Statistical modeling, classification, and sensor management

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Statistical modeling, classification, and sensor
management
DARPA-MURI Review 2003

• Alfred Hero
• Univ. Michigan
• Ann Arbor

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Target Search Scenario
HighRes Spot Scan
LowRes Spot Scan
Strip Scan
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Sensor Deployment Architecture
Our Research themes
Sequential Sensor Management
Image Reconstruction
Adaptive Detection
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Research Loci

• Image modeling and reconstruction
• Markov random field (MRF) polarimetric models
  (HoryBlatt)
• 3D Imaging with uncalibrated sensor nets
  (RangarajanPatwari)
• Adaptive detection and classification
• Pattern matching and modeling (Costa)
• Distributed detection and classification
  (BlattPatwari)
• Sequential sensor management
• Myopic information-driven approaches (Kreucher)
• Non-myopic approaches (KruecherBlatt)
• Common theme adaptive robust non-parametric
  methods

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Detection Target or Clutter Alone?
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Detection Target or Clutter Alone?
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Target Returns Not Additive or Gaussian
SNR0dB
SNR6dB

• 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 (azimuth35,45,55,
  elev180)

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Polarimetric Field Modeling and Reconstruction
h-pol. incidence
v-pol. incidence

• Field Distribution On FDTD Box (2 GHz)

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MRF empirical histogram
Conditional Markov transition histogram
estimated from training data
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Causal MRF Field Synthesis
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Example K-NN MRF Extrapolation
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Non-parametric MRF density estimator

• General penalized MRF transition density estimate
  
• y is observed data
• parameter b enforces smoothness
• function g(f) captures data-fidelity
• g(f)f2 standard L2 quadratic regularization
• g(f)f L1 regularization for denoising
• w(x) smoothing within and across neighborhoods

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Cartoon illustration of density estimator
K-Nearest Neighbors Estimator
Penalized MRF transition Density Estimator
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Visual Validation of MRF Model
g(f)f
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MRF Transition Density Comparisons
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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

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A Planar Sample and its Euclidean MST
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Convergence of Euclidean MST
Beardwood, Halton, Hammersley Theorem
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Pattern Matching
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MST Estimator of a-Jensen Affinity
Two well separated Classes
Two overlapping Classes
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MST Estimator of Friedman-Rafsky Affinity
Two well separated Classes
Two overlapping Classes
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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
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Target-Image Manifold
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2D manifold
Embedding
Sampling distribution
Sampling
A statistical sample
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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)

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Illustration for 3 land Vehicles
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loglogLinear fit to asymptote
LS-Soln d13 H120(bits)_
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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?

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Flat Sensor Aggregation Architecture
Distributed Estimation and Detection
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Distributed M- Estimation
Ambiguity function for Cauchy distributed points
on a manifold
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A slice of ambiguity function
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Key Theoretical Result

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

Ref BlattHero2003
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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.
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M-estimator Aggregation Algorithm
Sample Covariance Analysis
Estimation of Gaussian Mixture Parameters (EM
)
Aggregation To Final Estimate
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Illustration
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

Local maximum
Global maximum
Ambiguity function.
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Local/Global Maxima Discrimination Algorithm
Bad estimates
Bad estimates
Inverse FIM
Good estimates
Empirical covariance
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Addition of other Discriminants
Value-added due to local acquisition and
transmission of likelihood values
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Hierarchical Sensor Aggregation Architecture
Distributed Estimation and Detection
Sensor 6
Sensor 5
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Detection Flat vs Hierarchical Architecture

• Flat Rago, Willett, et al
• Hierarchical, w/ and w/o Feedback
• Each sensor is limited with identical r
• At low PF, Hierarchical outperforms Flat

Optimal 7-Sensor
r 0.30
r 0.10
Legend
Flat
r 0.03
Hier. w/o Feedback
Hier. w/ Feedback
Optimal 1-Sensor
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Sequential Adaptive Sensor Management

• Sequential only one sensor deployed at a time
• Adaptive next sensor selection based on present
  and past measurements
• Multi-modality sensor modes can be switched at
  each time
• Detection/Classification/Tracking task is to
  minimize decision error
• Centralized decisionmaking sensor has access to
  entire set of previous measurements

Single-target state vector
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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 (BlattKreucher)
• MDP value function approximations and rollout
  methods
• Bayesian path averaging
• Reinforcement feedback and learning

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Sensor scheduling objective function

• Prospective value of deploying sensor s at time t

Sensor agility
Prediction
Retrospective value of deploying sensor s
Available measurements at time t-1
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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 ED(s,t)Z
• Computation complexity
• Robustness to model mismatch
• Decisionmaking relevance

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Value Function Alpha Divergence

• Properties of Renyi divergence
• Simpler and more stably implementable than KL
  (KreucheretalTSP03)
• Parameter alpha can be adapted to non-Gaussian
  posteriors
• More robust to mis-specified models than KL
  (KreucheretalTSP03)
• Related directly to decision error probability
  via Sanov (HeroetalSPM02)
• Information theoretic interpretation

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Relevance of alpha-D to Decision Error

• Consider testing hypotheses
• Sanovs theorem optimal decision rule has error
• Implication nearly-optimal decision rule for H1
  is
• if can generate good estimate of alpha-D

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Multi-Target Bayesian Filtering

• Joint multiple target posterior density (JMPD)
  jointly represents all target states (Kastela)
• Update eqns must generally be approximated

Model Update (Prediction using prior kinematic
model)
Measurement Update (Bayes Rule)
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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
time t-1
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Particle Filtering Illustration

• Initialize simulate random samples (particles)
  from proposal density

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Particle Filtering Illustration

• Model Update
• Propose new particles from existing particles
  based on drawing samples from the importance
  density

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Particle Filtering Illustration

• Measurement Update Reweight particles density
  according to
• Resample the particles if necessary

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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 updating
CP updating
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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
  (Pf0.1)
• No sensor management

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Tracking Simulated Target Motion w/o SM
Sensor makes measurements on a grid The sensor is
characterized by a probability of detection and
a probability of false alarm.
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Real Target Motion
Ten real targets Motion taken from recorded GPS
measurements During a battle simulation exercise
at NTC.
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Real Target Motion
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Multiple Model for Real Target Motion

• Target state vector
• Three different models
• Target is moving
• Target is stopped
• Target is accelerating

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Multiple Model for Real Target Motion

• Model switching transition matrix

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Tracking Real Multitarget Motion w/o SM
Staging area
Ten real targets Motion taken from recorded GPS
measurements During a battle simulation exercise
at NTC.
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Quantitative Results Adaptive Partitions
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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-managed50 dwells per
  second

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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.

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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 a.
• 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 a.

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Choice of Alpha Mismatched Models
Snapshot of information map for ten target GPS
simulation
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Choice of Alpha Mismatched Models

• Under target kinematic model mismatch using a 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 a.5

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Multimode Radar Mode and Dwell Point Selection

• 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)

• MTI Mode
• Each detection cells is 100m x 100m
• Measures strips 1x25 cells long
• Pd 0.9, Pfa .001
• Detects targets with velocity gt 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

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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

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Non-Myopic Search Tree
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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
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Myopic Target lost 22 of the time
Non-myopic Target lost 11 of the time
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• 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.

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Foci for 2nd Year

• Non-parametric polarimetric backscatter modeling
  for multistatic target detection
• Target and clutter model reduction and pattern
  matching
• Adaptive non-myopic sensor scheduling and
  management

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Personnel on A. Heros 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

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Personnel on A. Heros 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

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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

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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.

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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.

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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.

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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. ThelenN. 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

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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)