Journal of Electrical and Computational Innovations(JECI)

WR Systems, Ltd., Fairfax, USA

Publications

• Research Article   
  Properties of the Toeplitz Covariance Matrix Numerical Likelihood Ratio Maximization: Convex-Like Optimization Behavior
  Author(s): Yuri Abramovich*, Victor Abramovich and Tanit Pongsiri
  
  Abstract In this paper, we continue to investigate the well-known problem of the numerical likelihood maximization of the positive definite Toeplitz covariance matrix of complex Gaussian data. In our recent papers, we demonstrated that direct LR maximization, using Vandermonde parameterization, applied to initial Toeplitz matrices distant from the true Toeplitz covariance matrix, predominantly yields an inappropriate solution with negative eigenvalues [1,2]. Yet in all cases where the MATLAB fmincon routine converges to a positive definite Toeplitz matrix, the process converges to the same solution as if initiated by a true Toeplitz covariance matrix, irrespective of the initialization one. We also demonstrated that the optimized likelihood ratio (LR) exceeded that of the true Toeplitz covariance matrix and that, by starting fmincon iterations from the true covariance matrix �?�?ï.. Read More»
  

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