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

Abstract 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.

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