Statistical modeling, classification, and sensor management

Sequential Adaptive Multi-Modality Target Detection and Classification using Physics-Based Models: Review 03

Statistical modeling, classification, and sensor management

Alfred Hero

Univ. Michigan

Ann Arbor

DARPA-MURI

Review 2003


Target Search Scenario

LowRes Spot Scan

Strip Scan

HighRes Spot Scan


Sensor Deployment Architecture


Research Loci• Image modeling and reconstruction

– Markov random field (MRF) polarimetric models (Hory&Blatt)– 3D Imaging with uncalibrated sensor nets (Rangarajan&Patwari)

• Adaptive detection and classification– Pattern matching and modeling (Costa)– Distributed detection and classification (Blatt&Patwari)

• Sequential sensor management– Myopic information-driven approaches (Kreucher)– Non-myopic approaches (Kruecher&Blatt)

Common theme: adaptive robust non-parametric methods


Detection: Target or Clutter Alone?


Detection: Target or Clutter Alone?


Target Returns Not Additive or Gaussian

– 1cm x 1cm x 1mm plate at 1m from ground

– Plate under forest canopy (10 deciduous trees)

– 2GHz SAR illumination

– Aggregate of three look angles (azimuth=35,45,55, elev=180)

SNR=0dB SNR=6dB


Polarimetric Field Modeling and Reconstruction

• Field Distribution On FDTD Box (2 GHz)

v-pol. incidenceh-pol. incidence


MRF empirical histogram

Conditional Markov transition histogram

…estimated from training data


Causal MRF Field Synthesis

Causal kNN predictor:

Non-Causal MRF model:


Example: K-NN MRF Extrapolation


Non-parametric MRF density estimator• General penalized MRF transition density estimate

• y is observed data• parameter enforces smoothness• function g(f) captures data-fidelity

– g(f)=|f|^2: standard L2 quadratic regularization– g(f)=|f|: L1 regularization for denoising

• w(x): smoothing within and across neighborhoods


)|(ˆ| iixi xNx NyP

Cartoon illustration of density estimatorK-Nearest Neighbors Estimator

),(ji xx NNd

iy~

Penalized MRF transition Density Estimator

),(ji xx NNd

)|(.ˆ| iiyi yNy Nf )|(ˆ

| iixi xNx NyP


Application: MRF synthesis and denoising

g(f)=|f|


Target Modeling and Classification

• Pattern matching in high dimensions– Standard techniques (histogram, density estimation) fail due to

curse of dimensionality

– Entropic graphs recover inter-distribution distance directly

– Robustification to outliers through graph pruning

• Manifold learning and model reduction– Standard techniques (LLE, MDS, LE, HE) rely on local linear

fits and provide no means of getting at sample density

– Our geodesic entropic graph methods fit the manifold globally

– Computational complexity is only n log n


A Planar Sample and its Euclidean MST


Convergence of Euclidean MST

Beardwood, Halton, Hammersley Theorem:


Pattern Matching


MST Estimator of -Jensen AffinityTwo well separated Classes Two overlapping Classes


MST Estimator of Friedman-Rafsky AffinityTwo well separated Classes Two overlapping Classes


Target model reduction• 128x128 images of three land vehicles over 360 deg

azimuth at 0 deg elevation

• The 3(360)=1080 images evolve on a lower dimensional imbedded manifold in R^(16384)

Courtesy of Center for Imaging Science, JHU


Target-Image Manifold


A statistical sample

Sampling distribution

2D manifold

Sampling

Embedding


Geodesic Entropic Graph Manifold Learning and Pattern Matching Algorithm

• Construct geodesic edge matrix (ISOMAP,C-ISOMAP)• Build entropic graph over geodesic edge matrix

– MST: consistent estimator of manifold dimension and process alpha-entropy

– MST-Jensen: consistent estimator of Jensen difference between labeled vectors

• Use bootstrap resampling and LS fitting to extract rate of convergence (intrinsic dimension) and convergence factor (entropy)


Illustration for 3 land Vehicles

0 200 400 600 800 1000 12000

1

2

3

4

5

6

7

8

9x 10

5 MST Length for 3 Land Vehicles (=1,m=20)

n

Ln

1020 1022 1024 1026 1028 1030 1032 1034 1036 10388.5

8.52

8.54

8.56

8.58

8.6

8.62

8.64x 10

5 MST Length for 3 Land Vehicles (=1,m=20)

n

Ln


loglogLinear fit to asymptote

6.925 6.93 6.935 6.94 6.94513.652

13.654

13.656

13.658

13.66

13.662

13.664

13.666

13.668

13.67

13.672logMST Length and Linear Fit for 3 Land Vehicles (=1,m=20)

log n

log

(Ln)

y = 0.91*x + 7.3

log(Ln)

Linear fit

LS-Soln:d=13H=120(bits)_


Distributed Multisensor Estimation and Detection

• Distributed M-estimation (Blatt)– Ambiguity function is often multimodal: local and global M

– Distributed measurements make local M more difficult

– We develop method to discriminate between local/global M

– Use unsupervised clustering and Fisher information matching

• Distributed change detection (Patwari)– Bandwidth and computation constraints

– Multilayer vs flat store-detect-forward architecture

– We study perfromance loss due to bandwidth constraints

– How much information should be sent to what layers?


Flat Sensor Aggregation Architecture

Sensor 1 Sensor 2 Sensor N

Processing unit

Final estimator

Distributed Estimation and Detection


Distributed M- Estimation

Ambiguity function for Cauchy distributed points on a manifold


A slice of ambiguity function

Global maximum

Local maxima


Key Theoretical Result

• The asymptotic distribution of M-estimate is (asymptotically) a Gaussian mixture

• Parameters

M

m

mm

Tm

mK

m tCtC

ptf

0

1

2/ˆ )()(

2

1exp

2)(

Ref: Blatt&Hero:2003


Validation of Key Result – QQ-plots

M-estimates are clustered into two groups. Each group is centered according to the analytical mean and normalized according to the analytical variance.


SampleCovariance

Analysis

M-estimator Aggregation Algorithm

Estimator 1

Estimator 2

Estimator N

Estimation of

Gaussian Mixture

Parameters

(EM)

AggregationTo FinalEstimate


Local maximum

Ambiguity function.

Global maximum

Model:

• 200 Sensors• 100 snapshots per

sensor• Snapshots are 1D

Gaussian 2-mixture• Known covariance• Unknown means• Sensors generate

i.i.d. M-estimates of means and forward to central processor

Illustration


Local/Global Maxima Discrimination Algorithm

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

1

2

Bad estimates

Good estimates

Empirical covariance

Inverse FIM Bad estimates


Addition of other Discriminants

00.5

11.5

22.5

3

0

0.5

1

1.5

2

2.5

3-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1

2

lo

g f(

y i; 1,

2) -

E{

log

f(y i;

1, 2)

}

Value-added due to local acquisition and transmission of likelihood values


Hierarchical Sensor Aggregation Architecture

Processing unit

Final estimator

Distributed Estimation and Detection

Sensor 1 Sensor 2 Sensor 3 Sensor 4

Sensor 5 Sensor 6


Detection: Flat vs Hierarchical Architecture• ‘Flat’ [Rago,

Willett, et al]

• Hierarchical, w/ and w/o Feedback

• Each sensor is limited with identical

• At low PF, Hierarchical outperforms Flat

Optimal 1-Sensor

Optimal 7-Sensor

= 0.30

= 0.10

= 0.03

Legend

FlatHier. w/o Feedback

Hier. w/ Feedback

2 3 6 74 5

1

2 3

6 74 5

1

Optimal 1-Sensor

Optimal 7-Sensor

= 0.30

= 0.10

LegendFlat

Hier. w/o Feedback

Hier. w/ Feedback


Sequential Adaptive Sensor Management• SequentialSequential: only one sensor : only one sensor

deployed at a timedeployed at a time• Adaptive:Adaptive: next sensor selection next sensor selection

based on present and past based on present and past measurementsmeasurements

• Multi-modality:Multi-modality: sensor modes can sensor modes can be switched at each timebe switched at each time

• Detection/Classification/Tracking:Detection/Classification/Tracking: task is to minimize decision errortask is to minimize decision error

• Centralized decisionmakingCentralized decisionmaking: : sensor has access to entire set of sensor has access to entire set of previous measurementsprevious measurementsSingle-target state vector:

x

y


Sequential Adaptive Sensor Management

• Myopic information-based strategies (Kruecher)– Multi-target tracking capabilities

– Fully Bayesian approach

– Non-linear particle filtering with adaptive partitioning

– Renyi-alpha divergence criterion

• Non-Myopic strategies (Blatt&Kreucher)– MDP value function approximations and rollout methods

– Bayesian path averaging

– Reinforcement feedback and learning


Sensor scheduling objective function

Sensor agilityPrediction

Retrospective value of deploying

sensor s

Availablemeasurements

at time t-1

•Prospective value of deploying sensor s at time t:


Information-based Value Function• Incremental information gained from data collected

from using sensor s. Can be measured by divergence

• Requires posterior distributions of future target state X given future Z and given present Z, resp.,

• Main issues for evaluation of E[D(s,t)|Z] – Computation complexity– Robustness to model mismatch– Decisionmaking relevance


Value Function : Alpha Divergence

• Properties of Renyi divergence – Simpler and more stably implementable than KL

(Kreucher&etal:TSP03)– Parameter alpha can be adapted to non-Gaussian posteriors – More robust to mis-specified models than KL

(Kreucher&etal:TSP03)– Related directly to decision error probability via Sanov

(Hero&etal:SPM02)– Information theoretic interpretation


Relevance of alpha-D to Decision Error• Consider testing hypotheses

• Sanov’s theorem: optimal decision rule has error

• Implication: nearly-optimal decision rule for H1 is

if can generate good estimate of alpha-D


Multi-Target Bayesian Filtering• Joint multiple target posterior density (JMPD) jointly represents

all target states (Kastela)

• Update eqns must generally be approximated

11111 ||| kkkkkkk dppp xZxxxZx

1

1

|

|||

kk

kkkkkk

p

ppp

Zz

ZxxzZx

kkkkkkk dppp xZxxzZz 11 ||| where

Model Update (Prediction using prior kinematic model)

Measurement Update (Bayes Rule)


Particle Filter (Metropolis) Approximation• Propose (draw) a set of particles based on some importance

(proposal) density q chosen to be as close to the posterior as possible

• Weight the particles using the principle of importance sampling

• Resample particles using above density to avoid degeneracy

time t-1

time t

kkp

kq zxx ,| 1

N

p

kp

kkp

kk wp1

)()|( xxZx kk

pkp

kp

kp

kp

kkp

kp q

ppww

zxx

xxxz

,|

||1

11


Particle Filtering Illustration

Initialize: simulate random samples (particles) from proposal

density

00 | Zxp

N

pppw

1

000 )( xx


Particle Filtering Illustration• Model Update:

Propose new particles from existing particles based on drawing samples from the importance density kkkkkk pq ZxxZxx ,|,| 11

11111 ||| kkkkkkk dppp xZxxxZx


Particle Filtering Illustration

Measurement Update: Reweight particles density according to

• Resample the particles if necessary

kk

pkp

kp

kp

kp

kkp

kp q

ppww

zxx

xxxz

,|

||1

11


Multitarget Tracking: Adaptive Proposals•When targets are well separated in measurement space, each target-partition of particle evolves independently.

•In this case can use independent partition (IP) updates

•When targets become “close” target-partitions become dependent•In this case should use coupled partition (CP) updates

•Adaptive strategy: use IP unless CP is deemed necessary IP updating CP updatingCP updating


Numerical Experiment• Simulation conditions

– Linear target motion model: isotropic diffusion

– GMTI sensor with dwells over uniform grid– Non-linear return: Rayleigh target and clutter rv

– Target detector operates with fixed threshold (Pf=0.1) – No sensor management


Tracking Simulated Target Motion w/o SM

Sensor makes measurements on a gridThe sensor is characterized by a probability of

detection and a probability of false alarm.


Real Target Motion

Ten real targetsMotion taken from recorded GPS measurements

During a battle simulation exercise at NTC.


Real Target Motion


Multiple Model for Real Target Motion

• Target state vector

• Three different models– Target is moving:

– Target is stopped:

– Target is accelerating:

Tyxyx ] [

y

x

dyd

dxd

ydy

xdx

etc. ,]E[with

processes noise whiteare

and ,

22 dtqd

dd

xx

yx

0 ydxddydx

y

x

dyd

dxd

ydy

xdx

ˆ

ˆ

[-k...k]on onsaccelerati discrete

ddistributeuniformly are

ˆ and ,ˆyx dd


Multiple Model for Real Target Motion

• Model switching transition matrix

acceltoaccelstoptoaccelcvtoaccel

acceltostopstoptostopcvtostop

acceltocvstoptocvcvtocvk1k

ij

ppp

ppp

ppp

jmimP

______

______

______

}|{

001

352

0304930

...

...


Ten real targetsMotion taken from recorded GPS measurements

During a battle simulation exercise at NTC.

Staging area

Tracking Real Multitarget Motion w/o SM


Quantitative Results : Adaptive Partitions

Method FlopsCP Updating 1.25E+08IP Updating 6.74E+06

Fully Adapative - Mean 5.48E+07Fully Adaptive - Sample 5.35E+07


Comparison of Managed and Non-Managed Performance

• We illustrate the benefit of info-gain SM with AP implementation of JMPD tracking 10 moving targets.

• GMTI radar simulated: Rayleigh target/clutter statistics• Contrast to a periodic (non-managed) scan: same statistics• Coverage of managed and non-managed=50 dwells per second


Tracker Comparison Managed vs. Non-Managed• Monte Carlo tests (left) show performance with SM using 50 looks similar to periodic scan with 700

looks – SM makes the tracker 12 times as efficient in terms of sensor resources needed.

• More extensive runs in similar scenario (right) with 3 targets show performance with SM using 24 looks similar to periodic (non-managed) performance with 312 looks

– SM makes the tracker approximately 13 times as efficient in this scenario.– Performance of managed scenario with 24 looks at SNR = 2 (3dB) similar to performance of periodic management at

SNR = 9 (9.5dB) – approximately a 6.5dB performance gain.

Utility of Sensor Management : Three Simulated Targets


Choice of Alpha: Matched Models• When filter model matches the actual

target kinematics very closely, the performance of the algorithm is insensitive to the choice of .

• Simulation: Three targets moving according to a nearly constant velocity model with diffusive component q. Filter has exact model of target motion with correct q.

• Results: Tracker performance nearly identical for all values of .

),0(~1

qINk

kkk

v

vxx


Choice of Alpha: Mismatched Models

Maximum at (4250, 2450)Maximum at (3450, 650)

~

Snapshot of information map for ten target GPS simulation


Choice of Alpha: Mismatched Models• Under target kinematic model mismatch using = ½ yields better performance.• Simulation: Ten targets with trajectories taken from real, recorded data. The filter

kinematics are mismatched to vehicles with nearly constant velocity.

• Results: Fewest lost tracks over 50 Monte Carlo trials with avg RMS std RMS

0.1 49.57 24.780.5 47.28 11.84

0.99999 57.43 44.22


Multimode Radar: Mode and Dwell Point Selection• MTI Mode

– Each detection cells is 100m x 100m– Measures strips 1x25 cells long– Pd = 0.9, Pfa = .001– Detects targets with velocity > MDV

• FTI Mode– Measures cells that are 100m x 100m– Measures spots 5x5 cells on the ground– Pd = 0.5, Pfa = 1e-12– Detects stopped targets

• Particle Filter–Multiple model (stopped and moving)–Adaptive Proposal Method–100 Particles, 3 Targets

• Sensor Management–Expected gain for each modality/pointing angle calculated before each measurement.

–12 Looks/time step each of 250km2 (total approximately 10% of surveillance area)


Myopic vs Non-Myopic Strategies

• Myopic SM computes only one-step ahead• Non-myopic SM looks ahead multiple steps• Even two step look-ahead can be of value• Simple illustration:

– Non-myopic information gain criterion

– Two targets in two cells

– At even time instants only one cell is visible


Non-Myopic Search TreeS5

S6

S7

S8

S9

SA

SB

SC

SD

SE

SF

SG

SH

SI

SJ

SK

S1

S2

S3

S4

A

<D>=1.1

B<D>=.9

C

<D>=.1

C

<Dc>=1.1

C

<Dc>=1.1

C

<Dc>=1.1

D<D>=.001

D<Dd>=.001

D<Dc>=.001

D<Dd>=.001

p=0.5

D = 2.2

p=0.5D = 0

p=0.5

D = 1.8

p=0.5D=0

S0


Posterior at t=0, P(X0|Z0) Prediction at t=1, P(X1|Z0)

One Realization of

p(X2|Z1) when right

target measured

Left Target

Measured

Right Target

Measured

One Realization of

p(X2|Z1) when left

target measured

Myopic scheme uses only this information

Non-myopic scheme makes use of this information


Comparison of Greedy and Non-Myopic (2 step) decision making

Myopic: Target lost 22% of the time

Non-Myopic: Target lost 11% of the time


Non-myopic:Target lost 11% of the time

Myopic:Target lost 22% of the time


• Before time 190 (the crossover point):– At even time instants, only

one target is visible and the myopic/nonmyopic strategies agree 100% of the time.

– At odd time instants, the right method is to measure the right target. The myopic/nonmyopic strategies agree about 85% of the time.


Foci for 2nd Year

• Non-parametric polarimetric backscatter modeling Non-parametric polarimetric backscatter modeling for multistatic target detectionfor multistatic target detection

• Target and clutter model reduction and pattern Target and clutter model reduction and pattern matching matching

• Adaptive non-myopic sensor scheduling and Adaptive non-myopic sensor scheduling and managementmanagement


Personnel on A. Hero’s sub-Project(2002-03)

• Krishnakanth Subramanian, 1st year MS student– Birla Institute of Technology– 50% GSRA

• Michael Fitzgibbons, 1st year MS student– Northeastern Univ.– 50% GSRA

• Cyrille Hory, Post-doctoral researcher– University of Grenoble– Area of specialty: data analysis and modeling, SAR, time-frequency


Personnel on A. Hero’s sub-Project(ctd)• Jose Costa, 3rd year doctoral student

– IST Lisbon– Portugese fellowship, summer GSRA

• Chris Kreucher, 3rd year grad student– UM-Dearborn, Veridian Intl– Veridian support

• Neal Patwari, 2nd year doctoral student– Virginia tech– NSF Graduate Fellowship, summer GSRA

• Doron Blatt, 2nd year doctoral student– Univ. Tel Aviv– Dept. Fellowship, summer GSRA

• Raghuram Rangarajan, 2nd year doctoral student– IIT Madras– Dept. Fellowship, summer GSRA


Publications(02-03): Estimation-Classification

• J. Costa and A. O. Hero, “Manifold learning with geodesic minimal spanning trees,” submitted to IEEE T-SP (Special Issue on Machine Learning), July 2003.

• A. O. Hero, J. Costa and B. Ma, "Convergence rates of minimal graphs with random vertices," submitted to IEEE T-IT, March 2003.

• J. Costa, A. O. Hero and C. Vignat, "On solutions to multivariate maximum alpha-entropy Problems", in Energy Minimization Methods in Computer Vision and Pattern Recognition (EMM-CVPR), Eds. M. Figueiredo, R. Rangagaran, J. Zerubia, Springer-Verlag, 2003

• D. Blatt and A. Hero, "Asymptotic distribution of log-likelihood maximization based algorithms and applications," in Energy Minimization Methods in Computer Vision and Pattern Recognition (EMM-CVPR), Eds. M. Figueiredo, R. Rangagaran, J. Zerubia, Springer-Verlag, 2003


Publications(02-03): Sensor Management

• C. Kreucher, K. Kastella, and A. Hero, “Sensor management using relevance feedback learning,” submitted to IEEE T-SP, June 2003

• C. Kreucher, K. Kastella, and A. Hero, “Multitarget tracking using particle representation of the joint multi-target density,” submitted to IEEE T-AES, Aug. 2003.

• C. Kreucher, K. Castella, and A. O. Hero, "Multitarget sensor management using alpha divergence measures,” Proc First IEEE Conference on Information Processing in Sensor Networks , Palo Alto, April 2003.

• C..Kreucher, K. Kastella, and A. Hero, “A Bayesian Method for Integrated Multitarget Tracking and Sensor Management”, 6th International Conference on Information Fusion, Cairns, Australia, July 2003.


Publications(02-03): Sensor Management(ctd)

• C. Kreucher, C., Kastella, K., and Hero, A., “Tracking Multiple Targets Using a Particle Filter Representation of the Joint Multitarget Probability Density”, SPIE, San Diego California, August 2003.

• C. Kreucher, K. Kastella, and A. Hero, “Information-based sensor management for multitarget tracking”, SPIE, San Diego, California, August 2003.

• C. Kreucher, K. Kastella, and A. Hero, “Particle filtering and information prediction for sensor management”, 2003 Defense Applications of Data Fusion Workshop, Adelaide, Australia, July 2003.

• C. Kreucher, K. Kastella, and A. Hero, “Information Based Sensor Management for Multitarget Tracking”, Proc. Workshop on Multiple Hypothesis Tracking: A Tribute to Samuel S. Blackman, San Diego, CA, May 30, 2003.


Publications(02-03): SP for Sensor Nets

• N. Patwari and A. O. Hero, "Hierarchical censoring for distributed detection in wireless sensor networks,” Proc. Of ICASSP, Hong Kong, April 2003.

• N. Patwari, A. O. Hero, M. Perkins, N. S. Correal and R. J. O'Dea, "Relative location estimation in sensor networks,” IEEE T-SP, vol. 51, No. 9, pp. 2137-2148, Aug. 2003.

• A. O. Hero , “Secure space-time communication," to appear in IEEE T-IT, Dec. 2003.

• M.F. Shih and A. O. Hero, "Unicast-based inference of network link delay distributions using mixed finite mixture models," IEEE T-SP, vol. 51, No. 9, pp. 2219-2228, Aug. 2003.


Synergistic Activities(02-03)• Veridian, Inc

– K. Kastella: collaboration with A. Hero in sensor management, July 2002-– J. Ackenhusen: collaboration with A. Hero in mine detection, Oct. 2002-– C. Kreucher: doctoral student of A. Hero, Sept. 2002-

• ARL– NAS-SED: A. Hero is a member of yearly review panel, May 2002-– B. Sadler: N. Patwari (doctoral student of A. Hero) held internship in

distributed sensor information processing, summer 2003• ERIM Intl.

– B. Thelen&N. Subotic: collaborators with A. Hero, Oct. 2002• Chalmers Univ.,

– M. Viberg: A. Hero is Opponent on multimodality landmine detection doctoral thesis, Aug 2003

• EMMCVPR: – “Entropy, spanner graphs, and pattern matching,” plenary lecture, July 2003


Cross-Fertilization to Other Sponsors(02-03)• NSF-ITR

– “Modular strategies for internetwork monitoring,” A. Hero, PI (2003-2008)

• NIH-P01– “Automated 3D registration for enhanced cancer

management,” C. Meyer, PI (2002-2007)

• NIH-R01– “Radionucleides: radiation detection and quantification,” N.

Clinthorne, PI (2002-2005)

• Sramek Foundation– “Genetic pathways to diabetic retinopathy,” A. Swaroop, PI

(2002-2005)

Documents

Statistical modeling, classification, and sensor management