New Methods for MLE of Toeplitz Structured Covariance Matrices with Applications to RADAR Problems

Abstract: This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization of the equivalent problem. Both the strategies are based on the Majorization Minimization (MM) framework and hence enjoy nice properties such as monotonicity and ensured convergence to a stationary point of the equivalent MLE problem. The proposed algorithms are also extended to deal with MLE of other related covariance structures, namely, the banded Toeplitz, Toeplitz-block-Toeplitz, low rank Toeplitz structure plus a scalar matrix (accounting for white noise), and finally Toeplitz matrices satisfying a condition number constraint. Through numerical simulations, it is shown that new methods provide satisfactory performance levels in terms of both mean square estimation error and signal-to-interference-plus-noise ratio.