Computationally Efficient Distributed Multi-Sensor Multi-Bernoulli Filter

Abstract

This paper proposes a computationally efficient distributed fusion algorithm with multi-Bernoulli (MB) random finite sets (RFSs) based on generalized Covariance Intersection (GCI). The GCI fusion with MB filter (GCI-MB) involves the computation of the generalized MB (GMB) fused density determined by a set of hypotheses growing exponentially with object number. Hence, its applications with multiple targets are quite restrictive, which further motivates an efficient fusion algorithm. In this paper, we propose a novel approximation of the GCI-MB fusion. By discarding the hypotheses with negligible weights, the GCI-GMB fusion amounts to parallelized fusions performed with several smaller groups of Bernoulli components. As such, the computation of the GMB fused density is significantly simplified, with the number of hypotheses reduced dramatically and a practical appealing parallelizable structure achieved. Based on the proposed approximation, a computationally efficient GCI-MB fusion algorithm which can harness large amount of objects is devised. Furthermore, we present the analysis on both the characterization of the $L_{1}$ -error and the computational complexity of the proposed fusion algorithm compared with the standard GCI-GMB fusion. Our analysis shows that the proposed fusion algorithm can reduce the computational expense as well as memories dramatically with slight approximation error. Numerical experiments using the Gaussian implementation for a challenging scenario with twenty objects demonstrate the performance of the proposed fusion algorithm.