Estimating parameters of sinusoids from noisy data using bayesian inference with simulated annealing

Abstract

In this paper, we consider Bayesian analysis proposed by Bretthorst for estimating parameters of the corrupted signals and incorporate it with a simulated annealing algorithm to obtain a global maximum of the posterior probability density of the parameters. Thus, this analysis offers different approach to find parameter values through a directed, but random, search of the parameter space. For this purpose, we developed a Mathematica code of this Bayesian approach and used it for recovering sinusoids corrupted by random noise. The simulation results support the effectiveness of the method.