Robust Kalman Filter with Fading Factor Under State Transition Model Mismatch and Outliers Interference

Abstract

In practical applications, due to the complexity of the system, the process equation of the state space model is difficult to match the actual state transition model. In addition, the unreliability of the sensor will cause the measurement to be accompanied by outliers. In this paper, a novel robust Kalman filter with fading factor is proposed to improve the accuracy of state estimation for the linear system under state transition model mismatch and outliers interference. Firstly, in order to modify the state transition model, this filter introduces a fading factor which is modelled as the inverse gamma distribution to update the state prediction covariance. Then, aiming at the phenomenon that the measurement noise does not follow the Gaussian distribution and has nonzero mean characteristics due to outliers interference, the measurement noise is modelled as the generalized hyperbolic skew Student’s t distribution. Finally, the state estimation is realized by using the variational Bayesian. The simulation results show that the estimation accuracy of the proposed filter is higher than that of the Kalman filter and the strong tracking filter.