Bayesian model selection and estimation of multiple cisoid models

In this paper we address the problem of Bayesian model selection and estimation, of signals that consists of a sum of complex sinusoids (“cisoids”). This kind of signal models are abundant in a wide range of engineering applications, but has usually been treated in a non Bayesian way. The recent development of Markov Chain Monte Carlo methods (MCMC) have opened up the possibility to use Bayesian methods to analyze this kind of signals. Here we present a new combined model selection and estimation method for the case of signals with additive white Gaussian noise and known variance. We demonstrate its use on cisoids closely spaced in frequency, using the Jeffrey prior.