A distributed social-learning Kalman filter

Distributed target tracking systems are increasingly deployed in practical applications where non-Gaussian and time-varying process noise frequently arise. Under such conditions, conventional distributed Kalman filtering approaches that rely on fixed noise covariance assumptions often suffer from severe performance degradation. In this paper, a Distributed Social-Learning Kalman Filter (D-SKF) is proposed to address distributed state estimation under Non-Gaussian and time-varying noise statistics. The proposed framework formulates noise covariance uncertainty as a finite hypothesis set and enables each node to infer the active noise regime through social learning based on local likelihood evaluation and neighbor information exchange. The identified noise hypothesis is then incorporated into the filtering process to adaptively adjust the estimation gain.Theoretical analysis establishes the boundedness of the estimation error and the convergence of the distributed belief update. Simulation results demonstrate that the proposed D-SKF achieves superior estimation accuracy and robustness compared with existing distributed Kalman filters and robust variants.