Numerical Techniques for the Maximum Likelihood Toeplitz Covariance Matrix Estimation: Part II—Hermitian Toeplitz Matrices

Independence of the normalized likelihood functions (likelihood ratios, LR) with the argument being the true Toeplitz covariance matrix creates a statistical lower bound for the optimized maximum likelihood, since in this case the pdf does not depend on this true covariance matrix. Analysis of the likelihood ratio maximization results using the MATLAB fmincon routine demonstrated that for a large enough sample volume, the optimized solution is either unacceptable, mainly due to the negative eigenvalues in the solution, or meets the global LR maximum criteria. The method proposed to modify the initialization of the fmincon routine to achieve the global LR maximum in every trial.