initial inputs adaptive front end signal processing
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Initial Inputs: Adaptive Front-End Signal Processing. W. Clem Karl Boston University. Long term aims. Methods robust to sensor configuration & sparsity of data “Submissive sensing” matched to backend management Works with wide range of configurations

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Presentation Transcript
long term aims
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

new bu signal processing
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

multistatic radar
Multistatic Radar
  • Sensing Model
  • Different choices for K(t), rx, tx possible

Reflectivity

Tx frequency

Tx/Rx geometry

Transmit Freq

B = bistatic angle

uB = bistatic bisector

wtx = transmitted frequency

From Wicks et al

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

many sensing options
Many Sensing Options…

Case 2: Stationary Tx, Moving Rx, UNB waveform

Case 1: Stationary Tx/Rx, Wideband waveform

Case 3: Stationary Tx, Moving Rx, Wideband waveform

Case 4: Monostatic Tx/Rx, Wideband waveform

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

multistatic comments
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

reconstruction formulation
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

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

example unb multistatic sar
Example: UNB Multistatic SAR
  • UNB (single frequency)
  • Ntx=10, Nrx = 55 Sparse coverage
  • Uniform circular coverage
  • Fourier support (resolution) µ UNB frequency

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

results
Results

FBP, cw = 2MHz, SNR = 15dB

FBP, cw = 4MHz, SNR = 15dB

Extension of FBP

Truth

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

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

LS-L1

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

understanding performance
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 µ (mutual coherence)2

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

initial work
Initial work
  • Compare different monostatic and UNB multistatic radar configurations
  • Mutual coherence
  • Measure of diversity of sensing probes

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

different sampling strategies
Different Sampling Strategies

Monostatic

Multistatic

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

results1
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

results cont
Results (Cont)
  • Example reconstruction for Ntx/Nq=10 case
  • Reconstructions confirm prediction

Ground Truth

Monostatic

Multistatic

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

dynamic scenes moving targets
Dynamic Scenes: Moving Targets
  • Augment model to include velocity
  • Discrete form of forward model:

Static targets at a reference time

Phase shift due to motion

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

overcomplete dictionary approach
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!

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

overcomplete problem solution
Overcomplete Problem Solution
  • Idea: sparest solution should automatically identify correct velocity and scattering
  • Solution via custom made large-scale interior point method

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

example 1
Example #1:
  • Multistatic configuration with Ntx= 10, Nrx = 55
  • Dictionary does not contain true velocities

Truth

CW = 4MHz, OD

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

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