Optimum Passive Beamforming in Relation to Active-Passive Data Fusion

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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

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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/fac
tsheets/22_UDF_e.shtml
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Passive Beamforming

• A form of spatial filtering
• Narrowband delay-and-sum beamformer
• Planar wavefront, linear array
• Suppose 2N1 elements
• Sampled array output xn a(?)sn vn
• Steering vector w(?)
• Beamformer output yn wH(?)xn
• Direction of arrival estimation precision
  limited by length of array

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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(?)
• Minimize wRxw subject to wa(?)1
• Direction of arrival estimation much more
  precise, but very sensitive to mismatch

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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

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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(?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

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Robust Capon Beamformer Li, et al, 2003

• A natural extension of the Capon beamformer
• Directly addresses steering vector uncertainty by
  assuming an ellipsoidal uncertainty
  setminimize aR-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

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Questions?