• C)W X

MINE-LIKE TARGET WET 7TB-9TB .183 30 0% 12 12

MINE-LIKE TARGET DRY 7 TB- 9 TB .483 15 0% 5 3

MINE-LIKE TARGET ICY 7 TB- 9 TB .423 30 0% 9 9

BRASS CYLINDER ICY 5TB- 7TB .675 30 0% 9 9

*PERFORMANCE FOR RID=30 cm WAS NOT OBTAINED IN THIS CASE.

RID ý IDENTIFICATION RANGE, MEASURED FROM CENTER OF TARGET

3. Choose the identification thresholds to be the minimumvalues of (Toi) and -,,(To). evaluated from the desired-target waveforns measured within the identification range.

An example is given below to clarify the above procedure. Fromthe waveforms measured from a mine-like target in a wet ground con-dition, we evaluated their detection parameters (as tabulated inTable 5) and deterinlned the minimum and maximum of these parameters.The rargus of these paraimeters were used as the desired ranges of thedetection paranieters in the detector. With the extracted resonancesfrom the measured waveforms (as given in Table 6), ,ind the conditionsgiven in Section D of this chapter, we chose the range of Toi values

... o' from (Tr-TB4 ) t•"2TN*'.rn this" cas6 fM= 4 2 8 MHz, thus

TN T , it

* 1denotc's qIrvitest i nteger,

72

10 R

LrLcm .- N

HO K tw

-. 1 m L

Ln WN

V 4E 4)

IN

uF LJ L2 IN l y

I-icC)I -

3 1) o3

H I - E4

4, ' ' M -7'

73

TABLE 6AVERAGE EXTRACTED RESONANCES OF THE MINE-LIKE

TARGET IN A WET GROUND CONDITION

POLE POLE(REAL)* (IMAG)

-1.71536397E8 .6.1601933 E7-5.73125538E7 kl.32122486E8-2.87494683E8 .t2.27030133E8-1 ,82908509E8 .3.0741l(43E8-9. 76454733E7 '4. 28447900E8

*Real and imaginary parts of theextracted poles are in nepers/sand Hz, respectively.

With the values of Tni we evaluate the values of p(Tni) andfor' the all measured desired-target waveforms. The mninimum of thesevalues are chosen to be the identification thresholds. This is illu-strated in Table 7.

Table 8 summarizes a set of sinqle-look identification perform-ance based on the additional preprocessing and the multiple-thresholdalgorithm. Note that the size of the ensembles of waveforms consider-ed indicates a better estimate of the identification statistics. Inobtaining this set of identification performance, the region of Tvalues was chosen to be from (TN-TB) to 2TN. Details concenring theidentification results are given in Appendix E.

The identification statistics discussed so far' were obtainedwith the identifier "tuned" to the right ground condition, e.g., thewet-ground resonances of the mine-like target were used to identifythe nine-like target in that wet ground condition. If the identifieris not tuned, identification performance will degrade, e.g., for thewav.eforms ýnni~ered in .Talj. 4.Awl, tb dry-.,Qtvnd. resonancea .wvre ., .

used to identify the mine-like target in wet ground, perforttance de-graded to PI-90%, PFA= 16 .6%. Methods for on-location calibration ofthe ground condition and automnatic tuning of the identification radarto ground condition is currently being pursued. One method is based onthe backscattered waveforms from thin wires measured using the samepulse radar system. Onr.location calibration of the ground conditionand automatic tuning of the identifier to the ground condition arediscussed in Chapter IX.

K ,I.' .-

74

3t0

V, a' C , U,I,..........-2CKD N

I I*

1 g I a , 0

- 00

=1-, I'D .

4a '

75

Identification is degraded when the radar frequencies do notproperly span the target resonances. This is demonstrated in Chap-ter V.

TABLE BSUMMARY OF SINGLE-LOOK IDENTIFICATION PERFORMANCE OF THE

SHORT-CABLE SYSTEM BASED ON ADDITIONAL PREPROCESSINGAND MULTIPLE-THRL 3HOLD ALGORITHM

Pi-1 lO0% For All Cases

NUMBER OFWAVEFORMS

DESIRED TARGET TA RID - SToi OTHi "THA •I.PFA • •,

4TB .948

5TB .667

MINE-LIKE TARGET WET,I 6TB -. 209 .25937 30 0% 9 70

77 TB .243

8TB -. 061591TB -. 118

lOTB .224

5T1B .445

6T8 -. 4887 TB .127

MINE-LIKE TARGET WET,2 8TB .243 .30050 30 5.7' 9 709TB .289

10Th .221

l12TU -. 43629I12TB -.259

I________- --

76

TABLE 8 (Cont.)

5TB .610

6TB .510

7TB .614

BRASS CYLINDER WET 8TB .386 .34073 30 .97% 9 10391B -. 139

lOTB .543liTB .389

12TB .691

5TB .197

6TB .4817TB .600

ALUMINUM SPHERE WET 8TB -. 106 .42942 37 6.12% 8 989TB .218

lOTB .189

1ITB .103

12TB .341

I..4 .• " -, • • • •--'-•-i-.- " ••••-;'T"-- "-

CHAPTER VEFFECTS OF RADAR BANDWIDTH ON THE CHARACTERIZATION

AND IDENTIFICATION OF SUBSURFACE TARGETS

A. IntroductionThq target resonances present in the backscattered waveforms

depend on the bandwidth of the radar system. Target resonancesresiding near the band edge(s) or outside the bandwidth of thi. radarsystem are either weakly excited or not excited at all. Thus, whenthe radar bandwidth is reduced, the number of target resonances presentin the backscattered waveformis will decrease accordingly. In thisstudy, a set of data was obtained with an additional 200 ni of con-necting cables(RG-8) inserted in the system to keep the equipment in-doors during inclement weather. These cables acted as a low-passfilter with attenuation of 30 dB at 400 MHz and thus reduced the radarbandwidth. Such bandwidth reduction was found to degrade identifica-tion performance for certain subsurface targets under consideration.

B. Processed Waveforms Obtained Withthe Lonj-Cab11-e Sys te-

Typical processed waveforms obtained with the long-cable systemare shown in Figure 25. A quick comparison between the waveforts inFigures 7, 9 and 25 indicates the severe loss of high frequency inthe wavefonrms of the mine-like target and wood board. Furthermore,there was a significant loss of signal amplitude for all waveforms.

C. Extracted Resonances

The avera.p extracted resonances of the long-cable wavefol'msfrom the suhsurface targets are given in Tables 9 and 10. A coiupari-son between the extracted resonances in Tables 3 and 9, 10 indicatesa qeneý'ral ToVs f high-frequency resonances iaithe long-cable, wave- . ...forms. The loss of high-frequency content causes Lhe high frequencyresonances to he either weakly exciLed or not excited at all. Acomparison between the resonances extracted from the two sets ofmine-like target waveforiw (as plotted in Figure 26) shows that, inthe long-cable system), the resonance of the mine-like target at 300Mhz was not excited, while the resonance at 400 MHz was only weaklyexc i ted.

77

78

uiI0I

C SL

Liin(N~

saew-#wo-

79

5000

0 LONG CABLE 0 -400

0 SHORT CABLE

0 --300N

0D 0

00200

oD

100

00

I I 0-800 -600 -400 -200 0

al (106 NEPERS/S)

Figure 26. Average extracted resonances from the long andshort-cable mine-like target waveforms.

"..

1• •,•, •; . =. -

F:m • °• -"-'i,. • ' .... L••:•,' J ..•.......•• I ... ." -= •...,, ,i iii I

80

LLJ LU LU LUJ LU

UJ ct QI)'. 001.0CO

cc t- l MW cw 41 +1I fl +1-Ht

ooo-~o LU LO

__i LUL7. N C) - ' LU) LU Ch C-rV1 M

I-, I.-, N 0 C L Ld LLL

CLL LO ~ j LA0 0 > -*) >- .L JLJLJLJC L l

1 C).. In C) (3 I Iu < - IN L1 + 04

Li.U -cc C)

CL 1- LULS.JLULUm 0 ._- I-) I-LD RrM CD<LU a. r-%~D. M Owwtr. d r- ro

00 u N - C1 aw :1 - 0..C 2fl '.0 C . .~L .LUA

C) --I C) IJ M- +I ti +I fI.- j CC -j

LL" LUJ 00-jw- EwLJLJLU u(l _CC) LI) 60C -V -0

1- wf CC LU CL. 0¶ Li Lt 0 o0C- .. 1.LI) 0'. U C) -.. J0. N O' -t0Or'

LULU U: oD ce I=o " c

LU -j ;TlU

MQ J~ L.) LL fy CLU~~0 Ne LL

Lii Li IN-'~

V) -j(T. ) m 011111" CLLJ J LL LLJilm ~j LI UjW IL

(x In.~ oL )C? " R

81

D. Tarqet Identification Performance

Single-look identification performance is sunmiiarized in Table If,*As expected, identification performance degraded. The drastic degra-dation in the perforiance for the identification of the mine-liketarget and the wood board clearly demonstrated the importance of highfrequencies for the identification of these two targets.

TABLE 11SUMMARY OF SINGLE-LOOK IDENTIFICATION PERFORMANCE OF THE

LONG-CABLE SYSTEM. ADDITIONAL CABLE LENGTH-200 m.PI=1 O0% For All Cases

NUMBER OFWAVEFORMS

Lh.JDESIR17D TARGET TM To TH R PFA

0• RHID PFA Ce j 'n •"

oz(cmi)

MINE-LIKE TARGEF DRY 7 TB .675 30 33.55% 9 152

BRASS CYLINDER DRY lOTB .600 30 4.49% 9 156

ALUMINUM SPHERE DRY lOTB .867 52 9.29% 12 140

COPPER SHEET DRY 9T, .964 40 4.35% 11 138

WOOD BOARD WET 7T8 .823 45 23.98% 11 138

The importance of the high-frequency resonances of the mine-liketarget stems from the fact that its high-fre(uency resonances aredominant (see residues of target resonances in Appdenix C). An attemptto identify this target without strongly exciting its dominant reson-ances results in the poorer identification performance. To improvetarget ideuntification performance, the radar must be able to transmitand receive more high-frequency enerqv in the vicinity of these high-order resonances. The short-cable system discussed previously repre-sented an improvement over the long-cable syst.ilm. However, much more

*TIlis set of identification results was obtained based on thresholdidentification with one value of fo and without detection andfiltering.

82

Sillprove•nijlIt Ld:a be mcde in the various cumponents of the pul se radarsystem to provide a better "match" between the systew bandwidth and

the bandwidth in which the dominant target resonances reside. One

of these components is the antenna system.

For the identification of the plastic mine-like target, the1¾ crossed-dipole antenna with arm length of 0.6 1 (2 feet) did not pro-vide a "good" match between the radar system bandwidth and the band-width of the target resonances. The extracted resonances shown in

Figure 14 indicated that tV- antenna resonante Wds not even tledr Lhehigh-order resonances of the mine-like target. Such mismatch ofbandwidths results in the low level of correlation coefficients astabulated in Table 8. For better characterization and identificationof the mine-like target, the frequency of the antenna resonance needsto be increased. One easy way to accomplish such increase is toreduce the size of the antenna. In this study, a smaller crossed-dipole antenna with arm length of 0.15 ni (0.5 feet) was built to pro-vide a better match of bandwidths for the identification of the mine-like target. Mine identification is the subject of Chapter VII.

In the next chapter, we study the effects of target depth and1, size on the characterization and identification of subsurface targets.

i.

"I'

-.- us-aN"., n 2.,aa .c~J.v~,. y ' ~niLu rr ... .,, ~ , .i .- ~ .t . a. i

CHAPTER VIEFFECTS OF TARGET DEPTH AND SIZE ON THE CHARACTERIZATION

AND IDENTIFICATION OF SUBSURFACE TARGETS

A. Introduction

To study the effects of target size and depth on the character-izatinn and Identification technique, two sets of targets wereburied (see Figures 27 and 28). The first set consisted of a seriesof different-size brass cylinders buried at different depths. Thesecond set consisted of a series of different-length 0.3125 cm (1/8-inch) diameter thin brass wires buried at the depth of 5 cm (2inches). Backscattered waveforms were obtained using the subsur-face pulse radar at various antenna locations. Locations of theantenna center are shown as dots in Figures 27 and 28.

1B. Processed Wavefortiis

Processed waveforms from the cylinder and the wire targets areshown in Figures 29-31. From these waveforms, the following observa-tions are made:

1 . All these wavetorvis exhibited some transient behavior,signifying the possible existence of one or more naturalresonances.

. 2. A comparison between the brass cylinder waveforms shownin Figures 9 and 29 indicates that the signal level ofthe waveform from the brass cylinder at 5 cm depth wasapproximately 12 dB higher than that of the waveformfrom the brass cylinder at 30 cm depth. This signifieda propagation loss of over 10 dB -)er 30 cm (I foot).

3. A burst of signal energy appeared in the early-tim.portion of the waveforms from the brass cylinders at90 and 150 cm depth. This was caused by a phenoulenonknown as the "Trench effect"[22].

Rain, snow and evaporation changed the moisture contentof the ground arid the distribution of moisture was per-turbed by the Trench walls. At times diring the r(ourseof a year the groLynd in the trench was found by directmeasurement to be drier and at other times wetter

83

84

UlEU

CLS

* jI1.1 w

cu)

WZ z L

u Lu.

•5

N

60 cm LONGTHIN WIRE W E

1I cm

X< ANTENNA30 cm LONG ORIENTATION 45cm LONGTHIN WIRE * THIN WIRE

DEPTH OF ALL THIN WIRES 5 cm (2 INCHES)DIAMETER OF ALL THIN WIF -S m 0.31 cm ( 1/8 INCH

Figure 28. Layout of the buried thin wires,

86

tE

6--v

0

0

L >1JN

z *-

UU

0 ZCA

CL I.

I, -

0~>1

0 0-I

Nd

I IE

4j 0 N i000W

LC)

C3-

than the ground outside the trench. Thus, the trench be-came a scatterer. The trench signal obscured the cylindersignal and made the task of target identification difficult.

4. Careful study of the waveforms of Figure 31 from the thinwires indicated that the time interval between zero cross-ings increased according to the increase in the wire size.Such phenomenon was not observed in the cylinder waveforms.

C. The Extracted Resonances

1. Effects of target depth

To see the effects of depth on the complex resonances, theaverage extracted resonance of the 30cm long cylinders at differentdepths are shown in Figure 32, From these resonances, we make thefollowing observations:

Sa. The high-frequency content in the backscattered waveformswas highly attenuated as target depth increases. The"highest-order resonance which was present in the 5 and30cm deep cylinder waveforms was absent from the wave-forms of the deeper rylinders.

b. All resonances with imaginary parts smaller than 400 MHzwere present in the cylinder waveforms of all depths.

c. The lowest-order resonance was the antenna resonance(0.6m long antenna). This resonance was present in almostall the waveforms of all targets at all depths collectedusinq this antenna.

d. The imagni nary part of thfa target resonances of the brasscylinder occurred in integer multiples of the imaginarypart of the lowest-order target resonance. This seemedto suggest that the extracted resonance of the brasscylinder were caused by the multiple scattering mechanismsalong the length of the cylinder only (i.e., the dipolemode)[21], the creeping-wave modes were not present in thewaveforms. The absence of the creeping wave type reson-ances was furthejr emphasized when we compared the extractedresonances of the same-size thin wire at the depth of 5 cmto the cylinder resonances (see Figure 32). The same lower-order resonances were extracted. This proved the absenceof the creeping-wave modes, for the creeping-wave modesof the thin wires have resonant frequencies which are toohigh to be present inside the bandwidth of our radar sys-tem. The absence of the creeping-wave modes is attributedto the high loss suffered by the creeping waves as ittraveled around the circumference, and the cross-polari-zation effects of the crossed-dipole antenna system,

90

500

0 THIN WIRE, 5 cm DEEP

0 CYLINDER, 5 cm DEEP

A CYLINDER ,30cm DEEP

0 CYLINDER ,90cm DEEP 400

V CYLINDER , '50cm DEEP

LENGTH OF TARGETS*30cm V

0200N

S~aoo

100

.0-800 -600 -400 -200 0

l (106 NEPERS /S)

Fiquru 32. Average extracted resonances of the 30cmlong cylinders at different depths.

91

With the absence of the creeping-wave type resonance.,frow the point of view of the target resonances, the thinwire and the cylinder are indistinguishable. Separationof these two targets i5 possible only when discriminantsether than the lower resonances are used. One suchpossible discriminant is the forced response of the back-

scattered waveforms which contains information about theprofile area of the target[48].

e, The fact that the extracted resonances of the 30cm longcylinder are related solely to the length of the cylindersuggests the use of these resonances to estimate theparameters of the ground. If we consider these resonancesto be an approximation to the resonances of the same-sizecylinder in a homogeneous medium illuminated by a planewave, the imaginary parts of these resunances can beapproximated by Equation (54)[21]

fn n , n n = 1,2,3... (54)2L~rr

where L is the physical length of the cylinder, c is thespeed of light in free space and "r is the relative die-lectric constant of the medium. Using Equation (54) andthe extracted resonances of the 30cm long cylinder asgiven in Figure 32 the relative dielectric constant isestimated to be approximately 20 at the resonant frequencyof approximately 100 MHz. This estimate agrees closelywith the estimate from other methods currentl, beinginvestigated in the ElectroScience LaboratoryL58].

The complex resonances of the 30cm long cyl ir~ers and thinwire relate very simply to their physical size. This simple rela-tionship disappears when the size of the target increases beyond acertain threshold. This is demonstrated in the following discussion.

2. Effe:ts of tarL•e.size

As target size increases, we expect tile target resonances to belower in frequency. Such expectation turns out to be warranted whenwe consider the extrdcted resonances of the dIifferent-sizc thin wiresat. the depth of 5 cm as shown in Figure 33. Again, the imaginaryparts of target resonances occur in simple multiples of the imagi-nary parts of the lowest-order target resonance, and as tile length ofthe wire increases up to 60 cm, the frequency decrea:.e, according toit,, size. This expectation turns out to be unwarranLed when thelength of Lhe cylinder increases to uver 90 cm at the depth of 30 cm.

92

500

u 30cm LONG30 45 cm LONG

A 60cm LONG -400

DEPTH OF THIN WIRES 5cm

o -300N

0

k 200

' 0•. [0

ANTENNA . 100

0 o-800 -600 -400 -200 0

Figure 33. Average extracted resonances of the

S~different-size thin wires at 5 cmi depth.

i

93

Extracted resonances of the different-size cylinders at the depthof 30 cm are shown in Figure 34.

Although resonances of the large-size targets are no longerrelated to their sizes in simple form, however, there are stillresonance- presant in the backscattered waveforms. Hence identi-fication of these targets is still possible. Some identificationresults are presented in the next section.

500O 30cm LONG0 90 cm LONG 0

A 150cm LONG

V 300cm LONG A - 400

CYLINDER DEPTH ,30cm

0A• 0_ 300N

ID

0

0 200A

AV• o -- 100

-800 -" -'600 -400 -200 '00

1 (106 NEPER /S/ )

Figure 34. Averaqu extracted resonances of the different-size cylinders at 30 cm depth.

• ir' | I '•- -'-' - .-'-- -... I -. I -

94

0. Target Identification

Some single-look identification performance results are givenin Table 12. Based on these results, the following observationsare made:

1. All false alarm probabilities were less than 8%. In somecases, estimates of Pi=1 lO0%, PFA= 0 % were obtained.

2. Identification range decreased as target depth increased.

In the nexL chapter we focus our attention on the detectionand identification of mine-like targets in more extensive and practi-cal situations. Improvements over the Terrascan-like pulse radar aremade for the implementation of a portable on-location real-time sub-surface target identification radar.

TABLE 12SUMMARY OF SINGLE-LOOK IDENTIFICATION PERFORMANCE

FOR THE BRASS CYLINDERS OF DIFFERENT SIZESPI 1 lO0'i% For All Cases

BRASS CYLINDER NUMBER OFS-..1 WAVEFORMS... .... ...... .... .. .. I D PFA ..... O• . .

I LNGTII DLiPTII R. . . .A(ui) (cm) South- East-*

North West - _

30 JO 30 30 3.08,:,' 11 65

90 30 60 30 7.25 9 69

150 30 105 30 02I'l, 17 65

300 30 150 30 01 9 65

300 90 150 15 7.9,1 7 38

300 150 150 15 0% 9 3

*See Figure 27.

F . .. .NS#4.i4

,~t~. ~ #s~vt.. .t • nmII I .t I I . I- I

CHAPTER VIIELECTROMAGNETIC MINE DETECTION AND IDENTIFICATION

A. Objectives

This chapter focuses on the detection and identification of mine-like targets. First a second model of the mine-like target was buriedat the same depth of 5 cm. Measurements were obtained over the twoisolated mine-like targets for comparisoia and identification. Second,to simulate a realistic mine identification situition a set of wave-forms was obtained over a section of a rouqh road in which numerousfalse targets existed. These false targets were caused by the debrisexisting In the old country-style road, and thus represented a set ofrealistic false targets in a mine field. The set of rough road measure-ment was used for evaluition of "typical" false-target discrimination.Third, a sniall antenna of arn length 0.15 in (0.5 foot) was built andused to provide better characterization and identification of the mine-like target. Performance of the small-antenna system is presented anddiscussed.

B. A Second Model of theMiin e-Like Tariet

Typical processed waveforms from the two mine-like targets atthe same relative antenna-target geometry are shown in Figure 35,There are minor differences in these two wavefonns. This can beattributed to the minor difference in the structure of these twotargets, clutt ter 1ud the differene in the gjround conditions atthe two target loc1at. ionn. Complex natural resonances of the twomodels of the mine-like target were extracted fron their backscatteredwaveforms using Prony's method. The average extracted resonances ofthe two models are shown in Figure 3b. Again the slight differencein the locations of these two sets of resonance is attributed to thepossible slight difference in the structure of the two models, clutterand the difference in the ground conditions at the two target sites.

95

.

96

II-/ .4..)

0)

0)

0

It) U�I

0)

0

0

.4..)I.hJ --J

H 002/

U,

Ut�&J LA. 0U, '4-

0)

'Nj3

0)

0)U0

C-,

0)

I.-

C,

.4

_______________

97

5OO

0 FIRST MODEL

O SECOND MODEL-400

300

D00 200

0 O~

CD- 1 00ANTENNA ,

10-800 -600 -400 -200 0

C (106 NEPERS/S

Figure 36. Average extracted resonances of the twomine-like targets.

- - ,r.....--.....

9R

I. Kse 1inryeL Mu,,,•urremenrtsi Wn t -h-e Rou•yh Road

A set of 53 (difference) waveforms was collected over 53 loca-tions in a 40m section of a rough road adjacent to the Electro-Science Laboratory. These echoes were probably a result of debrisexisting in this old country-style road. There were numerous suchfalse targets observed. Pictures of the rough road is shown inFigure 38.

The measurement locations were chosen to ensure significantfalse-target signal levels for a more realistic and difficult testof the identification method. Figure 38 shows a typical false-targetwaveform.

D. Mine Identification

The predictor-correlator identification method was applied tothe waveformis from the two mine-like targets and the rough road-bedFor' identificition of the two mine-like targets and false-target dis-crimination. Single-look identification statistics are given inTable 13,

This set of identification statisticq basically established thefact that the predictor-correlator identification method did Indeedsuccessfully identify different models of the mine-like target atdifferent locations. Furthermore the method successfully separatedthe mine-like target from the set of false targets which were typi-cal of the false tarceLts found in a realistic mine field,

The pulse radar system discussed so far represented a workable(and successful) mine identification system, however two obviousimprovements could be made. First, there was the bandwidth mismatchproblem (as discussed in Chapter V) that resulted in low-level valuesof Lhe correlation coefficient. The bandwidth mismatch problem couldbu c(rrected by introducing an antenna system with a higher-frequencyaintenna resmnance. Second, the size of the crossed-dipole antenna(1.2 in (4 tfet) maxinium dimension) was a bit too large for a practicalmine identification system. There existed a single solution to thetwo problems mentioned above, This solution was the reduction in theantenna size. Since the 0.6m lon (arm length) antenna had a resonance at 65 Mliz, a 0.15m (0.5 foot) long antenna would have a resonanceat 260 MHz which was close to the nild-frequency of the resonance band-width. A crossed-dipole of 0.15 m anii length was therefore built forimproved mine identification purformance[59]. Perfornmance of thisantennd on the identification of the mine-like target is discussed inthe next section.

I ~99

4.,

Figure 37. The rough road for fal se-target measurements.

* yr.. -

I*� 00

11 01..

0

4-,

I :580 r�

4-,

cJ'4,

I -C

0F U

0EI.-

ciciI.-

a:.0�I-ciI0�

I

- ,.a. �

101

TABLE 13SINGLE-LOOK IDENTIFICATION STATISTICS: THE FIRST AND

SECOND MODEL OF THE MINE-LIKE TARGET VSTHL FALSE TARGETS IN THE ROUGH ROAD-BED.

Pi=100%

INUMBER OF

WAVEFORMSDESIRED TARGET - T0 i RID PFA -

m~ (cm) t

F O 4 TB .948

5T3 .667MINE-LIKE TARGET WET,1 6TB -.209 .25937 30 1.85% 9 53FIRST MODEL 7TB .243

8TB -. 06159 TB -. 118

lOTB .224

5TB .445

6TB -. 488

MINE-LIKE TARGET WET,2 7TB .127 .30050 30 3.70% 9 53

SECOND MODEL 8T8 .243

9TB .289

lOTB .221

lITB .436

12TB .259

102

E. A SmaIlI Antenna for Improved_ .Performancei n Mine I dentiFication

A picture of the small crossed-dipole antenna is shown in Figure39. This antenna was used to obtain a set of measurements over the5 cm deep targets. Typical processed waveforms are shown in Figure 40.For comparison purposes, Figure 41 shows the processed wfveforms ob-tained using the 0.6m long antenna over the same target locationsFrom Figures 40 and 41, we note the following improvements obtainedusing the 0l.15m lonq antenna. First, thp fl.15m long antenna offersa gain of at least 6 dB in target signal level. Second, the level ofthe no-target signal obtained using the 0.15m long antenna is gener-ally lower. Third, the tiOe interval of the target signals obtainedusing the 0..15m lung antenna is only half as long. This reductionin interval size would effectively reduce the computation time forevaluating the correlation coefficient by a factor of two.

Due to the minimization of the length of the inter-connectingcables at the balun-antenna connection of the small antenna, the balunreflection exists in the early-time portion of the waveform. In thisregion, the primary target signal level is much higher than the levelof the balun reflection. This severely suppresses the effects of thebalun reflection. The decrease in cable length is also a contributingfactor to the 6 dB gain in signal level. With the balun reflectionmoved in, the stop-time te of the error-calculating interval in theProny's and the predictor-correlator identification pr~cesses had tobe changed. In this study, the choice of te for the small-antennasystem was based on the resonances of the mine-like target. The valueof te was chosen to yield an error interval of size equal to fivetimes the period of the lowest imaginary part of the t~arqet resonances(125 MHz), This resulted in the te value of ts+lOOTB.

Figures 42-44 shows more waveforms and their FFT's obtainedusing tne 0.15m long antenna. From the FFT's of the waveforms, itis found that most energy resided in the frequency region of 100 Mto bOO MHz wit.h the most dominant frequency in the region of about30(0 MHz (as compared to 70 MHz for the 0.6m long antenna).

The set uf wavufornis obtained with the small antenna over the5cm deep targlets was processed for pole extraction and identifica-tion of the mine-like target. Average complex resonances of the mine-like target extracted from these waveforms are shown in Figure 45.For comparison purposes, the extracted resonances from the minf-liketarget waveforms obtained with the 0.6m long antenna in a similarground condition are also shown in Figure 45. The locations of thetarget resonances from both antennas were almost identical. However,

the imaginary part of the antenna resonance increased by a factor of 4when the length of the antenna arm was reduced from 0.6 m to 0.15 m.

103

tAC

Lu 4

Co

4-.

cm.

104

00 0 Q0D OD 0o o

0 wj

W-2 L

I- I- 9Ww ' 4--Ij I

r wD w

W. U

0 0wICLol

w E U) U

LA4

105

In in 0

[o 0 s

0L 0 W

w 5w

LLi

106

6-E E

wwILJ

LDDW w0 owIn e

CZ 0 2

-1000 00

C~L

- n-

~10

2~ W~

U LL.0J .

ww

ED 0

4 w1

I- CA

LU UJO1(0c0

%Mmih--

IIaim

CL cr

'Li-

r

LA

109

500

0 0.15m LONG ANTENNA

D 0.6m LONG ANTENNA ()'2/ 400

0300ANTENNA POLE----

O0

100

ANTENNA POLE -_..,

. I Io-800 -600 -400 -200 0

a (106 NEPERS/S )

Figure 45. Average extracted resonances from the mine-liketarget waveforms taken using the O.15m and theO.6m long antennas in similar ground conditions.

110

Complex resonances of the various 5cm deep targets are shownin Fiqure 46. The antenna resonance was present in almost all targetwaveforms measured. The complex resonances of these targets were inthe same general area of the complex frequency plane as the antennaresonance. This was expected to present a difficult test to theidentifier.

Single-look identification statistics obtained using the smallantenna in identification of the mine-like target is shown in Table14. Typical ,(T) curves are shown in Figure 47. From Table 14 andFigure 47, the following observations are made:

1. Target identification performance estimates based on theextracted resonances of the mine-like target was PI=l0O%,PFA= 1 . 7 2 % within a 30 cm radius of target center. Withina 45 cm radius, identification performance was PI=IOD%,PFA=6.90%. This set of statistics was obtained with anensemible of 13 mine-like target and 58 false-target wave-formls. These performances represented an improvement overthe performance obtainable with the 0.6m long antenna.The 0.6m long antenna system was unable to identify themine-like target in a distance of more than 30 cm fromthe target center.

2. In addition to the range improvement, a quick comparisonbetween the identification statistics given in Tables 8and 14 indicates that the level of p(T) values for thewine-like target were generally improved. It is expectedthat thiý will produce improved identification in the pre-sence of greater amounts of clutter. It has already beenobserved that target identification in the presence ofclutter has been improved.

3. The region of To values for optimum identification per-formance was in the neighborhood of TN-6TB. However,this region of To values was shifted toward small Tovalues. This was attributed to the shift to dominance ofto the hiuh-frequency poles due to the shift in theantenna resonance. Note that the region of To includedTN.

Because of the change in the bandwidth of the small-antennasystem a band-pass filter was used in the preprocessor ofthe identifier to suppress out-of-band clutter and noise.The transfer function of the band-pass filter is shown inFigure 48.

In the next chapter, we discuss the implementation of the small-antenna mine identification system as a microcomputer system. Targetidentification performance will be given.

'I

111

600

0 MINE-LIKE TARGET0 COPPER SHEET v 500A ALUMINUM SPHERE

SWOOD BOARD )

0 400V

ANTENNA POLE 03O

0

13 200lVA

0a A V 100

0

Il. ., I I I-1000 -800 -600 -400 -200 0

a (106 NEPERS/S)

Figure 46. Average extracted resonances from the waveforms ofthe 5cm deep targets obtained with the smallantenna.

112

MUISIO fO

In

>--

LUW

-V)

I-

LU.L

-4 LUMLIL-

1.1-j __o_ co 13__

~LLD

LLLH

113

0

"MINE-LIKE TARGETI----- OTHER TARGET

it z

w°

I'

20 0.2 18 024 30

0*

Figure 47. Typical ,(nT) curves for the identification of themine-like target using the small-antenna system.

H M)

200 500 2560 Mz

Fitqure 48. Transfer function of the preprocessorfilter used in the 3mall-antenna sys-tem for target identification.

r

CHAPTER VIII

A MICROCOMPUTER SYSTEM FOR REAL-TIME ON-LOCATIONSUBSURFACE TARGET IDENTIFICATION

A. Objectives

This chapter discusses the implementation of the pulsc radaridentification system as a microcomputer system for real-time on-location identification of subsurface targets. The identificationradar, is implemented with an SDK-80 microcomputer[60] in conjunction

with the Terras~an. The processing algorithms are stored In thesystem as microprogramst ArithmoLic operations are performid by a

hardware arithmetic processing unit and data can be recorded by a

cassette recorder. Thus the microcomputer system can serve either asa real-time identification system or as a data-recording system.

B. Structure of the Microcomputer

The basic structuru of the microcomputer target identificationsystem is shown in Figure 49. The major components and their corre-spondilng functions are the following:

I. Terrascan System: the raw backscattered waveform is

• i de byT-- --- -the crossed-dipole antenna in analogform. This inalog waveform is samplied by theTerrascan system which essentially serves as a sampl-

ing oscilloscope and provides various flexibilitiessuch as gain, time delay, and dc offset to the wave-form. The sampled raw waveform Is displayed on theneon di,;play and then fed to the analog board as adiscrete-time signal.

2. Analna Board: besides converting the sampled raw wave-form to digital form using an 8-bit AI/D converter,the analog board provides a keyboard for inputtingto the microcomputer system. Various operatingmodes of the microcomputer system are Initiatedthrough the command codes entered from the keyboard.The analog board also provides 6 LEn) displa~y lightsfo- displaying echoes of the input command codes,various system operating information, and Important

114

-Br -.. ,-

AAPU

ANTENNAN A NAO DP

SMEMER

G ENERATORSCASSETTE -

RECORDER

SYSTEM

Figure 49. Block diagram of the microcomputer systemfor un-location subsurface targetidentification in real time,

information concerning the received waveform (suchas peak timing, peak values, etc.).

3. SDK-3O: this is the microcomputer unit. All operatingsystem progrwims, signal-preprocessing, detection andidentification and data-recording operations arestored as microprogranis in the SDK-80[60], Thesemilcroprograms are executed when the proper commandsare entered from the keyboard. The SDK-80 is an 8-bit machine running at a clock rate of 2 MHz.

4. Arithmetic ProcessinL UnitIAPU_: the hardware arithmeticprocess--in unit is interfaced to the SDK-80 micro-computer for high-speed arithmetic calculations. TheAPU provides various flexibilities such as floating-point nr fixed-point arithrnetir. single or double pre-cisiori, function (such as trigonometric functions,etc.) generations, etc.

---- ~--

116

5. Memory Board: 8K memory bytes (8 bits/byte) for datastorage.

6. Cassette Recorder: used for data recording

Similar systems had been built and documented under differentstudies[67] at the ElectroScience Laboratory. Except for the additionof the hardware arithmetic processing unit, the system developed andimplemented in this dissertation has basically the same design andhardware. Thus, only the details concerning the APU are given inAppendix I. Details concerning the other modules of the microcomputersystem are well documented in various reports[67].

C. Implementation of the Microcomputer Systemfor Subsurface Target Identification

Pictures of the microcomputer system and its components areshown in Figures 50 and 51. Two major operations, namely targetidont.i ficition arid d1t0a rocording wor 'Imnplemented in the microcomputorsy lum, Thu tdt'ut IdutiHfictito process perfolrned by the microcom-puter is outlined in Figure 52. All processes except the automatictuning process have been implemented. The tuning process is discussedin Chapter IX. In short, when the target identification mode is beingexecuted, the Terrascan samples the received analog waveform, displaysand feeds it to the analog board for A/D conversion. The digitalwaveform is then fed to the memory board where the average waveformis formed. The average waveform goes to the preprocessing unit forreduction in clutter/noise. This preprocessed waveform arrives at thedetector for a screening operation. The detector screens out wave-forms whose energy, peak timing and peak amplitude are out of the de-sired ranges. The "in-range" waveform would then be fed to the pre-dictor-cnrrelator for target identification. "Out-of-range" waveformsare considered as "undesired-target" waveforms. The correlation coef-ficients and the processed waveforms are stored in the 8K memory whichis transferred to the cassette recorder when filled. For targetidentification based on the predictor-correlator method, only thedifference equation coefficients corresponding to the desired targetneed to be stored in the microcomputer for the evaluation of p(T), thecomplex resonances are not stored. For multiple-threshold identifica-tion, a set of coefficients corresponding to each chosen value of Toineeds to be stored. Note that these coefficients depend on groundcondition, thus, for on-location subsurface target identification inreal time, an automatic tuning process is necessary. Automatic tuningof the identification radar to the ground condition is discussed inChapter IX.

A list of executable commands and their detailed descriptionsare given in Table 31 of Appendix I.

117

II

LC)0

ý41 Lt

118

ANALOG BOARD 4SDK8 BORD8K MEMORY BOARD

()THE MICROCOMPUTER

* * KEYBOARD .

(b) *rEANALOG BOARD

Figure 51. The microcomputer and Its components.

119

EPROMS FOR S0J30A

MICROnROGRAM

IF

(d) THE 8 K MEMORY BOAR~D

Figure 51 (cont'd). The microcomputer and its componenlts,

120

r (n~pI. SAMPLES OF POESDWVFRMEASURED RAW WAVEFORM PROCESSED At1 FnT(DIStACRTE TIME) 01 .

ANALOG PRE-PROCtESsoR DETECTOR

BOARD O EOFAOIONVERT MEMORY BOARD (DAVIRAGING DEKTMNOT

linT.) STORE THE1, TO RAW WAVRFORMS *AMPLITUDE OPEAK VALUE OUT

DIGITAL.4 IN MEMORY A OFFSET OF RANGE ?FORM Q90 DI'FFERENCE cJVENERoy OUT

r/ \ nLERIN OF RANGE?

(DIGITAL)/

TO CASSTTERECORDER

00R10ICTOR -CORNELATOR 0IONVIFIER

*N RANGE" PROCElSSE WAVIFORM 0ES1RED TARGET

SPICFY (7j) ND p (7, )>(

To,&~~~~O T.TPRDCTR>OR9TO TRSHL

GROUNDTIOIDITION

F~~gure 52, The identific ~~Atoprcs imennednthmicocmpte system.DTRGT'

121

The following notes with regard to the implementation of themicrocomputer identification system are important:

1. Due to hardware constraints in the Terrascan, a waveformobtained with the microcomputer system contained only 128 data points.The waveforms obtained with the digital computer controlled systemcontained 256 data points. Thus, we were faced with possible loss ofresolution in time (i.e., a large,, sampling period must be used inorder for 128 samrFes to cover a 50 ns time window) or frequency (i.e.,smaller time window must be used). Careful study of the small-anteanawaveforms from the mine-like target revealed the fact that the energyof practically all waveforms resided in a time window of 25 ns (seeFigure 40). Hence, by choosing a time window for 25 ns and 128 samplesfor the mine identifier, both time and frequency resolution were main-tained.

2. Besides frequency and time resolution of the waveforms, theother important considerations are data precision, flexibility andspeed. In this system, double-precision floating-point* arithmeticis used to perform the major calculations such as the evaluation ofthe correlation coefficient A(T) and the FIR filtering in the prepro-cessinq unit. The floating-point format offers large dynamic range,flexibility and ease of implementation. The function-generation capa-bility (such as trigonometric functions, transcendental functions, etc.,arv available f0' floating-point numbers only) of the APL! provides tre-mendous flexibilities in the implementation of digital signal processingtechniiques. These, together with the fact that scaling operation Is notneeded for floating-point operations, makes the floating-point formatan ideal choice for a "first-generation" computze,' system. The tremend-ous aoKunt of scaling operations in the fixed-point calculations makesthe calculations difficult to track and furthermore, the great amountof scalitiq often causes loss in data precision. The trade-off in us-inql the floating-point foriwit is the computing speed. Floating-pointoperations usually take more comiputing time than the correspondingfixed-point operitions. Furthermore, the 25-bit mantissa offers less"nominal" data precision than the 32-bit fixed-point formated number.With tne choice of data format, we now estinmte the computing timeneeded for an identification decision. The major areas requiringsignificant emnunt, of computations are the following:

F'oa'tlng-puint number in this system is represented by a 7-bitexponont and a 25-bit mantissa.

122

a. Arithmrtic averaging

This procLss forms the arithmetic average of C'] raw waveforms from.the same antenna location and orientation for reduction of noise. Here,the major part of the computation time goes to the sampling of the Nlwaveforms. The sampling time At Is inversely proportional to the repeti-tion frequency of the radar source, i.e., the impulse generator, and

N1 N2

where

N1 number of waveforms required to form the average,

N2 number of samples in a waveform, and

RF * repetition frequency of the impulse generator.

In the present system, N1 -10, N -128 and RF=256. Thus Atw5 seconds.If the repetition frequency can be increased to 10 KHz*, At will bedecreased to 0.125 second.

b. 90w-difference

This process forms the difference between two waveforms from two* antenna orientations (one of which is a 900 rotation from the other)

at the same antenna location. The differencing operation basicallyincreases the sampling time by a factor of 2. In the final systemapplications, this process is probably not needed. At any rate, theantunna rotation process will represent a major time factor.

c, Calculation o

This process evaluates the correlation coefficient p(T) at allchosen values of Toi's for multiple-threshold Identification, Notethat with the choice of floating-point format, the expression for p(T)given in Equation (24) can be manipulated for minimum computation time,In floating-point calculations, due to the shifting of exponents re-quired for the add/subtract operations, the amount of time required toperform an add/subtract operation can be larger than that required fora multiply/divide operation. Table 15 lists the computation time re-quired by the APU to perform each of the four basic floating-pointarithmietic operations. The maximum difference in the average computa-tion time for the four operations are less ihan 23% of the minimum

*This is believed to be within state-of-the-art technology.

........... **'* .

123

TABLE 15COMPUTATION TIME REQUIRED BY THE APU TO PERFORM

THE FLOATING-POINT ARITHMETIC OPERATIONS

FLUATING NUMBER OF CLOCK CYCLES*POINT

OPERATION MINIMUM MAXIMUM AVERAGE**

ADD 56 350 203

SUBTRACT 58 352 205

MULTIPLY 168 168 168

DIVIDE 171 171 171

* 1 clock cycle = 500 ns"**AVERAGE = (MINIMUM+MAXIMUM)/2

average computation time. Thus it seems reasonable to manipulate theexpression for ,(T) to minimize the total number of operations. Basedon the above criterion, the following expression for p(T) is implement-ed in t0c predictor-correlator of the microcomputer system for targetidentification. t

>' e2 (t)

t =t +m +0 T

,T) - fl.T titr+m0 T (56)rir(t) (rN(t)'e(t)) + C 2(t)

L=ts +moT t-t- +moT

where

e(t) = rM(t)-rc(t)

The number of aritimietic operations required to evaluate r,(T) at a Tvalue of To1 is given in Table 16.

L , .. i

124

TABLL 16NUMBER OF ARITHMETIC OPERATIONS REQUItRED

TO EVALUATE p(T) OF EOUATION (56) ATTHE VALUE OF T=Toi

OPERATION NUMBER OF OPERATIONS

ADD (N+2)(M-NIoi)-I

SUBTRACT M-NIoi

MULTIPLY (N+1)(M-N1Ioi)+l

DIVIDE 1

In Table 16,

N number of resonances of the desired target usedfor identification purposes,

M (te'ts+TB)/TB, and

10i Toi/TB

Note that M-NI 0 is the number of instantaneous error samples inthe error interval.

With the small antenna system and for mine Identification, N=-O,M=1Ol 1o =4,5,6,7 and 8 (see Chapter VII). The total computation timeranges fromO .26 seconds to 0.64 seconds with an average of 0.45 seconds.

d. The filtering operationIn t,-Fepreprocessor

Because of the unavailability of the FFT package in the micro-computer system, the digital filtering operation in the preprocessorwas performed in the time domain via the following relationship[55,56]

N'rM(nTB) = h(iTB)rl(nTB-iTB) (57)

where

125

rM(nTB) the processed filtered waveform,

rl(nTB) -- the processed unfiltered waveform,

h(iTB) impulse response of the digital filter, and

N' order of the digital filter.

The impulse response of the digital bandpass filter given inFigure 47 was obtained by taking the inverse FFT of the digital filtertransfer function. This impulse response and transfer function areshown in Figures 53a and b, respectively. Using this time-domain fil-ter, a set of identification results was obtained using the in-housecomputer for the identification of the mine-like target based on thesmall-antenna waveforms previously obtained (see Chapter VII). Identi-cal estimates of identification performance were obtained (i.e., P

00%, PFA1. 7 2 % for RID=30 cm, and P 10 0%, P 6FA.6 9 0 % for RID45 ct).

The time-domain filter shown in Figure 53b is a FIR filter witha large order of N'=128. Thus, tremendous computation time will beconsumed in the filtering operation if it is to be impelemented in themicrocomputer system. To save computation time, the order of this FIRfilter was lowered to 37 by using a "windowing" technique with a Kaiserwindow[55,56,61]. The Kaiser window, the "windowed" impulse responseof the filter and the FFT of the windowed impulse response are shownin Figure 53c-e. Identification performance estimates obtained usingthe in-house computer with this windowed filter was P=1 lO0%, PFA- 8 . 6 2 %for RID-:45 cm. Thus, performance only slightly degraded. This filterwas incorporated into the microcomputer system for real-time identifi-cation of the mine-like target. The windowed time-domain filterhas 37 coefficients and is symmetric about its center. Based onEquation (57) and Table 15, the average time required for the filteringoperation on a small-antenna waveform is 0.5 seconds (vs 2 seconds forthe unwindowed filter). The digital filter can be replaced by an ana-log filter placed at the front end of the receiver in the final identi-fication system.

e. Detection

Operations performed in the detection include peak detection,energy calculations, etc.

f. E xecut.ion of coniiiu ter. r .in.st.r-uc-t.ion.s'

The amnount of time taken for execution of the computer instruc-L iuns depends on the efficiency of the microprogram written.

In sunmiwnarizing, the amount of time required for an identificationdecision in the identification of the ,line-like target with the exist-ing small-antenna microcomputer system is estimated to be approximately11 seconds with 0.45 seconds of average predictor-correlating time.

0 ,

20 25TIME Ino)

hI

0 104 ii 1512 2018 252FREQUENCY (MHv)

(a) (b)

IfiF/•Ig-Ld LtI

9 5 10 Is 20 25 5 014 -7 a

TIME (pa) A TIME (no)

Cc) (d)

---- t

H M

a

6 TII I t t. I I 1

0 504 IOCh1 1512 2010 2520FREQUENCY iMM:)

Figure 53. Design of thie orraceswor FIR filter fortdargtL identification with the smaIl 1-diltelnlia microcomputer qysLem,

ji

127

The decision time goes down drastically to about 0.7 seconds if therepetition frequency o.f the pulser can be increase-d- to-_-10-Fz, and thefiltering operation in the preprocessor can be performed with an ana-log filter. Using state-of-the-art technology, both these conditionscan be easily met.

Based on the simulated identification results obtained with themicrocomputer conditions (i.e., 128 samples per waveforrml, FIR filter-Ing), the microcomputer identification system is expected to identifythe mine-like target with the same level of performance as the resultspreviously presented in this dissertation.

D. Calibration of the Mi crocomputerTarget I�ent ficaton Systeni

Calibration of che microcomputer system includes the following:

1. Time scale

The timle scale was calibrated by comparing two waveforms from thesame target, One of the waveforms was obtained with a fixed length of pcable added to the system. Th~e time window waLs calibrated at 25 ns.

However, the impedance mismatch at the trigger pick-off circuitory ofthe Torras-an limited the reflectionless time window to 20 ns (seeFigure 54). The secondary reflections caused b this impedance mis-match occurred at a time which was 20 ns from the transmit receiveco•upling, This reduction in the size of the reflectiunless time windowwas later found to limit the identification range of the radar system.

2 Apit~ude sca__le.

Operations performed in the detector required accurate calibrationiof the peak amplitud,, peak timingn as wull as the energy of the mine-like tairget waveformts. These calibrations were performed by collectinga sut of waveforms over the wine-like target and tabulating Ohe variousdetection thresholds based on the set of waveForms

J , .n~rou~nd c.on dition

On-location ground-condition calibration is discussed in ChapterIX. At. the present time, the in-situ complex resonances of the mine-like target waveforms were obtained by analyzing the waveforms collectedin 2. using Prony's method. The difference equation coefficients asso-ciated with these resonances were then used for real-time target iden-tification. Real-time identification performance of the microcomputersystem is discussed In the next section.

,!,

128

A102-

76-

1 SI REFI..ECTION CAUSED

lz25- IKF

A -

-SI

SIGNAL FROM_77- MINE-LIKE TARGET

-102

rliuuru b4. Typ-ical procusso mnelnu1ike target wavefonuiruccivced by the miicrocomputer ý,yteii,

129

E. Real-Time Identification Performance

TCentfcti- on ystm

1. Identification performance

Two sets of identIfication data were obtained for the identifi-cation of the mine-like target in two different ground conditions.The first set was obtained using the poles and thresholds as given inTables 27 and 30 of Appendix G for real-time identification of themine-like target, Real-time identification performance of Pi10l0% andPFA--% was obtained for RID-30 cm (based on 9 mine-like target wave-forms and 21 other-target waveforms). It was found that, for RID-45 cmidentification performance degraded to P 2 PFAO0 This reductionin identification range was attributeo tý the presence of the unwantedreflections from the trigger pick-off in the lotter portion of the time

window.

The •.rond set of identification data was obtained under a dif-

ferent and rapidly changing grou condition, A uet of measurementsover the mine-1 ke target was collected over a lightly wet ground forcal lbrating the ground condition, target resonances, and the variousdetection and identification thresholds. However, there were rapidweather changes betwoeri the time of data analysis (fnr ,alibratinns)and real-time identification, There was heavy rainfall during the

interim period, and in one day, even a moderate snow storm. Thesedrastic weather changes altered the ground condition, and with the.Fy:tem tuned Lu the previously calibrated conditions, it was found thatthe level of the correlation coefficients for the mine-like target wave-fonme, was generally lowered. Hence to ensure a 100% identificationprobability, the identification thresholds had to be lowered. Thus,with an untuned system and using lower threshold values (see AppendixI for details), a set of real-time identification data was obtained.Identification data based on 17 mine-like target and 13 other-targetwaveforms were P1 1OO'; and PFAzO'7 for RID= 3 0 cm. Thus, lowering thethreshold values seems to be an effective means to counter the problemof uncertain ground conditions for this penetrable "desired target",This a.pect of thin system warrants a detailed future investigation,

2. Speed

The two sets of identification d.ta dincussed in the above sub-sucrion were obtained with N1 (the number of raw wavefori|s required toform an average waveform) set equal to 8. Thus, for a pulse repetitionrate of 256 Hz, the amount of time required for the microcomputer sys-tem to form an average difference waveform was 8 seconds. The amountof Limt! taken for the correct identification of the . One-like targetwas clocked at approximately 2.5 seconds, Thus, the total real-timcfor a correct Identification of the mine-llko target was Lipproximate-ly 10.5 seconds. The amount of time required for false-ta,.Cetor no-target discrimination was less than 10.5 seconds, In the

L p,*hIrtý,i,:f -1A1' 1, n~~4,d~r,,M~. ~ ,4~~~7 ',: ,,.~. ti . 4 ,,"4*4liA,4';49y 4'4 njd eV

1I(inplemuntation of later generations of this identification, system, it

is expected that, the identification speed will drastically increasewith the increase in pulse repetition vate, decrease in N1 , elimina-tion of the 900 difference operation, and morn efficient microprograms.

3. Precision

To find the precision of the correlation coefficients calculatedin the microcomputer system, correlation coefficients were calculatedfor a waveform using the microcomputer system. These correlationcoefficients were then compared to those calculated by the in-housecomputer system for the same waveform. It was found that, the two setsof results differed in the 10th bit of the mantissa of the floatinq-point formatted numbers. No error was observed in the exponents. Thus,using the 25-bit floating-point format of Lhe APU resulted in C 0.i,truncated error in the correlation coefFicients. This is expected tohave little effect on the identification performance.

F. Possible Future Improvements on

In addition to the impedance mismatch at the trigger pick-offcircuitory of the Terrascan, a few other aspects of the microcomputersystem can he modified to improve identification performance.

1. The samplingnsystem in the Terrascan

The Terrascan system was originally desi ned for low-frequencyoperation (i.e., frequencies less than 200 MHz), as such its samplingsystem Is therefore slow. The slow sampling system causes loss in high-frequency content of the received waveforms, Figure 55 shows two wave-forms, one received by the Terrascan and the other by a faster samplingsystem, Frnm the same target at the same antenna location and orienta-tion. The loss of high-frequency content in the waveform received bythe Terrascan system i., quite apparent,

With the identification pprformiance obtained thus far using themicrocomputer system, the high-frequency loss in the Terrascan samplingsystem does not seem to affect identificaLinn performance for theidentification of the mine-like target considered in this study. How-ever, such high-frequency loss will almost surely degrade performancewhen the system is used to identify smaller mines.

2. Thedna!Micrane in si•a level

The microcomputer system currently uses an 8-bit A/D converterto convwrt the received analog waveformts to digital form. This resultsin a 48 dB dynamic range in signal level. For the identification oflow-level signals rhe dynamic range needs to be increased.

.... ". ..- ] " 7 ' .- " • T " ' .' " i. .." . . . .. .... . ... . [ i ........ ....

131

127 1000A

j 102- -6 00I ' - MICROCOMPUTER

78 ---- FAST SAMPLER60

-J 5 400 E

25-200 I

An0

o0i TIME (ns)-20

U.

____ ___ ___ ____ ___ ___ ___ ____ ___ ___ ___ -1200

Figure 55, Processed mine-like tar'get waveforms receivedby the microcomputer and the fast samplingsystem.

132

3. Gain control of the Terrascan

The gain control of the Terrascan system offers a limitedrange of gains in large discrete steps. Such large discrete stepsmay result in large truncation error.

In summarizing, a microcQmputer system has been implemented forreal-time subsurface target identification. Real-time single-lookidentification performance of Pi=l00% and PFAN0 % for RID: 3 0 cm wasobtained with a total of 26 mine-like target waveforms and 34 other-target waveforms for the identification of the mine-like target indifferent ground conditions. The amount of time required for a correctidentification of the mine-like target was approximately 10.5 seconds.The amount of time required for a correct other-target or no-targetdiscrimination was less than 10.5 seconds.

The microcomputer system built in Ahis study was intended to bea "first-generation" system. Many possible modifications of the systemwere recommended in this chapter for better identification speed, dataprecision, and identification performance. The most important modifi-cation is the process of automatic tuning of the radar system to theon-location ground condition. This is the topic of Chapter IX.

.. ......

.1

I l

CHAPTER IXA METHOD FOR REAL-TIME ON-LOCATION TUNING OF IH.

IDENTIFICATION RADAR TO THE GROUND CONDITION

A. Objectives

*, ,. The importauce of tuning the radar system to the ground conditionwas illustrated in Chapter IV. An un-tuned subsurface identificationraoar system yielded degraded performance. This chapter discussesa possible method for automatic tuning of the radar system to theground condition. Emphasis 's on the ý,implicity of thr, method and the"possibility of incorporatini such method into the microconiputer systemfor on-lo.:ation target icdenLification in real time.

B. The Use of Backscattered Waveforms-rom-H-T-hin •Wres t o Es temt e-"

Ground Parameters

The bdckscattered waveforms from the buried thin wires as shownin Chapter V1l possess the following properties which are useful inIthe calibration of giound conditions:

1. The uiaveforms contain complex natural resonances whichare related to the ground parameters in a simple fashion.

2. lhe wire waveforms arc. of high amplitude, thus theestimate of the resonances will be accurate.

3. The lowest-order target resonance of the thin wires arethe most dominant. (Se2 Appeidix J). This implies th,tthe thin wire waveforms can be closely characterized 0ýa •ingle resonance. Thus,

11l ,t-t' )rM(t) = 2aI e cos(.l (t-t') (58)

where

rM(t) processed waveform

133

134

S I = 'I +j(,i I complex resonance,

F; = residue associated witn r, , and

t' -: start time of the transient signal from the wire.

For a thin wire, the first resonance can be approximuted byEquation (58)

- 0.0828 (59)i~Lr

T1 C0.9251 _c

rL

"where

ground conductivity (homogeneous medium assumed),

, ground permittivity,

c speed of light in free space,

• = relative dielectric constant of the ground, and

L length uf wire

The complex natural resonance given by Equation (59) is a goodapproximation to the first natural mode of a thin wire with a lenyth/diameter ratio of 100 buried in a homogeneous medium of good dielec-tric (i.e., medium with d small loss tangent of (/(d-,-<I)[52,69].Here, it is used to estimate the ground parameters based on the wave-formis from the buried thin wires and is found to yield reasonableresults.

Sinco the waveform is dominated by a single resonance, thevalues of 1 and 1 can be easily estimated from the decaying envelopeand the peak timing at two samples of the waveform, thus, the groundparameters can be estimated via the following equations:

o .9251 (tI- -to)C] 2

andJ (60)

2, [tl-to)'l ,,n M 0)0

-MO-

S~135

where r(t ) and r(t ) are the sample value-, of the measured waveformat time t8 and tl, ýespectively.* All other parameters are as pre-viously defined.

Using Equation (60), the ground parameters represented by thewave~orm shown in Figure 56 are estimated to be ,r= 1 4 and u=24 m$/rn.**These estimates are found to be very close to the estimates obtainedsuing different techniques currently being investigated in anotherstudy at the Elc-ctroScierce Laboratory[58]. The method outlined inEqua•tion ý60) is attrictive, for it uniquely characterizes the groundcondition by two sample values of a thin-wire waveform.

C. Automatic Tunij.g. 9f he Identi f i cati onRadar to the Ground Conditior.

The knowledge of the ground parameters basiLally solves theautomatic tqruund-condition tuning problem for the real-time identifi-cation of simple targets such as the brass cylinder and the aluminumsphere whose resonances are related to the ground parameters in aknown analytical fashion[21,63]. How.ver, it does not solve the tun-ing problem for tile real-time identification of plastic mines, forthe analytic relations between the complex natural resonances of theplastic mine-like target and the ground parameters are not known.lo date, the characterization of t,-rqets, should it be free-space orsubsurface targets, is o relatively new research problem, Further-more, research efforts have mostly been concentrated in the character-ization of perfectly conducting targets only. Characterization ofdielectric targets ,uch as the plastic mine-like target with complexnatural resonances via andlytical method has not been previouslytreated. This could be achieved but it represents a substantialresedrch effort beyovnd the scope of the present study. In this studywe sugest. solving the automati: tuning problem for identificationof minv;S experimentally with the procedure outlined as follows:

Step 1: Es;timate the qround parameter by using the methodoutlined by Lquation (60).

* Equation (60) Is valid only when rM(tn) and rM(tlI are both non-zero and that !lr(t 1 -tO)=2nn where --1,2 3.

** Note that these rc;timates are, of co.Arse, accurate only atFurthermore, the loss tangent, based on the estimated values of

and d, is found to be 0.252.

-.

..1LZL~ ~.~-

�2'

� 36

4-0

* ¾t.*�*SF-

.1 *

a

* S

S..US-

4-

EIS-

Si w.1�

SiJ V

o o�'4-

301-S

C)

U-

-� C-

137

Step 2: Determine the loci of the complex resonances of themine-like target experimentally as the ground para-meters vary. Ground parameters can be controlledby using different kinds of soils, or by increasingthe moisture and salt content of the ground. Thus,the loci of the natural resonances (or the coeffici-ents am's) can be determined as a function of tl-to,rM(tO), and rM(tl) and stored in ROM's in the micro-computer identification system for on-location targetidentification in real time.

To make the above method even more attractive and practical, the, thin wire does not have to be buried for ground-condition characteri-

zation. Figure 57 shows waveforms obtained 4from a thin wire Idyingat different locations on the surface of the ground,* Again, the wave-form is dogninated by one (pair) resonance and thus, the ground conditionis uniquely characterized by the values and timing of two sample pointsof the waveform. In the case of the on-surface wire however, becauseof the fact. that part of the wire is in the air, the ground parametersare no longer estimated accurately by Equation (60). Nevertheless, theunique information about the ground condition is assumed to be contain-ed in the two samples of the waveform. Thus far, this assumption isfound to be valid. The on-surface wire waveforms given in Figure 55indicate different decaying envelopes and zero-crossing intervals fordifferent ground conditions.

The method of ground-condition tuning outlined above amounts toan extensive experimental effort and is planned for the future.

• The wire has to be in good contact with the ground.

- ,,.

138

op 0

'4-

Inn

0 0 0 U

CHAPTER XSUMIARY, CONCLUSIONS AND RECOMMENDATIONS

A. Swarmaryc

At the tine research in this report was initiated, thec laini that electromagnetic signals were impractical for subsurface

exploration because of attenuation had already been refuted. Refer-ences in this report contain additional evidence refuting this claim,We demonstrate that the received signals from objects beneath thesurface of the earth can also be interpreted intelligently. That is,that much wlore than simple ray tracing with a postulated reflectioncoefficient at somýe depth is possible. We show conclusively, usingreal subsurface probing data, that the target can be identified.It is emiiphasized that the identification is not simply a seismic-typem11ap subject to interpretation and qualificatfon by the observer butan actual processing scheme which inquires as to the presence of aparticular target. We also stress that the methods developed 'in thisdissertation are field-oriented and operate in real time. The para-graphs below itemize the specific progress which has been made.

The predictor-correlator vethod for characterizing and identi-fying subsurface targets was studied and extensively tested using realradar measurements obtained with a Terrascan-type subsurface pulseradar. Measurements were obtained over three sets of targets. Thefirst set consisted of five similar-size targets including a plasticmine-like target, a brass cylinder, an aluminum sphere, a coppersheet and a wood board. These targets were buried at a depth of 5cm (2 inches). The second set consisted of a series of different-size(maximum diiiension varies from 30 cm to 300 cii) brass cylinders buriedat different depths (depth varies froemi 30 cm to 150 cimi). The thirdset consisted of a series of thin wires buried at the depth of 5 cm(2 inches). The method of characterization and identification uses thecomplex natural resonances as the discrindlnants for the identifier andthe method of linear prediction for evaluation of the correlation coef-ficients for threshold identification. The complex natural resonancesof the desired target are determined a priori and the difference equa-tion coefficients related to these resonances are. stored in the identi-fication system for real-time on-location target identification. Theidentification process is simple and involves only simple algebraicoperations.

139

-. •.s- • ' . -I

140

The characterization and identification methods were found to besuccessful and a "first-generation" microcomputer system was built foron-location identification of mines in real time. A simple method forautomatic tuning of the identification radar to the ground conditionwas suggested. This method is simple to use and can easily be incorpor-ated into the microcomputer system for real-time target identificationpurposes. The significant findings are:

1. The identification method was extensively tested, withmeasurements over the subsurface targets, and found tobe extremely successful. Single-look identification.sta.tjsjtiqis fo~rý the identification of the mine-like targetin differeni ground conditions w're "tmatb . .. .be'

00% .25'/' for R 3t cm over an ensemble of 55ipiine-like arget w avefo rms, and ~22" other-target waveforms.*The S/C of the ensemble of mine-like target waveformsranged from 0.21 tO 3.5.

2. A microcomputer system was implemented for real-time sub-surface target identification using the techniques develop-ed in this study. Single-look identification statisticsfor the identification of the mioe-like target were esti-mated to be P - 1 00%,1 PFA- 0 % for RIDm30 Ln11 over an emsembleof 30 mine-liie target waveforms and 30 other-target wave-forms. The amount of time required for a correct identifi-cation of the mine-like target was 10.5 seconds, a correctdiscrimination of an other-target or no-target requiredless time.

3. Identification performance degraded when the radar systemwas not tuned to the right ground condition

4. Identification performance degraded when the radar fre-quencies did not properly span the target resonances.

S. Single-look identification performance was characterizedby a correlation coefficient vs. sampling interval (p(T))curve. Optimal identification performance occurred whenthe sampling interval T was in the ii1viediate neighborhood Kof TN (see Equation (51)), Thus, one knows a priori thevalue or the region of values of the sampling intervalneeded for design and Implementation of the identificationradar.

* Identification statistics given herr, is estimated from the ensembleof all wine-like target waveforms collected using the Terrscan-l Ike sysLoms.

-- 77.

141

6. All subsurface targets considered were characterized bya small and finite number (5 pairs or less) of resonances.These resonances were invariant with respect to radarlocation.

7. The resonances of the plastic mine-like target were foundto be internal resonances, with their imaginary partsindependent of ground condition. The resonances of thebrass cylinder were found to be external resonances;both their imaginary and real parts were dependent onground conditions.

8. The extracted resonances of the brass cylinders werefound to be the dipoles modes along the length of thecylinder, Furthermore, they closely approximated theresonances oF the same target buried in a homogeneousmedium with plane-wave illumination. This discoverysuggested a good way to estimate the ground parameters(see Section VI1-B),.

9. The high-frequ'ncy content of the backscattered waveformswas highly attenuated as target depth Increased, Identi-fication rnrige decreased as target depth increased,

10. Up to a certain threshold, the frequency of the targetresonances decreased according to the increase in targetsize, and target resonances depended solely on the scatter-

I ing mechanisms of the targets, Beyond the threshold, in-crease in target size did not warrant the decrease in thefrequency of the resonances. In this case, target reson-ances would depend on the scattering mechanisms as well asother ciuantities such as the antenna pattern, etc.

The sitnif ihinit contribut Ions of this relort are:

1. 7he problem of applying Prony's Method to real radar measure-ments for extraction of the complex resonances was consider-ed as one of parameter optimization. This approach yieldedlegitimate target resonances from waveforms with S/C as lowas 0.?1 (see Chapter III),

2. The predictor-correlator method was extensively tested withreal radar measurements, and found to yield practicalsingle-look identification performance. Furthernure, itwas found that there existed a limited range of T values inwhich optimum identification performance orcurred. (SeeChapter IV).

# MAb•~~l.~i4 M. ~ i tlv~ t~iitM

142

3. A microcomputer system was implemented for real-time on-location subsurface target identification using the tech-niques developed in this dissertation. The system wasfound to yield practical single-look identification per-formance with a 10.5 second identification time (seeChapter IX).

B. Conclusions

We have now provided a successful method for the identificationof subsurface targets at shallow depth. The method is based on singleradar returns and is simple to implement# Based on this method a micro-computer system has been implemented for on-location identification ofsubsurface targets in real time. Some modifications have to be madefor the microcomputer identification radar system to be practical, themost important being a method to calibrate the ground parameters (e,Vi,o) in real time and to adjust the resonances of the desired targetaccordingly for real-time subsurface target identification in differentground conditions. This is now being implemented and is expected to beincorporated in the final system.

C. Recommendations for Future Work

The subject of subsurface target characterization and identifica-tion is in its infancy. The results obtained in this study representsa significant step forward, but much remains to be done. The followingitems are highly recommended for future research:

1. The taks of automatic on-location tuning of the subsurfaceradar to the ground condition is crucial to the problem ofsubsurface target identification. The consideration of thewaveform values of the on-surface wire waveforms suggestsa feasible way to solve this problem.

2. The relationships between the extracted resonances of thetargets and the various system parameters such as targetsize, depth, antenna pattern, air-ground interface, etc.,need to be exploited for a better understanding and inter-pretation of the extracted resonances.

3. Application of the characterization and identificationtechnique to deeper targets needs to be expanded. In thisregard very little deep electromagnetic probing has beendone.

4. Identification of subsurface targets in the presence ofother objects.

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60. INTEL .CS_8_0 Desii.n Kit User's Guide, INTEL Corporation, 1976.

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i

APPENDIX ADERIVATION OF PRONY'S METHOD FOR TRANSIENT WAVEFORMS

WITH MULTIPLE-ORDER POLES

This appendix derives Prony's method for the extraction ofresonances from waveforms with multiple-order poles,

With multiple-order poles the transient waveform can beexpressed as

N 'Mi sitrft) : + bjiPt a-lr )12 .e(61)i =l J=2

where

P = O, if Mi ,. 2

p 0 1, if Mi 2

and where Mi is the multiplicity of the ith pole.

The corresponding expression of Equation (61) in the complexfreqiency domain is

a j=Mi b )

Si l\ (s-si)J

In discrete form, Equation (61) can be written as

N Mi snTr(nT) : (\ + )' hj ip(nT)j'l) ae (63)i ij--2 i1 a

With the following z-transforwtl pairs[54]

s rT

,- 1-i5

150

l~t.tfl~sLIk~z~a nflz &fniIt afl It V.,.. It C

151

r I(nT)esi T] e Te l z I

ses Z" 1) 2-T z-1 T

1-e z 1 )2

4[(nT)JeSi _ (Tz •I) 1 (64)d) SiTz.1-e z•

where t,[] is the z transform operation. We can transform Equation

(63) into the z domain, viz.,

,.[r(nT)] N + ) bjiP zT ai=-- j2 dzQ J=l Si z"

b-e zl

b e - 'Tz'l siT z

a siT T 1 2

N (,1 1-e- z3

d T 2e Z- I+e i T"1

+ 4.eb Tz 4--

+ MSl T dz) I ( iesTzY (65)1-e

Each tertll in the right hand side of Equation (65) is a rationalfunction of z- with its denominator one degree higher in z-1 than thenumerator. Thys. when the series is summed, it becomes a rationalfunction of z in the form of

,,,( r ( n T )) = C z + . ..- -_ 'L +)(r~nT do+dIlz'l + .. dLz-L

152

where the polynomial of z-1 in the denominator is one degree higherthan that in the nunerator. The denominator polynomial is commonlyreferred to as the characteristic polynomial and its related to thepole locations si by

L i N SiTzlMiZl'i , IT( -e z -1) L = i ' (67)1i-O icli 1

Multiply both sides of Equation (67) by zL, we obtain

L N iT)Mi

iO (z-eI

or

L N MiZ ,, (11 , (z-z) (68)

m-O ic1

where

m L-i; m I O,l1..L

siTzi e (69)

Equation (68) is analogous to Equation (11),

We now proceed to write Equation (66) as

do+dlz'l + ..- dLz' L)ý,[r(nT)] , co+clz + L+l

With the relationship[54]

,, [z'(r(nT))] = r(nT-iT) (71)

where ] is the inverse z transform operation. We obtain theinverse z transform of Equation (70)L r L- ].

X dir(nT-iT) = . X, (.72)iO ' i O

-. .. . ... - " " . .

153

Since the right-hand side of Equation (72) is zero for noL, hence

LI dir(nT-iT) 0 ; n > L (73)

i=0

Now with

n a L + K; K 0,',2"

in = L-i and

we obtain the desired difference equation,

LX ,,lrK+m = 0, K = 0,1,2, (74)

where rK+n--r(KT+mT). This difference equation is identical to theProny difference equation in Equation (12) except for the change oforder. Thus, the sample values of a transient waveform with the pre-sence of multiple-order poles satisfies a Prony difference equationof order L, where

NL ' M- . (75)

i--I

With rquation (74) wt, can solve for the coefficients , s, and sub-sequently solve for the si by Equation (67). We can a so solve forthe poles si, as was done in the simple-pole case, by solving Equations(I2) and (01) with N chmnged to L. Thus, the same procedure taken tosOlve for the pole locations in the simple-pole case can also be usedin the multiple-order-pole case. However the procedure for the calcu-lation of the residues requires a slight modification,

The calculation of the residues is done by solving Equation (63),which differs from Equation (8) because of the presence of the termsinvolving (nT), and the fact that there are L unknowns rather than N.With the a•sumption that the ith pole is of order Mi, Equation (63)cam be written as

154

Miterms

ro = a,+a + "'+0+ + ---+0+ - - - - a

M1terms

rl =a~l,+a 2z2+...+aizi+T(b 2ial)zi+f2(biai)zi+...+T '- (bM41ai)z 1 +

Mi1 terms *+N

r2 ýazzl+a2z2±...+ZIZý+T(b,,iai)zi+lL(h3ii2z+-- +T (b llz+

**+ 2 (75)N N

Froim Equation 7~5)~ we see that, in solving for the residues inthe presence of mlultiple-order poles, the, matrix Eqtqation (15) mustbe modified as follows

DE F

where

A'n

2 ~ ~ ~ r z . z7

ý1~ .2 . 1

ohf

a a

31 +2

a ibM ~ al'+Mil

a 1+1 a i+mi

a Nd

r0

r.

r

r1+1

~i+Mi -2

r+ -1

APPENDIX RDERIVATION OF PRONY'S METHOD AND ITS VARIATIONS

This appendix derives the variations of Prony's method due tothe constraints aj=l (Interpolation method) and

N 21

111- 0

(Eigenvalue method). Computer codes (in Fortran Language) for thesemethods are also included.

A. _Th!e Interp[olIa t ion Method

In the interpolation method, the Prony difference equation canbe written as

, 0 r(t)+ýI r(t+T)+- " i-lr(t+(il- )T)+,- *ci +Ir(t+(i+1 )T)+ -

+ atNr(t+NT) -- ,r(t+il) (76)

Thus the matrices A, B and C shown in Equation (13) need to be

modified as

AB E C (77)

whl. reror rr ri ri+ I.. rN •

A : rl ~ • '' i+l, r +2 ''' 'N+1 i

Ar

rMN~r _1Nl rMN++ r~-rM-N rM-N+ "N+i' -N+i+l M

156

157

"12

(,i+l

I,.L

Equai on(7)cnb ue+oI~efr h of~ ~

ri+1

_rM-N*i _

Equcitiun ( 77) can be used to ;olv e for the coeffic' nLs c< ,• , .

"- i N in the interpolation method, Once the cuo.!fic~enisire •nown, we can solve for the poles and residues by foilowing theidenticdl procedure outl ined in the Classical Method (Chapt.ter III).

3. T h.e L v a.19 u_ Me t-c1d"

Under the constrdint

NII2 l

the instamtcmfn(eow error in the error-evaluation process of Prony ismodifid t,. follows

N Ne(t ,+NT) t r ( t+iiiT) -2 (78)

In mdtrix form, the instantaneous error can be written as

,,jr.!tj , ~ n~n .~ii ih-..-t -ni..b ~ t~ n ~ L t,

IA L59

e(ts+NT) rM(ts) rM(ts+T) "" rM(ts+NT) ru0e(ts+NT+T) rM(tS+T) rM(ts+2T) rM,(ts+NT+T) ?2

. • (79)

e(t 6 +MT-T) rM(tY+MT-NT-T) rM(ts+MT-NT) rM(ts+MT-TD LNJ

The total square error over the fitting interval (t s,ts +MT-T) is

L1 C cTr1

BT ATA B

:B *B (80)

where L1 is the total squared error 2ve¶ the fitting Interval. [ ]T

denotes the transpose operation. A, = A'A, is the data covariancenla t i Y,[5 3 ] .

Solving for Matrix B by minimizing L1 under the constraint

N

is a s tandard eijenvaluu problem. Via the eigen-analysis, thesolution matrix k is the .iqen-vector corresponding to the minimum;eiqenvalue of the covariance Matirx

Thus, Equation (81f) can be used to solve for the coefficients"Once these coefficients are known the identical proce-

dure outlined in the Classical Prony's method can be used to solvefor the poles ind residues.

Collipul.er codes for the Prony's method and its variations aregvi 1) iwe 1how. The program names "SEMI" implements the Pruny's methodunder the constraints of ti 1, m-O,1,2... N (See Chapter III). Theprogram "Sen2"' implements the Prony's method under the constraint of

Both programs are well coninented and user oriented.

axa~~:L~4I-~2

.- ~-J~a,.Ak..~t - ULtiL~L~Lhfl~~.' ,l&L--A-.--'- ~ L-~~-- 'J

159

0 ECC to *-.1A.4 fir 1. 11 1 %- I -' Of~ LAR1I ¶ ' I 1jll'I.Wt I 1e Alf PI.f ' 1)

w WI "t '". IS' 0441.!fA t, t47n~t.fAt.1% 1611 So . h rJj'

*CLC 1~4 1) " 1 I I t II'fr '7' a ~A"t. 1~' OF ~ Y.4p.

7 cL' f L Pt b I aI u' r 06:0'UL 1 -

SCL':

j CL 11I.,, t 0 TTbll"TK I. J *.I~ S.'* '"OI -,4*~i I

1~rcf I *V

IS. C ~ m 1. C ~ 1

re v: t. ti * rs I I

I~~~~ IL ., w. f3*

*Src:

~, CL': *., Itoe.

(9 piug 1 o .3-j~ I )9j 5

160

r..ti I I~t

0. b.SIA FIS' Is W i 1 i'tg

It f9 1 ,-b

9u 5I, ý r i if I I p ~

'14

7. F I% k:.~*.~'I* uS4J TI" eg

Is L *

1) ~ f e "F .'

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APPENDIX C

This appendix tabulates the extracted resonances of the mine-like target at different antenna locations in icy ground. The poles,residues as well as the minimum-error-case parameters associated

with the Prony Process are given. These parameters are N, IBS, III,and M and are defined as follows.

N Number of poles

IBS Interval between samples, i.e., T=IBSxTB

III The start time of the fitting interval in theProny process is ts+(iiI-l)x2xTB

,M Number of samples used in the fitting interval isMxN.

185

186

TABLE 17EXTRACTED RESONANCES OF THE MINE-LIKE TARGET

AT VARIOUS ANTENNA LOCATIONS IN ICY GROUND

ANTENNA LOCATIQNO_ CENTER N-II, IBS=5, 111=5, M=3EO0.632E-2

POLE POLE RESIDUE RESIDUE(REAL PART) (IMAG PART) (REAL PART) (IMAG PART)

-. 6165323E8 ±..5980379E8 .1627237E0 ±.22C3193EO-. 9816088E8 t.1153422E9 -. 1200819EO t. 4662508E-1-. 2972145E9 ±.3199646E9 -. 6727021E0 ±.2528001E-1-. 2574395E9 t .4525337E9 -. 2245525E0 ±.9734140E-1

_________ CETERN=11, IE3S=7, III-1, M-215 cm EAST OF CENTER L, S60lE ,M1ý_=O. 604E-3

POLE POLE RESIDUE RESIDUE(REAL PART) (IMAG PART) (REAL PART) (IMAG PART)

-. 7955556E9 +.7207162E8 -. 3441590E0 r.5773295EO-. 9747022E8 t.1327517E9 -. 2914887E-1 t.4185661E0"-.2185998E9 t,1964866E9 .1786104Ei ±.6787741E0-. 2235657E9 t..2570622E9 .1210215EI A,1496749EI-. 2108089E9 t.3265433E9 -. 2914887E-1 V.4185661EO

N=1O, IBS=4, 111=2, M=215 cm SOUTH OF CENTER :0375E-2.

* POLE POLL RESIDUE RESIDUE(REAL PART) (IMAG PART) (REAL PART) (IMAG PART)

-. 4419169E8 +.5302244E8 -. 1283107E0 t.266B165EO-. 1687482E9 L..1862940E9 .1938945E0 :L.4774533EO-. 1866233E9 +.2797166L9 .2234024E-1 ±..5512929E0-. 3106326E8 ±..3993629E9 -. 5570095E-1 ±.4816288E0-. 4141821E9 t.5571886E8 ,7225376EO T.9451689EO

• Real and imaginary parts of the extracted resonances are inNepers/s dnd Hz, respectively.

. .... >. .. . ... . .. ....-

II187

TABLE 17 (Cont.)

15 cm WEST OF CENTER N-7, IBS-9, II=3, M3L __0.448E-2

POLE POLE RESIDUE RESIDUE(REAL PART) (IMAG PART) (REAL PART) (IMAG PART)

-. 82b269IE8 ±.7159227EH .4703710E0 ±.2550093E0-. 63661OOE8 ±.1213223E9 .f435532E-1 T.1370926EO-. 2474290E9 ±..2123833E9 .3750488E0 f.2747979E0-. 1196715E9 i.2833333E9 .1486354E9 0.0000000

15 cm NORTH OF CENTER N=12, IBS=6, 1 5, M=2c=0. 287 -3

POLE POLE RESIDUE RESIDUE(REAL PART) (IMAG PART) (REAL PART) (IMAG PART)

-.123869?E9 .5956967E8 -. 756820iEO T.4133825EO-. 1455328E9 ±.1044725E9 .4427186E0 ±.3773904E0

-. 2976452E9 ±.2543575E9 .1G51730EO ±.4133825E0-. 3582517E9 i.3319750E9 .3949756E0 T.7346425E0-. 3250828E9 i.4250000E9 .2408422E0 O.0O00000

30 N1EAST1F ENTERS=O.247E-2

POLE POLE RESIDUE RESIDUE

(REAL PART) (IMAG PART) (REAL PART) (IMAG PART)

-. 9395545L8 ±..7131887E8 -. 3951318E0 TF.1237333El-. 1369431E9 :E.1220007E9 -. 1243418EI t.8057936E-I

k-.3187709E9 ±,.2553445E9 -. 1835029El T.6562829EO-2052859E9 ±.3777737E9 .1061165E0 ±.9037383E-1

-. 2686828E9 f.4250000E9 -. 2203826E0 0.0000000

_5_ ý OF CENTER N=13, IBS=6, 111=2, M=2

_ SOUTH E=0.406E-3

POLE POLE RESIDUE RESIDUE(REAL PART) (IMAG PART) (REAL PART) (IMAG PART)

-. 7440484E8 f.5768431F8 .2634359E0 ±.3522781E0-. 2734229E9 4.1749879Eq -. 5841965E0 4.1580445EI-. 2451866E9 i.2385293E9 .1394630E1 4.1721972E0-. 2480318E9 ±.2889975E9 .6811801EO ±.1354053EI

2653034E9 ±.3814169E9 -. 6790937E0 ±.11B7006EI-... . . .

188

TABLE 17 (Cont.)

30 cm WEST OF CENTER N=13, IBS=6, 111=3, M-2L-0.685E-2

POLE POLE RESIDUE RESIDUE(REAL PART) (IMAG PART) (REAL PART) (IMAG PART)

-. 1174326E9 _t.9037581E8 -. 7656702E0 +.8719310E0-. 2722184E9 A.,1783297E9 .3367912E0 T.1380838EO-. 2442735E9 i..3781778E9 -. 2437025E0 +,.4363209E-1

'30 cm NORTH OF CENTER N=12, IBS=6, I11=2, M-2:30 cNRT=0.171E-2

POLE POLE RESIDUE RESIDUE(REAL PART) (IMAG PART) (REAL PART) (IMAG PART)

I• -~~.39291 71EB +.246E 3064080E0 :F. 2378655E-2

-..3953903ES .1162181E9 -. 8984933E-1 ±.4503131E-1-,2863506E9 +.1847860E9 -. 2726371E1 '-.3413519EO-. 2130829E9 t+.2626060E9 -. 1131884EI TF.711625IE0-. 3845860E9 t.2977974E9 .2613163E1 1,.2442230EI-. 3482679E9 +,3921698E9 .1288635EI _.1489745EI

POLE POLE(REAL PART) (IMAG PART)

-. 7493116E8 +.L6347621E8-. 9981995E8 +.. 1146405E9-. 2416503[9 +..1535799E9-. 2809195E9 !--.3074991E9-. 2885261E9 +•.4076659E9

a-."

APPENDIX D

This appendix tabulates the average extracted resonances ofmine-like target waveforms obtained using the 12m long antenna.

Table 18

AVERAGE EXTRACTED RESONANCES OF THE MI.IE-LIKETARGET WAVEFORMS OBTAINED USING

THE 12m LONG ANTENNA

POLE POLE(REAL)* (IMAG)

-242.9760E6 144.343SE6-381.1344E6 ,233.987lE6-407.1770E6 *319.0055E6-373.7482E6 .ý413.1869E6

*Real and imaginary parts of theextracted resonances are in Nepers/sand Hz, tespectively.

189

gj

APPENDIX E

This appendix lists the Fortran program for performing the target I

identification process (SRTlD2), it also tabulates some of the target

identification results described in Chapter IV. Detail correlation

coefficient values are given.

190

am ,---r lo .-..............-

191

I CtC .seI~ Al- AtIS.T1-

%kW4 ~U '0'Lq ..CF nt A P T M~lft~ i'.1 I IF IfjT1IM

CLCI, ' **f r%, tf It £4. Yt 1-it I,#-....... i * *4 O.. 444

j 4 ILL' 1. I hr~t. l It

I'd V. XLLIJU L S

j~Lt. Lt!'1''9'P~ I- - .t1

1' I tL Kfk 0vI;b- ýlf

IF It~ j(c oi'i* *S(91 I * P 4 I. 'vw A O, T V,. Lr t 1 9 ALP A II P

S., cc': ', TL~. $-t * 1 :1Pr.' ' t 1.

15 CV:LiClf71 '

L9 ccc v PIi T IS~ PI U* F

S~ ¶.. cc I P L,.T ' I z=;Or.-tT 7~ S I 1 f 7' L

r. c 'Ji r- ~~'j ~3 C~r .in I III ,; I. .TI'

*.,s £u'CIi,*I ~A L

3t gCt *

.4-1. *C r u i*f~L4q

to r

192

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r I: t /I .J l oI IT

IE7 l *1 tob 9 I l]r .4 1 .I

I -

4).' 7 77 TAr~lI11L(

jt AI L Wi '1-j;

I3 'u? =I.10 = 1-Il.i Lj r LI I TI

L~ rc,

' rLr tee*~ *, -r1 tLl

47 L C , *'#.

rCI

1) .J v i

u ps' 1=1 .7

IU, 1U'"i~ T)sTil- (I

193

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cu c

,I• ? ] t %I Y, i .u-1 LP Ir, Si

Joe 73 u2

1 5.. ; 1. ' i, •. ' ' •' I tt.c( A

1J.•-• A2 2 1'.= .F

low"= (L')

lB."' Yf(II1, *t .I' •r1 -UQ's

jL'- Cqdf'7 I *r-F&J 1l:T,," (j.IP

1,.' e. i

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1I 7 v Pg. It I Til-',l t,

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1.•i 1.,j6 t,, V 10,

pl . I tf 9TJ

l b•, C~tl •| g .**,- !,~

r r

194

a kb

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I Z, 3k biIV . F I t'It rc'

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t, ~~I T .I III L_ ~ I A isg.

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is -)% *I ... ~ * ~ .'d ,1 Iu

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d gor 2% t: .4 L A I I U ". 0

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261 ~ I '..j zt ? .".T',-

1 31*

92p 14 ip (A F ,4 ~ .I II'%'aDL'-I'1

g'IXIIgell Sw rg,v pof Zt P1 1.

196

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doeu jCuL 1:t3d I T

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.Sd,'L Ouj*i IN.. tLN

I %J Via -11 .- i11 ~ *I "I i T )S to( "'*f I If~ OI

3dt. 1', fillZ 11-l I.1 9 I

197

j I" q :'I I 4'I**1 .

~ I 13 I t& I

345. St 1k.f

iLt. P'.UPI A (

3b'e C,,lzIt

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j%? -4 1s' *.a m*1i

.5"7 fI 1r P P i

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L ''1 -&IL -~ 1 *'''IL

v 5 k , I A ' I - -Li 1 1: i' k. k

ti.~ -= " 't

4 rCC

#AII kT kL I~ ) If 1I-I I. I I (1 10! C*J$I IPL r rf. I~

-o-A %~: 0 O. r' I L., Ir X' t p

46 14# S.j 1 1 1:t.

4. . L I 1. r' 10 1.'

64J AU 1 L - A W T of. A J * ?J""I'I

..4 1. ur , rv 3 1e )A 3

a', IJI tq~ -' I It .11. 'I .g I 1.3' ý q*mnj~ el ?.j

199

4e47 CCC *s'b

44 Cccc

4-:1L is ti It qpI OII~bhA

40. 1 cr z

P73.%

.6 b ~A 1.L

rLr

17t )47.! I.L2ZV

F4 7s rlIU<.

TABLE 19VALUES OF THE CORRELATION COEFFJCIENT FOR THE

IDENTIFICATION OF THE MINE-LIKE TARGETIN WET GROUND

WAVEFORM ANTENNA p(9TB)LOCATION

EIS .593C .167C .785C .363

15 cmE .170MINE-LIKE 15 cmS .596TARGET '15 crn,W .382

15 cm,N2930 cmn,E .18330 cm,S 1 .29430 cm, W .76630 crni,N .28845 cmn,E -.47845 cmn,S .678

I C -.678BRASS 15 cmi, S 1 -.380CYLINDER 30 cm,S .448

45 cm,W ...447

ALUM INUM 7 cmn,S - .337SPHERE 22 crn,S -. 387

37 cimlS -. 061

7 cmN -. 727COPPER 10 cml, S -.384

ISHEET 25 cm, S -. 02613 cm.NE - .06528 cm,NE - .183

201

TABLE 20VALUES OF THE CORRELATION COEFFICIENT FOR THE

IDENTIFICATION OF THE MINE-LIKE TARGETIN DRY GROUND

"WAVEFORM ANTENNA (9TLOCATION

L .57515 cm,E .685

MINE-LIKE 15 cmS .709TARGET 15 cm,W .483

15 cm,N .538

BRASS C -.779CYLINDER-77

ALUMINUM 7 cm,S -. 080SPHERE

COPPER 10 cm,S - 291

SHEET

tI

•JI

202

TABLE 21VALUES OF THE CORRELATION COEFFICIENTS FOR THE

IDENTIFICATION OF THE MINE-LIKE TARGETAND THE BRASS CYLINDER IN DRY GROUND

DESIRED TARGET DESIRED TARGETWAVEFORM ANTENNA MINE-LIKE = BRASS

LOCATION TARGET CYLINDERp(8TB) P(5TB)

C .525 .64815 cm,E .434 .64615 cm,S .423 .49115 cm,W .477 .651

MINE-LIKE 15 cm, N .837 .922TARGET 30 cmE .6P7 .738

30 cm,S .535 .16830 cni,W .396 .831

30 cm,N

C -. 266 .95415 cm,SN .228 .983

BRASS 30 cm,SN .146 .951CYLINDER 15 cm,EW .228 .979

30 cmEW -. 049 .991

- .. .. .... . .. . - . . .

203

I# Itit

L&Jn

L III

F 00

LA W

Lu-

LDJ

x! !m61-J i-FT4k

InA

03 en Wn 0

vn o~ -0

'm 0 IN* ccI

o D

V Lii 0Aw. -1-

IL V -

- i

a ; 0.

I S --- c--C

205

CO. --j- ~

LA. C->O ~ N N F

U-1

pqzw We"

APPENDIX F

This appendix tabulates the average extracted resonances ofthe different-size, different-depth cylinders and the thin wires(discussed in Chapter V).

206

206

20l7

"R 1C

Q -a a U,f".

61~

NI

-No-

IL'

208

U, r-

11, IWO

cm~ VI'a wa'

UJ i

C49'

Li.

I

APPENDIX G

This appendix tabulates the average extracted resonances ofthe waveforms from the two models of the mine-like target and thesmall-antenna mine-like target waveforms.

TABLE 27AVERAGE'EXTRACTED RESONANCES OF THE MINE-LIKE TARGET

1 POLE POLE(REAL)* (IMAG)

-1.75363970EB ±6.61019133E7MINE-LIKE TARGET -5.73125538E7 ±l.32122486E8MODEL NO. 1 -2.87494683E8 t2.27030133E8O.6m ANTENNA -1.82908509E8 A-3.07411043E8

-9.76454733E7 ±4.284479OOE8

MINE-LIKE TARGET -1.49959862E8 17.56869867E7MODEL NO. 2 -9.64557560E7 L.64502020E8O.6m ANTENNA -2.09351880E8 i2.27711640E8

-1.91461498E8 ±2.89778957E8-1.91729062E8 ±4.14181320E8

-6,90468500E7 *.•131552700E8MINE-LIKE TARGET -2.80111200E8 ±2.22590300E8MODEL NO. 1 -2.35432000[8 .2.69826400EBO,15m ANTENNA -5.03972000E7 -t2.994208OOE8

-1.22024400E8 4 4.04685600E8

*Real Part in Nepers/s, Imaginarv Part in Hz.

I .209

' IA

I' K.

APPENDIX H

This appendix tabulates the identification results for identi-fication of the mine-like target with the small-antenna system.

210

5. -. *-;.*

211

LAJAIn4 LL

LL, -- -

Ww I

-a g O N.N 0

212

TABLE 29FIR FILTER COEFFICIENTS USED IN THE PREPROCESSOR

OF THE MICROCOMPUTER IDENTIFICATION SYSTEM

-1

"1 7. re ( ib ý - •1 -E). , "/ -" u b• e .".•)t ' ' b , - i •

"13• tZ • * .i7J3eI E" -e

' .4 -, ' J . . • - J.1 7 P - )5

,56~ ~ ~ ~ ~t 1-q 1""01 ... L?.F.

St., H P,. 4 4 - - , ,.: • "

1' t) r.( ."• -

213

"f f

4.0

04

-L t- 0

L J m--

I-I

II /I

4) LU l '

L. 4

L C:)9 -

cm JLUI4

- - elM

APPENDIX I

This appendix gives detail descriptions of the APUE68] and themicro-program that implements the various system control and targetidentification processes.

A . The APU and Its InterfacewithF -- e-- SDKC-805

The connection diagram of the APU is given in Figure 58.

CONNECTION DIAGRAM

00

0014 1

Too %Vo

Figure SG. Connection diagramn for the APU.

214

215

Interfacing the APU with the SDK-80 requires the generation ofthe various control signals. In this study, the APU is interfacedto the SDK-80 as a memory location, and the control signais are gen-erated as follows:

1. CS: chip select

The chip-select signal is generated by using addresslines A13, A14, and AI5 nf the 8080A processor in theSDK-80. The signal generation circuit is shown inFigure 59. The chip-select signal C is low when theaddress lines A13, A14, A15 are all high.

A13 9I0

A14_ 12 - 3A15 -- 13 74 I

Figure 59. The chip-select (Cs) signalfor the APU.

2. C/D: ronimand/data

The C/D signal is tied directly to the address lineAý of the 8080A processor.

3. I0: tied directly to M"WT of the 8080A processor.

4. IOW; tied directly to WW line of the 808A processor.

5. PAUSE: tied directly to the ready line of the 8080Aprocessor.

6. CLK: tied directly to ý2 of the 8080A processor.

7. EALK, SVACK, SVREQ, RESET, E-0: unused.

8. To eliminate possible loading problem, two additionalsignals are generated tc inhibit the ROM's and RAM's of theSDK-80 when the APU is being addressed. These two controlsignals (El and E3) are given in Figure 60.

.21

j. Z0 I-C0

o ~ E

to -o NO

LaJ4J

0

CQ CQ

In i

S.4

N qN

217

Asurtmary of the APU conuands is given in Table 31.

TABLE 31APU COMMAND SUMMARY

SCommand Cod.t Command Cm~dDtcoto 16 S I4 3 2 1 10 Mnsimons,.ComnOcrpo(1

FiXiO POINT SINGLE. PRECISION

0 O SAOO SubladTOS fo~nOSNOS..iuivtoS NOaS Po sacIII 0 WWIL U~.11pi~es NOS tiv TOS Result to NOS Poo SlackIsl __ SOV s'.r NOS be TOS n.0~.i, to NOS Pooptc

FIXED POINT DOUBLE PAICISIONA4 3 0 0 ~ 0 DADO A,t.h.TO$ 10NOS Resultr to NOS Poo Stack.

1% 00U M Subtracts TOS fromNOS R..wit o NOS Poo Stack1 0 IVU Mut~p~esNOS e TS Rsul toNOSPio Stack.

011 ODIV O..rl-s NOS brv TOS A-s.wlt to NOS Poo Stec'.

FLOATING POINTa 01 0 5~ FADO Adds. TOS to NOS Rewir to NOS Pop Slack.

0 1 0 0 0) sue Subptracts TOS Ilp., NOS Re~ult to NOS. Poo Stack.AC 100t0~ IMUL Ml.Ir-pitrri NOS hy TOS R.suft to NOS Poo Stack

a C'V O..'.tNOS ovTOS R,.vlt to NOS POO StackDERIVED FLOATING POINT FUNCTIONS 421

- G 1 I ,. fT SR wt0 0 1 Cclv". of TOS ResulIt .n TOS

A:0 'C .0 0 1:00 TAN Tanry'nofITOS Resul~t ATOS0 00 01 AS N 1A-%* .tSn#of TOS R".InTOS

00 At OS I.w Com-rn ofTOS 0....u.t A TOSa 0 a I 0I AT AN rr....Tanny- of TOS AeI.r.ir r TOS

a 0 1 0 ~0 NOP N~t- .o.... ,w% a-a fTn eut- O

1) 0 1 0 1 0 F: %P C.;-n..t, TO Iro-) a~ot.' TO ., Rw to- TO1S rcoo ,.pppn omC 1 0 1 1 l 1'% qn'.' TOS I ,, a-l. "C% . Id dn to thetrr Do.*,- .,Rý1 to.,SPo.Sac

I 0 S~iDAT ConIPULATIO COMMArNDS d.I431 .~ o.the~gp.1l.m0 1 0 0 0o O CN., Ov T'o. 1.n . ... 0nI.1pn Ord nTS

A4, 1 0 1 1 0rO C sO Char.,,.y TqrOS tdo- #1at$. eorom Ifip..t c .n d o an forS.V. I 0 0 F: CNS Cho-V. is .TOS Na oat.n q po .A ovnle ~v .10 oormn formalS

AtI 0 0 P~D Co -%TOS P..,ngep.C,.o- do..,, op',rc% oo lr d or'ý TO 0 IIOJI DOAtlbS%P 0 1 m proiS Chnr s~ ofcpr i ....p ptcsoo ~rl oovw oi.nd on TOS t OAt J 0 1 0 0 PSOF Pu~nqp ItJIq of doub. DPrI ,.dpm Operand 0. TOStoNO

a f .0 0 1 POPS P Chag'. p'r,t Of flo.., orr." ooDrarrd an..TC 15 c ' TOS

: 1 t 0 0 Pros Push s.Ai~r ol,q prc-1o f-d.. DO-.t Oofrani 1on. TOS to 0 NOS mt OS

0t 1 0 1 1 TooI Put .cnu.t~rgi Orec.1.rr fwerl po ..to oi.a on TOS tod NOSC *1 1, a I CIN:or o.'.~,oub'. pcor.treed Do~n TOS e~ro TSon NOS

. .£ I I a C. 0 00's Poo.g. mtlP.I' wfi rrrI 1-d Onat moS nd N~O TS 0Sw orTO

- PU.PI Pull Ilootmqr po-m comin,?' "- nn,, TOS Prrin,mu TOS Lrwcn'., NOS.

A".' A( '-' -s .Top : 'it% %14.11.N..l 0. Slack2 LI .P *.-, 'I . , r'1l'l."I ow f.%o1rr0. th. Cg.,nf~r, of1 II. Slack Oftl fft* resulit Can bir C0,.n1ed O to be "611 raPf" eommwi@d

I ~* .Ii'.9.S' ..- a. fl$), FIXD, Ik.S. FLTDI *'tha ItI dat.'qOO' et formal to b ge . ofr.d ktweunr..dbItts Si nd$0"I Fie 0l

218

B. The Microprogram for theMicrocomputer System

The various functions of the microcomputer systems are imple-mented as commands listed in Table 32. The microprogram thatimplements the various commands is given following Table 32.

TABLE 32TABLE OF COMMANDS IMPLEMENTED IN

THE MICROCOMPUTER SYSTEM

COMMAND DESCRIPTIONS

CODE

F Restart

A Display a menmry waveform on theOsc il lo scope

8 Branch to another ROM

7 Displays data values of interest

6 Change or enter the number of waveform

taken to form an average waveform

H Change or enter number of samples perwaveform

2 Change or enter the sequence numberfor, the next waveform

1 Initiate Recording sequence via thepush button

0 Record a waveform, and perform theidentification process

B Dump memory onto tape

D Check if data transmission torecorder is error-free

-z

219

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is . LUC Sf~j $VJ UL~ICt. S?,&Tr 'Lt4

1 1 1ýT V9 1HF.4 C,,S3CTIr Tru.L RECUID~fIr. V~rjSju,, ej0 1 P T4rSKPtA.'i.E "ICROCS11PLAIM. SYSTEM PRGA.

17 I IS U~'i 61N' Tole mlNO TEN AIAII', LJ0II7IV Tr' rCi'i Idd POINT WAYUCkISO~

I IT Hias Tmra 0.I LIlT? C ILI! CAT& P~rCLSSI:,G UhIPIO

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ie 1 I IJO% A A% rP:"

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220

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~to,U P uI wsT c~l, ue"r mtAA6'. H&ý SlUCKO -Alll aL ))# .

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ou s~ b~ t r PIAI Cal LF11.

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11!31'U J I L(:101 FPLIC-t.1 ,p IS 15 l.¶0M UPf LOCATIONr

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C. Details in Obtaining the SecondSet of Identification DatA Withthe Microcomputer System

i. _Dfffre nce equation coefficients

Table 33 tabulates the difference equation coefficients usedin the microcomputer system for identification of the mine-liketarget.

2. Detection thresholds (RID-30 cm)

tMAX RANGE -14,49 (TB)

MAX RANGE •12,82

EM RANGE " 0.639, 0.862

The sane detection thresholds were used for identification of Ithe mine-like tarqet in both ground conditions.

3. Identification thresholds (RID-30 cm)

Table 34 tabulates the identification thresholds for identifi-cation of the mine-like target in the two different ground conditions.

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-yI TABLE 34IDENTIFICATION THRESHOLDS FOR THE IDENTIFICATION OF THE

MINE-LIKE TARGET WITH THE MICROCOMPUTER SYSTEM

0" 2To T O2 T0 3 T0 4 T0 5 ''

GROUND'" T4TB Tz5TB T-6TB T=7TB T=BTB

CONDITION .522 .801 .615 .677 .780 .79177l

(TUNED)L|

CONDITION .500 .500 .250 .125 .500 .400002

(UNTUNLD) L

I ..

W

APPENDIX J

Table 35 tabulates the extracted resonances and their corres-ponding residues of the thin-wire (30cm long, 5cm deep) waveform.

Tab'le 35EXTRACTED RESONANCES FROM THE 30cm LONG, 5cm DEEP THIN WIRE

ANTENNA LOCATION = CENTER OF WIRE

POLE * POLE RESIDUE RESIDUE(REAL) (IMAG) (REAL) (IMAG)

-. 1308792E 9 -. ;2243403E 9 -. 1708435E 0 .6741198E-1-. 4685945E 9 .2800813E 9 .1377038E 1 -. 2542809E I-. 2156001E 9 .'260306E 8 .2210962E 0 .1263321E 1-. 4685945E 9 -. 2800813E 9 .1377038E 1 .2542809E I-. 2156001E 9 -. 7260306E 8 .2210962E 0 -. 1263321E 1-. 170807eE 9 .3030841E 9 .5459014E-1 .2335131E 0

-I1209931E 9 126777E 9 -. 9631155E 0 -. 2862594E I-. 1209931E 9 -. 1126777E 9 -. 9631167E 0 .2862594E 1-. 1708073E 9 -. 3030841E 9 .5459009E-1 -. 2335131E 0-. 1308•792E 9 .2243403E 9 -. 1708435E 0 -. 6741193E-1-. 6272871[ " .1839096E-2 -. 2458968E-1 -. 4475425E-7

PARAMETERS: N-l1, ILBS7, M=2, Il1=4, ,.=0.391E-2

Two pairs of poles appear to have dominant residues, namely thepole pair- at 280 MHz and 112 MHz. However, the pole pair at 280 MHzhas a mu'ih more negative real part, thus, in the late-time region,

'urlHy tht, pole pair at 112 MHz is dominant. .. ..

Table 36 tabulal.e% the extracted resonances and their correspond- iinq resirlues fro• the 30cm long on-surface wire.

In the early-time region, the pole pair at 302 MHz is dominant.

• Real Part in Nepers/%. Imaqinary part in Hz.

258

I)

259

TABLE 3�EXTRACTED RESONANCES AND FROM THE ON-SURFACE THIN WIRE

(30cm LONG). ANTENNA LOCATION CENTER OF WiRE

POLE* POLE RESIDUE RESIDUE

(REAL) (iMAG) (REAL) (IMAG)

-.1462028E10 .OOOOOOOE 1 .2469165E 1 *6242044E-7-.3449277E 9 -.3023622E 9 *1591370E 1 -.1711432E 1-.3449277E 9 .3023622E 9 *1�9137OE 1 .1711432E 1-.1003984E 9 -.2404006E 9 -. 1003876E 0 .1049173E-1-.2344375E 9 .4529953E 9 -.2735412E 0 .1V13815E-1-.4641263E 8 .6872750E 8 - .6308170E-1 .7273762E-1-.2344375E 9 -.4529953E 9 -?.035411E 0 -.1113816E-1-.1003984E 9 .2404006E 9 -.1003877E 0 -.1049174E-1-.3901977E 8 -,1401513E 9 -.2077824E-1 -.2096944E-1-.3901977E 8 .1401513E 9 -.2077823E-1 *2096944E-1- .3232055E 9 .3787546E 9 -.3689420E 0 -.6241565E 0-.3232055E 9 -.3787546E 9 -.3680420E 0 .6241565E 0-.4641263E 8 -.6872750E B -.6308171E-1 *.7273161L-1

PARN4ETERS: N=13, IBS�5, M=2, II�1, �=O.3839O75E-3

I.,[

S *� � . �. 9 * , . . ffi . S .� .. .

*

*Real part in Nepers/s. Imaginary part in Hz.

1��

U --------------------------------- �.i�-. -. -