Efficient stochastic maximum a posteriori estimation for harmonic signals

In this paper, we address the problems of ML (Maximum Likelihood) parameter estimation and model order selection for harmonic signals using classical criteria. Solving these problems requires the maximization of complex multimodal functions. These optimization problems are shown as being equivalent to the estimation of joint and marginal maximum a posteriori (MAP) estimates under given Bayesian models. Efficient stochastic algorithms based on non-homogeneous Markov chain Monte Carlo methods are presented to solve these problems and their convergence is established. Computer simulations demonstrate the efficiency of these algorithms.