Modeling chaotic systems with hidden Markov models

The problem of modeling chaotic nonlinear dynamical systems using hidden Markov models is considered. A hidden Markov model for a class of chaotic systems is developed from noise-free observations of the output of that system. A combination of vector quantization and the Baum-Welch algorithm is used for training. The importance of this combined iterative approach is demonstrated. The model is then used for signal separation and signal detection problems. The difference between maximum likelihood signal estimation and maximum a posteriori signal estimation using a hidden Markov model is illustrated for a nonlinear dynamical system