增强多目标跟踪：基于幅度信息的δ-GLMB滤波器

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本文主要探讨了"基于带幅度信息的δ-GLMB滤波器的多目标跟踪"这一研究领域。多目标跟踪在许多实际应用中，如军事、交通监控等，是一项关键任务，它涉及对目标数量和状态进行实时估计。传统的多目标跟踪方法可能受到背景杂乱信号的干扰，而幅度信息通常比这些杂乱信号更强烈，这对于提高跟踪性能具有显著潜力。传统的多目标跟踪算法，如概率数据关联(PDA)或粒子滤波，可能不足以充分利用这种幅度信息。为此，研究人员提出了将幅度信息融入到随机有限集(RFS)框架下的δ-Generalized Labeled Multi-Bernoulli(δ-GLMB)滤波器。δ-GLMB滤波器是一种强大的多目标跟踪工具，因为它能够处理不确定性并生成精确的目标轨迹，尽管目标数量是未知且动态变化的。在本文中，作者Changshun Yuan、Jun Wang、Shaoming Wei和Hong Xiang针对这个问题进行了创新性的研究。他们将幅度信息有效地整合到了δ-GLMB滤波器的设计中，通过建立更准确的杂乱和目标似然性模型，从而提升跟踪精度。作者特别设计了一种新的更新方程，利用幅度似然函数来处理这一融合过程，这在理论上和实践上都是一项突破。通过模拟实验，他们在一个线性多目标跟踪场景中展示了带幅度信息的δ-GLMB滤波器相较于传统方法的优越性能。实验结果清晰地表明，利用幅度信息可以显著改善多目标跟踪系统的鲁棒性和准确性，特别是在复杂环境中，如目标与杂乱信号强度对比强烈时。关键词包括：随机有限集（Random Finite Set）、多目标跟踪（Multi-Target Tracking）、δ-GLMB滤波器（δ-GLMB Filter）、幅度信息（Amplitude Information）以及贝叶斯滤波（Bayesian Filtering）。这篇文章对于寻求在多目标跟踪中利用额外信息源以提升性能的科研人员来说，提供了有价值的新思路和技术支持。

Multi-target Tracking Based on δ-GLMB Filter with

Amplitude Information

Changshun Yuan , Jun Wang , Shaoming Wei , Hong Xiang

School of Electronic and Information Engineering

Beihang University

Beijing, China

Abstract—In many multi-targets tracking scenarios, the

amplitude returning from targets are typically stronger than

those from clutters. This information could be used to enhance

the tracking performance by establishing more accurate clutter

and target likelihoods. In this paper, we incorporate the

amplitude information into the δ-Generalized Labeled Multi-

Bernoulli (δ-GLMB) filter, which is based on the random finite

set (RFS), and can output target tracks. In addition, we present

the novel update equation of the δ-GLMB filter using amplitude

likelihood function. Simulation results demonstrate the better

performance via a linear multi-target scenario.

Keywords—random finite set; multi-target tracking; δ-GLMB

filter, amplitude information; Bayesian filtering

NTRODUCTION

Multi-target tracking is to jointly estimate the unknown and

time-varying number of the targets and the corresponding

multi-target states from the rarely perfect measurements [1].

For many sensors such as sonars, lasers and radars,

measurements not only contain the targets’ positions, but also

come with the signal amplitude. The signal amplitude from a

target is usually stronger than that of clutter. So, it provides a

kind of valuable information to decide whether the

measurement is from a target or from clutter.

The amplitude information as a measurement has been used

in the traditional multi-target tracking to improve the tracking

performance, such as Viterbi data association [2] and multiple

hypotheses tracking (MHT) [3]. However, the computational

load of the aforementioned techniques increases exponentially

as the number of measurements and targets increases due to the

necessary process of associations.

In recent time, a RFS approach was proposed by Mahler,

which could avoid associations [1]. In particular, the

development of the probability hypothesis density (PHD) [4],

the cardinalized probability hypothesis density (CPHD) [5] and

multi-Bernoulli (MB) [6] filters have demonstrated the

efficiency and practicability of the RFS approach. Meanwhile,

many researchers have incorporated the amplitude information

into the PHD, CPHD and MB filters with Gaussian Mixture

(GM) and sequential Monte Carlo (SMC) implementations [7,

12]. But targets are indistinguishable in these filters, which in

principle, are not multi-target trackers.

Vo recently proposed a δ-GLMB filter based on the labeled

RFS to address target trajectories and their uniqueness [8, 9].

To data, all of the works on the δ-GLMB filter have not

considered the amplitude information. Inspired by the results in

[7,12], this paper proposes a GM-δ-GLMB filter using

amplitude information, which is called AI-GM-δ-GLMB filter.

We introduce the likelihood function with amplitude

information, and incorporate it into the update step of the GM-

δ-GLMB filter. Simulation results for a linear multi-target

scenario are presented to demonstrate the improvements in

performance of multi-target tracking.

This paper is organized as follows: The background on

labeled RFS and δ-GLMB RFS is provided in Section 2.

Section 3 describes the proposed AI-GM-δ-GLMB filter.

Section 4 shows the simulation results for a linear multi-target

scenario. Conclusions are finally given in Section 5.

II. B

ACKGROUND

This section provides a brief review of the labeled RFS

and δ-GLMB RFS. The details on intuitive interpretations and

mathematical proofs are given in [8].

A. Labeled RFS

To estimate each target track in the multi-target scenario,

each state

∈x

is augmented by a unique label

{

}

: 

∈= ∈

, where



represents the set of positive

integers and all

are distinct [8]. Meanwhile, each target is

identified by an ordered pair of integers

()

,= ki

, where

the new-born time, and

∈i

is a unique index to distinguish

new-born targets at the same time [8].

The definition of labeled RFS is given in [8]. A labeled

RFS with state space



and label space



is an RFS

×

such that each realization has unique and distinct

labels. The labels of a labeled RFS

is defined as

() ()

{

}

=∈Xx:xX

, where

：

×→

is the projection

written as

()

 =x,

() ()

()



Δ=

is called

distinct label indicator [8].

In the following, the conventions that single-target state is

given by lowercase letter (e.g.

), while multi-target states

are denoted by uppercase letters (e.g.

X ,X

), spaces are

denoted by blackboard bolds (e.g.

,,,

), and the finite

subset of a space



is represented by

()



, are the same as

Proceedings of the 13th European Radar Conference

189

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