Optimum Passive Beamforming in Relation to Active-Passive Data Fusion

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Presentation transcript:

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 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 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 Most common form is Minimum Variance Distortionless Response (MVDR) beamformer (aka Capon beamformer) [Capon, 1969] Given cross-spectral matrix Rx and 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] 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] 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] 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

Questions?