Hidden Markov Modeling of Noise Periodograms Using Rayleigh Mixture Models

Abstract

In this paper, we derive an Expectation-Maximization algorithm for hidden Markov models (HMMs) with a multivariate Rayleigh mixture model (RMM) in each state. We compare the use of multivariate RMMs to multivariate Gaussian mixture models in the general case where the HMM is a dynamic model and for the special case where it has a single state and reduces to a static model. We evaluate the proposed method when used to model probability density of periodpgrams from real-life noise sources and white Gaussian noise, which we include for reference purposes.