Two efficient Kalman filter algorithms for measurement packet dropping systems under maximum correntropy criterion

This paper investigates the state estimation problem for the linear discrete-time system with both packet dropping and non-Gaussian noise. Specifically, maximum correntropy Kalman filter algorithms are derived under different packet dropping models. Both the cases with and without using the statistical characteristic of the packet dropping variable are discussed. For the state estimation using only the real-time known characteristic of the packet dropping variable, the maximum correntropy Kalman filter with packet dropping can be successfully derived by designing a coefficient matrix. Furthermore, it can degenerate to the Kalman filter with packet dropping when the kernel bandwidth tends to infinity. On the other hand, for the state estimation using both the real-time known and statistical characteristics of the packet dropping variable, the maximum correntropy suboptimal Kalman filter with packet dropping cannot achieve the degeneration due to the presence of mathematical expectation, but it still achieves an excellent estimation performance. Simulation results consistently indicate that the filter algorithm based on maximum correntropy criterion outperforms the one based on minimum mean square error criterion when the measurement packet dropping system is disturbed by non-Gaussian noise. This paper presents a novel idea and solution to the state estimation problem for the measurement packet dropping system with non-Gaussian noise.