Distributed State Estimation with Unknown Inputs and Heavy-Tailed Noises

This paper addresses the distributed filtering problem for linear systems subject to unknown inputs and heavy-tailed measurement noises. The unknown inputs are modeled using a non-informative prior distribution, while the heavy-tailed noises are modeled using a Student’s t distribution. Leveraging variational Bayesian methods, a local filter is designed to jointly estimate system states and unknown inputs in the presence of heavy-tailed measurement noises. Subsequently, a distributed filtering framework is proposed by integrating the designed local filter with the consensus on information method. Moreover, a sufficient condition is derived to ensure the boundedness of the estimation error covariance of the proposed distributed filter. Finally, simulation results from a target tracking system are presented to demonstrate the effectiveness of the proposed distributed filtering approach.