Distributed filter with fixed-lag smoothing for multi-satellite target tracking under noise outliers

To address degraded tracking accuracy caused by time-varying heavy-tailed noise (HTN) in multi-satellite cooperative target tracking, this paper proposes a distributed Kalman filter with fixed-lag smoothing. The objective is to develop a robust distributed filtering framework that jointly handles time-varying heavy-tailed process and measurement noise, finite-round consensus fusion, and smoothing-window adaptation under resource-limited multi-satellite tracking. Unlike conventional filters, the proposed filter models the prior distribution of the unknown noise as a mixture of two Gaussian distributions (MTG), with the covariance of one of the Gaussian distributions adaptively adjusted using an auxiliary variable based on a power term. The MTG parameters are iteratively calculated using a variational Bayesian method. Then, the MTG is extended to a distributed consensus filter to fuse localized information from a multi-satellite network. A fixed-lag smoothing method based on the information filtering framework is subsequently derived. Moreover, to achieve efficient collaborative state estimation under time-varying HTN, this paper proposes a dynamic event-triggered strategy to adjust the smoothing window length. Simulations demonstrate the superior performance of the proposed distributed smoothing MTG Kalman filter.