ECHO-ECHO CORRELATION - DTIC · Echo-Echo Correlation (EEC) is a method for e.:ploiting the...

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0 0 Technical Report 336 ECHO-ECHO CORRELATION Comparative Study of Echo-Echo Correlation and Replica Correlation During the US/UK Joint Sonar Project Shows EEC to be a Superior Detection Process Under a Variety of Conditions MD Green 15 August 1979 LU DDCFinal Report OCT I. 199 Approved for public release, distribution unlimited.r NAVAL OCEAN SYSTEMS CENTER SAN DIEGO, CALIFORNIA 92152 -,.-. _• .• _. . . ..

Transcript of ECHO-ECHO CORRELATION - DTIC · Echo-Echo Correlation (EEC) is a method for e.:ploiting the...

Page 1: ECHO-ECHO CORRELATION - DTIC · Echo-Echo Correlation (EEC) is a method for e.:ploiting the (assumed) stationarity of the medium and target to allow each echo in a train of three

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Technical Report 336

ECHO-ECHO CORRELATIONComparative Study of Echo-Echo Correlation and

Replica Correlation During the US/UK Joint SonarProject Shows EEC to be a Superior Detection Process

Under a Variety of Conditions

MD Green

15 August 1979

LU DDCFinal Report

OCT I. 199

Approved for public release, distribution unlimited.r

NAVAL OCEAN SYSTEMS CENTERSAN DIEGO, CALIFORNIA 92152

-,.-. _• .• _. . . . .

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NAVAL OCEAN SYSTEMS CENTER, SAN DIEGO, CA 92152

AN ACTIVITY OF THE NAVAL MATERIAL COMMAN% D

SL GUILLE, CAPT, USN HL BLOODCommander Technical Director

ADMINISTRATIVE INFORMATION

The work reported on in this document was funded by the NOSC IndependentResearch Program (61152N, ZR78).

Released by Under authority ofR. A. McLennan, Head R. 1). Thuleen, IleadSonar Systems Division Weapons Control and Sonar

Department

ACKNOWLEDGMENTS

The author wishes to thanik Dr. Jon Reeves and Darrell Marsh, both of NOSC,for their earher work in this field and for their support and encouragement.

-. z

,// I

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UNCLASSIFIEDSECUI'.ITY CLASSIFICATION OF THIS PAGE (Whe~n Data Entered)

DOCUENTAION AGEREAD INSTRUCTIONSBEFORE COMPLETING FORMA

I. REPORT NUM13LVW GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER

TIIECHO-L HOWQRRELATION 5 S TyP OF REIOAT & PERIOD COVERED

k lu- c k LwIrc ,epdk *.

Nav l ý Oc a System Centerf

9I. CERONROLING ORGFICEIO NAME AND ADDRESS 10. PROGRAM ELMNP~j ,TS

Naval O.cean Systemr Center 15 I5AugeO 79 '

San Diego, CA 92152 56&&

14, MON ITORIN G Ak.EM.C._)AM.EA ADPRESS(tl different fromi Conhroliing Office) IS. SECURITY CLASS. (of this report)

/1' UNCLASSIFIED

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Approved for public release; distribution unhimited

17. DISTRIBUTION STATEMENT (of the abstract entered In Block 20, It different front Report)

Ill. SUPPLEMENTARY NOTES

1S. KEY WORDS (Continue on reverse etid* it necessary end identify by block numbher)

active sonar, signal processing, replica correlation, echo-echo correlation

20. AUatI\ACT (Continue on reverse side It neceeseay and Identlify by block number)Thsreport provides a theoretical and computer-aided study into EEC signal processing and presents the

results of EEC analysis on selected p~ortionls of data recorded during the US/UK Joint Sonar Project. A limitedcomparison with replica correlation anal) sis is also provided. Unique characteristics of the EEC pro'-ess are iden-tified and discussed, and its advantages over the RC process are suggested. ,

DD I JA,47 1473 EDITION OF I NOV Sb IS OBSOLETE UCASFES/N 01 02-LfP.01 4-6601 UCASFE

SECURITY CLASSIPICATION OF THIS PAGE (mfet eja ~Entebetl

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: UNCLASSIFIED

UUNCLASSIFIED

SCSECUITITY CLASSiCiCATIO o TFCI PAGO THIS D Date Entre

iIfIl

• :I

: I

)

*I UCASFE

*KugyCASFCTO FTHSiAEWm~DaMtd

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SUMMARY

In active sonar, large time-bandwidth product echoes from submerged objects areofti.. identified through the use of a matched filter, or replica correlator. The theoreticalchar:.cteristics of replica correlation (RC) are well known, but are predicated upon the echobeing identical to the transmittvL pulse, except for the presence of white Gaussian noise.When the ocean and target combine to filter the incident pulse in a random manner, the1' replica may no longer b, a match for the echo.

Echo-Echo Correlation (EEC) is a method for e.:ploiting the (assumed) stationarityof the medium and target to allow each echo in a train of three or more closely spacedechoes to be used as a match for the following echo. This results in a correlation techniquethat is insensitive to, "echo splitting," target doppler, and pulse type. The sampled outputof the correlator may be reduced by an almost arbitrary amount, thereby reducing the falsealarm rate, but without affecting the probability of detection.

Lii

II

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CONTENTS

INTRODUCTION... page 3

ECHO-ECHO CORRELATION... 4

SIGNAL-TO-NOISE RATIOS... 7

FALSE ALARMS ... .8

COMPUTER SIMULATION... 10

COMPARISON OF ECHO DETECTABILITY... 13

EXPERIMENTS AT SEA... 16

Experimental Conditions... 16Signal Processing ... 17Experimental Results ... 17

CONCLUSIONS... 55

Location of Target Return ... 55Platform Stability ... 55Multipath and Echo Splitting Loss ... 55

Target Doppler Sensitivity ... 55Pulse Type Sensitivity ... 56False Alarms.. . 56SNR Enhancement. .. 56Characteristic Appearance ... 56

REFERENCES... 56

2

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INTRODUCTION

The problem of detecting the presence of an underwater target began to receiveattention during World War II as the danger from submarines and subsurface mines began toincrease. In subsequent years the problem has expanded to include avoidance of submergednavigational obstacles such as wrecks and sea ice. The primary means now in use to detectthese submerged dangers is sonar, which functions either by "listening" (passive reception)to the emitted sound of a target or by actively transmitting sound toward the target, then

* listening for the "echo," which is the reflection of the transmitted energy from the target.The echo will return to the receiver distorted to some degree by unwanted energy, which iscalled noise. The receiver system must contain some form of decision-making process whichanalyzes the returning energy with the goal of identifying, or detecting, the echo in thepresence of the noise.

An echo returned from a perfect reflector will be identical to the transmitted pulsep(t), provided the medium through which the energy travels does not distort the wave. Inthe actual sonar environment, the target seldom acts as a perfect reflector, and the mediumnearly always modifies the wave in several ways. A transmitted narrowband pulse of soundwill be characterized by: its pulse length r, its center frequency &2, its bandwidth B(B/2<I ), its initial phase 4, and by its power. The parameters may be modified by thetarget and the medium in such a way that statistical estimation of each becomes necessary.When the range and/or the relative velocity of the target is unknown, the time of arrival ofthe echo may also have to be estimated.

When the echo is so buried in noise that its immediate identification is difficult,signal processing is required to extract the echo. The primary form of signal processing nowin use with sonar, for narrowband pulses in which the product Br is much greater than I , iscalh'd Replica Correlation (RC). When the spectral density of the noise n(t), is also a nar-rowband function centered on S2, the received time function will be

z(t) = p(t) + 1(t)

= RQ[Z(t) exp (i2t)l (I)

= RQ[(P(t) c4P + N(t)) exp (ig2t)l

where

Z(t), P(t), and N(t) are the complex envelopes (Ref. (1)) of z(t), p(t), and n(t),respectively.

The observation period of v(t) is Tý>r. Assume the data are sampled according to the Shan-non sampling rule, at h samples per second. Replica correlation is defined as

11T

r(X) = >, pi + X) z(j)j= h

hT

hT M * X eo 2

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.,i

in which p(j), a replica of the transmitted pulse, is the optimum fcrm of the matched filterfor white noise. The time, ,max, of the largest amplitude of r(X) is taken as an estimate ofthe time of arrival of the echo.

Replica correlation presupposes that the echo is identical to the transmitted signalsave for the effects of noise. The medium and target will often combine to filter the trans-mitted signal in such a way that the received echo no longer duplicates the replica. In gener-al, it is not possible to predict the characteristics of this "external filter," and means arcrequired to compensate for its effects, although the techniques employed with replica corre-lation have not been notably successful when severe distortion of the pulse occurs. Theremainder of this paper presents a technique that eliminates the problems caused by theexternal filter.

ECHO-ECHO CORRELATION

If the external filter is fairiy stationary over a period of several pulse lengths, it ispossible to compensate for the pulse distortion by transmitting three or more closely spacedpulses, identifying one of the returning echoes, and using it as a "replica" for the remaining"pulses. Let the transmitted signal be a series of pulses

M

a(t) p(t - mL) (3)nIl

where L > r is the pulse repetition period,

M > 3 is the number of pulses,

and

ML' 4T.

The received sampled time function from a stationary target now is x(j), where

xO) = b(j) + nj) , < j hT (4)

where

M

b(j) q(j -niL)mn= I

qj) is the received echo from one transmitted pukse, p(j).

At any time jo, begin observing x C) in segments each hiL samples long. Let xk be the kthsegment. Define Echio-Echo Correlation (F-EC) as

4I

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(hL-Il)

Ck(X)= (L I xk) + X) Xk+l )j=0

jhL- RII L Rk *0+X (5)L X-Wj+k )Xk+i)I

- hL < X < hL

where Xk(J) is the complex envelope of xk(J).

There are two cases to be considered. First, assume that each individual echo, qQ(), 2 1,2, 3, is wholly contained within the adjacent segment, xk+k_1 C). Refer to Fig. 1, where the

Xk-2 - Xk_1 I xk I Xk+1 Xk+2 Xk+3

IFigurie 1

Senvelope of xOj) is shown; the noise is suppressed. Assume that the first echo, q(11), is con-tained in segment xk, that the individual echoes (IQ are identical, although they may nolonger resemble po), and that the noise in each segment, nk(J), is statistically independentfrom signal and from no!;.c in adjacent segments. Eq. (5) is used to obtain sample correla-lions of adjacent segments. There are seven input segments, which provide six correlationsegments. They are

IckE2 (X)l = 7 E{nk X2 (j+X)nk-lIW)} 0 (6)j=0

where E is the expectation over the noise distribution,

J = (hL- IX!)

JE[Ck+l(X)1 ;1 + ) q0)+k()] 0 (7)

7k Itn (X) I =) 'J 4i)+ .k

j=0

J

E[I ck(.t)l - Et[l( (t + X) + Ilk(t + ) 1q2MI2(t) k+ (t)I lItj=0i. (8)

q - I- (lt + X) q2(t0 dt

S~J=O

i;i

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1X1

F[Ck+l(X)l E{[q(JjX)+nlk+10j+X)] [q 3(6)+nk+2(J)])}

j=O (9)J

= - >I q2 (j + X) q 3(j)

j=0

E[ck+2(X)] = ( E{[q 3 (U+X)+n k+2(+X)I nk+3J)}) 0 (10)

j=0

ElCk+3(") ---J! E (lk.•3(0-N) lk+40j)} 0.()

j=0

Note that noise correlated with noise [Eqs. (6), (11 )1 gives zero correahtion, as does echocorrelated with noise [Eqs. (7), (10)1, while echo plus noise correlated with echo plus noisegives the autocorrelation of the 'cho [E.Ls. (8), (9)1. Each correlation segment is 2L seclong.

In the second, and more general, case, each echo will be split between segments, asshown in Fig. 2. Note that xk(J) contains a portit) of(q , while xk+1 (j) contains portions

I Xk2 x kI l Xk I Xkf 0 Xk12 X3

Figure 2

of both ql and q2, etc. As before Eqs. (6), (7), and ( II) show I Ik-'21 = I" [ck+ II= E[ck+31 = 0. H1owever, since xk() contains a part of q l(J) which is identical to thesimilar part of l2(J) in xk+l(j), El ck 1 will be a partial autocorrelation. Segment xk+ 1 0)contains a complete echo (although the parts are rearranged) as does segment xk+2(.j). Thus"E[ck+I(X)I follows Eq. (9), and produces a full autocorrheation. E lck+2(X)] again pro-duces a partial autocorrelation. Since one of the two cases will always occur for a fixedtarget, Eq. (5) will always produce a full autocorrClation function for at least one vVluC of k.

With both RC and EEC, the passage through the correlator of a sufficiently strongecho will result in a "peak" in the output which exceeds in amp)litudC the surrounding back-ground caused by noise passing through the correlator. When no piior knowledge of' thetarget's location is known, the output of the replica correlator must be computed for eve'yvalue of X to determine which r(X) is largest in magnitude. For 'EC, on the other hand,Fig. I ant Eq. (8) show that the peak must occur at the center of the output segment, X=O,for a f'ixcd target. Thus all values of c0k(?), for XWO and all k, need not be computed. Thereduction in computation ovei RC is apparent.

6-

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When the target moves with constant velocity relative to the transmitter/receiver,the effect is to change the pulse repetition period, L. If v is the relative target velocity, and

i •V the speed of sound, then L' is the echo repetition period,

SL'L I + 2v) (12)KV

*• The individual echoes, q2(j), are each frequency shifted relative to the transmitted pulse,V....but not relative to each other. Since v is unknown, it must be estimated; however, since

I v = (L'/L - 1 )V/2, L' determines v. If information about the target's maximum speed isavailable, then the difference IL-L'I < S. Thus it becomes necessary to evaluate ck(X) onlyfor IXJ < 6, and tie time Xmax 0 0 will thus determine (L-L'), hence L' and v. .

SIGNAL-TO-NOISE RATIOS

One of the primary measures of the effectiveness of a signal processing technique isits ability to imprcve the signato-noise ratio of the input z~j). Define the input signal-to-

, • noise ratio as

Si = F/o2 (13)

where (

F is the mean square amplitude of the echo, q(j), and 02 is the variance of nU).I)nThe output signal-to-noise ratio for RC [Eq. (2)] is

K SO = {Elr(Xm-ax) }21 (14)

2B1r(Si)

whereS~2

a2 is the variance of r(i)

and for EEC [Eq. (5)1 it is

2/2SO {E[ck(O)I}2'k+

Where

a is thle variance of' ck+2(X).. Cck+2

The dlerivations of these formulas are given in Ref. 2.

It is interesting to note that, because tile EEC peak occurs at Xmax 0, for a targetwhich is fixed relative to the receiver, the So predicted by Eq. (15) can be doubled. Let

71

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- -2

I.

9kX 1a (16) W

E: ck(O) = [Ck(X) + Ck(-X)l. (16)

Define the new output signal-to-noise ratio to be

-2-2

"a, = E[Ik(0) + / + X (17)where

- 4 = vart(k+2(X)) .

Now

E[-•k(0)1 = - E[ck(O)+Ck(O)] = E[Ck(0)]I

so that the signal part of S0 is unchanged from that of S0 . The noise variance is reduced byIa factor of two, however, since ,

-2 (01 = - var C+2X + Ck+2-] (18)

- - [va, k2~ + var Ck+2(-A)I

=- [2 var ck+2 (R)].

- ~(°k+2 (x)

Since, for X i4 0, ck+2(X) and ck+2(-X) have independent white Gaussian noise, one has

s= 2S 0 (19)

In the remainder of the paper, the use ofCk (N) will be referred to as the enhanced FlI(Ctechnique.

FALSE ALARMS

A processor decides that an echo is present when the output is sufficiently high.The decision level D is often determined as a function of one or more of the noise statistics.so that, when noise alone enters a correlator, the possibility exists that the output will ex-ceed the threshold. When this occurs, the reslts arc interpreted as a false alarm.

For Br>>- 1, the Central Limit Theorem (Ref. 3) ensures that the probability densityfunction (pdf) of the correlation of the noise will be Gaussian, both for RC I Eq. (2)1 andEEC [Eq. (5), (16)] However, in the estimation of sonar parameters, it is often the casethat the phase, 4, and carrier frequency. I2, are unimportant. Since the time functions of'interest are narrowband, the phase and carrier of the echo cnvelope can be eliminated bycomputing the magnitude of the complex functions [lE1. (2), (5), and (16)1. Thus

8 -

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I,

f O(X) Ir(X)I , for RC

Pk(X) ICk(X)l for EEC (20)

ak(W) = Ick(X)l for enhanced EEC.

These are the correlation "envelopes," which will follow the Rayleigh distribution (Ref. 4)so that the probability ofia false alarm, PFA, is, for RC

PFA( >D1) = exp de

S2

""exp -D2/2a2 (21)

and for EEC

IT A(P k > )2 xp (D 2! 2o D)) (22)( 4°2)

PFA(ak >)3) exp (D 3I4u2) (23)

where

Di, i= 1,2,3 is the respective threshold

,= 1,2 is the respective noise variance.tj'By forminig a ratio of Eqs. (22) and (23), and setting D3 2, one has

"" 1Yexp -D214 a2 < 1 (24)

forj•yt D2>0

which shows that using ak(X) in place of Pk(r) will always give a reduced PFA for a giventhreshold level. On the other hand, if PFA in Eqs. (22) and (23) are equal, then D3

.D2//T, so that the same result is obtained with a lower threshold for the enhancedV tec1 hniquIe.

9

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Jt was previously mentioned that one need compute ck(X) and/or ck(X), hen'ce pk(r)

and/or (k(X), only within some range, -5 < X < 5. By not cdmputing tile correlation forXI > 5, the opportunity for noise only output to exceed the threshold is reduced. Let

25 •5 (25)

which is seen to be a ratio between the necessary output duration, 25, and the maximumduration, 2L. The probability of a false alarm is thus reduced by the factor y.

COMPU I'ER SIMULATION

One method for checking the validity of assumptions made in deriving theoreticalequations is to make mcasunremenS oN computer simulated data and to compare these re-suits with the theoretical predictions. To that end, a pui ' t was generated and added tobandlinlited while Gaussian noise. This ilnput time function was used as z(t) from Eq. (1)and was passed through both the replica correlator and the Echo-'cFho Correlator. Theoutput was observed, and the signal-to-11oisC ratio So, lmeasured. When B-> I , the output ofthe correlator will be Gaussian, so that S0 may be comnpu ted from

F ( )(26)

where

F is the peak of the correlation output when pulse (plus 11oise) has passed throughthe correlator Y is the sample mean of the out put noise, U is the sample variance ofthe output not,1.WI

Equation (26) compares with Eqs. (14) and (15) when Y = 0. When the envelopes of zeromean Gaussian correlator outputs (lEqs. (-20)) are coilsidered, a more appropriate measure touse is (Ref. 5)

S= (27)

where

F and Y are as bcfore.

When Si is computed as the mean square pulse amplitude divided by the noise variance, Eq.(27) is an asymptotically unbiased estimate of So as predicted by Eq. (14) or (15) asappropriate.

The pdf of the noise outlput can be estimated by computing a histogram of the dataand comparing it with a theoreticý ' say by a "chi-squarcd Goodness of Fit Test"(Ref. 6). This estimate can be imin I averaging together several histograms of inde-pendent data. The mean, Y. and va, c, a- of the data are estimated as

10

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i MM

1 M (M ) (28)

X- 1

and

(Y W Y) (29);..'1,162 MM-I >,(Y(X)-Y) (9

x=- I:!!• t:X=l

where MM >l ht and Y(X) are samples of O(X), Pk(X), or ak(X), as appropriate. The FalseAlarm Rate K is estimated by counting the number of times in the observation period, T,that the noise only portion of the correlation exceeds a threshold, D. This threshold isusually a multiple of" the output sample noise standard deviation, o.

The wavwfoi-ms used in the sea trials were either Linear Period Modulated (LPM)pulses, or Pseudo Random Noise (PRN) pulses. See Reference 7 for a discussion of LPMsignals. A set of three identically generated LPM pulses were generated in the computer andimbedded in bandlimited white noise. Tne pulse bandwidth was 15-70 lHz, and the pulselength, r, was 0.853 sec. The pulse repetition period, L, was 1.333 sec. The noise band-width, to the 3-dB points, was approximately 15-70 lHz. See Figure 3, which represents thecase in which each echo is wholly contained in a segment, xk(t) (Fig. I ). Equation (20) was

I.! evaluated from these data with results as shown in Figs. 4 and 5, for RC and EEC,

3.750

II 1.875

I-.

z 0.000

ECHO ECHO ECHO

S-3.7500.00 0.25 0.50 0.75 1.00

TIME

Figure 3. Computer simulated x(t) iRef, Eq. (4)],

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1.2

SEGMENT OF INTEREST EEC

0.9

0.6

0.3

0.02 3 4

SEGMENT

Figure 4. EI!( output.

1.2I SEGMENT OF INTEREST ENHANCED EEC

0.9

• a.

.0.3

0.0 -

- I12 3 46

SEGMENT

Figure 5. ElntHh lced 1I1(,' ml put.

12

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respectively. Ten trials using the same pulse train mixed with independent noise sampleswere conducted and the results averaged. The input signal-to-noise ratio Si, calculated as themean square pulse amplitude divided by the input noise variance, was 2.85 dB, and theaverage output signal-to-noise ratio S0 , calculated by Eq. (27). was 22.36 ± 0.90 dB forPk(i), and 25.14 ± 0.8 dB for akO). The predicted So, using Eq. (15), was 23.1 dB. Asimilar test was conducted for a case of arbitrarily located echoes (with respect to segmentorientation - Fig. 2), with results very nearly the same as just described. Figure 6 shows aplot of the probability of false alarms exceeding a threshold, D, versus the threshold, givenas fractions of the output mean, - Eq. (28). Note that the measured data points fit thetheoretical curves very closely.

0.6

w 0.4S.-J0EEC

L. ENHANCED0. COMPUTED

'a' - 65'BT' - 27

ca 0.2

0.1

,0,1 I-oLl

0 .5 1.0 1.5 2.0 2,5 3.0 3.5 4.0 4.5 5.

THRESHOLD (FRACTION OF MEAN)

Figure 6. Probability of false alarms.

COMPARISON OF ECHO DETECTABILITY

The relative ability of two signal processing techniques to extract a recognizableecho from noise is a measure of the efficiency, of one technique versus the other. The fol-lowing comparison method is due to Brown (Ref. 2, pp 2-30), with modifications to suitthe mole restricted nature of this inquiry.

Define the False Alarm Rate, K, to be the number of false alarms which occur insome unit of time, and assign K to both techniques. Determine the Si necessary for eachtechnique to attain this K for a 50% probability of detection. For Br 1 1, an acceptableestimate of K is

' A

K PFA" B. (30)

13

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Using Eqs. (24), (25), and (26), we have

K = PFA(0> D) B1 - PFA(p>D,)) B2 PFA(x >D 3 ) B2 (31)

where

Bi is i= 1, 2 bandwidth.

Solving Eq. (32) for Di, we obtain

Di (_2 ^ 1/2tDI (K)/B1 1 ) 1

D2~~ ~ =(22 , 1/2D ( a2 n2 n (K)/ 1/B2

D3 -4o n2 (K)/B-) V2"D, (32)

The mean, YR and the variance R, of the Rayleigh distributed noise out of the corr,_lator/detector is related to the variance, u-, of the input noise, n(t) [Eq, (I)I by the following(Ref, 5):

YR= 0n0/U/2R°n ) f un (33)

An "effective signal-to-noise ratio," di, is givCn fOr each technique .s

di = 2t log I[(D xRi)/URil

=20 log [(Di - uj 1iV/ý12)//Poi, (34)

Equation (34) is equivalent to Eq. (26). In order to determine Si 1'rom Eq. (14) or I(15), it is first necessary to ,'ompute So f'rom Eq. (27), which is not linearly related to di.The non-linearity may be removed by application of (modified) Brown's curves, thuIS trans-

forming di to an estimate of SO comparable to that obtained from Eq. (27).

As a numerical example, let n l = on2 = 1.0, B1 = B = B = 400 lIz, r = I sec, so 10

log (2Br) = 29 dB, and letK= 10-2 false alarms per sec. Thus, from Eqs. (22), (23) and

(24)

D= D2= 4.61

D3 = 6.51

and from Eq. (34)

d = d2 = d3 = 14.21 dB1

From Fig. 7 we obtain, for RC, Si = 12-29 -17 dB, while from Fig. 8, for IEC, Si 6.5-14.5 =-8.5 dB, and for the enhanced -l'EC [Eq. (16)1 Si 5.5-14.5 =-9.5 d B.

14

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< ~ -

cld

00 Iw ~0

0

00 0

(On

000

(N

000p

I I I ? I . V I "

7 7

15WAL

Page 20: ECHO-ECHO CORRELATION - DTIC · Echo-Echo Correlation (EEC) is a method for e.:ploiting the (assumed) stationarity of the medium and target to allow each echo in a train of three

TThe preceding example shows RC to require 7.5 dB to 8.5 dB less Si to attain the•. , •given K, which implies that RC is superior to EEC as a detection tool. However, this exam-

pie required two assumptions. First, the echo was not distorted by the external filter sothat, for RC, the processing gain of Eq. (15) holds. Experimental results have shown, how-

i' ever, a loss of up to 15 dB from the anticipated So -- a loss that would not occur withl EEC.

Second, the false alarm rate assigned for RC may be arbitrarily reduced for EEC simply bynot computing values ol'Pk(X) or Qk(,), as appropriate, for IX, > &. Figure 9 shows a plotof K vs. di for different values ofy [ Eq. (25)1 . To complete the previous example, ify = 0.01, then for K = 10-2, the EEC technique requires that di = 10.5 dB. From Fig. 8,the required Si is now -11.5 dB., or an equivalent gain in detection capability of 3 dB.

14

10 12 -

X = -> EEC "y - 0.2

+8- = EEC y - 0.01

WHERE

6 " OUTPUT SECON DS/CE LLL - INPUT SECONUS/CELL

10-3 10-2 10-1 100

FALSE ALARM RATE (K)

Figure 9. Falsc al•rn rate vs. detectioni index.

EXPERIMENTS AT SEA

EXPERIMENTAL CONDITIONS

Tests were conducted during June of 1977 at a site located approximately at 46.5°Nlatitude, I 2.8W latitude. The water deptlh was approximately 4 150 metres, fnd the seastate was a moderate three. The transmit/receive platform was I IMS MATAPAN, a convert-ed WW II battle destroyer with a side-mouonted planar array sonar. The submarine tlargewas at a depth of 100 m. The majority of the trials occurred during parallel course (zerorelative velocity) operations with a target aspect angle of approximately 100 deg. The sonarbeam depression/elevation angle (D/I') ranged from 45 to 26 (leg relative to the mcanl seasurface. The acoustic path was a single bottom b)ounce, and 0ei limiting interferen cc aboutthe echo was reverberation from the sea surface above the target (see Fig. 10). All

16

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D/

Figure 10. Experimental geometry.

k

transmissions were corrected for the motions of the platform, but the received signal wasnot so corrected prior to recording on magnetic tape.

SIGNAL PROCESSING

The narrowband signals were sampled at 1024 sarmples/sec - approximately 2.5times the Nyquist folding frequency. For RC, a replica of the transmitted pulse was alsosampled. The correlations (Eq. (20)) were computed via a Fast Correlation technique (Ref.7), and the results plotted. For EEC, the output segments are for II < 6 = 10-3 seconds ofcorrelation. To'e input segment duration was the pulse repetition period, L = 0.5 sec or 0.6sec, depending on the Lest, givingy = 2 X 10-3, or 1.67 X 10-3, respectively.

EXPERIMENTAL RLSULTS

Although the object of this experiment was to compare echo detectability using RC

and EEC, only a limited aimount of data were obtained, and the errors and uncertainties inthe data made quantitaVtve measurements impossible. However, a qualitative comparison ispossible from the plots that follow. These plots are presented in groups, with the first plotin each group being a representative received time function*, z(t) [Eq. (1)], for that groupof transmissions. Following this RTH are the individual RC and EEC plots for each trans-mission ("ping") in the group. The groups are characterized by D/E angle and pulse type, asindicated in Table 1. Each RTH has a heavy horizontal line marked "Echo Time." Becausethe target was equipped with a delayed acoustic tratisponder, it is possible to determinerather precisely the expected echo time from the target. Each c rrelation plot has a similarline marked "Period of interest," indicating the anticipated echc zorrelation time.

Figure 1 I b shows EEC output as anticipated from theory. There is a single strongpeak with two smaller side peaks equally spaced on either side of it. These three peaksoccur precisely at X = 0 for their respective segments. Note that the corresponding RC plot,Fig. 1I a, does not show an acceptably high enough echo correlat•'n to reasonably declarean echo to be present. Most of the remaining plots in this group show more than the antici-pated two or three peaks for EEC, which, it is assumed, is accounted for by some unknownacoustic paths, The nature of these paths is beyond the scope of this report. It is apparent,

*The received tiinc function here is referred to as a Reverberation Time History (RTH). Since the back-ground interference for these tests is dominated by acoustic returns from environmental scatterers, hence"reverberation."

17 I.

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Table 1 Experimental parameters.

Figure DIE BW 19, Ping Numbers

11 26 400 LPM 438-442

12 26 600 LPM 443-447

13 35 500 PRN 224-225

14 35 400 LPM 219-223

15 40 400 LPM 147-155

16 45 400 LPM 82-87

Where: D/E in degrees, BW is pulse bandwidth ill lIz, and PT is pulse type.

however, that at this D/E, EEC provides a much more satisfactory target indication thandoes RC, which often has the echo correlations nearly buried in the background.

At steeper D/E angles (shorter ranges), the RC plots begin to improve see Fig. 14c.However, the EEC plots are still superior in So see Fig. 14d, Several of the EEIC plots,such as 14f and 14h, were suppressed by the large spike at the left hand side, but tile So is,in fact, higher than that for the corresponding RC.

At the steeper D/E angles of' 35 and 45 deg, the high output from EEC inl lhe firstseven to fifteen segments indicates correlated echoes froni the bottom. As ami example, seeFig. 15h1. These returns may serve to suppress the scale for the remainder of' the plot, butthe geometry of Fig. 10 shows them to occur well before any possible target echoes, so thatthey do not, in fact, affect the signal-Wo-noise ratio of the target echo.

Figure 16, which shows the results for the steepest 1)/l of' 45 deg, not only has moirccorrelation peaks for both RC and EEC than anticipated, but the E"EI!C peaks are not cen-tered at X = 0 for their respective segments. While a definitive reason for cither anonialy isnot apparent, the off-center peaks were most likely caused by the vertical acceleration ofthe receive platform during the reception time of' thie target echoes. For the most shallowD/E of 26 deg, any vertical acceleration of' the r'eceive platforni would have produced onrly a1minor projection along the beam axis, and, as shown in Fig. I I , t lie peaks are constrained toX= 0.

The enhancement process discussed earlier ( Eq. (20)) was not used on these databecause of the peaks not being constrained to segment center (X = 0).

In order to compare empirical results with t heoretical predictions, one requirementis that the background noise statistics be the same as those used in the predictions. 'I ficvarious RTII plots show pronounced variation,; in background intensity, so fhat the conceptof noise stationarity does not hold. 1lowevei, it is possible to reduce the ef'f'ects of a slowlytime varying background by the number of methods. One might pass the coi'rclator/detector output through a s:uitable high pass filter, or, perhaps, since the correlation may beaccomplished with the cross spect ruin, by dividing tile cross spectru in by tile auto powerspectra of' both components in the correlation. It applars, however, that the t-lV(' plots have

18

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0 0

06

Cj)

199

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0.020

0.018

0.016

0.014

0,012 -PERIOD OF INTEREST4

0.010 -

0.008 -

0.006 -

0.004 -

0.002

24,369 26.238 28.107 20.976 31.844 33,713 35.582

T I ME (sac)

VigwlC II~~ RC (ping 443).

1.2 PERIOD OF INTEREST

0.91

>, 0.6

0.3

0.00L

0.0 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0 27.0 30.0

SEGMENT(e

Figure II b. EEC (ping 443).

20

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77

0.014

0.013

0.011PERIOD OF INTEREST

0.010

0.009

0.007

0.006

o.004

0.003

0.001

24.369 26.238 28.107 28.976 31.844 33.713 35,582

TIME (soc)

Figure I Ic. RC (ping 444).

1.2 PERIOD OF INTERES7

0.9

>- 0.6

0.3

0.0 T

0.0 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0 27.0 30.0

SEGMENTS

Figure I lId. EEC (ping 444).

21 -!

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o.013

0.012

PERIOD OF INTEREST

0.010

0.009

0.008

0.007

0.005

0.004

0.003

0.001

24.369 26.238 28,107 29.978 31.844 33.713 35.582

TIME (sec)

Figure I Ic. RC (ping 445).

1.2

PERIOD OF INTEREST

0.9

>- 0.6

0.3

0. 0 L l -

0.0 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0 27.0 30.0

SEGMENTS

Figure II f. iEC (ping 445).

22

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0.010

0.009

'0.008 PERIOD OF INTEREST

(9 0.007

0.006

0.005

0.004

0.001

9,•369 26.238 28,107 29.976 31.844 33.713 35.582

TIME (sac)

Figure 1 I g. RC (ping 446).

1.2- PERIOD OF INTEREST

Figure II 1h. EF1& (ping 446).

23j

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0.010

0.009

0.00800 PERIOD OF INTEREST

0.007

0.006

0.005

0.004

0.0010.002

0.001

24,369 26.238 28.107 29,976 31,844 33.713 35.582

TIME (sec)

U--igurc Ili. EC (ping 447).

12 PERIOD OF INTEREST

0.9 1

-0.6:

0.3

00, .3.0 60 9 12.0 15.0- 18.0 21.0 24.0 270 30.0

SEGMENTS

JjFigure I Ij. FE( (ping 447),

24

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0 u0

0Ow R

100

o o

C-4 -'

4)

CD

Co -odrf/GP

25o

Page 30: ECHO-ECHO CORRELATION - DTIC · Echo-Echo Correlation (EEC) is a method for e.:ploiting the (assumed) stationarity of the medium and target to allow each echo in a train of three

0.019

0.017

0.015

0.014

0.012 PERIOD OF INTEREST

0.010

0,008

0.0061

S~0,0040.002

21.870 23,739 26.608 21.477 29.345 31.214 33.083

TIML (sc)

Figure 12a. RC (pilg 439),

PERIOD OF INTEREST

0.9

>- 0.6-

0.3-

0.00,0 3.0 6.0 90 12.0 15.0 18.0 21.o 24.0 27.0 30.0

SEGMENTS

Figure 121). -i- (pilg 439).

I2

Page 31: ECHO-ECHO CORRELATION - DTIC · Echo-Echo Correlation (EEC) is a method for e.:ploiting the (assumed) stationarity of the medium and target to allow each echo in a train of three

-~~~~~~ ---- w*---v -- __-~-. r~

I

0.018

0.016I

0.014

0.0 12

0.011 PERIOD OF INTEREST

[-

0.009

Il ME (soc)

Figmie 1 2c. RC' (p'ing, 440).

I PLI1I0OFUPINTEREST

0.31

0.0 40.0 3.0 6.0 9.0 12.0 1. .0 21.0 24.0 27.0 30.0

SEGM E NI S

oigoic 1I2d- --- (-In440).

27

I) - •. . "-

Page 32: ECHO-ECHO CORRELATION - DTIC · Echo-Echo Correlation (EEC) is a method for e.:ploiting the (assumed) stationarity of the medium and target to allow each echo in a train of three

0.017

0,016-

0.014

0.012

PERIOD OF INTEREST

0.01020,007

0.0091, ~~0.007 o

0.003

0.002I~~ ~ ~ -.. . ....------

24,369 26.238 28,107 29,976 31,844 33.713 35.582

TIME (svc)

Iigu e 1 2c. RC (ping 441).

1.2

PERIOD OF INTEREST

0.91

>0.6 -

0.3-j0.

0,0 3.0 0.0 9.0 12.0 16.0 18.0 21.0 24.0 27.0 30.0

SEGMENTS

Fig ere 121. IFE(' (ping 441).

28

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0.017

0.015

0.014

0,012

0.010 PERIOD OF INTEREST

0.0090.00 7!l W0.005

0.003

0.002

24.369 26.238 28.107 29.376 31,844 33,713 35,582

TIMEL (soc)

Iigsm., 12g, 1C (ping 442).

1.2 PEFIOD OF INTEFREST

0.9

>' 0.6

0.3

' ~ ~~0.0 *, fi-ll7.;/_; !'F','•,-•:"

0.0 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0 27.0 30.0

SEGMENTS

Figuic I 2h. IFIIC (ping 442).

29

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0

0

0uV

000

L,~

300

Page 35: ECHO-ECHO CORRELATION - DTIC · Echo-Echo Correlation (EEC) is a method for e.:ploiting the (assumed) stationarity of the medium and target to allow each echo in a train of three

RI i .- -.... . ..-- -- -.... ' "-- ' •.--- ,v ,•' , .. .. ... . . .. . .... .

1PEI OF INTEREST

0.9-

>- 0.6

0.3j

0. "11 i IA f _r

0.0 3.0 6.0 9.0 12.0 15,0 18, 21.0 24.0 27.0 30,0SEGMENTS

Figue 1.Ju, ITI& (ping 224).

1.2

0.8

>- 0.6 PERIOD OF INTEREST

0.3

0.0T0.0 3.0 6.0 9.0 12.0 15.0 18.0 21,0 24.0 27.0 31r.0

SEGMENTS

Figuic 131. EAl-T (ping 225).

31• .

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0

09- w 0O

dlf/UP /

32-

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0.010

4 01009

o~U PLRIOD OF INTLREST

0.006

0.00b

0.004

0.001

1 b/4b 1/400 19.234 20.9/8 22,722 24,467 20.211

TIME (see)

0,9

PLRiODOr) INTEREST

0.0 b.0 10.0 15.0 20.0 26 0 30.0

SEGMENTS

Figmei 141). kI+C (ping 2 19).

33

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PERIOD OF INTEREST

0.010

0.008

0.008

0.007'

0.006

0.003

0.003

0,002

12.182 19,026 21,670 23.415 2b. 159 26.903 28.648

TIME(scK IFigmei 14c. RC (ping 220).

1.2 PElHIUU OF INTWiLEST

0.9

>-0.6

0.3

0.0 3,0 6.0 9.0 12.0 15.0 18.0 21.0 24.0 27.0 30,0

S LGM E NTS

Figme l4d. FI& (ping 220).

34

t .o....oo-.-

Page 39: ECHO-ECHO CORRELATION - DTIC · Echo-Echo Correlation (EEC) is a method for e.:ploiting the (assumed) stationarity of the medium and target to allow each echo in a train of three

S •i . ...... . . . .. '--- . .. • .. . . -.I-- .- . . .. .... .. - "-,

0.010PERIOD OF INTEREST

* 0.009

01008

0,007

0.006

0.004

0.003

0.002

0.001

17.466 19.210 20.955 22.699 24.443 26.187 27.932TIME (sue)

Figuire 14c. RC (ping 22 1).

1.24

PERIOD OF INTEREST

>0.6

0.3

0.009-

0. .0.0 15.0 20.0 25.0 30.0

SEGMENTS

0,4002

Page 40: ECHO-ECHO CORRELATION - DTIC · Echo-Echo Correlation (EEC) is a method for e.:ploiting the (assumed) stationarity of the medium and target to allow each echo in a train of three

PERIOD OF INTEREST0.010 [--0.009

0.008

0.007

0.006

0.005

0.004

0.003

0.002

0.001

1 . .............

17.466 19.210 20.955 22.699 24.443 26.187 27.932I TIME (see)F~igure 14g. RC (ping 222).

0.9

pp

PERIOD OF INTEREST

- 0.600

0.30

'•" 0.00

0.f 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0 27.0 30.0SEGMENTS

Figure 14h. L•C (ping 222).

36

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PERIOD OF INTEREST

0.010

0.009

0.008

0.007

0,0oc

0.003

0002

17.466 19.210 20.9b5 22.699 24.443 26 187 27,932TIME (rue)

IVlgulrc 14i. RC" (pilg 22.1).

1.2

0.9 PERIOD OF INTEREST

>-0.6

03

IA

0,.06 3,0 6 0 9.0 12.0 15.0 18.0 21.0 24.0 27.0 304)0

SEGMI-N US

Fiue 14J.ll'C ( ig 3 .i

;. ~37

Page 42: ECHO-ECHO CORRELATION - DTIC · Echo-Echo Correlation (EEC) is a method for e.:ploiting the (assumed) stationarity of the medium and target to allow each echo in a train of three

0

do

9

.0

w

I- ..

oi

co(DL (Y)I

d ri/GPt

38

-Add",,

Page 43: ECHO-ECHO CORRELATION - DTIC · Echo-Echo Correlation (EEC) is a method for e.:ploiting the (assumed) stationarity of the medium and target to allow each echo in a train of three

PERIOD OF INTERETST

iI

11.982 13,824 15,686 17.548 19.410 21,272 23,134

TIME (soc)

Ftigure 15a. R•C (pinlg 147).

1.2

0.9PERIOD OF INTEREST

>- 0.6

0,30

0.0 4.0 8.0 12.0 16.0 20.0 24.0 28.0

SEGMENTS

Figuic 151) . FII'( (puing 147).

Page 44: ECHO-ECHO CORRELATION - DTIC · Echo-Echo Correlation (EEC) is a method for e.:ploiting the (assumed) stationarity of the medium and target to allow each echo in a train of three

UNCERTAIN PERIOD OF INTEREST

12.238 13.976 15.714 17,452 19.190 20,927 22.665

"TIME (see)Vigure 1Sc. RC (ping 148),

1.2PEH IOU OF: INTERE3STI

0.9

> 0.6 -

0. 1 -1 f I f I I I0.0 4.0 8.0 12.0 16.0 20.0 24.0 28.0

SEGIVMENTS

",,igLJ 15d. 11"(' (Iping 148).

S40k

Page 45: ECHO-ECHO CORRELATION - DTIC · Echo-Echo Correlation (EEC) is a method for e.:ploiting the (assumed) stationarity of the medium and target to allow each echo in a train of three

It i

SPERIOD OF INTEREST

II

T

12.2 43 13 .97 0, 15,74 12 1 9, 190

H gw ' IM E (sue)

Fti re 151., F . (pIng 149).

1.41

PEIHIOLU OF IN'TEl'lE8T

0,13

>- 0.6,

0,0O. 4.0 8.0 12.0 113.0 20.0 .( 4.0 28.

•SEU(3M UNT S

I' l~Iigue 151, l-lCt (iping 149)).

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PERIODS OF INTEREST

(UNCERTAIN)

12,238 13,976 15.714 17,452 19.190 20,027 22.665

TIME (sou)

Figure 15g, R(C (pinhg 1,50).)

1,2

0.9

>" 0.6 PPERIODS OF INTERESI

(UNCEIITAIN)

0.3

0.0 4.0 8.0 12.0 16.0 20.0 24.0 28.0

SEGMENTS

Figure 1511, VFC(' (ping 15(0).

42

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PERIOD OF INTEREST

ri(UNCERTAIN)

12.238 13.975 15.714 17,452 19.190 20.927 22.665

TIME (see)

'iguic 1.51. 1c (pi=lg Is11).

1,2

>" 0.6 PERIOU OF INTEREST

(UNCERTAIN)

0.3

0.0 t TI

0,0 4.0 8.0 12.0 16.0 20.0 24,0 28.0

SEGMENTS

,_igur 1 SI. FI1 (ping 15 1).

43

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PERIOD OF INTEREST

I I!

II

12.238 1.,'/6 1,7r4 17.462 19.190 20.27 2=,'5

TIME (sac)

Figmw; 15k. RC (pinig 152),

1,2

0.9 PERIOD OF INTERESTI'I

>- 0.6

r 0.3

*: I 0.0 1I .

0.0 3.0 .0' 9.0 12.0 15.0 118.0 21.0 24.0 27.0 30.0

% • SEGMENTS

Figure 151. FFIC( ping) 152).

44

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"PERIOD OF INTEREST

(UNCERTAIN)

S.236* 13976 1 714 17,452 19.190 20. 27 22, 65

TIME (sac)

V I'igitnc I Sill, RW (ping 153).

1.2

PERIOD OF INTEREST

(UNCERTAIN)

0.3

10 0.0 t3.0 .0 9.0 12.0 15.0 1•.0 21.0 24.0 27.0 3l.OI• i;SEGMENTS

[• i ]•'igIme 15.a. IlEC (ping 153).

45

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PERIOL OF INTEREST

II I

12,238 13.976 15.714 17,462 19,190 20.927 22,605

TIME (se)

igui-c 15 o. RC (ping 154).

1.2 PERIOD OF INTEREST

0.9

" III

>-0.6

0.3

0.0 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0 27.0 30.0

K ~SE GM ENTSFge151) I±( (ping 1 54).

46

.......... .

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r

PERIOD OF INTEREST

;I

13,738 15.476 17.214 18,852 20.690 22,427 24.165

TIME (sac)1

t guro I 9q. RC (ping 155).

1.2

PERIOD OF INTEREST

0.9

03

fil I

0.0 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0' 27.0 4.Q

SEGME NTIS

lVigurc 15qr. REC (ping 155).

47

* - - -- 0.

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00OD (D

dH/EI0

48N

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PERIOD OF INTEREST

(UNCERTAIN)

'I I

11.362 13,224 15.086 16.948 18.810 20.672 22.634

TIME (sac)

Figure 16a. RC (ping 82).

!I

PERIOD OF INTEREST

(UNCERTAIN)

0.3

1A

0.0-T, t-- ....r

0.0 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0

SEGMENTS

Figurc 16b. EEC (ping 82).

49

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PERIOD OF INTEREST

(UNCERTAIN)

11.362 13.224 15.086 16.948 18.810 20.672 22.534

TIME (sec)

Figure 16c. RC (ping 83).

1.2

PERIOD OF INTEREST

0.9 1

>- 0.6

0.3 I

0.0 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0

SEGMENTS

Figuce 16d. EEC (ping 83)

I 'IQ

S... • . : :.... ... '.•' .•.. . . ,0

Page 55: ECHO-ECHO CORRELATION - DTIC · Echo-Echo Correlation (EEC) is a method for e.:ploiting the (assumed) stationarity of the medium and target to allow each echo in a train of three

PERIOD OF INTEREST

F I

i

11.362 13.224 15.086 16.948 18.810 20.672 22.634

TIME (sec)

Figure 16c. RC (ping 84).

1.2 PERIOD OF INTERESTr

0,9 [

)-0.6

r0.3

0.0 le

0.0 3.0 6.0 9.0 12.0 15.0 18,0 21.0 24.0

SEGMENTS

Figure 161f. FEC (ping 84).

51

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PERIOD OF INTEREST

11.362 13.224 16,086 16.948 18.810 20.672 22.534

TimE (sac)

FigUr-C 16g. RC (ping 85).

H1.2

0.9-

II

PERIOD OF INTEREST)-0.6 --

0.3

0.0 -

0.0 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0

SEGMENTS

Figure 1601. [1 (pintg 85).

!i•!' 52

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0.020IPERIOD OF INTEREST

0.018

0.016

0.014*

0.012

0.010

0,0081

0.006

F ~0.004-

0.002

11.369 13.238 15.107 16,976 18.844 20.713 22.582

TIME (sec)

Figure 16bi. RC (ping 80).

1.2 PERIOD OF INTEREST

0.9

)- 0.6

0.3

0.01 l 1

0.0 3.0 6.0 9.0 12.0 15.0 18.0 21.0 24.0

SEGMt-Ni S

Figure 16 . LLCT (ping 86).

53

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. , [,

PERIOD OF INTEREST

0.029

"0.026

0.023

0.020

0.0 17

0,014

0.011

0.009

0.006

0.003

11.369 13.238 15,107 16976 18.844 20,713 22,582

TIME (goo)

Figure 16k. RC (ping 87).

12

0.9PERIOD OF INTFREST

>-0.6

0.3

0.0 [ I r I il 12 .

0.0 3.0 6.0 9.0 12.0 1.0 18.0 21.0 24.0

SE GM ENTS

Figule 161. I-C (ping 90).

54

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a rather characteristic appearance (see Fig. 11, for cxample) not available with RC, and sucha "normalization" would destroy this appearance. Further work is required on this point.

Although the data are sparse, the EEC results appear to improve with respect to RCas the range increases. Compare Fig. 11, the longest range, with Fig. 16, the shortest. Thisis perhaps a result of the increased multipath interference with range degrading RC.

All of the previous discussion presul)posed identical input signals to (white) noiseratios as the basis for SNR comparison between EEC and RC. In the case of' practical sonarcomparisons, it must be pointed out that a transmission of three pulses suitable for EEC

for RC for a comparable input etcho to reverberation level, Si. The EEC pulse train causes a

three-fold increase ill background reverberation for each individual returning echo. Againstthis loss must be measured the gain inherent in multipath recombination that is characteris-tic of liEC, as well as the reduction in false alarm rate,

CONCLUSIONS

Il cho-Echo Correlation has a number of c haracteristics that distinguish it from repli-ca correlation aind whech suggest that EEC may be a superior detection tool under a varietyof environmental and operational situations. A summary of' the characteristics is givenbelow:

LOCATION OF TARGET RIETUIRN

The 0peak echo cori'clatioln will always be found at a known or estimable location inthe cori'elator outl)ut: at segmenCt center f'or the fixed target case or within a short timespan about the segment celiter lor the m1oviing largert con0dition. Such a priori knowledge isnot available f'ori re pl ica correlationi.

IPLATFORM STABILITY

Sonnar pnlatform motioln will shift the output echo peak about the segment center in apossibly i'aldom i manner. Without a1 sIabilizcd, or motion coimpensated platf'orm , the analy-sis of 1,ai'get dol)lcir wuldtl be difficult.

MULTIPATII AND ECIIO SPLITTING LOSS

EEC is relatively i lse-tivc to multi pIe irCturns of' both types provided the target isu0 1.1 tdergoing high accelerations. Replica correlation may be severely degraded.

TARGET D)OPPLER SENSITIVITY

EFIC may suf'fei a ininor loss in correlator amplitude caused by echo tu imicationl, but

is inselsitiv' to vclocity-indu,.cd frequcncy distortion.

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PULSE TYPE SENSITIVITY

For moton ompesate plttbr, EC is wholly insensitive to I)Us type. As anl

example, doppler-distorted PRN is handled with the same fi'lters as any for other pulse type,but tile replica correlator must have a large bank of doppler-shifted rpicas to handle justthis case alone,

FALSE ALARMS

Since thle lpeak return occurs about the segment center, the probability of detectionis idepedent(witin dpple contraints) of' the number of samples displayed inl the ot

greatlyp red ucn g (w the n I plseal rm rate. R e l c o r l ti n r q i e h a l u u 5 il ) eput. Thus, only a small portion ofthell Output for each segmenit need 1)e displayed, thereby

displayed, wi th a in uch hligher false alarm rate.

SNR ENHANCEMENT

Knowing the precise location ot' thle. correlator peak allIows thle Li5C of' Eq. ( 10),naniely, ck (N) =ck (X) + ck(-X) where ck (X) is the standard EEC Output inl a segmlenlt.ck(N) will hiaveý a 3 dB g~ain inl signal-to-noise ratio ovI' ck (X)

CHARACTERISTIC APP~EARANCE

Replica Correlation inl a reverberation background pro0vites dIistinlguishiable delec-ItionIs only inl term1s of'Uamplitude abovc bauckgr'ounld. EEV-C1.returns, inl additionl, maIy o11ler acharacteristic appearance that is a useful aid inl detection.

REFERENCES

I.I lelIstrom ), C.W., Statistical The ory of Signal lDetectionl, Pergamon Press, New York,1968,1p. 13.

2. T1racor Corporation, Technical Memiorandumn 66-203-4, "A Comnparisonl of' the Pecr-formaiice of Several Signal P~rocessors,'' by lP.l. Brown, March 1966, pp. 39-42 andI61-65.

3. D~avenport , W .B., and Root, W. L., Randoml SiIWIaS an1d Noise, McGraw I fill, New York,1958, pp. 81-84.

4. Whalen, A.lD., Detection of'Signals inl Noise, Academin i Press, New York, 197 1, pp.K. 102-105oraion ReferenceolData I'or Engineers, New York, 1965, 1),99 1.

6. Bnda, J.., nd iersl, G.,Randm Dta:Analysis and Measurement Prloced ures,Whiley-lnterscience, New York, 1971, pp. 1). I 2

7. Naval Ocean Systems Cen ter, NOSC TR 228, "Re plica Correlation of' Li near PeriodModulated ( LPM) Signals,'' by M.D. Green, J one 1978.

56 7