a. hero, afosr muri review 11/08 adaptive radar sensing strategies afosr muri integrated fusion,...

A. Hero, AFOSR MURI Review 11/08

Adaptive radar sensing strategies

AFOSR MURI

Integrated fusion, performance prediction, and sensor management for ATE

(PI: R. Moses)

A.Hero

Univ. of Michigan – Ann Arbor

2nd Year Review, AFRL,11/08


Outline• I. Broad aims of our research

• II. Progress in sensor management

– New effort: multiple platform radar provisioning with guaranteed uncertainty

– Continuing effort: sparsity constrained spatio-temporal search using convex resource allocation criteria

• III. Progress in front-end processing and fusion

– New: graphical models for distributed decomposable PCA

– New: graphical models for hyperspectral image unmixing

• Information items

– Synergistic Activities

– Personnel

– Publications


I. Broad aims of our research• Integration of modeling, inference, planning

– Integration of multi-platform data

– Performance prediction

– Information-directed sensor management

• Constraints

– Limited time/energy/resources

– Brute force optimal approaches are intractible

• Components of our research approach

– Sequential resource allocation

• Multiresolution wide area search

• Multiple platform provisioning

– High level fusion with hierarchical graphical models

• Decomposable PCA

• Hyperspectral unmixing

– Performance prediction

• Guaranteeduncertainty management

• Bayesian posterior analysis

This talk

Agile Multi-Static Radar system illustration


Part II: Sensor Management

• II.A Performance prediction: multitarget

multiplatform multifunction radar systems

• II.B Adaptive wide area search: sparsity-

constrained multiresolution radar search


II.A Performance prediction: multitarget multiplatform multifunction radar systems

High confidence target regions

time=t time=t+targets targets


Target track update

time=t time=t+


Trac

k up

date


Wide area search

time=t time=t+


Wide area search


Objective: performance prediction

• Radar constraints: – multipulse radar can be allocated to multiple

tasks: target tracking, wide area search,...– number of radar pulses affect MSTE/ROC and

time spent on a given task

• Objective: predict overall system capabilities – maximum number of targets that can be

reliably tracked with a given number of radars?

– system loading and load margin available for other tasks (discrimination, kill assessment, search)?


Our approach • A guaranteed uncertainty management (GUM)

framework– Radar system performance prediction– Guarantee specified level of track/detection

accuracy (std error of 2%, 5% FA and 1% M)– Specify stable regime of system operation

• An combination of information theoretic uncertainty management and prioritized longest queue (PLQ) resource allocation– related to optimal multiprocessor policy of

Wasserman&etal:2006 for multi-queueing systems.


Uncertainty management and PLQ

ServiceLoad

TargetUncertainty

Policy is analogous to optimal processor allocation in heterogeneous multiple queueingsystems (Wasserman&etal:2006)


PLQ Stability Analysis• Radar load for nth target after secs ellapsed

• As radar load grows superlinearly in time system stability is the central issue

• Cumulative service time to revisit all N targets


Track-only stability condition• For stable operation of radar system

where (balance equation)

• Track-only system capacity: = maximum number of targets for

which solution exists


Multi-tasking stability: load margin

• Assuming radar operates below capacity headroom exists for other tasks.– Search load:– Discrimination load:

• Condition for stability with additional load

• Excess capacity and occupancy


Illustration: 24 Swerling II targets

• C-band radar (4Mhz)• PRI=1ms (150km)• Range res=150m• # pulses=10

– (Pf,Pd) = (0.000001, 0.9999)

• Target speed=300m/s• Speed std error=30m/s• Direction std error=18deg

Load curve lies above diagonalMax number of trackable targets is 23

• System is underprovisioned• Stable track maintenance impossible

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.2

0.4

0.6

0.8

1

1.2

1.4

Single target service time (secs (PRI

Np)-1)

Tar

ge

t re

visi

t pe

riod

(se

cs)

N=24, R=1, RevisitR=0, =0%, Nmax

/R=23

Tcell

Radar load curveStability lineOptimal load curve


Illustration: 12 Swerling II targets

• C-band radar (4Mhz)• PRI=1ms (150km)• Range res=150m• # pulses=10

– (Pf,Pd) = (0.000001, 0.9999)

• Target speed=300m/s• Speed std error=30m/s• Direction std error=18deg

•Track-only load curve below diagonal•Can handle up to 23 targets •With12 targets extra 0.2 secs to spare • System has excess capacity

• Load margin is 0.176 and occupancy is 70%


Discussion• Take home message: GUM performance prediction framework specifies

capacity and stability of radar systems with information theoretic performance measures

• Theory can be used to evaluate radar systems for given scenario• The system capacity and stability depend on the presribed maximum track

and detect uncertainty • Priority longest queue (PLQ) allocation policy is a natural but not the only

radar resource allocation policy that can be studied in this framework.


II.B. Adaptive wide area searchSt

age

1W

ide

area

sea

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Stag

e 3

Ref

ined

sea

rch

Stag

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Ref

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sea

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Stag

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Problem setup (same slide as last year)

• Set of all cells • ROI• ROI indicator• Spatio-temporal energy allocation policy

• Observations • Uniform spatial allocation:• Ideal spatial allocation:• Optimal N-step allocation: multistage stochastic control problem

• Simpler objective: find two-step optimal allocation that minimizes


Recall optimal strategy


Recall comparisons

Wide area SARacquisition

Optimal two step SARacquisition

Overall energy allocated is identical in both cases


Year 2 progress on ARAP: M-ARAP

• Extend ARAP to account for

– time constraints (number of chips acquired)

– radar beam shape (footprint)

– extended targets

– multi-resolution search implementation

• Modified measurement model incorporates

spatial point spread function H(t)


Simulation of M-ARAP for MTI • Uniformly attenuating beampattern

• FOV is 66 x 66 km with pixel dimensions of 20 × 20 m

• Radar resolution cell is 100 × 100 × 150 m.

• Sparsity level p = 0.0007 was selected Q = 4082

• Identical targets with target reflection distribution modeling an

aircraft similar to an Airbus A-320.


Simulation of M-ARAP for MTI • Target velocities are isotropically normally distributed

• Swerling II noise model

• Clutter (rain) intensity was random between 0-6 [mm/hr] and

spatial correlation on the order of 1x1 km.

• Maximal clutter velocity was 30 m/sec

• Standard single pass MTI filter is compared to a two pass

multiresolution ARAP search

• M-ARAP search has lower MSE localization error, fewer false

alarms and higher detection rate than MTI for equivalent time

and energy.


M-ARAP for MTI tracking radar


Correct detection probability vs

false discovery rate


Optimal energy allocation


Discussion• Take home message: can attain 7dB MSE reduction at SNR of 5 dB using

only N=Q/P samples• M-ARAP searches for P sparsely distributed but clustered targets over Q

search cells with minimum time and energy constriants• Objective function J is related to the KL information divergence and the

Fisher information under a Gaussian measurement model. • J only depends on the cumulative energy allocated to each voxel in the

image volume (deferred reward)• Features of two-step M-ARAP search algorithm

– motivated by pooled statistical sampling (syphylis studies of Dorfman:AnnMathStat1943)

– assigns energy to regions with high posterior probability of containing targets– is an index policy with threshold k0– is a multi-resolution extension of the two-stage ARAP search algorithm presented

at last review.– Is low computational complexity - O(Q)


Part III: High level fusion

• III.A Distributed decomposable PCA

• III.B Hyperspectral imaging and unmixing

• Common theme: application of hierarchical

graphical models


III.A Decomposable PCA• Principle components analysis (PCA) is a model-free

dimensionality reduction technique used for high level

data fusion (variable importance, regression, variable

selection)

• Deficiencies:

– PCA does not naturally incorporate priors on

• Dependency structure (graphical model)

• Matrix patterning (decomposability)

• Scalability problem: complexity is O(N^3)

– Unreliable/unimplementable for high dimensional data

– Ill-suited for distributed implementation, e.g., in sensor

networks


Networked PCA• Network model: measure sensor outputs Xa, Xb, Xc

– Two cliques {a,c} and {b,c}

– Separator {c}

• Decomposable model: covariance matrix R unknown but

conditional independence structure is known.

• PCA of covariance matrix R finds linear combinations

y=UTX that have maximum or minimum variance


DPCA formulation• Precision matrix K=R-1

• For decomposable model K has structure

• General representation


1 dimensional DPCA• PCA for minimum eigenvector/eigenvalue solves

• Key observation:

• This constraint is equivalent to

• where


Extension to k-dimensional DPCA• k-dimensional PCA solves sequence of eigenvalue

problems

• Dual optimization


k-dimensional DPCA (ctd)

• Dual maximization splits into local minimization with

message passing

• Message passing


Tracking illustration of DPCA • Scenario: Network with 305 nodes representing three

fully connected networks with only 5 coupling nodes

• C1 = {1, · · · , 100, 301, · · · , 305}, C2 = {101, · · · ,

200, 301, · · · , 305}, and C3 = {201, · · · , 300, 301, ·

· · , 305}.

• Local MLEs computed over sliding time windows of

length n = 500 with 400 samples overlap.

• Centralized PCA computation: EVD O(305)^3 flops

• DPCA computation: EVD O(105)^3 flops + message

passing of a 5x5 matrix M


DPCA min-eigenvalue tracker

Iteration 1

Iteration 2

Iteration 3


DPCA network anomaly detection

SNVA

STTL

LOSA KSCY

HSTN

DNVR

CHIN

IPLS

ATLA

WASH

NYCM

Multiple measurement sites (Abilene)


DPCA anomaly detection

PCA (centralized)

DPCA (E-W decomp)

DPCA (E-W-S decomp)

DPCA (Random decomp)


Discussion• Take home message: Combination of model-free dimensionality reduction

and model-based graphical model can significantly reduce computational complexity of PCA-based high-level fusion

• Complexity scales polynomially in clique size not in overall size of problem. Example: 100,000 variables with 500 cliques each of size 200

– Centralized PCA: complexity is of order 1015

– DPCA: complexity is of order 106

• If can impose similar decomposability constraints on graph Laplacian matrix, be extended to non-linear dimensionality reduction: ISOMAP, Laplacian eigenmaps, dwMDS.


III.b Hyperspectral unmixing• Hyperspectral imaging model

Y = MA + N

• Y: L x P matrix over L spectral bands and P pixels

• M: L x R matrix of R endmember spectra

• A: R x P matrix of endmember mixture coefficients

• N: L x P noise residual matrix

• Hyperspectral unmixing problem is to estimate A given M

and Y. Usually broken into two steps (ENDFINDR, VCA)

– Endmember extraction algorithm (EEA)

– Inversion step to extract mixing coefficents


Sample endmember spectra

• Concrete Redbrick


Key observation• Mixing coefficients supported on R-1 dimensional simplex

• This suggests a natural dimensionality reduction approach

to estimation of mixing coefficient matrix A


Hierarchical Bayesian model• Graphical model structure induces posterior

• T: projected endmember spectra

• C: projected mixing coefficents

• e,s: mean and variance of projected endmember

spectrum


Moffet field hyperspectral image

AVIRIS image


Unmixing results


Discussion• Take home message: by using a unified graphical

model approach to hyperspectral unmixing can

significantly improve performance wrt state-of-the-art

(N-FINDR, VCR)

• Other Bayesian prirors can lead to sparsity

preserving solutions


Synergistic Activities• Related funded activities

– NSF (Cozzens) Transductive anomaly detection– ARO (Harmon) Sparsity penalized 3D inverse scattering– ARO (Prater) Sparsity penalized 3D molecular imaging MRFM– ONR (Martinez) Network tomography and discovery

• DoD panel participant:

– National Research Council Workshop on Disrupting IED Terror Campaigns and Predicting IED Activities (Mar. 2008)

– Army Research Office CISD Strategic Planning Meeting (Aug 2008)

– NSF/IARPA/NSA workshop on the science of security (Nov 2008)

• Industry interactions

– Techfinity (MDA funded) Guaranteed uncertainty management for missile defence

– SIG (ATR Center dunded) information-driven dimensionality reduction


Personnel

• Supported by MURI grant:– 2008- : G. Newstadt (2nd year MS) – 2007-2008: C. Kim (2nd year MS)– 2007-2008: E. Bashan (Graduated July 2008)

• Other (unsupported by UM)– Ami Wiesel (Post-doc, Umichigan)– N. Dobigeon (Univ of Toulouse)– S. Damelin (Prof at Georgia Southern)– Venkat Chandrasekeran (MIT Grad Student)


Publications (2007-2008)• Appeared

– E. Bashan, R. Raich, R.; A.O. Hero, “Optimal two-stage search for sparse targets using convex criteria,” . IEEE Trans. on

Signal Processing Vol. ?, Issue 10, Oct. 2008 Page(s):?. – E. Bashan, “Efficient resource allocation schemes for search ,”

PhD Thesis, University of Michigan, May 2008.– H. Bagci, R. Raich, A. E. Hero, and E. Michielssen, "Sparsity-

Regularized Born Iterations for Electromagnetic Inverse Scattering," Proc. of IEEE Antennas and Propagation Symposium, June, 2008.

– A. Hero, Guaranteed uncertainty management (GUM) for sensor provisioning in missile defense, mid-term research report to the US Missile Defense Agency and Techfinity, Inc, Mar 2008.

• Submitted– N. Dobigeon, J.-Y. Tourneret, S. Massaoui, M. Coulon and A.O.

Hero, 'Joint Bayesian endmember extraction and linear unmixing for hyperspectral imagery,' IEEE Trans. on Signal Pocessing, submitted Sept 2008.

– A. Wiesel and A.O. Hero, 'Decomposable Principal Components Analysis,' IEEE Trans. on Signal Processing. submitted Aug 2008.

a. hero, afosr muri review 11/08 adaptive radar sensing strategies afosr muri integrated fusion,...

Documents

multipulse radar

load marginassuming

number of radar pulses

system capacity

time system stability

multiresolution radar

secs ellapsedas radar

nth target