The Labeled Multi-Bernoulli Filter

Abstract

This paper proposes a generalization of the multiBernoulli filter called the labeled multi-Bernoulli filter that outputs target tracks. Moreover, the labeled multi-Bernoulli filter does not exhibit a cardinality bias due to a more accurate update approximation compared to the multi-Bernoulli filter by exploiting the conjugate prior form for labeled Random Finite Sets. The proposed filter can be interpreted as an efficient approximation of the -Generalized Labeled Multi-Bernoulli filter. It inherits the advantages of the multi-Bernoulli filter in regards to particle implementation and state estimation. It also inherits advantages of the -Generalized Labeled Multi-Bernoulli filter in that it outputs (labeled) target tracks and achieves better performance.Index Terms-Bayesian estimation, conjugate prior, marked point process, random finite set, target tracking.

Box-Particle Labeled Multi-Bernoulli Filter for Mltiple Extended Target Tracking

“…Labeled single-target state and multi-target state are denoted by x and X , respectively. The recursion of LMB filter is carried out on    as follows [9].…”

“… denotes the clutter density, and the clutter is modeled as Poisson model [9]. D p represents the detection probability, it is state independent, and 1…”

“…The simulation results are divided into two parts: Firstly, multiple linear extended targets are tracked by the proposed BP-LMB filter and the traditional point-particle LMB filter (PP-LMB filter) [1], [9]. Secondly, the BP-MM-LMB filter is compared with the single-model BP-LMB filter (BP-CV-LMB filter) and multi-model PP-LMB filter (PP-MM-LMB filter) in the scenario containing multiple rapidly maneuvering extended targets.…”

“…Similar to classical LMB filter, the birth process is modeled as a multi Bernoulli RFS [9], i.e. The state transition functions of CV model and CT model are described by (43) and (44) [18].…”

“…Subsequently, the Generalized Labeled Multi-Bernoulli (GLMB) and the δ-GLMB RFS were proposed as the specific subclasses of labeled RFS [8]. As an accurate and computationally efficient approximation of the δ-GLMB filter, the labeled Multi-Bernoulli (LMB) filter has been proposed in [9]. Both Gaussian Mixtures (GM) and sequential Monte Carlo (SMC) techniques have been implemented for these RFS based filters [6], [10].…”