State estimation under non-Gaussian Levy and time-correlated additive sensor noises: A modified Tobit Kalman filtering approach

The Tobit Kalman filter (TKF) is a powerful tool in solving the state estimation problem for linear systems with censored measurements. This paper is concerned with the Tobit Kalman filtering problem for discrete time-varying systems subject to non-Gaussian Levy and time-correlated additive measurement noises. By referencing to the measurement differencing method, the time-correlation of the measurement noises is transformed into the cross-correlation between the equivalent measurement noise and the process noise. Then, by resorting to the Levy-Ito theorem, the non-Gaussian Levy measurement noises are transformed into equivalent Gaussian noises with unknown covariances. Based on the transformed Gaussian measurement noises, a modified recursive TKF is designed where the unknown noise covariances are carefully calculated. Simulation results are provided to illustrate the effectiveness of the proposed filter. (C) 2018 Elsevier B.V. All rights reserved.