序列蒙特卡洛多伯努利滤波器在扩展目标跟踪中的应用

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"序列蒙特卡洛多伯努利滤波器在扩展目标中的应用" 本文主要探讨了序列蒙特卡洛（Sequential Monte Carlo，SMC）多伯努利滤波器在处理扩展目标（Extended Targets）跟踪问题上的应用。多伯努利滤波器（Multi-Bernoulli Filter, MBF）是一种在随机有限集理论框架下用于多目标跟踪的有效方法，它考虑了目标可能的出生、死亡以及同时存在的不确定性。然而，尽管针对扩展目标的MB滤波器已经被导出，但在非线性非高斯模型下的具体实现仍然缺乏。在这篇研究论文中，作者Meiqin Liu、Tongyang Jiang和Senlin Zhang提出了一个序列蒙特卡洛技术与测量分割算法相结合的ET-MB滤波器（Extended Target Multi-Bernoulli Filter）。这个创新性的实施方式旨在解决非线性非高斯模型下的扩展目标跟踪挑战。序列蒙特卡洛方法，又称粒子滤波（Particle Filter），是一种在高维空间中进行概率密度函数近似的统计方法。在多目标跟踪问题中，通过模拟一系列代表状态分布的随机样本（粒子）来估计目标的状态。而测量分割算法则有助于提高滤波器的性能，通过将测量分配给不同的粒子，可以更好地捕捉目标的复杂特性，特别是扩展目标，这些目标可能具有较大的尺寸或形状。论文展示了SMC-ET-MB滤波器在模拟实验中的优秀性能，与标准的SMC-MB滤波器相比，对于处理扩展目标测量模型时，其估计精度更优。这表明了所提出的滤波器在处理非典型目标如飞机、船只等大型物体时，能够提供更准确的跟踪结果。关键词：随机有限集，多伯努利滤波器，扩展目标，序列蒙特卡洛该研究对于多目标跟踪领域的理论发展和技术应用具有重要意义，特别是在雷达和传感器网络等领域，对提高目标识别和跟踪的精确度有显著贡献。此外，这种方法也对未来的智能交通系统、航空航天和军事防御等应用提供了重要的理论支持。

The Sequential Monte Carlo Multi-Bernoulli Filter

for Extended Targets

Meiqin Liu

∗†

,Tongyang Jiang

∗†

, and Senlin Zhang

†

∗

State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou 310027, P.R. China

†

College of Electrical Engineering, Zhejiang University, Hangzhou 310027, P.R. China

Email: {liumeiqin,jiangtongyang,slzhang}@zju.edu.cn

Abstract—The multi-Bernoulli (MB) ﬁlter for extended targets

has been derive d recently. However, the implementation of the

extended target (ET) MB ﬁlter for nonlinear non-Gaussian

models has not been presented. In this paper, we propose the

sequential Monte Carlo (SMC) implementation of the ET-MB

ﬁlter for estimating multiple extended targets by using the SMC

technique and measurement partitioning algorithm. Simulation

results demonstrate that the estimation performance of the SMC-

ET-MB ﬁlter is superior to that of the standard SMC-MB ﬁlter

for extended target measurement models.

Index Terms—Random ﬁnite set, multi-Bernoulli ﬁlter, extend-

ed targets, sequential Monte Carlo

I. INTRODUCTION

In multi-target tracking, the objective is to simultaneously

estimate the number of targets and their states from a sequence

of noisy measurements. Generally, each target is assumed to

be a point which produces at most one measurement per

scan. This assumption is valid when the target is far away

from the sensor or the resolution of sensors is low. For the

high resolution sensor, or the distance between the target and

sensor is small, the sensor may be able to resolve individual

features on the target. Each target may generate more than

one measurement per scan, and the assumption of point targets

is not appropriate. Hence extended target tracking arises. An

extended target is deﬁned as a target that potentially generates

more than one measurement per scan [1].

Extended target tracking has attracted more attention in

recent years. Among various extended target tracking ap-

proaches, we are interested in the random ﬁnite set (RFS)

approach. The RFS approach provides another kind of methods

for target tracking [2],[3],[4]. In the RFS approach, targets’

states and measurements are treated as RFSs. With RFS

models, Mahler has proposed the multi-target Bayes ﬁlter

that propagates the multi-target posterior density recursively

[2],[5]. Since the optimal multi-target Bayes ﬁlter is generally

intractable, some approximated multi-target Bayes ﬁlters have

been proposed, such as the probability hypothesis density

(PHD) ﬁlter [5] which propagates the ﬁrst order moment of the

multi-target density, cardinality PHD (CPHD) ﬁlter [6] which

propagates the ﬁrst order moment and cardinality distribution

of the multi-target density, and the multi-Bernoulli (MB) ﬁlter

[2],[7] which propagates the parameters of an MB distribution

to approximate the multi-target density. These ﬁlters have been

implemented by using Gaussian mixture (GM) and sequential

Monte Carlo (SMC) techniques [7],[8],[9],[10]. The PHD,

CPHD, and MB ﬁlters are usually considered for estimating

multiple point targets. Using a Poisson model of extended

target measurements [11], Mahler has derived the PHD ﬁlter

for extended targets [12]. The GM implementation of the

ET-PHD ﬁlter has been presented in [1],[13]. A Gaussian

inverse Wishart implementation of the ET-PHD ﬁlter has been

proposed to jointly estimate targets’ states and extensions. The

CPHD ﬁlter for extended targets has been derived in [14], and

the GM implementation of the ET-CPHD ﬁlter was presented

in [15]. Subsequently, a Gamma Gaussian inverse Wishart

implementation of the ET-CPHD ﬁlter was proposed to jointly

estimate targets’ states and extensions in [16].

Recently, the MB ﬁlter for extended targets has been pro-

posed in [17]. A GM implementation of the ET-MB ﬁlter

for linear Gaussian models was proposed in [18]. However,

the GM-ET-MB ﬁlter cannot be directly applied to nonlinear

non-Gaussian models. With the assumption of point targets,

the SMC-MB ﬁlter has been proposed for nonlinear models,

which obtains higher estimation accuracy than SMC-PHD and

SMC-CPHD ﬁlters, as the SMC-MB ﬁlter does not need the

extra clustering method to extract target states. Hence, in this

paper we propose the SMC implementation of ET-MB ﬁlter

for extended targets. Using SMC techniques and the existing

measurement partitioning algorithm, the SMC-ET-MB ﬁlter

for estimating multiple extended targets is presented in this

paper.

The rest of this paper is organized as follows. Section

II reviews the ET-MB ﬁlter for extended targets. The SMC

implementation of the ET-MB ﬁlter is presented in Section

III. Numerical results for a simulation scenario are offered in

Section IV. Finally, the conclusion is drawn in Section V.

II. T

HE ET-MB FILTER

The MB ﬁlter propagates parameters of an MB distribution

to approximate the multi-target Bayes ﬁlter. It propagates a

time varying number of target tracks in time. Initially, the

MB ﬁlter was proposed for handing point targets. Recently,

based on a Poisson model measurement likelihood proposed

by Gilholm [11], Zhang [17] has derived the MB ﬁlter for

extended targets. In this section, the ET-MB ﬁlter is reviewed,

for more details see [17]. The ET-MB ﬁlter consists of

prediction and update.

18th International Conference on Information Fusion

Washington, DC - July 6-9, 2015

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