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This work considers Maximum Likelihood Estimation (MLE) of a Toeplitzstructured covariance matrix. In this regard, an equivalent reformulation ofthe MLE problem is introduced and two iterative algorithms are proposed for theoptimization of the equivalent problem. Both the strategies are based on theMajorization Minimization (MM) framework and hence enjoy nice properties suchas monotonicity and ensured convergence to a stationary point of the equivalentMLE problem. The proposed algorithms are also extended to deal with MLE ofother 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 acondition number constraint. Through numerical simulations, it is shown thatnew methods provide satisfactory performance levels in terms of both meansquare estimation error and signal-to-interference-plus-noise ratio.

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