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A Moving Target Tracking Method Based on Adaptive Tensor Decomposition in Bistatic MIMO Radar
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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。
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关键词:
- 双基地多输入多输出雷达 /
- 阵列信号处理 /
- 动目标跟踪 /
- 自适应张量分解 /
- 并行因子
Abstract: Moving target tracking is a fundamental task in bistatic Multiple-Input Multiple-Output (MIMO) radar systems, as it is essential for improving sensing accuracy and real-time adaptability in dynamic environments. This paper proposes a tracking algorithm based on Adaptive Tensor Decomposition (ATD) to address accuracy degradation caused by target dynamics and high-dimensional data coupling. A third-order streaming tensor is first established to model the time-varying, multi-dimensional structure of received signals from moving targets, which jointly incorporates the Direction Of Departure (DOD) and Direction Of Arrival (DOA). A dynamic mapping is then derived from the tensor to characterize the relationship between the target’s spatial state and the factor matrices. Next, a random dimensionality reduction strategy is integrated into the adaptive tensor decomposition, which iteratively updates the factor matrices that contain target state information, thereby enabling real-time and robust tracking of target angles. Finally, numerical simulations are conducted to evaluate the tracking performance of the proposed method. The results demonstrate that it provides continuous and stable tracking of moving targets under low Signal-to-Noise Ratio (SNR) conditions. Compared to classical approaches, the proposed algorithm reduces computational time by one to two orders of magnitude, demonstrating its effectiveness and real-time applicability in complex and dynamic environments. -
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 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 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。 
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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) $
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