Recursive EM algorithm with adaptive step size

We study the recursive EM algorithm with adaptive step size (REMA) in this work. Recursive EM is a stochastic approximation procedure for finding the maximum likelihood (ML) estimate. Favorite features of recursive EM include strong consistency, asymptotic normality and simple implementation. However, the convergence rate associated with recursive EM is not optimal. To obtain a good convergence rate without losing the advantage of simple implementation, we propose an adaptive procedure to determine the step size at each recursion. More importantly, this approach provides a guideline for automatic design of the step size. Feasibility of REMA in practical application is demonstrated by its application to the direction finding problem. Numerical results show that the proposed method leads to satisfying convergence behavior in various scenarios.