Variational robust filter for a class of stochastic systems with false and missing measurements

Abstract

This paper investigates the state estimation problem for a class of stochastic system under randomly occurring measurement anomalies, and the Kalman filter is combined with variational Bayesian (VB) method to cope with the simultaneous occurrence of false and missing measurements. First, to unify the false and missing measurements into a modified measurement model, a categorical distributed vector is employed to establish a new measurement model including randomly occurring measurement anomalies. Next, the conjugate prior distributions for the unknown measurement anomaly parameters are determined, in which the probabilities of the measurement anomalies are modeled as Dirichlet distribution and the false measurement is described by Gaussian-inverse-Wishart distribution. Then, based on the constructed measurement model and VB inference, a variational robust KF is designed to simultaneously estimate the state and measurement anomaly parameters. Finally, the estimation performance of the proposed filter is illustrated through a simulation example.