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Progress in structured covariance estimation

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1 Author(s)
Fuhrmann, D.R. ; Dept. of Electr. Eng., Washington Univ., St. Louis, MO, USA

The author summarizes recent work on the problem of computing maximum-likelihood estimates of structured covariance matrices, as it applies to problems in array processing and spectrum estimation. Two areas are discussed; the existence of positive definite solutions when the number of observations is less than the dimension of the matrix, and the efficient implementation of the algorithm expectation-maximization for estimating Toeplitz matrices. For the Toeplitz case, it is shown that, for a single observation vector, the probability of generating a positive definite solution can be very small, whereas when the Toeplitz covariance matrix is constrained to have a nonnegative definite circulant extension, a positive definite solution will exist with probability

Published in:

Spectrum Estimation and Modeling, 1988., Fourth Annual ASSP Workshop on

Date of Conference:

3-5 Aug 1988