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变分贝叶斯概率数据关联算法

恽鹏 吴盘龙 李星秀 何山

恽鹏, 吴盘龙, 李星秀, 何山. 变分贝叶斯概率数据关联算法. 自动化学报, 2022, 48(10): 2486−2495 doi: 10.16383/j.aas.c200407
引用本文: 恽鹏, 吴盘龙, 李星秀, 何山. 变分贝叶斯概率数据关联算法. 自动化学报, 2022, 48(10): 2486−2495 doi: 10.16383/j.aas.c200407
Yun Peng, Wu Pan-Long, Li Xing-Xiu, He Shan. Variational Bayesian probabilistic data association algorithm. Acta Automatica Sinica, 2022, 48(10): 2486−2495 doi: 10.16383/j.aas.c200407
Citation: Yun Peng, Wu Pan-Long, Li Xing-Xiu, He Shan. Variational Bayesian probabilistic data association algorithm. Acta Automatica Sinica, 2022, 48(10): 2486−2495 doi: 10.16383/j.aas.c200407

变分贝叶斯概率数据关联算法

doi: 10.16383/j.aas.c200407
基金项目: 国家自然科学基金(61473153)航空科学基金(2016ZC59006)资助
详细信息
    作者简介:

    恽鹏:南京理工大学自动化学院博士研究生. 主要研究方向为目标跟踪和鲁棒滤波. E-mail: yunpeng0409@163.com

    吴盘龙:南京理工大学自动化学院教授. 主要研究方向为目标跟踪, 信号处理和火控系统. 本文通信作者. E-mail: plwu@163.com

    李星秀:南京理工大学数学与统计学院副教授. 主要研究方向为目标跟踪和信号处理. E-mail: xxlwpl@126.com

    何山:南京理工大学自动化学院博士研究生. 主要研究方向为目标跟踪和火控系统. E-mail: heshanhshs@163.com

Variational Bayesian Probabilistic Data Association Algorithm

Funds: Supported by National Natural Science Foundation of China (61473153) and Aeronautical Science Foundation of China (2016-ZC59006)
More Information
    Author Bio:

    YUN Peng Ph.D. candidate at the School of Automation, Nanjing University of Science and Technology. His research interest covers target tracking and robust filtering

    WU Pan-Long Professor at the School of Automation, Nanjing University of Science and Technology. His research interest covers target tracking, signal processing and fire control systems. Corresponding author of this paper

    LI Xing-Xiu Associate professor at the School of Mathematics and Statistics, Nanjing University of Sci-ence and Technology. Her research interest covers target tracking and signal processing

    HE Shan Ph.D. candidate at the School of Automation, Nanjing University of Science and Technology. His research interest covers target tracking and fire control systems

  • 摘要: 针对杂波环境下的目标跟踪问题, 提出了一种基于变分贝叶斯的概率数据关联算法(Variational Bayesian based probabilistic data association algorithm, VB-PDA). 该算法首先将关联事件视为一个随机变量并利用多项分布对其进行建模, 随后基于数据集、目标状态、关联事件的联合概率密度函数求取关联事件的后验概率密度函数, 最后将关联事件的后验概率密度函数引入变分贝叶斯框架中以获取状态近似后验概率密度函数. 相比于概率数据关联算法, VB-PDA算法在提高算法实时性的同时在权重Kullback-Leibler (KL)平均准则下获取了近似程度更高的状态后验概率密度函数. 相关仿真实验对提出算法的有效性进行了验证.
  • 图  1  场景 1 下 3 种算法的位置 RMSE

    Fig.  1  The RMSE of position from three algorithms in scenario 1

    图  2  仿真场景 1 下 3 种算法的速度 RMSE

    Fig.  2  The RMSE of velocity from three algorithms in scenario 1

    图  3  仿真场景 2 下 3 种算法的位置 RMSE

    Fig.  3  The RMSE of position from three algorithms in scenario 2

    图  4  仿真场景 2 下 3 种算法的速度 RMSE

    Fig.  4  The RMSE of velocity from three algorithms in scenario 2

    表  1  一步状态更新过程中所需的加减运算与乘除运算次数

    Table  1  The number of addition and subtraction operations and multiplication and division operations required in the process of one-step state update

    算法加减法运算次数乘除法运算次数
    PDA$\begin{aligned} &{r^3}{n_{k + 1} } + {r^2}(m{n_{k + 1} } - {n_{k + 1} } + 2) + \\ &\qquad r({n_{k + 1} } + 1 + 2m) + 2{n_{k + 1} } - 1 +\\ & \qquad m{n_{k + 1} } - m\end{aligned}$$\begin{aligned} & {r^3} + {r^2}(2{n_{k + 1} } + m + 3) + \\ &\qquad r(2m + 1) + m{n_{k + 1} } + 1 \end{aligned}$
    DW-PDA$\begin{aligned} & {r^3}{n_{k + 1} } + {r^2}(m{n_{k + 1} } - {n_{k + 1} } + 2)\; + \\ &\qquad r({n_{k + 1} } + 1 + 2m) + 4{n_{k + 1} } - 3 + \\ &\qquad m{n_{k + 1} } - m\end{aligned}$$\begin{aligned} &{r^3} + {r^2}(2{n_{k + 1} } + m + 3)+ \\ &\qquad r(2m + 1) + m{n_{k + 1} } + 4{n_{k + 1} } + 1\end{aligned}$
    VB-PDA$\begin{aligned} & {r^3}{n_{k + 1} } + {r^2}(m{n_{k + 1} } - 2{n_{k + 1} } + 1)\; + \\ & \qquad2mr + 2{n_{k + 1} } - 1 + m{n_{k + 1} } - m \end{aligned}$$\begin{aligned} & {r^3} + {r^2}m + r(2m + 1)+\; \\ &\qquad m{n_{k + 1} } + 1 + {m^2} \end{aligned}$
    下载: 导出CSV

    表  2  场景 1 下 3 种算法的 TRMSE

    Table  2  The TRMSE of three algorithms in scenario 1

    算法位置 TRMSE (m)速度 TRMSE (m/s)
    PDA6.8920.873
    DW-PDA6.7920.839
    VB-PDA6.7420.872
    下载: 导出CSV

    表  3  场景 1 下一次蒙特卡洛仿真实验所需的计算时间

    Table  3  The computational time at one Monte Carlo simulation experiment in scenario 1

    算法计算时间 (ms)
    PDA56.52
    DW-PDA58.72
    VB-PDA46.70
    下载: 导出CSV

    表  4  仿真场景2下3种算法的TRMSE

    Table  4  The TRMSE of three algorithms in scenario 2

    算法位置TRMSE (m)速度TRMSE (m/s)
    IMM-PDA8.4091.874
    IMM-DW-PDA8.1011.818
    IMM-VB-PDA7.9671.784
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-06-11
  • 录用日期:  2020-09-07
  • 网络出版日期:  2022-09-19
  • 刊出日期:  2022-10-14

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