Distributed Consensus Multi-Distribution Filter for Heavy-Tailed Noise

Abstract

Distributed state estimation is one of the critical technologies in the field of target tracking, where the process noise and measurement noise may have a heavy-tailed distribution. Traditionally, heavy-tailed distributions like the student-t distribution are employed, but our observation reveals that Gaussian noise predominates in many instances, with occasional outliers. This sporadic reliance on heavy-tailed distributions can degrade performances or necessitate frequent parameter adjustments. To overcome this, we introduce a novel distributed consensus multi-distribution state estimation method that combines Gaussian and student-t filters. Our approach establishes a system model using both Gaussian and student-t distributions. We derive a multi-distribution filter for a single sensor, assigning probabilities to Gaussian and student-t noise models. Parallel estimation under both distributions, utilizing Gaussian and student-t filters, allows us to calculate the likelihood of each distribution. The fusion of these results yields a mixed-state estimation and corresponding error matrix. Recognizing the increasing degrees of freedom in the student-t distribution over time, we provide an effective approximation. An information consensus strategy for multi-distribution filters is introduced, achieving global estimation through consensus on fused local filter results via interaction with neighboring nodes. This methodology is extended to the distributed case, and the recursive process of the distributed multi-distribution consensus state estimation method is presented. Simulation results demonstrate that the estimation accuracy of the proposed algorithm improved by at least 20% compared to that of the traditional algorithm in scenarios involving both Gaussian and heavy-tailed distributions.