On variational Bayes for identification of nonlinear state-space models with linearly dependent unknown parameters

Abstract

In this paper, we propose a parameter estimation method for nonlinear state-space models based on the variational Bayes. We show that the variational posterior distribution of the hidden states corresponds to a posterior distribution of the states of an augmented nonlinear state-space model. From this, we can obtain the variational posterior distribution of the hidden states by implementing a variety of existing smoothing algorithms. Moreover, we assess with a simulation the predictive power of the proposed algorithm and the reliability of the estimated parameter.