多路径场景下的多目标跟踪：MP-GLMB滤波器

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"多路径广义标记多伯努利滤波器是一种针对雷达目标跟踪问题的新型算法，尤其适用于处理因多径传播导致的目标产生多个检测的情况。该算法基于标记随机有限集（Labeled Random Finite Set, LRFS）理论，能够有效估计目标数量及其状态轨迹。" 在传统的多目标跟踪算法中，通常假设每个目标在每次扫描时最多产生一个检测信号。然而，在超过地平线雷达（Over-the-Horizon Radar, OTHR）系统中，由于多径传播效应，单个目标可能产生多个检测信号。为了解决这个问题，本文提出了多路径广义标记多伯努利滤波器（Multipath Generalized Labeled Multi-Bernoulli, MP-GLMB）算法，它能够有效地在存在多个检测信号的系统中追踪多个目标。 MP-GLMB滤波器的核心在于利用标记随机有限集框架，这一框架不仅能够估计目标数量，还能跟踪每个目标的状态轨迹。与现有的多路径概率假设密度（Probability Hypothesis Density, PHD）滤波器和多目标多伯努利（Multi-Target Multi-Bernoulli, MeMBer）滤波器相比，MP-GLMB滤波器在模拟实验中显示出了更优的跟踪性能。在介绍部分，作者们强调了多目标跟踪问题的复杂性，特别是当目标数目未知且随时间变化时。他们指出，OTHR系统中的多径传播增加了跟踪的难度，因为这会导致目标表示为一组非独立同分布的检测。MP-GLMB滤波器正是为解决这一挑战而设计的。文章进一步可能会详细讨论MP-GLMB滤波器的数学模型和实现步骤，包括如何处理多径检测、如何更新和预测目标状态、以及如何通过LRFS理论进行目标合并和分割。此外，可能会有对比实验结果，展示MP-GLMB滤波器在精度、鲁棒性和计算效率方面的优势。这篇研究论文对多径传播环境下的多目标跟踪技术进行了深入探索，提出了一种新的滤波器方法，对于雷达目标跟踪领域具有重要的理论和实践价值。通过采用MP-GLMB滤波器，可以提高在复杂条件下多目标跟踪的准确性和效率。

Multipath Generalized Labeled Multi-Bernoulli Filter

Bin Yang, Jun Wang, Wenguang Wang, and Shaoming Wei

School of Electronic and Information Engineering, Beihang University, Beijing, China

Email:young

being@126.com

Abstract—Traditional multitarget tracking algorithms assume

that each target can generate at most one detection per scan.

However, in the over-the-horizon radar (OTHR), a target may

produce multiple detections because of multipath propagation.

In this paper, we propose a new algorithm, called multipath gen-

eralized labeled multi-Bernoulli (MP-GLMB) ﬁlter, to effectively

track multiple targets in such multiple-detection systems. The

proposed technique is based on the labeled random ﬁnite set

(RFS), which estimates the number of targets and the trajectories

of their states. The proposed MP-GLMB ﬁlter is compared with

the multipath version of the probability hypothesis density (PHD)

ﬁlter and the multi-target multi-Bernoulli (MeMber) ﬁlter, and

simulation results show that our algorithm has improved tracking

performance.

I. INTRODUCTION

Multitarget tracking problem involves estimating an un-

known and time-varying number of targets and their corre-

sponding trajectories by using measurements from sensors.

Three major algorithms, namely, the Multiple Hypothesis

Tracker (MHT), the Joint Probabilistic Data Association Fil-

ter (JPDAF) and algorithms based on the random ﬁnite set

(RFS) theory have been proposed to deal with problems in

multitarget tracking, such as nonunity probability of detection,

presence of spurious measurements (clutter), and uncertainty

of measurement-target association [1], [2], [3], [4], [5].

In these algorithms, a common assumption is that one target

produces at most one measurement in every scan, which is

valid in single-detection systems. However, in many practical

scenarios, one target can generate more than one detection

per scan. A well-known example of such a system is the

over-the-horizon radar (OTHR) [23], [24], [25], [26], which

radar signals from the same target are propagated by multiple

paths (MPs) due to multiple ionospheric layers. These multiple

detections (MDs) in receiver of OTHR bring beneﬁt and

disadvantage to the tracking algorithms simultaneously. If the

MDs from multipath propagation can be exploited effectively,

the performance of the tracking algorithm will be improved

greatly. But the tracking with MDs needs to solve not only

measurement-target association, but also measurement-path

association, which requires complex algorithm. Based on the

JPDA framework [8] and the MHT framework [9], MD-JPDA

ﬁlter [29] and MD-MHT algorithm [28] were proposed, re-

spectively, to tracking multiple targets with multiple detections

in OTHR. Since the RFS approach, such as the probability

hypothesis density (PHD) ﬁlter [10], [14] and the multi-target

multi-Bernoulli (MeMber) ﬁlter [5], [12], can avoid the data

association, the MD-PHD ﬁlter [31] and the MP-CBMeMBer

ﬁlter [32] have been proposed as tractable Bayesian ﬁlters with

low complexity in OTHR.

However, these RFS-based ﬁlters only estimate target states

at individual time instants and not provide target trajectories.

In order to overcome this limitation, [15], [16] appended an

unique label to RFS, which called labeled RFS, and linked

the target states with the same label at different scan to form

the trajectory of targets. Since the generalized labeled multi-

Bernoulli (GLMB) RFS is conjugate prior to the multitarget

point measurement model, the GLMB ﬁlter and the δ-GLMB

ﬁlter have been proposed as tractable Bayesian multitarget

trackers.

In this paper, we develop a GLMB ﬁlter, which called MP-

GLMB ﬁlter, for multipath multitarget tracking. First, we de-

rive the likelihood function of the multipath observation model.

Then, we provide the recursion of the GLMB density with

multipath observation likelihood inspired by the GLMB ﬁlter

for extended target tracking [33], which is another multiple

detection tracking problem. Furthermore, we propose a joint

prediction/update formulation [18] of the MP-GLMB ﬁlter and

implement it by using Murty’s algorithm [20], [21].

The rest of the paper is organized as follows. In Section II,

we present the problem description of the multipath system and

the background on labeled RFS ﬁltering. The derivation and

implementation of the MP-GLMB are provided in Section III.

Simulation results are given in Section IV. Finally, in Section

V, conclusions are discussed.

II. P

ROBLEM DESCRIPTION AND BACKGROUND

In this section we provide the mathematical preliminaries

of the multipath multitarget tracking problem in OTHR. We

also brieﬂy review the background of the labeled RFS.

A. Multipath System

)OD\HU

(OD\HU

5DGDU

7DUJHW

Fig. 1: OTHR multipath propagation modes.

The OTHR can detect targets beyond the horizon by using

internal reﬂection of high frequency radio waves through the

ionospheric layer. There are two major ionospheric layers E

and F scatter the radar signal from transmitter to targets and

2018 21st International Conference on Information Fusion (FUSION)

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