Title :
Progress in structured covariance estimation
Author :
Fuhrmann, Daniel R.
Author_Institution :
Dept. of Electr. Eng., Washington Univ., St. Louis, MO, USA
Abstract :
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
Keywords :
estimation theory; matrix algebra; probability; spectral analysis; Toeplitz matrices; algorithm expectation-maximization; array processing; matrices; maximum-likelihood estimates; nonnegative definite circulant extension; observation vector; positive definite solution; probability; spectrum estimation; structured covariance estimation; Array signal processing; Covariance matrix; Direction of arrival estimation; Eigenvalues and eigenfunctions; Laboratories; Matrix decomposition; Maximum likelihood estimation; Signal processing; Spectral analysis; Symmetric matrices;
Conference_Titel :
Spectrum Estimation and Modeling, 1988., Fourth Annual ASSP Workshop on
Conference_Location :
Minneapolis, MN
DOI :
10.1109/SPECT.1988.206182