Performance analysis for parallel grouping‐based labeled multi‐Bernoulli filter

Abstract

The Labeled Multi-Bernoulli (LMB) filter exhibits “size effect”, namely, the number of hypotheses constituting the multi-object posterior increases super-exponentially with the size of the entire current label space. To alleviate this “size effect”, a promising solution, Parallel Grouping-based implementation of the LMB (PG-LMB) filter has been proposed in [1]. While it can achieve great improvement on computational efficiency through parallel LMB filtering within smaller size of groups, several important theoretical issues remain to be further addressed. On the basis of [1], this paper further exploits the rationale behind the PG-LMB filter and provides a comprehensive performance analysis. At the core of the PG-LMB filter is an Inter-Group Independence Approximation (IG-IA) of the exact posterior. One major contribution of this paper is to propose a principled grouping criterion based on which the upper bound of the approximation error between the IG-IA and the exact posterior can be established explicitly. Another contribution is to exploit the “low dimensional” compression property of the IG-IA, taking advantage of which, the PG-LMB filter has the potential to achieve performance gain under limited computational resources, benefiting its application in low-cost and miniaturized processing platforms.