跳变马尔可夫系统下的多模型Vo-Vo滤波器

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"这篇研究论文探讨了一种基于跳变马尔可夫系统（Jump Markov System, JMS）的多模型Vo-Vo滤波器，用于跟踪高度动态的目标。Vo-Vo滤波器，也称为广义标记多伯努利（Generalized Labeled Multi-Bernoulli, GLMB）滤波器，提供了一个闭式解法，适用于高斯混合实现的多模型版本。在涉及大量目标随机出现和消失的复杂场景中，论文检验并比较了所提出方法的性能，结果表明该方法在跟踪精度上优于其他技术，并且对应用和滤波器参数的变化（如杂波率和模型转换概率）具有高度鲁棒性。" 文章首先介绍了贝叶斯滤波器在多目标跟踪问题中的普遍应用，如联合概率数据关联（JPDA）、多假设跟踪（MHT）、概率历史密度（PHD）、条件概率历史密度（CPHD）以及标记多伯努利滤波器等。这些滤波器虽然广泛使用，但在处理高度动态的目标时可能面临挑战。论文的核心是提出了一种新的多模型Vo-Vo滤波器解决方案，它利用了JMS的概念来适应目标动态性的突然变化。Vo-Vo滤波器，特别是其GLMB形式，允许对每个目标进行独立的、带有标签的概率表示，从而能更精确地跟踪多个相互干扰的目标。通过引入JMS，滤波器可以更好地处理目标的出现和消失，以及动态特性的随机变化。论文中，作者们推导出了多模型Vo-Vo滤波器的闭式解法，这对于高斯混合实现尤其重要，因为这种实现方式能够处理非高斯噪声和复杂的观测情况。此外，通过对比实验，论文展示了在具有挑战性的场景下，新方法相比于现有技术在跟踪准确性上的优势。实验涉及了多种目标动态变化的情况，包括目标的随机出现和消失，这模拟了实际环境中的复杂性。在评估中，新方法表现出了对各种参数变化的鲁棒性，例如杂波率（clutter rate）和模型转换概率。杂波率是指在雷达或传感器观测到的虚假目标数量，而模型转换概率则反映了目标状态变化的不确定性。即使在这些参数大幅度变动的情况下，多模型Vo-Vo滤波器仍能保持稳定的跟踪性能。这项工作为多目标跟踪提供了强大的工具，特别是在动态环境和高杂波环境下，其性能提升和鲁棒性使得该方法有潜力在实际的监控、安全和自动驾驶等应用场景中发挥重要作用。通过创新的多模型处理和闭式解法，论文提出的Vo-Vo滤波器为未来的研究和工程实践开辟了新的可能性。

The Multiple Model Vo-Vo Filter

Wei Yi, Meng Jiang, Reza Hoseinnezhad

Abstract—A Jump Markov System (JMS) multiple model

solution is presented for tracking highly dynamic targets using

the Vo-Vo ﬁlter (also known as Generalized Labeled Multi-

Bernoulli or GLMB ﬁlter). The closed-form solution is derived for

Gaussian mixture implementation of the multiple-model Vo-Vo

ﬁlter. The performance of the proposed method is examined and

compared with the state of art in challenging scenarios involving

numerous appearing and disappearing targets with randomly

time-varying dynamics. The results demonstrate that in such

applications, the proposed method can outperform the competing

techniques in terms of tracking accuracy, and is highly robust

to variations in application and ﬁlter parameters such as clutter

rate and model transition probabilities in the JMS.

I. INTRODUCTION

AYESIAN ﬁlters, in general, are the most popular type

of solutions developed and used for multi-target tracking

problems. The most commonly used Bayesian multi-target

ﬁlters include JPDA [1], MHT [2], PHD [3], CPHD [4], Multi-

Bernoulli [3], [5], and Labeled Multi-Bernoulli (LMB) [6]

ﬁlters, and most recently the Vo-Vo ﬁlter (also called Gener-

alized Labeled Multi-Bernoulli or GLMB ﬁlter) [7], [8].

The

main advantage of the above ﬁlters is the neat and efﬁcient

machinery they provide to harvest all the information that is

available in relation to the trackable targets. In general, the

application-speciﬁc information regarding the target dynamics,

birth and survival are used in the prediction step, then the

measurements (normally acquired by sensors) are processed

in the update step of the ﬁlter.

In their standard form, the above multi-target ﬁltering

solutions are implemented based on the assumption that the

states of all targets follow the same stochastic dynamic model

at all times. Examples of such models include Brownian

motion models, nearly constant velocity (NCV) models, nearly

constant acceleration (NCA) models and coordinated turn (CT)

models [10].

In many real world applications, assuming that all targets

evolve according to the same dynamic model at all times, is

far from accurate. For example, in trafﬁc monitoring, the dy-

namics of some slower targets may ﬁt well to an NCV model

while faster maneuvering targets may follow an NCA model

more closely. In battleﬁeld surveillance applications with radar

tracking, a maneuvering target may ﬂy very differently at

different times, hence its dynamics would match different

models in different periods of time. In such applications, the

W. Yi and M. Jiang are with University of Electronic Science and Technolo-

gy of China, Chengdu, Sichuan, P.R. China, 611731. Fax: +86-028-61830064,

Tel: +86-028-61830768, E-mail: kussoyi@gmail.com.

R. Hoseinnezhad is with the School of Engineering, RMIT University,

Victoria 3083, Australia, Tel: +61-3-9925-6135, E-mail: rezah@rmit.edu.au.

This work was supported by the Australian Research Council’s Discovery

Project Program, via the ARC Discovery Project grants DP130104404 and

DP160104662, and supported by the National Natural Science Foundation of

China under Grants 61301266, the Chinese Postdoctoral Science Foundation

under Grant 2014M550465 and Specail Grant 2016T90845.

We follow Mahler who used the name “Vo-Vo ﬁlter” in his book [9].

standard implementation of the aforementioned ﬁlters (with

a ﬁxed motion model) may not be able to accurately track

multiple rapidly maneuvering targets. Thus, new Bayesian

multi-target ﬁlters that consider multiple models characterizing

different maneuvers are necessary to describe the motion of

maneuvering targets.

To incorporate multiple models into existing Bayesian

multi-target ﬁltering schemes, the popular approaches in the

literature are the Jump Markov System (JMS) approach [11]

and its practical approximation, namely, the interacting mul-

tiple model (IMM) algorithm [12]. In the IMM algorithm, a

mixing step is added to the ﬁlter (in addition to prediction and

update steps). While the original solution [12] was developed

for ﬁltering of linear systems with Markovian switching coef-

ﬁcients (dynamic multiple model systems), the IMM approach

to hypotheses merging was used to devise multiple-model

extensions of the JPDA [13] and MHT [14] ﬁlters. In JMS

approach, the target state is augmented with an additional

motion model label, and the augmented state of each target

evolves with time according to a ﬁnite state Markov chain [11].

This approach has been employed to formulate multiple-model

extensions of PHD [15], GM-PHD [16], CPHD [17], multi-

Bernoulli [18] and LMB [19] ﬁlters.

This paper incorporates multiple models into Vo-Vo ﬁl-

ter [7], [8] and gives the speciﬁc closed-form solution for

multiple-model extension, called MM-Vo-Vo ﬁlter, based on

the JMS approach. The Vo-Vo ﬁlter uses a special class of

random ﬁnite set (RFS) distribution called generalized labeled

multi-Bernoulli (GLMB). Multi-target Bayesian ﬁltering of

GLMB random ﬁnite sets enables the estimation of target

tracks as well as their states.

The GLMB prior is closed under the Chapman-Kolmogorov

equation, and more importantly, it is a conjugate prior for the

point measurement set likelihood model. Vo-Vo ﬁlter is one

of the few stochastic multi-target ﬁlters in the literature that

satisfy this conjugacy property. This important characteristic

and the efﬁcient implementation of the Vo-Vo ﬁlter presented

in [8], have led to its outstanding performance in terms of both

tracking error and computational cost. As a result, the Vo-

Vo ﬁlter has been increasingly adopted in many applications

from track-before-detect [20], to tracking with superpositional

sensors [21], to visual tracking [22]. This paper addresses an

important gap in the literature in relation to using Vo-Vo ﬁlter

to track maneuvering targets with dynamics that can follow

multiple models [23], [24]

We introduce speciﬁc recursion formulae for Vo-Vo ﬁltering

of augmented target states under multiple motion models.

MM-Vo-Vo ﬁlter uses JMS to extend the standard Vo-Vo

recursion to allow for multiple target motion models. This

extension is implemented using Gaussian mixture approxi-

mations. The multiple model implementation is validated a-

gainst its respective standard implementations of PHD, CPHD,

LMB and Vo-Vo ﬁlters in a challenging scenario involving

up to ten appearing and disappearing targets that change

their motion behaviour at different random times. The OSPA

These two papers have independently proposed methods for maneuvering

target tracking based on Vo-Vo ﬁlter.

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