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Efficient Multiple Emitter Localization for Large-Scale/Low-Cost Multimodal Sensor Networks

Philip J. Haney BAE Systems – Technology Solutions August 29, 2013

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The views expressed are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. Approved for Public Release; Distribution Unlimited. Cleared for Open Publication on 6/6/2013. Non-Technical Data – Releasable to Foreign Persons.

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Outline • Need for Robust and Efficient Multimodal Emitter Localization

• Existing Approaches

• Pseudo Maximum Likelihood (PML) Function

• Cramer-Rao Lower Bound and Computational Complexity Analyses

• Distributed Network Tracking

• Simulated Performance Results

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Motivation for Large-Scale Ground Sensor Networks • Advancements in wireless communications

and sensing technologies have led to ongoing interest in developing large-scale ground sensor networks [1-4]:

• Remote Battlefield ISR • Homeland Security/Border Control • Law Enforcement

Maintaining Cost in Large-Scale Ground Sensor Networks • Networks approaching 100s to 1000s

of nodes introduce cost concern

• Cost-feasibility typically achieved through incoherent combination of inexpensive sensors dispersed throughout surveillance region of interest

• Low-cost sensors: • Characteristically exhibit non-

linear/non-Gaussian modalities • Present various challenges for

achieving accurate localization and tracking throughout network

Innovative solutions required to effectively

exploit multimodal sensor information

4

-5 0 50

0.2

0.4

0.6

0.8

1

1.2

Velocity (m/sec)

Allowable Range to Target

RmaxRmin

IndividualGaussian

terms Uniformdistribution

Range (m)

Common Multimodal Emitter Localization Approaches • Computationally efficient approaches [5-7]:

• Based on simple intersection or triangulation techniques

• Produce sub-optimal performance • Generate numerous false tracks (“ghosts”)

• Robust and optimal approaches [8-15]: • Based on multiple hypothesis tracking or

Sequential Monte Carlo methods • Computationally expensive • Not suited for large-scale, low-cost

sensor network applications Fo

rest

Lay

ers

Hypotheses

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Need for robust and efficient

multimodal emitter localization

Range (m)

Pseudo Maximum Likelihood Function • A robust and computationally efficient approach to the multimodal

emitter localization problem has been developed: • Based on a pseudo maximum likelihood (PML) function • Peaks of PML strongly indicate number and locations of true emitters • PML peaks used to associate sensor measurements in emitter-rich and/or

cluttered environments

• Proposed PML localization approach: • Efficient (in Cramer-Rao Lower Bound sense) • Computational complexity that is linear in the number of measurements

Pseudo maximum likelihood provides robust and computationally

efficient emitter localization in multimodal sensor networks

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• Goal is to estimate two-dimensional emitter location (xe ,ye) from set of multimodal measurement data collected over network

• Heterogeneous network assumed to consist of mixture of angle-only and range-only sensors

• Observed modalities therefore consist of some combination of the following:

where

Single Emitter Localization

rtrueobs

trueobsωrrωθθ

sensors angle of number

NNi

N

xxyyθ

ie

ietruei

},...,2,1{

),0(~

tan

2

1

Iω

sensors range of number

r

r

rrr

jejetrue

NNj

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},...,2,1{

),0(~

)()(

2

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Single Emitter Localization – Maximum Likelihood • For single emitter case, location can be estimated using maximum

likelihood (ML) approach

• ML surface generated by multiplying likelihoods corresponding to network available sensor measurements:

• Peaks of ML surface determined using grid-based optimization:

where

surfaceyx

mlml MLyx,

maxarg,

221 )()(,tan jjobserri

iobserr yyxxrr

xxyyθθ

jjii

r

ji

N

jrerr

N

ierrsurface rNNML

1

2

1

2 ,,

8

Multiple Emitter Localization • For single emitter case in

noiseless environments, standard ML optimization is sufficient and straightforward

• For emitter rich and/or cluttered environments, localization becomes significantly more complex

• Measurements from different emitter(s) or clutter included in ML optimization could mask true emitter location

Robust multimodal association/clustering required for accurate

localization in emitter rich and/or cluttered environments

Sensor Measurements ML Surface

Sensor Measurements ML Surface

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Multiple Emitter Localization – Pseudo Maximum Likelihood • Robust localization in emitter rich and/or cluttered environments is

achieved using iterative pseudo maximum likelihood (PML) process

• PML surface generated by summing likelihoods corresponding to network available sensor measurements:

• Peaks of PML surface determined using grid-based optimization:

where

surfaceyx

pmlpml PMLyx,

maxarg,

r

ji

N

jrerr

N

ierrsurface rNNPML

1

2

1

2 ,,

10

221 )()(,tan jjobserri

iobserr yyxxrr

xxyyθθ

jjii

Multiple Emitter Localization – Iterative PML Approach • Due to additive nature, PML function avoids

problem of peak suppression arising from misassociated measurements or clutter

• PML function provides key data association component for achieving accurate localization in emitter-rich or cluttered environments

• Iterative emitter localization performed by: 1. Generating PML surface from available

sensor measurements 2. Associating individual sensor measurements

to PML peak 3. Generating ML location estimate using

associated measurements 4. Removing associated measurements from

problem space and reiterating

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Sensor Measurements

PML Surface ML Surface

Multiple Emitter Localization – Iterative PML Illustration • Simulated scenario consisting of three emitters and five sensors (three

angle sensors and two range sensors)

• Each sensor (red circles) generates four detections: • One corresponding to each emitter (green squares) • One due to clutter (i.e., false alarm)

Iteration 1

Iteration 2

Iteration 3

Iteration 4

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• The Cramer-Rao lower bound (CRLB) is well known to express a lower bound on the estimation variance of a deterministic parameter [16,17]

• In its simplest form, the bound states that the variance of any unbiased estimator, , is at least as high as the inverse of the Fisher information

where

• An unbiased estimator which achieves the CRLB is said to be efficient

Cramer-Rao Lower Bound (CRLB)

13

ˆˆEJCRLB )()( 1

variancetmeasuremenfunctiontmeasuremen)(

)()()(

2

2

1

h

hhJ I

• Considering a parameter set based on the location of a single emitter, , and a network of angle-only/range-only sensor modalities,

the Fisher information can be extended as

where

and

PML Localization – Fisher Information and CRLB

14

)( ee y,x

rjjii

N

j

r

r

rN

i

hhhhJ

12

12

11 )()()()()(

22

1

)()()(

)(

jejer

ie

ie

yyxxh

xxyytanh

j

i

je

je

jeje

r

ie

ei

ieie

yyxx

yyxx

h

xxyy

yyxxh

j

i

22

22

1

1

)()(

)(

)()()(

2

2

1

ey

ex

crlb

crlb

~

~JCRLB

)()(

• CRLB investigated for iterative PML localization process:

• Hexagonal sensor array • Three angle-only sensors • Three range-only sensors

• Emitter locations based on various angle/range combinations:

• Angle – 0 to 90 degrees in 15 degree increments • Range – 0 to 200 meters in 1 meter increments

• CRLB analysis assumes: • σθ=5ₒ

• σr=1 meter • 1 measurement per sensor • 1000 Monte-Carlo runs per emitter location

PML Localization – CRLB Analysis

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Hexagonal Sensor Array

PML Localization – CRLB Analysis Results

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PML localization process is nearly optimal

CRLB ( ) / PML Std Dev ( )

PML Localization – Computational Complexity • Iterative PML process utilizes two-stage grid search:

1. 60x60 meter grid (2 meter resolution) • Centered around mean of node locations • PML surface generation • Coarse emitter localization • Computation complexity -

2. 10x10 meter grid (0.5 meter resolution) • Centered around coarse emitter localization results • ML surface generation • Fine emitter localization • Computation complexity -

)( 231measNO

)( 221measNO

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PML Surface

Sensor Measurements

ML Surface

Sensor Measurements

Computational complexity of two-stage PML process is linear in the number

of measurements making it suitable for low-cost hardware applications

Distributed Network Tracking • PML emitter localizations used to initiate and

sustain all tracking operations in DDF-based architecture

• Decentralized Data Fusion (DDF) [18] • Efficient method of distributed data fusion:

• Each node acts as a fusion node

• Robustness: • No single point of failure

• Modularity: • Nodes able to dynamically enter

and/or leave network

• Scalability: • Scales to number of targets

(independent of nodes/measurements)

• Commonality: • Coherent picture of fusion environment across

network regardless of local observability limitations

PML/DDF Node Flow Diagram

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Node 1

Node N

• • •

• Measures of performance for evaluating PML localization process drawn from Single Integrated Air Picture (SIAP) metrics [19,20]: • Network-centric approach to developing Common Operating Picture (COP)

of emitter environment • Intended for aircraft typically engaged in ISR-related missions • Direct application to ground-based multi-sensor/multi-emitter tracking

• COP metrics of interest: 1. Correctness 2. Completeness 3. Commonality 4. Accuracy

Distributed Network Tracking – Measures of Performance

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COP network-centric metrics used to evaluate emitter

localization as function of network track performance

PML Localization & Tracking Simulation – Simulated Parameters

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Simulated Parameter Value

Scenario Parameters

Region of Interest 200x200 meters

Number of Nodes 80 uniformly distributed (≈25 meter spacing)

Number of Emitters 5 dismounts with correlated random walk

Sensor Parameters

Modality Mixed angle/range

Detection Angle 360 degrees

Detection Range 30 meters

Angle Uncertainty 5 degrees

Range Uncertainty 1 meter

Node Position Error 0.5 meters

Node Orientation Error 3 degrees

Probability of Detection 90%

False Alarm Rate 1 per second (per sensor)

Communication Parameters

Range 40 meters

Transmit Rate 0.5 seconds

Probability of Drop 10%

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PML Localization & Tracking Simulation

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Summary • Advancements in wireless communications and sensing technologies have led to ongoing interest in large-scale ground sensor networks

• Cost concerns associated with large-scale sensor networks typically result in push toward utilization of low-cost sensors

• Low-cost sensors: • Characteristically exhibit non-linear/non-Gaussian modalities • Present various localization and tracking challenges

• Common multimodal emitter localization approaches: • Computationally efficient / sub-optimal performance • Optimal performance / computationally expensive

• Pseudo Maximum Likelihood (PML) provides: • Efficient and robust localization in emitter-rich / cluttered environments • Computational complexity that is linear in the number of measurements • Foundation for sustaining all track activity in fully decentralized sensor networks

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