Adaptive Fixed-Lag Smoothing Algorithms Based on the Variational Bayesian Method

Abstract

In this article, we address the adaptive fixed-lag smoothing (FLS) problem in the presence of unknown and slowly time-varying measurement noise covariance matrix (MNCM). Based on the variational Bayesian (VB) method, we use the VB inference to jointly estimate the system state and the unknown MNCM. According to different implementation methods, we propose two adaptive FLS algorithms: One is based on the augmented state-space models and another one is based on a sliding Rauch-Tung-Striebel smoothing. In addition, the evidence lower bound and the convergence criterion of the above two algorithms are given. The proposed adaptive algorithms are evaluated by a simulation example.