System Identification of Nonlinear State-Space Models with Linearly Dependent Unknown Parameters Based on Variational Bayes

Abstract

: In this paper, we propose a parameter estimation method for nonlinear state-space models based on the variational Bayes. It is proved that the variational posterior distribution of the hidden states is equivalent to a posterior distribution of the states of an augmented nonlinear state-space model. This enables us to estimate the probability of the hidden states by implementing a variety of existing filtering and smoothing algorithms. Using this technique, a system identification algorithm for nonlinear systems based on variational Bayes and nonlinear smoothers is proposed. It is expected to be more accurate than the existing results since it does not employ any additional approximations in executing the variational Bayes inference. Furthermore, a numerical example demonstrates the e ff ectiveness of the proposed method.