Constrained Maximum-likelihood Covariance Estimation for Time-varying Sensor Arrays

We examine the problem of maximum likelihood covariance estimation using a sensor array in which the relative positions of individual sensors change over the observation interval The problem is cast as one of estimating a structured covariance matrix sequence. A vector space structure is imposed on such sequences, and within that vector space we define a constraint space given by the intersection of a hyperplane Wi and the space of sequences of nonnegative definite matrices W2. Knowledge of the changing array geometry is used to reduce the dimension of the search space. An extension of the inverse iteration algorithm of Burg et aL is proposed for finding the maximum likelihood solution.