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

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. (C) 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Harbin University of Science and Technology