Variational Identification of Linearly Parameterized Nonlinear State-Space Systems

A variational Bayesian (VB) approach to the identification of linearly parameterized nonlinear state-space models (LP-NSSMs) is developed in this article. Conjugate priors over the unknown parameters are introduced, and the posterior distributions are approximated under the VB framework. In order to estimate the hidden states of the LP-NSSMs with random parameters, the augmented LP-NSSMs are established such that nonlinear smoothing methods can be applied. An extension to comprehensively tackling data anomalies, such as outliers and missing observations, is also considered to further improve the robustness of the presented method. Finally, a numerical example and the practical benchmarks are adopted to validate the efficacy of the proposed algorithm.