基于自适应张量分解的双基地MIMO雷达动目标跟踪方法

刘清 张海蕊 谢坚 陶明亮 王伶

刘清, 张海蕊, 谢坚, 等. 基于自适应张量分解的双基地MIMO雷达动目标跟踪方法[J]. 雷达学报(中英文), 待出版. doi: 10.12000/JR25107
引用本文: 刘清, 张海蕊, 谢坚, 等. 基于自适应张量分解的双基地MIMO雷达动目标跟踪方法[J]. 雷达学报(中英文), 待出版. doi: 10.12000/JR25107
LIU Qing, ZHANG Hairui, XIE Jian, et al. A moving target tracking method based on adaptive tensor decomposition in bistatic MIMO radar[J]. Journal of Radars, in press. doi: 10.12000/JR25107
Citation: LIU Qing, ZHANG Hairui, XIE Jian, et al. A moving target tracking method based on adaptive tensor decomposition in bistatic MIMO radar[J]. Journal of Radars, in press. doi: 10.12000/JR25107

基于自适应张量分解的双基地MIMO雷达动目标跟踪方法

DOI: 10.12000/JR25107 CSTR: 32380.14.JR25107
基金项目: 国家自然科学基金(62271412),西北工业大学博士论文创新基金(CX2025077)
详细信息
    作者简介:

    刘 清,博士生,研究方向为阵列信号处理、目标定位跟踪

    张海蕊,硕士生,研究方向为雷达目标检测、辐射源定位

    谢 坚,博士,教授,研究方向为阵列信号处理、电子侦察与对抗

    陶明亮,博士,教授,研究方向为雷达信号处理、遥感侦察与对抗

    王 伶,博士,教授,研究方向为卫星导航与通信、电子侦察与对抗

    通讯作者:

    谢坚 xiejian@nwpu.edu.cn

  • 责任主编:程子扬 Corresponding Editor: CHENG Ziyang
  • 中图分类号: TN959.1

A Moving Target Tracking Method Based on Adaptive Tensor Decomposition in Bistatic MIMO Radar

Funds: The National Natural Science Foundation of China (62271412), Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (CX2025077)
More Information
  • 摘要: 动目标跟踪是双基地多输入多输出(MIMO)雷达系统的核心任务之一,对提升系统的目标感知精度与动态响应能力具有重要意义。针对复杂场景下动目标跟踪性能易受状态变化、高维数据耦合等因素制约的问题,该文提出一种基于自适应张量分解(ATD)的动目标跟踪算法。首先建立包含运动目标波离方向(DOD)和波达方向(DOA)信息的三阶动态张量信号模型,以表征接收信号中时、空多维数据的时变结构。基于所建立动态张量模型,构建运动目标空间位置与张量因子矩阵间的映射关系,采用矩阵随机降维策略设计自适应因子矩阵更新机制,迭代分解包含目标状态信息的阵列流形矩阵,以实现对目标方向的实时稳健跟踪。最后,通过仿真实验分析所提算法的跟踪性能。仿真结果表明,所提算法在低信噪比(SNR)场景下可实现动目标轨迹的持续稳定跟踪。与传统动目标跟踪算法相比,所提算法在保证跟踪精度的同时降低了计算复杂度,跟踪运算时长可缩短1~2个数量级,满足双基地MIMO雷达系统对动目标的实时跟踪需求。

     

  • 图  1  双基地MIMO雷达动目标跟踪示意图

    Figure  1.  Moving target tracking by bistatic MIMO radar

    图  2  三阶张量的PARAFAC分解模型

    Figure  2.  PARAFAC decomposition of third-order tensor

    图  3  动态时变张量表征模型

    Figure  3.  Illustration of dynamic tensor model

    图  4  基于自适应张量分解的动目标轨迹跟踪

    Figure  4.  Target tracking based on adaptive tensor decomposition

    图  5  SNR=10 dB多目标跟踪结果

    Figure  5.  Multi-target tracking results at SNR=10 dB

    图  6  SNR=0 dB多目标跟踪结果

    Figure  6.  Multi-target tracking results at SNR=0 dB

    图  7  SNR=–10 dB多目标跟踪结果

    Figure  7.  Multi-target tracking results at SNR=–10 dB

    图  8  角度跟踪RMSE受信噪比影响对比

    Figure  8.  RMSE comparison v.s. SNR

    图  9  角度跟踪RMSE受阵元数目影响对比

    Figure  9.  RMSE comparison v.s. number of array elements

    图  10  角度跟踪RMSE受采样快拍数目影响对比

    Figure  10.  RMSE comparison v.s. number of snapshots

    图  11  角度跟踪RMSE受降维系数影响对比

    Figure  11.  RMSE comparison v.s. dimensionality reduction coefficients

    图  12  计算复杂度对比

    Figure  12.  Computational complexity comparison

    图  13  跟踪算法运行时长结果对比

    Figure  13.  Computing time comparison of different tracking algorithms

    1  动目标跟踪算法流程

    1.   Moving target tracking algorithm

     输入:接收端阵列原始采样信号$ {\boldsymbol{X}}(t) $
     步骤1:算法初始化
       初始化$ {\boldsymbol{A}}(0) $,$ {\boldsymbol{B}}(0) $为独立同分布的高斯随机变量,并设置$ r \lt MN $。
     步骤2:接收数据矢量化
       根据式(10)和式(11)对$ {\boldsymbol{X}}(t) $匹配滤波和矢量化,得到接收信号$ {\boldsymbol{y}}(t) $。
     步骤3:自适应张量分解
       3.1:随机选取$ {\boldsymbol{\varPsi}} (t - 1) $和$ {\boldsymbol{y}}(t) $的r行得到$ \bar {\boldsymbol{\varPsi}} (t - 1) $和$ {\boldsymbol{\bar y}}(t) $;
       3.2:构建关于$ {\boldsymbol{\beta}} (t) $求解的代价函数,根据式(38)计算$ \hat {\boldsymbol{\beta}} (t) $;
       3.3:构建关于$ {\boldsymbol{B}}(t) $求解的代价函数,根据式(45)计算$ {{\hat {\boldsymbol B}}}(t) $;
       3.4:构建关于$ {\boldsymbol{A}}(t) $求解的代价函数,根据式(48)计算$ {{\hat {\boldsymbol A}}}(t) $
     步骤4:角度更新
       4.1:根据式(49)、式(50)计算$ {{\boldsymbol{\varTheta}} _q}(t) $, $ {{\boldsymbol{\varPhi}} _q}(t) $,进行特征值分解并构造噪声子空间$ {{\boldsymbol{U}}_\vartheta }(t) $, $ {{\boldsymbol{U}}_\upsilon }(t) $;
       4.2:根据式(54)、式(55),构造求根多项式$ {f_\vartheta }(z) $, $ {f_\upsilon }(z) $,求解并根据式(56)、式(57)计算目标发射角$ {\hat \varphi _q}(t) $和接收角$ {\hat \theta _q}(t) $。
     步骤5:轨迹更新
       对$ t + 1 $时刻接收信号$ {\boldsymbol{X}}(t + 1) $重复步骤2—步骤4;
     输出Q个目标的DOD和DOA。
    下载: 导出CSV

    表  1  运算复杂度对比

    Table  1.   Comparison of computational complexity

    算法名称 运算复杂度
    AAJD $ O(4{M^3}{N^3}{Q^2} + 12{M^2}{N^2} + 5{M^3}{N^3} + 4{M^3}Q + 4{N^3}Q) $
    DPD $ O(2{I_{\rm d}}{Q^3} + 4{I_{\rm d}}MN{Q^2} + 5{I_{\rm d}}{M^2}{N^2}Q + M{Q^2} + N{Q^2} + 2Q{M^3} + 2Q{N^3}) $
    SOPD $ O(4{I_{\rm s}}{M^2}{N^2}Q + {I_{\rm s}}MN{Q^2} + M{Q^2} + N{Q^2} + 2Q{M^3} + 2Q{N^3}) $
    SDT $ O[16{Q^3} + {Q^2}(31MN + 31{T_{\mathrm{W}}} + 40) + Q(32MN + 10N + 20) + 2{M^3}Q + 2{N^3}Q] $
    本文算法 $ O(8r{Q^2} + 4rQ + M{Q^2} + N{Q^2} + 2{M^3}Q + 2{N^3}Q) $
    下载: 导出CSV
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  • 收稿日期:  2025-06-06
  • 修回日期:  2025-08-16

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