A Resilient Approach to Distributed Minimum Error Entropy Kalman Filter for Multi-Sensor Networked Systems with Non-Gaussian Noises

As system scale and complexity continually expand, distributed filters have become increasingly prevalent in multi-sensor networked systems. Conventional distributed Kalman filtering algorithms in the minimum mean square error criterion exhibit markedly limited efficacy in delivering precise state estimation when the Gaussian assumption is violated. This paper integrates the Cauchy kernel based minimum error entropy (CMEE) criterion with the Kalman consensus filtering framework. An online fixed point iteration equation is formulated through the upper bounds for the local estimation error covariance matrices, leveraging local measurements in conjunction with aggregated state estimates from neighboring nodes. Then, a distributed CMEE Kalman filtering algorithm is obtained by using a matrix inequality, without the computation of cross-covariance matrices between nodes, thereby reducing online computation cost. Finaly, the convergence of the proposed algorithm is established via the Banach fixed point theorem, and then the boundness of estimation error covariance is analyzed. Simulation studies verify effectiveness of the proposed algorithm.