Locally optimal maximum-likelihood completion of a partially specified Toeplitz covariance matrix
Y.L. Abramovich, N.K. Spencer · 2002
The problem of maximum-likelihood (ML) completion of a partially specified Toeplitz covariance matrix is crucial in several applications, such as the detection and estimation of more independent Gaussian sources than sensors (m>M) in minimum-redundancy sparse linear antenna arrays. Given the sufficient statistic in the form of the M-variate direct data covariance matrix R/spl circ/, we describe an algorithm that finds a positive-definite completed M/sub /spl alpha//-variate Toeplitz matrix (M/sub /spl alpha///spl Gt/M) with (locally) maximal likelihood ratio (LR). Simulations demonstrate that a statistically high LR is achieved, compared with L/sub 2/ optimisation.