Bailu Wang

Bailu Wang, Wei Yi, Reza Hoseinnezhad et al.

In this paper, we propose a distributed multi-object tracking algorithm through the use of multi-Bernoulli (MB) filter based on generalized Covariance Intersection (G-CI). Our analyses show that the G-CI fusion with two MB posterior distributions does not admit an accurate closed-form expression. To solve this challenging problem, we firstly approximate the fused posterior as the unlabeled version of $δ$-generalized labeled multi-Bernoulli ($δ$-GLMB) distribution, referred to as generalized multi-Bernoulli (GMB) distribution. Then, to allow the subsequent fusion with another multi-Bernoulli posterior distribution, e.g., fusion with a third sensor node in the sensor network, or fusion in the feedback working mode, we further approximate the fused GMB posterior distribution as an MB distribution which matches its first-order statistical moment. The proposed fusion algorithm is implemented using sequential Monte Carlo technique and its performance is highlighted by numerical results.

Suqi Li, Wei Yi, Reza Hoseinnezhad et al.

This paper considers the problem of the distributed fusion of multi-object posteriors in the labeled random finite set filtering framework, using Generalized Covariance Intersection (GCI) method. Our analysis shows that GCI fusion with labeled multi-object densities strongly relies on label consistencies between local multi-object posteriors at different sensor nodes, and hence suffers from a severe performance degradation when perfect label consistencies are violated. Moreover, we mathematically analyze this phenomenon from the perspective of Principle of Minimum Discrimination Information and the so called yes-object probability. Inspired by the analysis, we propose a novel and general solution for the distributed fusion with labeled multi-object densities that is robust to label inconsistencies between sensors. Specifically, the labeled multi-object posteriors are firstly marginalized to their unlabeled posteriors which are then fused using GCI method. We also introduce a principled method to construct the labeled fused density and produce tracks formally. Based on the developed theoretical framework, we present tractable algorithms for the family of generalized labeled multi-Bernoulli (GLMB) filters including $δ$-GLMB, marginalized $δ$-GLMB and labeled multi-Bernoulli filters. The robustness and efficiency of the proposed distributed fusion algorithm are demonstrated in challenging tracking scenarios via numerical experiments.

Suqi Li, Wei Yi, Reza Hoseinnezhad et al.

This paper presents an exact Bayesian filtering solution for the multi-object tracking problem with the generic observation model. The proposed solution is designed in the labeled random finite set framework, using the product styled representation of labeled multi-object densities, with the standard multi-object transition kernel and no particular simplifying assumptions on the multi-object likelihood. Computationally tractable solutions are also devised by applying a principled approximation involving the replacement of the full multi-object density with a labeled multi-Bernoulli density that minimizes the Kullback-Leibler divergence and preserves the first-order moment. To achieve the fast performance, a dynamic grouping procedure based implementation is presented with a step-by-step algorithm. The performance of the proposed filter and its tractable implementations are verified and compared with the state-of-the-art in numerical experiments.

Bailu Wang, Wei Yi, Suqi Li et al.

In this paper, we address the problem of the distributed multi-target tracking with labeled set filters in the framework of Generalized Covariance Intersection (GCI). Our analyses show that the label space mismatching (LS-DM) phenomenon, which means the same realization drawn from label spaces of different sensors does not have the same implication, is quite common in practical scenarios and may bring serious problems. Our contributions are two-fold. Firstly, we provide a principled mathematical definition of "label spaces matching (LS-DM)" based on information divergence, which is also referred to as LS-M criterion. Then, to handle the LS-DM, we propose a novel two-step distributed fusion algorithm, named as GCI fusion via label spaces matching (GCI-LSM). The first step is to match the label spaces from different sensors. To this end, we build a ranked assignment problem and design a cost function consistent with LS-M criterion to seek the optimal solution of matching correspondence between label spaces of different sensors. The second step is to perform the GCI fusion on the matched label space. We also derive the GCI fusion with generic labeled multi-object (LMO) densities based on LS-M, which is the foundation of labeled distributed fusion algorithms. Simulation results for Gaussian mixture implementation highlight the performance of the proposed GCI-LSM algorithm in two different tracking scenarios.

Suqi Li, Wei Yi, Bailu Wang et al.

As a fundamental piece of multi-object Bayesian inference, multi-object density has the ability to describe the uncertainty of the number and values of objects, as well as the statistical correlation between objects, thus perfectly matches the behavior of multi-object system. However, it also makes the set integral suffer from the curse of dimensionality and the inherently combinatorial nature of the problem. In this paper, we study the approximations for the universal labeled multi-object (LMO) density and derive several principled approximations including labeled multi-Bernoulli, labeled Poisson and labeled independent identically clustering process based approximations. Also, a detailed analysis on the characteristics (e.g., approximation error and computational complexity) of the proposed approximations is provided. Then some practical suggestions are made for the applications of these approximations based on the preceding analysis and discussion. Finally, an numerical example is given to support our study.