A multiply constrained minimum variance approach to multiple source parameter estimation

An extension of the minimum variance (MV) method of Capon for spatial source parameter estimation using sensor arrays is described. The method is advantageous in applications where asymptotically unbiased estimates of the powers and cross correlations associated with a subset of the entire set of signal arrivals are required, in that direction-of-arrival estimates for signals outside the subset are not required. The method is shown to arise out of the imposition of multiple constraints, one for each signal in the group of interest, in the development of the Capon estimator using an estimate of the signal-only (no noise) correlation matrix of sensor outputs. Success of the method is contingent on the condition that the signals in the subset of interest be uncorrelated with signals outside the subset. The algorithm for extracting the signal parameters of interest from the overall correlation matrix requires an estimate of the noise correlation matrix and direction-of-arrival estimates for members of the subset. This information may be obtained via the MUSIC algorithm.