information-based sensor-management for simultaneous ...€¦ · information-based...

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Information-Based Sensor-Management for Simultaneous Multitarget Tracking and

Identification

Christopher Kreucher ‡ *

Benjamin Shapo *

Keith Kastella *

Alfred Hero ‡

ASAP WORKSHOPMIT/LL

7 JUNE 2005

* ‡

22

The Resource Allocation Problem• Resource allocation refers to the

problem of scheduling the resources of agile sensors.

– How should the sensor choose which actions (mode, choice of waveform, where to point) to take with its resources?

– We take an information-based approach, where taskings are made using the principle that the sensor should take actions to maximize the expected gain in information

• We apply our methods to the problem of detection, tracking, and identification of multiple moving ground targets from an airborne platform.

33

Problem Motivation• JSTARS provides airborne far range

surveillance & target acquisition – Determines position & heading of targets.– The radar has many operating modes

• Wide area surveillance• fixed target indication• synthetic aperture radar • moving target indicator• target classification

• Next-generation JSTARS– Electronically scanned 2-D X-band radar – Several other sensor modes

JSTARS current tasking method

Maj. Michael Mras, sensor management officer, monitors activity while sitting at an operator workstation. Mras is one of the many 116th Air Control Wing airmen who detect enemy ground movement and relay information to airborne assets. "I monitor jobs that come in and juggle the different requirements and requests so the radar is not over-tasked at any one time”

44

Overview of our Approach• Our goal is to develop a general algorithm for balancing the

demands of an agile multi-mode radar• Resource allocation difficult due to inherent tradeoffs

– Many competing goals: e.g., detection, tracking, and ID– Each resource allocation addresses a subset of these goals– Want the allocation that properly balances competing desires

• We propose an integrated approach to state estimation and sensor resource allocation

– Estimation of Joint Multitarget Probability Density (JMPD)• JMPD p(X,T | Z) captures our uncertainty in both target number and

target states (position, velocity and identification)• Numerical challenges addressed by a multitarget particle filter with

adaptive sampling scheme– Use of the JMPD estimate for resource allocation

• Gaining information about the JMPD drives sensor allocations• Single metric trades between different types of information (e.g.

kinematic information versus identification information)– Resource allocation via approximate methods

• Choose action for maximum information gain• Numerical challenges addressed by function approximation

State Estimation

SensorManager

Target, Sensor and Terrain Models

data z

Estimation of the JMPD,

p(X,T |Z)

Maximizationof expected α-divergence

55

Talk Roadmap

I. Estimation of the Joint Multitarget Probability Density (JMPD)– Definition of the JMPD– The multitarget particle filter implementation

II. Use of the estimated JMPD to make sensor management decisions– The α- (Renyi-) Divergence– Computation of the divergence

III. Results– Sensor-Management performance gain– New method for tracking target ID

IV. Conclusions, and Future Work

66

I. Estimation of the Joint Multitarget Probability Density

I. Estimation of the JMPDII. Use of the estimated JMPD to make sensor

management decisionsIII. ResultsIV. Conclusions & Future Work

77

The Joint Multitarget Probability Density (JMPD)• Our resource allocation strategy is driven by information gain• Information content depends on uncertainty about target number, class, and

kinematic state. The mathematical model must reflect these couplings.

• The central element that summarizes knowledge of the system at time k is the joint multitarget probability density (JMPD),

estimated from a sequence of noisy measurements over k time steps, where–T is the number of targets, which is to be estimated along with the state X–X is a description of kinematic state (e.g., position and velocity) and ID of a target (e.g., tank)– Example: –Z is the measurements taken over k time steps

• The JMPD is hybrid continuous-discrete distribution with normalization

[ ]TTTTTT2222211111 ID y y x x||ID y y x x|ID y y x x &&L&&&&=X

88

The JMPD (II)• The temporal evolution of the JMPD is described by

– Kinematic model includes how existing targets move, how new targets arrive, and how existing targets leave the region

– Ancillary information that effects target motion incorporated through this model (e.g., terrain map)

• The sensor is described by the model– Sensor model describes how measurements z couple to target state X– Ancillary information that effects the sensor incoproated through this model (e.g.,

the visibility map)

• The JMPD is evolved via the Chapman-Kolmogorov-Bayes (CKB) recursion

Temporal Update

(“prediction”)

MeasurementUpdate

(“correction”):

99

Particle Filter Implementation of the JMPDParticle filtering is a method representing the JMPD and solving

the CKB equations numerically.a. Particles represent the density : The JMPD is approximated by a finite set of

weighted samples (“particles”) carefully chosen to cover important parts of the state space.

b. The temporal update is done via importance sampling : Given particles which represent the posterior at time k-1, samples from the prior at time k are drawn from an importance density q

c. The measurement update is accommodated by updating particle weights

1010

Particle Filter Illustration

True Target Location

Particles

1111

II. Information Based Resource Allocation Using the JMPD



1212

Information Based Resource Allocation

• The problem of Sensor Management is to determine the best way to task sensors, when sensors have many agilities (e.g., mode, waveform, pointing angle, …)

• We take an information-based sensor management route and rephrase the problem in terms of tasking the sensor to make the measurement that maximizes the information gain

– The JMPD characterizes uncertainty associated with the current estimate – We want to choose the action that makes the JMPD after the measurement maximally

informative relative to the JMPD before the action is taken – However, we cannot know the outcome of an action before it is taken. Therefore, we choose

the action that is expected to gain the most information. – Specifically, we choose the action m that maximizes the expected gain,

where Dα, the α- or Rényi- Divergence, is a measure of gain in information

1313

Measures of Gain in Information• The Rényi (α-) Divergence between the densities p1 and p0 is given by

• In our setting, we wish to measure the divergence between the JMPD before a measurement has been made and the JMPD afterward,

where, for notational convenience, we use

• The particle filter representation of the JMPD simplifies the Divergence to

( ) dxxqxpxpqpD

x∫ ⎟⎟

⎠

⎞⎜⎜⎝

⎛≡

)()(ln)(,

( ) dxxqxp1

1qpDx

1∫−

≡ − )()(ln, ααα α

( ) ∫−

≡⋅⋅ −−−

XZXZXXZZ αα

α α)|()|(ln)|(),|( kk11kkkk1k ppd

11ppD

1414

The Expected Renyi Divergence

• As stated earlier, we wish to take the action that is expected to maximize this divergence, so we use

• Which, in the case of thresholded measurements and particle filter representation of the JMPD is simply

• Computationally, this can be evaluated in O(M*Npart)

• Practically speaking, this method provides a nice metric as it can compare the effect of disparate sensing actions on a common ground; that of information gain.

1515

Sensor Management Algorithm – A SummaryIn summary, the information based multitarget tracking and sensor management algorithm proceeds as follows:1. Recursively estimate the JMPD via a

multitarget particle filter1. Time evolution (the Chapman-Komogorov)

equation addressed via adaptive particle proposals

2. Measurement update (Bayes’ rule) addressed via weight update

2. At each occasion where a sensing action is to be made, compute the expected gain in information for each possible sensing action m (e.g., pointing angle, mode, resolution, and waveform) using the α-(Rényi-) Information Divergence.

3. Select and take the action that gives maximal expected information gain.

1616

III. ResultsA. Information Metric PerformanceB. Innovative Approach to Tracking Target ID



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Results A: Information Metric Performance

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Simulation

• We present a simulation using a multimodality sensor:

– “ID” mode : models a HRR mode and associated signal processing into a confusion matrix.

• Target can be one of M classes (here 5)

• When pointed at a target, ID mode returns correct ID with p=0.6

• If pointed at an empty cell, ID call random

– “Detection” mode: models GMTI/SAR mode and associated signal processing into a process characterized by Pd & Pf

• When pointed at a target, gives a detection with probability Pd (here 0.5)

• When pointed at an empty cell, gives a detection with probability Pf (here .01)

• The goal is to choose which mode and where to point.

“Search” dwells

“Track” dwells “ID” dwells

Exploitation

Exploration

1919

Performance of the Renyi Divergence• The Renyi Divergence method of sensor management outperforms others

on the tracking and identification task– “Non-managed” scan sweeps through all cells and then repeats– Methods “A” and “B” point the sensor where targets are estimated to be

• Method A – chooses cells randomly from cells predicted to have targets and cells surrounding those predicted to have targets

• Method B – chooses cells probabilistically based on their estimated target count

2020

Results B: Innovative approach to tracking Target ID

2121

Innovative Method for Target ID• Traditional state representation of ID within target state vector:

Approximate Memory requirements: Nparts*5*T

• New representation:

where L = number of ID classes.– Equivalent to a grid tracker for ID only– Approximate Memory requirements: Nparts*(4+L)*T– Avoids decreasing ID diversity artifact over time

• Cost for one target, L=5 is a factor of 1.8 (same # effective particles) but performance more than pays for cost.

[ ]TTTTTT2222211111 ID y y x xID y y x xID y y x x &&L&&&& |||x =

,)p(ID )p(ID )p(ID y y x x

)p(ID )p(ID )p(ID y y x x )p(ID )p(ID )p(ID y y x x

L21TTTT

L212222

L211111T

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

L&&L

L&&L&&

|

||||

X

2222

ID

Sensor PCC = .3

Sensor PCC = .5 Sensor PCC = .8

Single Target tracker Pcc vs. time improves as sensor quality increases

Single Target tracker Pcc vs. time improves as sensor quality increases

2323

ID RESULT

Tracker PCC for 2 Methods (5 ID classes): Comparable FLOPS

ID SENSOR PCC/CELL

PF T

RA

CK

ER P

CC

NewMethod

OldMethod

2424

IV. Conclusions and Future Work



2525

Conclusions

• PF approximates the JMPD with enough fidelity to ID and track targets successfully

• Information-Based Sensor Management out-performsad-hoc sensor allocation methods

• New state representation for target ID out-performs traditional approach

2626

Future Work

• Combine Sensor Management with new ID representation

• Long-term scheduling

• Multi-Sensor extensions

• De-centralized processing

2828

Simulation Movie• We present a simulation using a

multimodality sensor:– “ID” mode : models a HRR mode and

associated signal processing into a confusion matrix.

• Target can be one of M classes (here 5)• When pointed at a target, ID mode returns

correct ID with p=0.6 • If pointed at an empty cell, ID call random

– “Detection” mode: models GMTI/SAR mode and associated signal processing into a process characterized by Pd & Pf

• When pointed at a target, gives a detection with probability Pd (here 0.5)

• When pointed at an empty cell, gives a detection with probability Pf (here .01)

• The goal is to choose which mode and where to point.

“Search” dwells

“Track” dwells “ID” dwells

Exploitation

Exploration

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