Efficient blind system identification of non-Gaussian autoregressive models with HMM modeling of the excitation

We have previously proposed a blind system identification method that exploits the underlying dynamics of non-Gaussian signals in [Li and Andersen, "Blind identification of Non-Gaussian Autoregressive Models for Efficient Analysis of Speech Signals," Proceedings of the International Conference on Acoustics, Speech and Signal Processing (ICASSP), May 2006, vol. 1, pp. I-1205-1-1208]. The signal model being identified is an autoregressive (AR) model driven by a discrete-state hidden Markov process. An exact expectation-maximization (EM) algorithm was derived for the joint estimation of the AR parameters and the hidden Markov model (HMM) parameters. In this paper, we extend the system model by introducing an additive measurement noise. The identification of the extended system model becomes much more complicated since the system output is now hidden. We propose an exact EM algorithm that incorporates a novel switching Kalman smoother, which obtains nonlinear minimum mean-square error (MMSE) estimates of the system output based on the state information given by the HMM filter. The exact EM algorithms for both models are obtainable only by appropriate constraints in the model design and have better convergence properties than algorithms employing generalized EM algorithm or empirical iterative schemes. The proposed methods also enjoy good data efficiency since only second-order statistics are involved in the computation. The signal models are general and suitable to numerous signals, such as speech and baseband communication signals. This paper describes the two system identification algorithms in an integrated form and provides supplementary results to the noise-free model and new results to the extended model with applications in speech analysis and channel equalization.