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水平集高斯过程的非星凸形扩展目标跟踪算法

陈辉 曾文爱 连峰 韩崇昭

陈辉, 曾文爱, 连峰, 韩崇昭. 水平集高斯过程的非星凸形扩展目标跟踪算法[J]. 电子与信息学报, 2023, 45(10): 3786-3795. doi: 10.11999/JEIT220997
引用本文: 陈辉, 曾文爱, 连峰, 韩崇昭. 水平集高斯过程的非星凸形扩展目标跟踪算法[J]. 电子与信息学报, 2023, 45(10): 3786-3795. doi: 10.11999/JEIT220997
CHEN Hui, ZENG Wenai, LIAN Feng, HAN Chongzhao. Non-Star-Convex Extended Target Tracking Algorithm for Level-Set Gaussian Process[J]. Journal of Electronics & Information Technology, 2023, 45(10): 3786-3795. doi: 10.11999/JEIT220997
Citation: CHEN Hui, ZENG Wenai, LIAN Feng, HAN Chongzhao. Non-Star-Convex Extended Target Tracking Algorithm for Level-Set Gaussian Process[J]. Journal of Electronics & Information Technology, 2023, 45(10): 3786-3795. doi: 10.11999/JEIT220997

水平集高斯过程的非星凸形扩展目标跟踪算法

doi: 10.11999/JEIT220997
基金项目: 国家自然科学基金(61873116, 62163023) , 甘肃省教育厅产业支撑计划项目(2021CYZC-02), 甘肃省科技计划项目(20JR10RA184)
详细信息
    作者简介:

    陈辉:男,教授,博士生导师,研究方向为目标跟踪和传感器管理

    曾文爱:女,硕士生,研究方向为扩展目标跟踪

    连峰:男,教授,博士生导师,研究方向为目标跟踪、信息融合与传感器管理

    韩崇昭:男,教授,博士生导师,研究方向为多源信息融合、随机控制与自适应控制、非线性频谱分析等

  • 中图分类号: TN911.7; TP274

Non-Star-Convex Extended Target Tracking Algorithm for Level-Set Gaussian Process

Funds: The National Natural Science Foundation of China (61873116, 62163023), The Industrial Support Project of Education Department of Gansu Province (2021CYZC-02), The Science and Technology Program of Gansu Province (20JR10RA184)
  • 摘要: 针对复杂环境下的非星凸形不规则形状扩展目标跟踪问题,该文提出基于能量泛函的水平集高斯过程扩展目标跟踪算法。首先,利用水平集随机超曲面模型(Level-Set RHM)通过多边形方法对形状内部进行建模。然后,用高斯过程(GP)学习Level-Set建模输入与输出的非线性映射关系,以求得边界函数最大值,并进一步推导Level-Set与GP相融合的非线性量测方程。在最优非线性滤波的框架下,最终推导得到水平集高斯过程(Level-Set GP)算法,并利用面积差作为不规则形状扩展目标形状估计的评价指标。仿真实验表明了所提算法对非星凸形不规则形状扩展目标形状估计的有效性。
  • 图  1  不规则扩展目标形状

    图  2  非星凸形扩展目标跟踪

    图  3  求边界形状函数最大值过程

    图  4  不同形状的跟踪效果

    图  5  不同形状的面积误差

    图  6  不同噪声下的面积误差

    图  7  动态目标跟踪

    图  8  不同时刻动态目标的面积误差

    图  9  群目标跟踪

    图  10  群目标面积误差

    算法1 Level-Set GP模型算法部分伪码
     输入:${\boldsymbol{x} }_{ { {k} } - 1|{ {k} } - 1}^{ {\rm{f} } } , { {\boldsymbol{F} }^{\rm{f} } }, {{\boldsymbol{Q}}_{ {k} } }, {\boldsymbol{x}}_0^{{\rm{p}}} , {{\boldsymbol{P}}_{ { {k} } - 1|{ {k} } - 1} }, {{\boldsymbol{C}}_{ { {k} } - 1|{ {k} } - 1} }, {\boldsymbol{F}}_{ {k} }^{{\rm{p}}} , {\boldsymbol{Q}}_{ {k} }^{{\rm{p}}}$
     步骤1 预测
     for$ {{ }}k = 1{{ : }}N $
       ${\boldsymbol{x} }_{ { {k} }|{ {k} } - 1}^{\rm{ {f} } } = { {\boldsymbol{F} }^{ {\rm{f} } } }{\boldsymbol{x} }_{ { {k} } - 1|{ {k} } - 1}^{{\rm{f}}}$;
       ${{\boldsymbol{P}}_{ { {k} }|{ {k} } - 1} } = {{\boldsymbol{F}}^{\rm{f}}}{{\boldsymbol{P}}_{ { {k} } - 1|{ {k} } - 1} }{({{\boldsymbol{F}}^{\rm{f}}})^{{\rm{T}}} } + {{\boldsymbol{Q}}_{ {k} } }$;
       根据式(10)—式(11),计算得到$ {{k}} $时刻扩展形状参数的预测值;
       ${{\boldsymbol{C}}_{ { {k} }|{ {k} } - 1} } = {\boldsymbol{F}}_{ {k} }^{{\rm{p}}} {{\boldsymbol{C}}_{ { {k} } - 1|{ {k} } - 1} }{({\boldsymbol{F}}_{ {k} }^{{\rm{p}}} )^{{\rm{T}}} } + {\boldsymbol{Q}}_{ {k} }^{{\rm{p}}}$;
     end for
     步骤2 更新
     for $ k = 1:N $
       for $ {{ }}j = 1:{\rm{num}} $
         根据式(43)计算$ k $时刻边界形状函数最大值;
         计算伪量测方程传递后的样本点$ h_{k,j}^* $;
         根据式(47)—式(52),更新扩展形状参数${\boldsymbol{x}}_{ {k} }^{{\rm{p}}}$和协方差${{\boldsymbol{C}}_{ { {k} }|{ {k} } } }$;
       end for
     end for
     输出:${\boldsymbol{x}}_{ {k} }^{{\rm{p}}} , {{\boldsymbol{C}}_{ { {k} }|{ {k} } } }$
    下载: 导出CSV
    算法2 面积差算法
     输入:$ {{x,}}{{y,}}{{X,}}{{Y}} $
     ${ {\rm{poly} } } 1 = { {\rm{polyshape} } } ({{x} },{{y} })$;
     ${{\rm{poly}}} 2 = {{\rm{polyshape}}} ({{X} },{{Y} })$;
     ${{\rm{intpoly}}} = {{\rm{intersect}}} ({{\rm{poly}}} 1,{{\rm{poly}}} 2)$;
     ${{\rm{intarea}}} = {{\rm{polyarea}}} ({{\rm{intpoly}}} (:,1),{{\rm{intpoly}}} (:,2))$;
     ${{\rm{unipoly}}} = { {\rm{union} } } ({ {\rm{poly} } } 1,{ {\rm{poly} } } 2)$;
     ${{\rm{uniarea}}} = {{\rm{polyarea}}} ({{\rm{unipoly}}} (:,1),{{\rm{unipoly}}} (:,2))$;
     ${ {\rm{trueshape} } } = { {\rm{polyarea} } } ({{X,Y} })$;
     根据式(54), 计算面积误差$\epsilon$。
     输出:$\epsilon$
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-07-27
  • 修回日期:  2023-01-04
  • 网络出版日期:  2023-01-14
  • 刊出日期:  2023-10-31

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