initial inputs: adaptive front-end signal processing
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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
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