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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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Initial inputs adaptive front end signal processing

Initial Inputs:Adaptive Front-End Signal Processing

W. Clem Karl

Boston University


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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