递归联合轨迹关联与传感器非线性偏差估计：广义贝叶斯风险视角

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"这篇研究论文探讨了在多目标多传感器跟踪系统中，如何基于广义贝叶斯风险进行递归联合轨迹间关联和传感器非线性偏差估计的问题。作者Mengxi Hao、Xianghui Yuan和Chongzhao Han来自西安交通大学的MOEKLINNS实验室和集成自动化研究所。他们提出了一种新的算法，该算法旨在解决在存在传感器偏差情况下复杂的轨迹关联问题，以避免因错误的轨迹关联导致的偏差估计不准确。通过将这两个问题联合解决，可以提高整体的跟踪性能。传统的轨迹关联和估计方法通常是分开处理的，但在实际应用中，这种分离处理可能会导致性能下降。论文提出的递归联合算法则将轨迹关联和非线性偏差估计融合在一个框架下，利用广义贝叶斯风险理论，优化了这两个过程的交互作用。广义贝叶斯风险是一种决策理论工具，它考虑了不确定性以及决策的后果，对于处理复杂系统的不确定性问题特别有用。在多传感器跟踪系统中，传感器的非线性偏差可能导致跟踪目标的误关联，进而影响到偏差估计的准确性。新算法的目标是通过改进的关联策略，减少这些负面影响，从而提高整个跟踪系统的稳健性和精度。为了验证新算法的有效性，作者进行了蒙特卡洛模拟实验，将提出的算法与传统的关联-然后-估计算法进行了对比分析。通过模拟实验的结果，论文展示了提出的算法在处理复杂关联问题和非线性偏差估计时的优势，进一步证明了联合处理这两个问题的优越性。这种方法对于未来多目标跟踪系统的设计和优化具有重要的理论指导意义和实践价值。" 这篇论文的核心知识点包括： 1. 轨迹间关联：在多目标跟踪系统中的重要任务，特别是在存在传感器非线性偏差时变得更加复杂。 2. 传感器非线性偏差估计：对跟踪性能有显著影响，错误的估计可能导致错误的关联结果。 3. 广义贝叶斯风险：用于决策理论，用于优化在不确定性和潜在代价情况下的关联和估计过程。 4. 递归联合算法：一种创新的方法，将轨迹关联和非线性偏差估计同时处理，提高了系统的稳健性和精度。 5. 蒙特卡洛模拟：验证算法有效性的常用方法，通过大量随机试验比较新算法与传统方法的性能。

Recursive Joint Track-to-Track Association and Sensor

Nonlinear Bias Estimation Based on Generalized Bayes

Risk

Mengxi Hao

MOE KLINNS Lab

Inst. of Integrated Automation

Xi’an Jiaotong University

Xi’an, China

mx.hao@stu.xjtu.edu.cn

Xianghui Yuan

MOE KLINNS Lab

Inst. of Integrated Automation

Xi’an Jiaotong University

Xi’an, China

xhyuan@mail.xjtu.edu.cn

Chongzhao Han

MOE KLINNS Lab

Inst. of Integrated Automation

Xi’an Jiaotong University

Xi’an, China

czhan@mail.xjtu.edu.cn

Abstract – Track-to-track association and sensor bias

estimation are two important problems in multi-target

multi-sensor tracking system. Track-to-track association

becomes more complex in the presence of sensor bias

and incorrect track association will lead to poor bias

estimation results. Solving these two problems jointly

would be attractive. This paper proposes a recursive joint

track-to-track association and nonlinear bias estimation

algorithm based on the generalized Bayes risk. The

proposed algorithm and the conventional

association-then-estimation algorithm are compared

with the Monte-Carlo simulation. Simulation results

show that the proposed algorithm has better track

association and bias estimation performance than the

conventional algorithm.

Keywords: generalized Bayes risk, recursive,

track-to-track association, sensor bias estimation, joint

decision and estimation.

1 Introduction

Track-to-track association and bias estimation, which

are generally tightly coupled, are of great importance in

multi-target multi-sensor tracking system. The coupling

gives rise to the difficulties.

Much work has been carried out on solving these two

problems separately. The “association-then-estimation”

strategy solves the bias estimation problem and assumes

the association was completely correct. The

“estimation-then-association” strategy solves the

association problem and assumes the bias estimation was

done. These two problems may affect each other and

should be considered jointly.

Several studies have been conducted on joint

track-to-track association and bias estimation problem

(JAE). [1] and [2] proposed a joint MAP bias estimation

and data association algorithm while this algorithm

describes the problem as an nonconvex mixed integer

nonlinear programming problem which is very hard to

solve. A joint association, registration, and fusion

approach based on expectation-maximization (EM) was

proposed in [3]. However it has a drawback that

expectation-maximization algorithm is a batch iterative

algorithm of which the convergence speed is slow when

solving complex cases. [4] proposed an extended product

multi-sensor cardinalized probability hypothesis density

(PM-CPHD) filter for spatial registration and data

association, which leads to a more difficult problem.

The optimal Bayes joint decision and estimation (JDE)

algorithm was proposed in [5] and was used to solve joint

tracking and classification problem in [6]. Moreover, the

optimal Bayes JDE algorithm was improved to recursive

JDE (RJDE) algorithm in [7]. Optimal Bayes JDE

algorithm was applied to solve JAE problem in [8].

However [8] used batch JDE rather than RJDE algorithm,

and only solved linear measurement problem.

In many applications, measurements are obtained

sequentially. So the computational demands of the batch

JDE algorithm will increase with an increase of data. Thus

RJDE algorithm would fit the problem more naturally. In

this paper, we try to apply RJDE algorithm to solve JAE

problem with nonlinear measurement and make it closer to

reality.

This paper is organized as follows. In Section 2 we

briefly describe the sensor bias model and association

problem. Section 3 gives a brief introduction to the RJDE

algorithm. The contribution of this paper is presented in

Section 4, where we use the RJDE method to solve JAE

problem with nonlinear measurement. Section 5 presents

simulation results. Finally, the concluding remarks are

given in Section 6.

2 Problem formulation

In this section, we present the association problem and

the bias estimation problem.

18th International Conference on Information Fusion

Washington, DC - July 6-9, 2015

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