Adaptive radar sensing strategies

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Adaptive radar sensing strategies

• Hero
• Univ. of Michigan Ann Arbor

2nd Year Review, AFRL,11/08

• AFOSR MURI

Integrated fusion, performance prediction, and
sensor management for ATE (PI R. Moses)?
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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

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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

Agile Multi-Static Radar system illustration
This talk
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Part II Sensor Management

• II.A Performance prediction multitarget
  multiplatform multifunction radar systems
• II.B Adaptive wide area search
  sparsity-constrained multiresolution radar search

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II.A Performance prediction multitarget
multiplatform multifunction radar systems
targets
targets
timet?
timet
High confidence target regions
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Target track update
timet?
timet
Track update
High confidence target regions
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Wide area search
timet?
timet
Wide area search
High confidence target regions
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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)?

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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
  Wassermanetal2006 for multi-queueing systems.

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Uncertainty management and PLQ
Policy is analogous to optimal processor
allocation in heterogeneous multiple
queueing systems (Wassermanetal2006)
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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

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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

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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

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Illustration 24 Swerling II targets

• C-band radar (4Mhz)?
• PRI1ms (150km)?
• Range res150m
• pulses10
• (Pf,Pd) (0.000001, 0.9999)?
• Target speed300m/s
• Speed std error30m/s
• Direction std error18deg

Load curve lies above diagonal Max number of
trackable targets is 23

• System is underprovisioned
• Stable track maintenance impossible

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Illustration 12 Swerling II targets

• C-band radar (4Mhz)?
• PRI1ms (150km)?
• Range res150m
• pulses10
• (Pf,Pd) (0.000001, 0.9999)?
• Target speed300m/s
• Speed std error30m/s
• Direction std error18deg

• 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

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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.

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II.B. Adaptive wide area search
Stage 2 Refined search
Stage 1 Wide area search
Stage 4 Refined search
Stage 3 Refined search
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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

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Recall optimal strategy
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Recall comparisons
Wide area SAR acquisition
Optimal two step SAR acquisition
Overall energy allocated is identical in both
cases
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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)?

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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.

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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.

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M-ARAP for MTI tracking radar
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Correct detection probability vs false discovery
rate
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Optimal energy allocation
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Discussion

• Take home message can attain 7dB MSE reduction
  at SNR of 5 dB using only NQ/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 DorfmanAnnMathStat1943)?
• 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)?

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Part III High level fusion

• III.A Distributed decomposable PCA
• III.B Hyperspectral imaging and unmixing
• Common theme application of hierarchical
  graphical models

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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(N3)?
• Unreliable/unimplementable for high dimensional
  data
• Ill-suited for distributed implementation, e.g.,
  in sensor networks

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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 yUTX that have maximum or minimum
  variance

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DPCA formulation

• Precision matrix KR-1
• For decomposable model K has structure

• General representation

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1 dimensional DPCA

• PCA for minimum eigenvector/eigenvalue solves
• Key observation

• This constraint is equivalent to
• where

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Extension to k-dimensional DPCA

• k-dimensional PCA solves sequence of eigenvalue
  problems

• Dual optimization

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k-dimensional DPCA (ctd)?

• Dual maximization splits into local minimization
  with message passing

• Message passing

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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

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DPCA min-eigenvalue tracker
Iteration 1
Iteration 2
Iteration 3
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DPCA network anomaly detection
Multiple measurement sites (Abilene)?
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DPCA anomaly detection
PCA (centralized)? DPCA (E-W decomp)? DPCA
(E-W-S decomp)? DPCA (Random decomp)?
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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.

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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

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Sample endmember spectra

• Concrete Redbrick

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Key observation

• Mixing coefficients supported on R-1 dimensional
  simplex

• This suggests a natural dimensionality reduction
  approach to estimation of mixing coefficient
  matrix A

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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

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Moffet field hyperspectral image
AVIRIS image
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Unmixing results
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Unmixing results
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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

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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

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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)?

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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.