On System Identification of Nonlinear State-Space Models Based on Variational Bayes: Multimodal Distribution Case

In this paper, we propose a parameter estimation method for nonlinear state-space models based on the variational Bayes. It is shown that the variational posterior distribution of the hidden states is equivalent the probability estimated by a nonlinear smoother of an augmented nonlinear state-space model. This enables us to obtain the variational posterior distribution of the hidden states by implementing a variety of existing nonlinear filtering and smoothing algorithms. By employing a Gaussian mixture distribution as a candidate probability density function of the hidden states, we propose an algorithm to compute multimodal posterior distributions which are not able to be handled by the existing results.