Alternating Maximization and the EM Algorithm in Maximum-Likelihood Direction Finding

Abstract

The classic expectation-maximization (EM) algorithm in maximum-likelihood direction finding updates the complete-data sufficient statistics by finding their conditional expectations. Besides, from the perspective of alternating maximization (AM) these sufficient statistics can also be updated by maximizing the complete-data log-likelihood function with respect to only the complete data, based on which both deterministic and stochastic signal models are considered. Theoretical analysis indicates that the proposed AM algorithm is equivalent to the EM algorithm for the deterministic signal model while outperforming the EM algorithm for the stochastic signal model. On this foundation, a sequential AM (SAM) algorithm and two iterative weighting schemes are proposed to improve the convergence of the AM algorithm. Numerical results show that the SAM algorithm yields faster convergence and the two iterative weighting schemes can be used to avoid the convergence of the EM and AM algorithms to an unwanted limit point efficiently.