MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 1

Initial Inputs:Adaptive Front-End Signal Processing

W. Clem KarlBoston University

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 2

Long term aims

Methods robust to sensor configuration & sparsity of data

“Submissive sensing” matched to backend management Works with wide range of configurations No “my way or the highway” signal processing

E.g. Circular SAR, Multistatic SAR, spatial-spectral diversity Understanding of performance

Presensing impact of sensing choices for management (e.g. frequency versus geometric diversity)

Understanding performance consequences of sensing choices Postsensing estimates and uncertainties for fusion

Methods for complex scenes, non-conventional uses, and greedy decision makers expect more, get more

Target motion 3D scene structure Anisotropic behavior

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 3

New BU signal processing

Multistatic imaging I: Physical modeling Sparsity-based reconstruction

Multistatic imaging II: Understanding performance Mutual coherence as predictor

Imaging dynamic scenes Overcomplete dictionary formulation Recursive assimilation of data

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 4

Multistatic Radar

Sensing Model

Different choices for K(t), rx, tx possible

B = bistatic angleuB = bistatic bisector

tx = transmitted frequency

Btx u

B

c

2cos

2

Tx frequency Tx/Rx geometryReflectivity

From Wicks et al

Transmit Freq

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 5

Many Sensing Options…

Case 1: Stationary Tx/Rx, Wideband waveform

Case 3: Stationary Tx, Moving Rx, Wideband waveform

Case 2: Stationary Tx, Moving Rx, UNB waveform

Case 4: Monostatic Tx/Rx, Wideband waveform

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 6

Multistatic Comments

Rich framework to study: sensor tradeoffs resource optimization waveform/sensor planning

Waveform diversity: UNB wideband Many transmitters few transmitters Etc…

Need new tools for processing non-conventional datasets

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 7

Reconstruction Formulation

Sparsity-based L2-L1 reconstruction using extension of previous SAR work

Leads to a second order cone program, effectively solved by an interior point method

11

22 ||||||||minargˆ fHfyf

f

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 8

Example: UNB Multistatic SAR

UNB (single frequency) Ntx=10, Nrx = 55 Sparse coverage Uniform circular coverage Fourier support (resolution)

UNB frequencytx

tx

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 9

Results

LS-L1, cw = 4MHz, SNR = 15dBLS-L1, cw = 2MHz, SNR = 15dB

FBP, cw = 4MHz, SNR = 15dBFBP, cw = 2MHz, SNR = 15dB Extension of FBPLS-L1

Truth

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 10

Understanding Performance

Want to understand performance consequences of different sensor configurations

Guidance for sensor management Compressed sensing theory says

reconstruction performance related to mutual coherence of configurations

# of measurements needed to reconstruct sparse scene (mutual coherence)2

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 11

Initial work

Compare different monostatic and UNB multistatic radar configurations

Mutual coherence

Measure of diversity of sensing probes

||||||||max][

ji

jTi

aa

aaA

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 12

Different Sampling StrategiesM

onos

tati

c M

ult

ista

tic

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 13

Results

Mutual coherence lower for multistatic configuration as number of probes are reduced

Monostatic Multistatic

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 14

Results (Cont)

Ground Truth Monostatic Multistatic

Example reconstruction for Ntx/N=10 case

Reconstructions confirm prediction

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 15

Dynamic Scenes: Moving Targets

Augment model to include velocity

Discrete form of forward model:

Lr

rvjrsstjKttxrx dreerfty itxirxitxirxref

ii

||

))((]))[((

,,)()(

Static targets at a reference time Phase shift due to motion

p

tppp nfvAy ref

Pixels

)(

A depends on unknown scatterer velocity v in pixel p, so nonlinear problem!

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 16

Overcomplete Dictionary Approach

Modify forward operator to include all velocity hypotheses

Pixel reflectively becomes a vector

New overcomplete observation model

A is now fully specified, so observation is linear…but solution f must be very sparse

We know how to do this!

],...,[)~

()]~(),...,~([)~

( 11 PNppp VvAvAV ΑΑAΑ

TPp

tpreff ],...,[ 1 ffff

nVnVyp

pp fAfA )~

()~

( Pixels

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 17

Overcomplete Problem Solution

Idea: sparest solution should automatically identify correct velocity and scattering

Solution via custom made large-scale interior point method

11||||||)

~(||minargˆ ffAf

f Vy

b

pv

tp

p

reff f̂maxˆ~

MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation 18

Example #1:

Multistatic configuration with Ntx= 10, Nrx = 55

Dictionary does not contain true velocitiesCW = 4MHz, ODTruth