Multi-Sensor Adaptive Signal Processing and Sensor...

Multi-Sensor Adaptive Signal Processing and Sensor

Management for Landmines

Multi-Sensor Adaptive Signal Processing and Sensor

Management for Landmines

Mark P. Kolba, Peter A. Torrione, Jeremiah J. Remus and Leslie M. Collins

Electrical and Computer EngineeringDuke University

Work supported by DARPA/ARO MURI

Mark P. Kolba, Peter A. Torrione, Jeremiah J. Remus and Leslie M. Collins

Electrical and Computer EngineeringDuke University

Work supported by DARPA/ARO MURI

Progress as of 2004 (Minneapolis meeting)

• Adaptive Feature Selection (JCFO) successfully applied to landmine problem

• Uncertainties incorporated into MIAP processor improve robustness

• Adaptive tracking technique improves GPR detection performance

• Encouraging sensor management results – simple problem, only simulated data considered

• Multi-sensor data from Georgia Tech processed –using adaptive fusion (had not considered sensor management).

Overview of Progress

• Sensor Management– New simulations– Comparison to theoretical predictions– Extensions and new developments– Processing Georgia Tech data– Application to Automated Mine Detection System

(AMDS) data• Ant system/Swarm algorithm application to mine

detection (not briefed due to time limitations.. maybe next year?)

Problem Statement

• Suite of available sensors• Performance and cost a

function of sensor modality

• Grid to be searched. Adaptively determine– where to go?– what sensor to deploy?– what sensor parameters to

employ?

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10Sensor path through cell grid for unconstrained sensor

Problem Formulation

• Search for N targets using M sensors– Sensors may be unimodal or multimodal

• Operate on a cell grid• Each cell has a state:

– Target– No target

• Possible observations:– Target present– No target present

• As observations are made, the state probabilities of each cell are calculated and updated

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10Cell grid containing five targets

Previously: Adaptive Discrimination-Based Sensor Management

• Initial algorithm based on Kastella1

• Select a cell which maximizes

• Can be calculated recursively

• Progress: Focus on considering assumptions that are inconsistent with the MURI application areas – most recent work particularly on considering uncertainty in sensor performance parameters needed in the formulation

1( , ) ( ) ln( ( ) / ( ))

S

sD P Q P s P s Q s

=

=∑D∆

1 K. Kastella, “Discrimination gain to optimize detection and classification,” IEEE Trans. Syst. Man, Cybern., vol. 27, no. 1, pp. 112-116, Jan. 1997

Progress• Extend to consider other priors on target locations• Extend to multiple sensors, each with different

performance, cost• Sequential detection in each cell once selected• Extend to consider unknown number of targets• Consider unknown Pd, Pf for each sensor 2 ways

– Extend Kastella approach to handle uncertainty OR– Need to estimate ROCs (performance degrades if

unknown)• Alternative (pure Bayesian) formulation• Comparison to Theory of Optimal Experiments

• Application to Georgia Tech data• Application to AMDS data• Swarm algorithm - alternative search algorithm

Problem formulation• Kullback-Leibler information, denoted D (for discrimination)

( ) ( ) ( )( )∑

= ==

==1

0ln,

s c

cc sSQ

sSPsSPQPD

P is the current state probabilities Q is the prior state probabilities Sc is the state of cell c s is one of the possible cell states

• State probabilities are calculated sequentially

( ) ( ) ( )( ) ( )∑

=−

−

==

==== 1

01,,

1,,,

jkccckc

kccckckcc

XjSPjSxP

XsSPsSxPXsSP

xc,k is observation k in cell c

Xc,k is observations 1, 2, . . ., k in cell c

• Sensors scheduled to make next observation to maximize expected discrimination gain

( ) ( )[ ] ( )ckckcckckc QPDXQPDEXD ,, ,,1,, −=∆ +

Performance metric• Probability of error, PE

– The N cells with highest probability of being a target should be the N cells containing targets

• PE = 1 if any of the N cells with highest P(Sc = 1) are not one of the N target cells

• PE = 0 if the N cells with highest P(Sc = 1) are the N target cells

• PE = a

if the N cells with highest P(Sc = 1) are the N target cells, and if there is a tie for highest P(Sc = 1); a = r / t, where t is the total number of cells tied and r is the number of those containing targets

Example: Multiple Sensors

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Performance of different sensor combinations

Discrimination Search: S1, S2, S3Discrimination Search: S1, S2Discrimination Search: S1Direct Search: S1, S2, S3Direct Search: S1, S2Direct Search: S1

S1: Pd = 0.9, Pfa = 0.4, Cost = 1S2: Pd = 0.9, Pfa = 0.1, Cost = 1S3: Pd = 0.99, Pfa = 0.02, Cost = 10

Uncertain PD and PF• Consider a real-world scenario

– Unknown ground– Unfamiliar obstacles– Unknown target and clutter types

• Assess prior distributions on PD and PF– Beta distribution (natural conjugate prior)

PD and PF are uncertain

nextfinished

Calculationcertain uncertain

Datacertain

uncertain

PD/PF

New problem formulation• State probabilities may no longer be calculated sequentially

( ) ( ) ( )

( ) ( )∑=

==

==== 1

0,

,,

|

||

tcckc

cckckcc

tSPtSXP

sSPsSXPXsSP

( ) ( ) ( ) ( ) dpfdpdpffpdfpfpdsSXPsSXP ckcckc ,,|| ,, ββ∫∫ ===

( )sSXP ckc =|, depends only on pd if c is a target cell and only on pf if c is a clutter cell

Thus, ( ) ( )pdpdbinckc nrnrPsSXP ′′== ,,||, β

( ) ( )pfpfbinckc nrnrPsSXP ′′== ,,||, β

if c is a target cell

if c is a clutter cell

r’ and n’ are the parameters of the beta prior

n is the number of observations, r of which were “target present”

( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( )nnrnrrnr

rrnnrrnnnrnrP bin +′Γ+−Γ+Γ′−′Γ′Γ−′−+′Γ+′Γ+Γ′Γ

=′′11

1,,|β

where

New problem formulation• We still use discrimination and expected discrimination gain

Method 1

( )[ ] ( ) ( )∑=

+++ ==1

0,1,1,,1, ,,

jkckcckckcckc XjxPQPDXQPDE

• There were two methods considered to calculate ( )kckc XjxP ,1, =+

( ) ( ) ( )∑=

++ =====1

0,,1,,1, |,|

skccckckckckc XsSPsSXjxPXjxP

( ) ( )( ) ( )dppfpsSjxP

sSjxPsSXjxP

ckc

ckcckckc

β∫ ===

=====

+

++

,|

|,|

1,

1,,1,

Assume that determination of P(xc,k+1) is independent of Xc,k. Then,

where p represents pd for a target cell (s = 1) or pffor a clutter cell (s = 0)

( )pfβ here is the original prior density for pd or pf, as appropriate

New problem formulation

Method 2

( ) ( ) ( )∑=

++ =====1

0,,1,,1, |,|

skccckckckckc XsSPsSXjxPXjxP

Assume that determination of P(xc,k+1) should take into account Xc,k. Then,

( ) ( ) ( )dppfpsSjxPsSXjxP ckcckckc β′′===== ∫ ++ ,|,| 1,,1,

( ) ( ) ( )( ) ( )

( )pfdppfpXP

pfpXPXpf

kc

kckc β

β

β ′′==∫ |

||

,

,,

where p represents pd for a target cell (s = 1) or pffor a clutter cell (s = 0)

( )pfβ′′ is the posterior density for pd or pf, as appropriate, given the data observed

( )pfβ′′ is a beta density with parameters r’’ = r’ + r and n’’ = n’ + n

r’ and n’ are the parameters of the beta priorn is the number of observations, r of which were “target present”

0.00180.00100.72890.9903

Effects of uncertainty

• State probabilities– Will be less differentiated from prior

– Method 1• ∆D based on prior

information only• Same as the calculation

under certainty

– Method 2• ∆D based on prior information

and all data taken in cell• Different than the calculation

under certainty

Prior

• Expected discrimination gain

0.01

Target cell Clutter cell

P(Sc = target)

certain certainuncertain uncertain

Observe: 1 1 1 1 1 1 1 1 Observe: 1 0 0 0

An alternative performance metric

• In addition to PE, consider “separation”• Use as a measure of confidence

– May be calculated using averages

– Or by using minima and maxima

– Or by combining the two methods

( ) ( )nN

SP

n

SPnN

icc

n

itc ii

−

=−

==

∑∑−

== 11targettarget

separation

( ) ( )targetmaxargtargetminargseparation =−==ii cc

itc

iSPSP

Discrimination gain comparison• Method 1

– Behavior easily explainable– State probabilities must reach

a certain value for sensor to move on

– Sensors can “stick”• Poor PE performance• Poor separation

• Method 2– Behavior is more complex– Sensors move on without

reaching a set value• Do not “stick”• More intelligent behavior• May move on too quickly• Can cause lower separation

performance

Obs # P(Sc = target) ∆D Obs # P(Sc = target) ∆D

M

M

M

mk

k

+M

M

M

8.0

8.0

M

M

M

1.0

1.0

M

M

M

mk

k

+M

M

M

8.0

8.0

M

M

M

06.0

1.0same different

Performance with uncertain calculation PD/PF: method 1

• Discrimination-directed search under uncertainty performs as well as or worse than discrimination-directed search with no uncertainty

• Low values of n (higher uncertainty) may lead to severe performance degradation (as seen in the second figure) when more targets are present

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1Performance under uncertainty with 1 sensor and 1 target

Number of measurements

Pe

disc: 0 dBn = 100n = 10n = 5direct: 0 dBdirect: 3 dBdirect: 6 dB

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1Performance under uncertainty with 1 sensor and 5 targets

Number of measurementsP

e



• Drastic differences in the separation for varying levels of uncertainty– The more uncertainty the worse the separation

• Poor separation performance means that decisions (target or no target) may not be made as confidently

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1Separation under uncertainty with 1 sensor and 1 target


Sep

arat

ion


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1Separation under uncertainty with 1 sensor and 5 targets


Sep

arat

ion


Analysis of results: method 1

• With 1 sensor and 1 target, the PE performance under uncertainty degrades only slightly– Uncertainty primarily affects the length of time spent

observing a likely target cell– With only one target, that target will be found in about

the same time even with uncertainty

• With 1 sensor and 5 targets, PE performance is severely degraded with low values of n (high uncertainty)– Sensor becomes stuck observing a single cell repeatedly

and never finds the rest of the targets

Theoretical analysis of results: method 1

• We can calculate the expected number of observations made in a cell when that cell is first observed

( )

=else

sequencen observatio ng terminatiain result and if

01

,nr

nrT

( ) ( ) ( ) ( )nrPnrNnrTnobsEK

n

i

r,,,

1 0∑∑= =

⋅=

( ) ( ) ( )( )

∑ ∑= =

−−

−

=

n

i

ri

j jrin

ijNijTrn

nrN1

,min

1

,,,N(r,n) gives the number of possible observation sequences for the given r and n

( ) ( )observed" target no" ,observed"target " |, , rkrXPnrP kc −=

Set K to a large enough value to achieve the desired precision


• With low enough n, the expected number of observations required before the sensor will move on becomes extremely high, resulting in the sensor becoming “stuck”

• “Sticking” when only one target is present will not harm performance since there are no other targets for the sensor to miss while stuck

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100Expected observations for 1 sensor, 1 target

n

E(o

bs)

uncertaincertain

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100Expected observations for 1 sensor, 5 targets

nE

(obs

)

uncertaincertain


• We may also calculate the expected separation after cells have been observed for the first time

( )

=else

sequencen observatio ng terminatiain result and if

01

,nr

nrT

( ) ( ) ( ) ( ) ( )nrPnrNnrTsnrSsepEK

n

i

rs ,,,,,

1 0∑∑= =

=

( ) ( ) ( )( )

∑ ∑= =

−−

−

=

n

i

ri

j jrin

ijNijTrn

nrN1

,min

1

,,,N(r,n) gives the number of possible observation sequences for the given r and n

( ) ( )observed" target no" ,observed"target " |, , rkrXPnrP kc −=

Set K to a large enough value to achieve the desired precision

( ) ( )nsobservatio no"" and yes"" with |,, , rkrXsSPsnrS kc −==


• At high values of n, the separation performance is comparable to the separation achieved in the certain case

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n

E(s

ep)

uncertaincertain

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nE

(sep

)

uncertaincertain


• Discrimination-directed search under uncertainty performs as well as or worse than discrimination-directed search with no uncertainty

• Performance degradation is more severe with smaller values of n (that is, with less prior knowledge about PD and PF), but is never as degraded as was observed with method 1

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1Performance under uncertainty with 1 sensor and 1 target


Pe


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1Performance under uncertainty with 1 sensor and 5 targets


Pe



• Drastic differences in the separation for varying levels of uncertainty– The more uncertainty the worse the separation

• Poor separation performance means that decisions (target or no target) may not be made as confidently

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1Separation under uncertainty with 1 sensor and 1 target


Sep

arat

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1Separation under uncertainty with 1 sensor and 5 targets


Sep

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• Separation performance appears comparable• PE performance is noticeably improved over

method 1, especially in the 5 target case– Sensor moves on and does not become “stuck”

• As before, the expected number of observations and the expected separation for the first observations made in the cells may be calculated


• Sensors observe in the target cell for about as long as in the certain case; when there are five targets, the sensor moves on more quickly than it would in the certain case

• Sensors will not “stick”

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n

E(o

bs)

uncertaincertain

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nE

(obs

)

uncertaincertain


• The separation under uncertainty never reaches the separation performance in the certain case; it is always significantly smaller

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n

E(s

ep)

uncertaincertain

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nE

(sep

)

uncertaincertain

Separation comparison

• Neither method is clearly better in terms of separation performance– With 1 target (when method 1 doesn’t stick), it outperforms method 2– With 5 targets (when method 1 does stick), method 2 is much better

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1Separation comparison for methods 1 and 2 with 1 sensor and 1 target


Sep

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method 1method 2

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1Separation comparison for methods 1 and 2 with 1 sensor and 5 targets

Number of measurementsS

epar

atio

n

method 1method 2

Uncertain PD and PF• Let calculation PD and PF be certain again

– Original SM mathematics apply

• Each cell has a PD or PF drawn from a beta density– Data will be generated using the PD or PF for that cell

next

finishedfinished


Datacertain

uncertain

PD/PF

Performance with uncertain data PD/PF: method 1

• Small values of n cause a sharp degradation in performance• Even small amounts of uncertainty have a more pronounced effect than

previously

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1Performance under uncertain data with 1 sensor and 1 target


Pe


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1Performance under uncertain data with 1 sensor and 5 targets


Pe



• Separation performance is fairly good even for large amounts of uncertainty

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1Separation under uncertain data with 1 sensor and 1 target


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1Separation under uncertain data with 1 sensor and 5 targets


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• Small values of n cause a sharp degradation in performance• Even small amounts of uncertainty have a more pronounced effect than

previously

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1Performance under uncertain data with 1 sensor and 1 target


Pe


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1Performance under uncertain data with 1 sensor and 5 targets


Pe



• Separation performance is fairly good even for large amounts of uncertainty

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1Separation under uncertain data with 1 sensor and 1 target


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1Separation under uncertain data with 1 sensor and 5 targets


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Uncertain PD and PF

• Now let both calculation and data PD and PF be uncertain– Return to the complex SM mathematics derived for the

uncertain calculation case

nextfinished

finishedfinished


Datacertain

uncertain

PD/PF

Performance with uncertain data and calculation PD/PF: method 1

• Low values of n degrade performance as expected• The five-target case performs very poorly at low values of n; these results

are due to the sensor “sticking”

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1Performance with uncertain data and processing with 1 sensor and 1 target


Pe


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1Performance with uncertain data and processing with 1 sensor and 5 targets


Pe



• Separation performance is rather poor for high uncertainty cases

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1Separation with uncertain data and processing with 1 sensor and 1 target


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1Separation with uncertain data and processing with 1 sensor and 5 targets


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• Uncertainty degrades performance as expected

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1Performance with uncertain data and processing with 1 sensor and 1 target


Pe


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1Performance with uncertain data and processing with 1 sensor and 5 targets


Pe



• Separation performance is better with method 2 than it is with method 1

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1Separation with uncertain data and processing with 1 sensor and 1 target


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1Separation with uncertain data and processing with 1 sensor and 5 targets


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Model Parameter Estimation –Alternative to Uncertainty Mitigation

• Response model (ROC) defined by two parameters: slope and median/offset/bias

• Need to estimate the parameters adaptively• Comparison of two methods for parameter

estimation– Bayesian adaptive estimation – Theory of Optimal Experiments

• Dual adaptation: ROC parameter estimation and sensor parameters/sensor movement/sensor selection

• Use Bayes rule to calculate the probability of a set of model parameters λ given the response r (Pd) at a specific input intensity x (Pfa).

• Select next input to minimize the expected entropy

• Update probability of model parameters using the outcome of the current trial

Bayesian adaptive parameter estimation

( | , ) ( )( | , )( | , ) ( )

prob r x probprob r xprob r x prob

λ

λ λλλ λ

=∑

( )[ ( )] ( ) ( | ) where ( ) ( | , ) log ( | , )r rr

E H x H x prob r x H x prob r x prob r xλ

λ λ= = −∑ ∑( 1) arg min( [ ( )])

xx t E H x+ =

1( ) ( | ( ) r, ( ) x)tprob prob r t x tλ λ+ = = =

• Find the parameter values that minimize the squared error between the collected data r and the model n(x,λ)

• Select the next input to maximize the information gained, calculated using

where column vector and B is the Fisher information matrix in the form

Parameter estimation using the Theory of Optimal Experiments

( )2ˆ arg min ( , )x

r n xλ

λ λ = − ∑

1( 1) arg max log |1 |T

xx t F B F− + = +

( , )( )i

n xF i λλ

∂=

∂

( ) ( )( ), ( ),( , )

t i j

n x t n x tB i j

λ λλ λ

∂ ∂=

∂ ∂∑

λ̂

Simulation Result: Estimating ROC Parameters

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0.001%

0.01%

0.1%

1%

Bias in median estimation

Trial

Per

cent

age

of tr

ue p

aram

eter

val

ue

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0.01%

0.1%

1%

10%

Variance in median estimation

Trial

Per

cent

age

of tr

ue p

aram

eter

val

ue

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1%

10%

Bias in slope estimation

Trial

Per

cent

age

of tr

ue p

aram

eter

val

ue

0 50 100 150 200 250 300

1%

10%

Variance in slope estimation

Trial

Per

cent

age

of tr

ue p

aram

eter

val

ue

Bayesian adaptiveTheory of Opt. Exp.




Observations

• Relative performance depends on parameters of simulation – some regions of slope/bias space better for one or the other.

• Overall, similar performance• TOE 5 times faster to compute than optimal

Bayesian approach

Simulation Results – Grid Search with Adaptive Estimation of Sensor

Performance

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Known Pd/Pfa20 iters10 iters5 iters

Georgia Tech Multi-Sensor Data

• Subsampled collection grid in 9 x 9 grid• Initial work with first 2 collections – less

complicated, fewer interactions• Used previously developed decision

statistics as sensor outputs in each grid• 81 samples in each grid available• Initially, each sensor has same cost, same

detection performance

Results – Collection 1

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Performance of discrimination-based and direct search techniques

Discrimination Search: S1, S2, S3Direct Search: S1, S2, S3Direct Search: S1Direct Search: S2Direct Search: S3

Results - Collection 2

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Performance of discrimination-based and direct search techniques

Discrimination Search: S1, S2, S3Direct Search: S1, S2, S3Direct Search: S1Direct Search: S2Direct Search: S3

Application to AMDS DataAMDS CT1, YPG

Lanes 15, 16, 21, 23, 25Summary

• 209 spots investigated. • SIMS are not included in the ROC curves generated by IDA. • 67 mines. 11- M AT 17-MM AT 6- M AP 33-MM AP• 81 Clutter items scored. 25- casings 43- Fragments 13-Fleshcettes• 40 Blanks.• Weather: bright sun, 60-70F, winds gusted to 30mph at times.

• Ground truth released 6/30/05

AMDS Data

• Cyterra radar– Various processors, including one from Duke

• Cyterra MD– Energy processor (prescreening)– Feature-based processor

• NIITEK radar– Various processors, including one from Duke

Duke-Cyterra MD Only CT1, YPG 4/2005, Each Point Rounded.

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Pd vs. Nonmines Pd vs Pba Pd vs. Clutter

Duke-NIITEK CT1, YPG 4/2005, Each Point Rounded.

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Duke3 Clipped-NIITEK/CyTerra Hybrid, CT1, YPG 4/2005.

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Blind Test Results Generated By IDA – Ground Truth Released

6/30/05

Cyterra MD EnergyNIITEK Radar

RVM Fusion of NGPR, CMD

Approach• Assume 3 processes to optimize: MD prescreener,

MD feature-based processor, GPR• RVM takes 209*3=627 operations to achieve a

specific performance, initial MD prescreenerrequires 209 operations

• Can the discrimination-based search optimize the use of the 3 processes to achieve the same performance in less operations?

• Only considered one performance point to date, since ground truth only available for approximately a month

Results

• Goal: 100% Pd at P others (Pfa) of 0.2

• RVM (direct search) requires 627 operations

• All operations assumed to be equal cost

• Discrimination search required 418 operations

• Assumes known Pd, Pf for each sensor

Duke3 Clipped-NIITEK/CyTerra Hybrid, CT1, YPG 4/2005.

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Accomplishments

• Implemented and evaluated all modifications to discrimination-based search algorithms

• Implemented and evaluated adaptive estimation approaches as an alternative to incorporating uncertainty into the search methodology

• Initial implementations tested on GT and AMDS field data, full versions of both approaches to be tested in the near future on both data sets

Future Work

• Test adaptive estimation techniques on GT data

• Test uncertainty-based techniques on GT data

• Test all techniques on other field data sets such as the AMDS data

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