A finite-time consensus distributed Kalman filter based on maximum correntropy criterion

Recently, the maximum correntropy criterion in information theoretic learning has been employed in the design of Kalman filters, which performs well under non-Gaussian noises problem. How to extend the maximum correntropy Kalman filter to the distributed framework has become a significant focus of many researchers. This paper utilizes consensus protocol to implement distributed fusion in sensor networks and Hankel matrices to improve the estimation performance of distributed Kalman filter. The consensus iteration values obtained by the consensus algorithm are stored in the sensor nodes, and the Hankel matrices are constructed from the differences of these iteration values. By calculating the normalized kernels of these Hankel matrices to obtain the final consistent estimates, a finite-time consensus distributed maximum correntropy Kalman filter is proposed. The proposed algorithm is able to reduce the number of consensus iterations and achieve accurate average consensus under non-Gaussian noises. Based on the stochastic stability lemma, we prove the stability of the proposed filter. Finally, numerical simulation examples are given to verify the effectiveness of the proposed algorithm.