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A Novel Method for Tracking Complex Maneuvering Star Convex Extended Targets Using Transformer Network
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摘要: 针对复杂的机动扩展目标跟踪问题，利用Transformer网络设计了一种有效的星凸不规则形状机动扩展目标跟踪方法。首先，该文研究利用alpha-shape算法建立了星凸形状的变化模型，实现了静态场景下的星凸形扩展目标的形状估计。然后，通过对目标状态转移矩阵进行重新设计，结合Transformer网络对机动扩展目标运动状态转移矩阵进行实时估计，实现了对复杂机动目标运动过程的精准跟踪。进一步地，将估计得到的形状轮廓与运动状态进行融合，最终实现了对星凸形机动扩展目标的实时跟踪。最后，通过构造复杂的机动扩展目标跟踪场景，利用多重性能指标测试算法对形状和运动状态的综合估计性能，验证了算法的有效性。
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关键词:
- 扩展目标跟踪 /
- 机动目标 /
- Transformer /
- 星凸形 /
- 弗雷歇距离-面积误差
Abstract: To address the challenges in tracking complex maneuvering extended targets, an effective maneuvering extended target tracking method was proposed for irregularly shaped star-convex using a Transformer network. Initially, the alpha-shape algorithm was used to model the variations in the star-convex shape. In addition, a recursive approach was proposed to estimate the irregular shape of an extended target by detailed derivation in the Bayesian filtering framework. This approach accurately estimated the shape of a static star convex extended target. Moreover, through the structural redesign of the target state transition matrix and the real-time estimation of the maneuvering extended target’s state transition matrix using a transformer network, the accurate tracking of complex maneuvering targets was achieved. Furthermore, the real-time tracking of star convex maneuvering extended targets was achieved by fusing the estimated shape contours with motion states. This study focused on constructing certain complex maneuvering extended target tracking scenarios to assess the performance of the proposed method and the comprehensive estimation capabilities of the algorithm considering both shapes and motion states using multiple performance indicators. -
图 2 利用alpha-shape算法提取目标形状
Figure 2. Target shape extraction using alpha-shape algorithm
图 16 形状自适应性测试的面积误差对比
Figure 16. Comparison of area errors for the shape adaptation tests
图 19 不同算法的单步运行时间对比
Figure 19. Comparison of single-step running time for different algorithms
1 结合Transformer的星凸形机动扩展目标跟踪部分伪代码
1. The pseudo-code of star convex maneuvering extended target tracking using Transformer algorithm
输入：$ {A_1},{A_2},{x_0},{P_0},{W_k},{U_k},{Q_k},{R_k},P_0^{{\text{cap}}} $ 步骤1：预测 for k = 1: steps % 量测集处理与形状初步处理 ${{\boldsymbol{\bar z}}_k} = \dfrac{1}{l}\displaystyle\sum\limits_{i = 1}^l {{{\boldsymbol{z}}_{k,l}}} $ ${{\boldsymbol{\tilde Z}}_k} = \{ {{\boldsymbol{\tilde z}}_{k,l}}\} $ ${{\boldsymbol{C}}_k} = {{\mathrm{as}}} (a,{{\boldsymbol{\tilde Z}}_k})$ ${{\boldsymbol{Z}}^k} = {{\mathrm{s}}} ({{\boldsymbol{C}}_k})$ % 静态形状预测 $ \mathcal{X}_k^ - - {\bar{\mathcal{X}} _k} = {\boldsymbol{A}}(\mathcal{X}_{k - 1}^ - - {\bar {\mathcal{X}} _k}) $ ${\boldsymbol{P}}_k^ - = {\boldsymbol{A}}{{\boldsymbol{P}}_k}{{\boldsymbol{A}}^{\text{T}}} + {{\boldsymbol{W}}_k}{\boldsymbol{W}}_k^{\text{T}}$ % 运动状态预测 $\hat \chi _{k - 1}^j = {\boldsymbol{F}}_k^i\chi _{k - 1}^j$ $ {{\boldsymbol{x}}_{k|k - 1}} = \dfrac{1}{m}\displaystyle\sum\limits_{j = 1}^m {\chi _{k - 1}^j} $ % 形态预测 $\mathcal{X}_{k,s}^ - = \mathcal{X}_k^ - + {{\boldsymbol{x}}_{k|k - 1}}$ end 步骤2：更新 for k = 1: steps % 静态形状更新 ${{\boldsymbol{K}}_k} = {\boldsymbol{P}}_k^ - {{\boldsymbol{H}}^{\text{T}}}{({{\boldsymbol{S}}_k}{\boldsymbol{HP}}_k^ - {{\boldsymbol{H}}^{\text{T}}} + {\boldsymbol{I}})^{ - 1}}$ ${\hat {\mathcal{X}}_k} = \mathcal{X}_k^ - + {{\boldsymbol{K}}_k}{{\boldsymbol{Z}}^k}$ ${{\boldsymbol{P}}_k} = ({\boldsymbol{I}} - {{\boldsymbol{K}}_k}{{\boldsymbol{S}}_k}{\boldsymbol{H}}){\boldsymbol{P}}_k^ - $ % 状态转移矩阵更新 ${{\boldsymbol{F}}_k} = {\text{TFMETT}}({{\boldsymbol{\bar z}}_k})$ % 运动状态更新 ${{\boldsymbol{\hat x}}_k} = {{\boldsymbol{x}}_{k|k - 1}} + {\boldsymbol{K}}_k^{{\text{cap}}}({{\boldsymbol{\bar z}}_k} - {{\boldsymbol{z}}_{k|k - 1}})$ ${\boldsymbol{P}}_k^{{\text{cap}}} = {\boldsymbol{P}}_{k|k - 1}^{{\text{cap}}} - {\boldsymbol{K}}_k^{{\text{cap}}}{\boldsymbol{S}}_k^{{\text{cap}}}{\left( {{\boldsymbol{K}}_k^{{\text{cap}}}} \right)^{\text{T}}}$ % 形态更新 ${\hat {\mathcal{X}}_{k,s}} = {\hat {\mathcal{X}}_k} + {{\boldsymbol{\hat x}}_k}$ end 输出：${\hat {\mathcal{X}}_{k,s}}$ 
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表 1 50次蒙特卡罗仿真测试中各种算法的平均单步运行时间
Table 1. Average single-step running time of various algorithms in 50 Monte Carlo simulation tests
算法 平均单步运行时间(s) RHM 0.38 GPR 0.41 TFMETT 0.26
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