Modified Kalman and Maximum Correntropy Kalman Filters for Systems With Bernoulli Distribution k-step Random Delay and Packet Loss

The simultaneous presence of uncertain data delays and data loss in a network control system complicates the state estimation problem and its solution. This paper redesigns the Kalman filter (KF) algorithm for systems with k-step random delayed data and data loss to improve estimation accuracy. A binary Bernoulli distribution is employed in the modified KF algorithm to model the received data with the knowledge of data delay and loss probabilities. Besides, the distribution of the non-Gaussian noise in the measurement system will degrade the performance of the conventional KF algorithm based on the minimum mean square error. Therefore, the modified KF algorithm is extended to the maximum correntropy Kalman filter (MCKF) algorithm to overcome the effect of non-Gaussian noise. The estimation accuracy of the modified KF and MCKF algorithms are experimentally compared under Gaussian and non-Gaussian noises, respectively. The simulation results demonstrate the excellent estimation performance of the proposed modified KF and MCKF algorithms under Gaussian and non-Gaussian noises, respectively.