基于随机有限集的非齐次马尔可夫链联合概率数据关联滤波器

朱昀; 梁爽; 吴晓军; 杨红红

doi:10.1631/FITEE.2000209

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基于随机有限集的非齐次马尔可夫链联合概率数据关联滤波器

常规文章 | Updated：2022-05-19

- 基于随机有限集的非齐次马尔可夫链联合概率数据关联滤波器
- A random finite set based joint probabilistic data association filter with non-homogeneous Markov chain
- 信息与电子工程前沿（英文） 2021年22卷第8期页码：1114-1126
- Affiliations：
  
  Key Laboratory of Modern Teaching Technology, Ministry of Education, Xi'an 710062, China
  School of Computer Science, Shaanxi Normal University, Xi'an 710119, China
  Academy of Advanced Interdisciplinary Research, Xidian University, Xi'an 710071, China
- Author bio：
  
  [ "Yun ZHU, yunzhu@snnu.edu.cn" ]
  Xiaojun WU, E-mail: xjwu@snnu.edu.cn
- Funds：
  
  Project supported by the National Key Research and Development Program of China (No. 2017YFB1402102), the National Natural Science Foundation of China (Nos. 61907028 and 11872036), the Natural Science Foundation of Shaanxi Province, China (Nos. 2020JQ-423, 2019JQ-574, and 2019ZDLSF07-01), the Fundamental Research Funds for the Central Universities, China (No. GK201903103), and the China Postdoctoral Science Foundation (No. 2018M640950)
- DOI：10.1631/FITEE.2000209
  中图分类号： TN713
- 收稿：2020-05-01，
  
  修回：2021-;7-14，
  
  纸质出版：2021-08
- Accepted：
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朱昀, 梁爽, 吴晓军, 等. 基于随机有限集的非齐次马尔可夫链联合概率数据关联滤波器[J]. 信息与电子工程前沿（英文）, 2021,22(8):1114-1126.

Yun ZHU, Shuang LIANG, Xiaojun WU, et al. A random finite set based joint probabilistic data association filter with non-homogeneous Markov chain[J]. Frontiers of Information Technology & Electronic Engineering, 2021, 22(8): 1114-1126.
朱昀, 梁爽, 吴晓军, 等. 基于随机有限集的非齐次马尔可夫链联合概率数据关联滤波器[J]. 信息与电子工程前沿（英文）, 2021,22(8):1114-1126. DOI： 10.1631/FITEE.2000209.

Yun ZHU, Shuang LIANG, Xiaojun WU, et al. A random finite set based joint probabilistic data association filter with non-homogeneous Markov chain[J]. Frontiers of Information Technology & Electronic Engineering, 2021, 22(8): 1114-1126. DOI： 10.1631/FITEE.2000209.

摘要

提出一种启发式方法，通过随机有限集理论优化数据关联跟踪算法的后验密度。具体而言，提出一种改进的联合概率数据关联滤波方法，即最近邻集合联合概率数据关联方法（NNSJPDA）。为提高边缘化的准确性，利用一种基于Kullback–Leibler散度的最近邻方法，对所有可能的数据关联事件中的目标标签进行转换。此外，进一步考虑目标标签向量的分布。后验密度转换后，可得到目标标签向量的转移矩阵。该转移矩阵随时间变化，使得目标标签向量分布的传播遵循非齐次马尔可夫链。证明了该链本质上是双随机的，并推导了相应定理。通过举例和仿真，验证了所提方法的有效性。本文结果可推广到相同随机有限集框架下的其他数据关联方法。

Abstract

We demonstrate a heuristic approach for optimizing the posterior density of the data association tracking algorithm via the random finite set (RFS) theory. Specifically

we propose an adjusted version of the joint probabilistic data association (JPDA) filter

known as the nearest-neighbor set JPDA (NNSJPDA). The target labels in all possible data association events are switched using a novel nearest-neighbor method based on the Kullback–Leibler divergence

with the goal of improving the accuracy of the marginalization. Next

the distribution of the target-label vector is considered. The transition matrix of the target-label vector can be obtained after the switching of the posterior density. This transition matrix varies with time

causing the propagation of the distribution of the target-label vector to follow a non-homogeneous Markov chain. We show that the chain is inherently doubly stochastic and deduce corresponding theorems. Through examples and simulations

the effectiveness of NNSJPDA is verified. The results can be easily generalized to other data association approaches under the same RFS framework.

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