Maximum Likelihood Structured Covariance Matrix Estimation and connections to SBL: A Path to Gridless DoA Estimation
Rohan R. Pote, Bhaskar D. Rao · 2022
In this paper, we revisit the framework for maximum likelihood estimation (MLE) as applied to parametric models with an aim to estimate the parameter of interest in a gridless manner. The approach has inherent connections to the sparse Bayesian learning (SBL) formulation, and naturally leads to the problem of structured matrix recovery (SMR). We therefore pose the parameter estimation problem as a SMR problem, and recover the parameter of interest by appealing to the Carathéodory-Fejér result on decomposition of positive semi-definite Toeplitz matrices. We propose an iterative algorithm to estimate the structured covariance matrix; each iteration solves a semi-definite program. We numerically compare the performance with other gridless schemes in literature and demonstrate the superior performance of the proposed technique.