State estimation for systems with unknown inputs based on variational Bayes method

This paper considers a probabilistic approach to state estimation for discrete-time dynamic systems with unknown inputs. A variational Bayes method is proposed to approximate the marginal posterior distributions of system state and input. In order to reduce the computational complexity, the complete-data likelihoods of system from the exponential family are considered, and the conjugate prior distributions are used to quantify the input. Then variational Bayesian learning procedures are derived to optimize the marginal distributions of the state and input. Specifically, recursive filtering for a linear Gaussian system is presented. As applications, state estimation for several important practical systems with unknown inputs is discussed. Related numerical simulations are provided to demonstrate the performance of the proposed method.