Group State Estimation Algorithm Using Foliage Penetration GMTI Radar Detections

Group State Estimation Algorithm Using

Foliage Penetration GMTI Radar Detections

Shozo Mori, Hui Hoang

Systems & Technology Research

Woburn, MA USA {Shozo.Mori,Hui.Hoang}@STResearch.com

17th International Conference on Information Fusion

Salamanca, Spain, 8 July 2014

Constantino Rago, Michael J. Shea,

Patricia L. Davey

BAE Systems,

Burlington, MA USA {Constantino.Rago,Michael.Shea,Patricia.Davey}@baesystems.com

Pablo O. Arambel

Raytheon Company

Sudbury, MA USA [email protected]

Chee-Yee Chong

Independent Consultant

Los Altos, CA USA [email protected]

Steve J. Alter

Independent Consultant

Needam, MA USA [email protected]

FUSION 2014

Salamanca Spain Paper 245

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Salamanca Spain Shozo Mori, Constantino Rago, Pablo O. Arambel, Hui Hoang, Patricia L. Davey, Michael J. Shea, Steve J. Alter, and Chee-Yee Chong - Group State Estimation Algorithm Using Foliage Penetration GMTI Radar Detections -

Acknowledgement

The research described in this presentation was supported by the

United States Defense Advanced Research Project Agency (DARPA) for

its FOPEN (Foliage Penetration) GMTI (Ground Moving Target Indicator)

Radar Exploitation and Planning (FOPEN-GXP) Program. BAE Systems

was a subcontractor to Syracuse Research Corporation (SRC), the

developer of the FORESTER radar.

The authors developed and implemented the group state estimation

(GSE) algorithm while they were all at BAE Systems, from 2010 to 2012.

The views and conclusions expressed by this presentation are those of

the authors and should not be interpreted as representing the official

policies, either expressed or implied, of DARPA, the U.S. Government,

or SRC. DARPA approved this paper for unlimited distribution.

The authors would like to express their sincere appreciation to Mr.

Vincent Sabio, Program Manager, DARPA Information Innovation Office,

for his steady and solid technical guidance throughout the entire course

of the algorithm development effort reported in this presentation.

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OUTLINE

• Foliage Penetrating (FOPEN), Ground Moving Target Indicator (MTI) Radar Extrapolation and Planning (FOPEN-GXP) Concept

• Group Tracking Algorithm: Two-Level algorithm – Individual Target Tracking

– Grouping, Merging and Splitting

• Processing Examples

• Conclusions

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Foliage Penetrating (FOPEN) Ground Moving

Target Indicator (GMTI) Radar Concept

• Foliage Penetrating (FOPN) Ground Moving Target Indicator (GMTI) radar for

FOPEN-GMTI Radar Exploitation and Planning (FOPEN-GXP) program is

airborne radar designed to detect hostile ground elements through dense foliage.

• Tracking using FOPEN GMTI radar is difficult because of (1) low state-dependent

detection-probability and (2) high-density structured false alarms.

• Data association is difficult but any multiple hypothesis tracking (MHT) will be

overwhelmed by significant uncertainty and data load (not a feasible solution).

• Detection-level target classification (vehicles,

dismounts, animals, etc.) is not possible.

• Need to track targets as groups and classify

them based on group activity patterns

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Our Approach

• Two-Level Tracking Approach

• Level 1: Individual (Group Members) Target Tracking

• Model a set of an unknown number of targets by

i.i.d. cluster finite point process (random finite set)

of stochastic processes*

• Calculate target density function

• Level 2: Group Tracking

• Group Forming, Merging, and Splitting

• Group Activity Analysis

• Group Identification

• No feedback to Level 1.

* S. Mori, and C.-Y. Chong, “Evaluation of Data Association Hypotheses: Non-Poisson I.I.D. Cases,” Proc. 7th International Conference on Information Fusion, pp. 1133 – 1140, Stockholm, Sweden, July 2004.

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Individual Target (Group Member) Tracking

Underlying Model

o I.I.D. cluster of finite point process (random finite set) of stochastic

process (position & velocity), 1(( ( )) )n

i t T ix t .

o NOT a stochastic process on a space of finite point processes (random

finite sets), 1(( ( )) )n

i i t Tx t .

Calculate Target Density

o A Posteriori First-Order Moment Measure: def

1( | ) ( ; )

n

iiB Y x B Y

o Radon-Nikodym derivative ( | )x Y of ( | )B Y is Probability Hypothesis

Density (PHD), or posterior first-order moment measure density, or

posterior intensity measure density, so that ( | ) ( | )B

B Y x Y dx .

Algorithm is: Sum-Of-Gaussian (Gaussian Mixture) Cardinalized PHD

(SOG+

CPHD)*: 1

ˆˆ ˆ( | ) ( | ) ( ; )N

UDT n n n

n

x Y x Y g x x V

1

def

1/2

(1/2)

( ; )

det(2 )TV

g V

V

e

* S. Mori, and C.-Y. Chong, “An Alternative Form of Cardinalized PHD Filter or I.I.D.-

Approximation Filter,” Proc. 10th International Conference on Information Fusion, Quebec,

Quebec, Canada, July 2007.

=informationY

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Individual Target Density Calculation

We use standard Cardinalized PHD (CPHD) filter, i.e., use i.i.d. cluster

approximation of a collection of all the orders of conditional Janossy measures

at the beginning of each measurement update (scan),

except for No target is born or killed

o A target is born. A target is detected for the first time.

Maintain undetected target density, ( | )UDT x Y

o A target is killed. A target stops or goes out of field-of-view.

Detection probability is state dependent as ( )DP x

Treat each Gaussian term, 1

21/2

ˆˆ ˆˆ ˆ( ; ) det(2 ) exp (1/ 2)

nn n n n V

g x x V V x x

as

a track with probabilistic weight ˆn

o Maintain parentchild relation (track history) activity analysis

o Processing structure similar to track-oriented MHT Replace optimal

data association selection for track pruning pruning using track

weights ˆn

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Track-Oriented Multiple Hypothesis

Tracking (MHT)

1

First Frame (SCAN)

Second Frame (SCAN)

0=

2 0

y11

y12

5 6 1

y21

y22 7 8 2 3 4 0

101L 1(1 ( ))DP x102L

211L212L

210L 221L222L

220L 201L202L

Track likelihood ( )k for each track is

updated by track-to-detection likelihood

kijL for i -th track and j -th detection for

each frame k .

1 1( )1 2( )

2 5( ) 2 6( )2 1( ) 2 7( ) 2 8( )

2 2( ) 2 3( ) 2 4( )

1U

0U

2U

2(1 ( ))DP x

Null Track =

Common track for

undetected targets

Measurement-to-

track assignment

Hypothesize miss

detections

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SOG (GM) CPHD Track Weight Updates

1

0=

2 0

y11

y12

5 6 1

y21

y22 7 8 2 3 4 0

101 11

11D

L W

Sum-of-Gaussian (SOG) target density function: ˆ

1

ˆˆ ˆ ˆ ˆ( ) ( ) ( ; )kN

k Uk k ki kii

x x g x x V

to represent

1 1( ( ); ) ,...,

ˆ ( )

ni i k k

kB

x t B y y

x dx

11v12

1U

0U

2U

101 11

12D

L W

20 2(1 ( ))DW P x

10 1(1 ( ))DW P x

201 21

21D

L W

201 22

22D

L W

211 21

21D

L W

212 22

22D

L W

221 21

21D

L W

222 22

22D

L W

210 20L W 220 20L W

21v22v

23v 24v25v 26v

27v28v

Number-of-Target (Cardinality) Probability

Distribution Update: 1

0 1ˆ ( ) ( , ) (( ) )kk

DT

mm

nk NTk D kj jp n C L n n r

Null Track =

Common track for

undetected targets

Measurement-to-

track assignment

Hypothesize miss

detections

First Frame (SCAN)

Second Frame (SCAN)

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Group-Level Tracking Group Formation, Group Merging, and Group Splitting

New group track: No term has a parent • Assign a new ID, and • Set the group cardinality as the sum of the weights of the individual terms.

Continuation group track: Each term has the same parent group track ID

• Assign the parent ID to the group track ID, • Derive the cardinality from the cardinality of the parent group updated with the estimated

cardinality of the child group. Merged group track: Some Gaussian terms are derived from two or more previous groups

• Assign a new group track ID, • Augment the lineage of the track with two or more parent group track IDs, and • Reset the cardinality to the cardinality of the new group.

Split group track: Gaussian terms from a single group separate

• Split the group into two or more groups (after identifying all the new groups, continued groups, and merged groups (as described above)),

• Assign a new ID, • Augment the lineage with the group track ID of the parent, and • Reset the cardinality to the cardinality of each new group.

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Raw GMTI (STANAG 4607) data (yellow triangles) collected on Ft. Stewart, Georgia (multiple dwells shown)

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Ground truth for the Ft. Stewart scenario in the previous figure, and the corresponding estimated group track position and

cardinality.

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Raw GMTI (STANAG 4607) data (yellow triangles) collected over Belize (multiple dwells shown)

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Ground truth for the Belize scenario in the previous figure, and the

corresponding estimated group track position and cardinality.

Estimated Group size ~1 to 2

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CONCLUSIONS

• We have shown the sum-of-Gaussian (SOG) group state estimation (GSE)

algorithm that the authors developed and implemented for DARPA’s Foliage

Penetrating (FOPEN) Ground Moving Target Indicator (GMTI) radar,

extrapolation and planning (FOPEN-GEP) in 2010 – 2012, at BAE Systems.

• The GSE algorithm works at two levels, individual target (group members)

level, and group level. The individual target level algorithm is a variation of

SOG CPHD, characterized by (i) no birth-death process (instead maintains

the undetected target density, and use state dependent target detection

probability), and (ii) track tree maintenance (maintaining parent-child

relations – aiding group activity analysis).

•The GSE algorithm was thoroughly tested through the data collected by the

FOPEN Reconnaissance, Surveillance, Tracking and Engagement Radar

(FORESTER) mounted on airborne frames at various locations, and under

diverse conditions.

Group State Estimation Algorithm Using Foliage Penetration GMTI Radar Detections

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