Wavelet-based method for nonparametric estimation of HMM's

In this letter, we propose a new algorithm for nonparametric estimation of hidden Markov models (HMM's), The algorithm is based on a "wavelet-shrinkag e" density estimator for the state-conditional probability density function s of the HMM's. It operates in an iterative fashion similar to that of the EM reestimation formulae used for maximum-likelihood estimation of parametr ic HMM's. We apply the resulting algorithm to simple examples and show its convergence. The proposed method is also compared to classical nonparametri c HMM estimation based on quantization of observations ("histograms") and d iscrete HMM's.