Variational Bayesian Two-Stage Kalman Filter for Systems with Unknown Inputs

Abstract

In this paper, we consider the probabilistic approach in adaptive state estimation for discrete-time linear stochastic time-varying systems with unknown inputs. When lack knowledge of noise, we regard the system state, unknown inputs and time-varying noise parameters as hidden variables with conjugate priors, and use variational Bayes method to side-step the complicated Bayesian inference. The proposed algorithm is based on optimal two-stage Kalman filtering technique that enables us to obtain marginal posterior distributions of hidden variables. A numerical example is provided to demonstrate the state estimation performance of proposed algorithm.