Non-Star-Convex Extended Target Tracking Algorithm for Level-Set Gaussian Process
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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。
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关键词:
- 扩展目标跟踪 /
- 非星凸形 /
- 水平集随机超曲面模型 /
- 高斯过程 /
- 非线性滤波
Abstract: To solve the problem of extended target tracking with non-star-convex irregular shape in complex environments, a level-set gaussian process extended target tracking algorithm based on energy functional is proposed. First, the interior of the shape is modeled by the polygonal method using the Level-Set Random Hypersurface Model (Level-Set RHM). Then, the nonlinear mapping relationship between the input and output of the Level-Set modeling is learned by using Gaussian Process (GP) to obtain the maximum value of the boundary function, and the nonlinear measurement equation based on the fusion of Level-Set and GP is further derived. Under the framework of optimal nonlinear filtering, Level-Set Gaussian Process (Level-Set GP) non-star convex extended target tracking algorithm is finally derived. And the area error is used as an evaluation index for the shape estimation of irregularly shaped extended targets. The simulation experiments show that the proposed algorithm is effective for the non-star convex irregular shape extended target shape estimation. -
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} } } }$ 
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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：$\epsilon$
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