Variational Bayesian Inference for Linear State Space Models with Multivariate Laplace Distributions

This paper presents a robust variational Bayesian (VB) method for identifying linear state space models (LSSM) with non-Gaussian observational noise. Appropriate prior information is introduced for the unknown parameters, and the posterior distribution is approximated within the variational Bayesian framework. An augmented LSSM with deterministic parameters is utilized to estimate the hidden states of the LSSM with random parameters. Additionally, data anomalies, including outliers, are considered, and the effectiveness of the proposed method is validated through a numerical example.