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Optimum Passive Beamforming in Relation to Active-Passive Data Fusion. Bryan A. Yocom Literature Survey Report EE381K-14 – MDDSP The University of Texas at Austin March 04, 2008. What is Data Fusion?. Combining information from multiple sensors to better perform signal processing

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optimum passive beamforming in relation to active passive data fusion

Optimum Passive Beamforming in Relation to Active-Passive Data Fusion

Bryan A. Yocom

Literature Survey Report

EE381K-14 – MDDSP

The University of Texas at Austin

March 04, 2008

what is data fusion
What is Data Fusion?
  • Combining information from multiple sensors to better perform signal processing
  • Active-Passive Data Fusion:
    • Active Sonar – good range estimates
    • Passive Sonar – good bearing estimates

Image from http://www.atlantic.drdc-rddc.gc.ca/factsheets/22_UDF_e.shtml

passive beamforming
Passive Beamforming
  • A form of spatial filtering
  • Narrowband delay-and-sum beamformer
    • Planar wavefront, linear array
    • Suppose 2N+1 elements
    • Sampled array output: xn = a(θ)sn + vn
    • Steering vector: w(θ)
    • Beamformer output: yn = wH(θ)xn
    • Direction of arrival estimation: precision limited by length of array
adaptive beamforming
Adaptive Beamforming
  • Most common form is Minimum Variance Distortionless Response (MVDR) beamformer (aka Capon beamformer) [Capon, 1969]
  • Given cross-spectral matrix Rxand replica vector a(θ)
  • Minimize w*Rxw subject to w*a(θ)=1:
  • Direction of arrival estimation: much more precise, but very sensitive to mismatch
cued beams yudichak et al 2007
Cued Beams [Yudichak, et al, 2007]
  • Need to account for sensitivity of adaptive beamforming (ABF)
  • Steer (adaptive) beams more densely in areas where the prior probability density function (PDF) is large
    • Cued beams are steered within a certain number of standard deviations from the mean of a Gaussian prior PDF
  • Use the beamformer output as a likelihood function
  • Use Bayes’ rule to generate a posterior PDF
  • Improvements:
    • Need to fully cover bearing
    • The use of the beamformer output as a likelihood function is ad hoc
bayesian beamformer bell et al 2000
Bayesian Beamformer [Bell, et al, 2000]
  • Also assumes a priori PDF
  • Beamformer is a linear combination of adaptive MVDR beamformers weighted by the posterior probability density function, p(θ|X)
  • Computationally efficient, O(MVDR)
  • The likelihood function they derive assumes Gaussian random processes and is therefore less ad hoc then using the beamformer output
  • Difficult to extend their likelihood function to other classes of beamformers
robust capon beamformer li et al 2003
Robust Capon Beamformer [Li, et al, 2003]
  • A natural extension of the Capon beamformer
  • Directly addresses steering vector uncertainty by assuming an ellipsoidal uncertainty set:minimize a*R-1a subject to (a-a0)*C-1(a-a0) ≤ 1
  • Computationally efficient, O(MVDR)
  • When used with cued beams its use could guarantee that bearing is fully covered