水下地形导航模型求解与导航区初选策略研究
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摘要
水下地形导航是辅助潜器惯性导航的一种方式,本文在水下地形函数插值逼近、水下地形导航模型求解和水下地形导航区初选三个方面进行了研究。
水深是位置的函数简称地形函数,是没有显式表达式的非线性函数。为避免地形线性化处理,采用插值的方式对地形函数进行逼近。把协调Delaunay三角化的思想融入自然邻点插值,提出协调自然邻点插值算法。与约束自然邻点插值相比,协调自然邻点插值简化了构建插值点二阶约束Voronoi单元的过程,使算法易于实施,同时保留了传统自然邻点插值定义域稳定、平滑度高、形函数满足克罗内克尔6函数特性等优点。提出端点三角形外接圆法进行协调Delaunay三角化中特征约束的细分嵌入,在保证附加点个数和网格质量与现有最好算法持平的基础上,时间复杂度接近线性。实验结果表明协调自然邻点插值比不规则三角网插值的插值误差低、反映细节能力强,可以满足地形导航中逼近地形函数的需要。
水下地形导航系统是一个非线性动态系统,建立了水下地形导航随机微分模型,探索变分法求解导航状态微分方程的可行性,在有限维函数空间里逼近状态概率密度函数。设计了递推伽辽金投影滤波器,使伽辽金投影滤波具有了递推特性。由于多维矩阵相乘编程实现困难,目前递推伽辽金投影滤波还没有用于状态维数大于二的系统。在一维空间进行的实验结果表明,目前递推伽辽金投影滤波可以在有限维函数空间内求得系统状态的概率密度函数,也可以跟踪系统状态的演变,但均方根误差较大,估计方差的收敛速度和光滑性比不上粒子滤波。
采用常用的导航滤波方法对水下地形导航随机微分模型进行差分求解。为适应地形的非线性,提出插值地形导航方法,使用协调自然邻点插值计算由地形图读出的水深。实验结果表明,对于同一种滤波算法,插值地形导航可以有效减少发散现象、降低估计误差和估计误差的波动幅度。
由于高精度水深测量成本高,提出以矢量电子海图中地形数据作为地形导航区初选的数据源。通过实验分析了地形参数与导航误差之间的关系,构建了基于矢量电子海图的水下数字高程模型,发现比例尺大于1：5万的电子海图可以作为地形导航区初选的数据源。
Underwater terrain navigation is a way for aiding inertial navigation. This thesis is focus on underwater terrain function approximating, underwater terrain navigation model solving and underwater terrain navigation cell choosing three aspects.
Terrain elevation is a nonlinear function of position, terrain function for short. There is no explicit function can describe this function, so interpolation method is used to approximate terrain function. A new interpolation method named "conforming natural neighbor interpolation" (Conforming-NNI) is proposed, in which natural neighbor interpolation is combined with conforming Delaunay triangulation. Compared to constrained natural neighbor interpolation, Conforming-NNI simplifies the procedure of constructing second order constraint Voronoi cells of interpolation target, making interpolation can be implemented more easily, and keeping the advantages of traditional natural neighbor interpolation, such as steady interpolation supports, high smoothness, and shape functions share keronecker delta property etc. An improved algorithm of node refinement scheme called "Endpoint Triangle's Circum-circle Method" (ETCM) is proposed for refining the feature segments in conforming Delaunay triangulation. Time complexity of ETCM goes to nearly linear, meanwhile new nodes quantity and mesh quality of ETCM are almost the same as the best of existing algorithms. Experiment results show that compared with TIN interpolation, interpolation error and the ability of reflecting details of Conforming-NNI is better. Conforming-NNI is competent for approximating terrain function.
Underwater terrain navigation system is a nonlinear dynamic system. In this thesis a terrain navigation stochastic differential model (TNSDM) is established, and the feasibility of solving state differential function in variational way is explored, in which the state probability density function (pdf) is approximated in a finite dimensional function space. A modified version of Galerkin Projection Filtering method named "Recursive Galerkin Projection Filter" (RGPF) is proposed, and detail solving procedure of n-dimensional state space is given. Due to programming difficulty of calculate multi-dimension matrix multiplication, RGPF has not been used in the system whose state dimension lager than one. In the simulation of one dimension state space, results show that RGPF can obtain the state pdf in finite dimensional function space, and can track the true state, but its root mean square error (RMSE) and stander deviation is larger than Particle Filter.
Common navigation filters are adopted to solve TNSDM in difference way. In order to avoid the divergency phenomenon caused by terrain linearization, interpolation terrain navigation method is proposed, in which Conforming-NNI is used to calculate the water depth from terrain map. Simulation results show that, for same filter, interpolation terrain navigation method can reduce divergency times, estimation error and error range.
Due to high cost of high precision water depth measurement, a scheme that the terrain data in vector nautical charts can used as the data source for terrain navigation cell primary selection is proposed. The relation between terrain parameters and navigation error are analyzed through experiments. Methods of constructing the underwater digital elevation model (DEM) based on vector nautical chart are proposed, and experiment results show that the primary navigation cell can be selected from the nautical charts whose scale is larger than 1:50000.
水深是位置的函数简称地形函数,是没有显式表达式的非线性函数。为避免地形线性化处理,采用插值的方式对地形函数进行逼近。把协调Delaunay三角化的思想融入自然邻点插值,提出协调自然邻点插值算法。与约束自然邻点插值相比,协调自然邻点插值简化了构建插值点二阶约束Voronoi单元的过程,使算法易于实施,同时保留了传统自然邻点插值定义域稳定、平滑度高、形函数满足克罗内克尔6函数特性等优点。提出端点三角形外接圆法进行协调Delaunay三角化中特征约束的细分嵌入,在保证附加点个数和网格质量与现有最好算法持平的基础上,时间复杂度接近线性。实验结果表明协调自然邻点插值比不规则三角网插值的插值误差低、反映细节能力强,可以满足地形导航中逼近地形函数的需要。
水下地形导航系统是一个非线性动态系统,建立了水下地形导航随机微分模型,探索变分法求解导航状态微分方程的可行性,在有限维函数空间里逼近状态概率密度函数。设计了递推伽辽金投影滤波器,使伽辽金投影滤波具有了递推特性。由于多维矩阵相乘编程实现困难,目前递推伽辽金投影滤波还没有用于状态维数大于二的系统。在一维空间进行的实验结果表明,目前递推伽辽金投影滤波可以在有限维函数空间内求得系统状态的概率密度函数,也可以跟踪系统状态的演变,但均方根误差较大,估计方差的收敛速度和光滑性比不上粒子滤波。
采用常用的导航滤波方法对水下地形导航随机微分模型进行差分求解。为适应地形的非线性,提出插值地形导航方法,使用协调自然邻点插值计算由地形图读出的水深。实验结果表明,对于同一种滤波算法,插值地形导航可以有效减少发散现象、降低估计误差和估计误差的波动幅度。
由于高精度水深测量成本高,提出以矢量电子海图中地形数据作为地形导航区初选的数据源。通过实验分析了地形参数与导航误差之间的关系,构建了基于矢量电子海图的水下数字高程模型,发现比例尺大于1：5万的电子海图可以作为地形导航区初选的数据源。
Underwater terrain navigation is a way for aiding inertial navigation. This thesis is focus on underwater terrain function approximating, underwater terrain navigation model solving and underwater terrain navigation cell choosing three aspects.
Terrain elevation is a nonlinear function of position, terrain function for short. There is no explicit function can describe this function, so interpolation method is used to approximate terrain function. A new interpolation method named "conforming natural neighbor interpolation" (Conforming-NNI) is proposed, in which natural neighbor interpolation is combined with conforming Delaunay triangulation. Compared to constrained natural neighbor interpolation, Conforming-NNI simplifies the procedure of constructing second order constraint Voronoi cells of interpolation target, making interpolation can be implemented more easily, and keeping the advantages of traditional natural neighbor interpolation, such as steady interpolation supports, high smoothness, and shape functions share keronecker delta property etc. An improved algorithm of node refinement scheme called "Endpoint Triangle's Circum-circle Method" (ETCM) is proposed for refining the feature segments in conforming Delaunay triangulation. Time complexity of ETCM goes to nearly linear, meanwhile new nodes quantity and mesh quality of ETCM are almost the same as the best of existing algorithms. Experiment results show that compared with TIN interpolation, interpolation error and the ability of reflecting details of Conforming-NNI is better. Conforming-NNI is competent for approximating terrain function.
Underwater terrain navigation system is a nonlinear dynamic system. In this thesis a terrain navigation stochastic differential model (TNSDM) is established, and the feasibility of solving state differential function in variational way is explored, in which the state probability density function (pdf) is approximated in a finite dimensional function space. A modified version of Galerkin Projection Filtering method named "Recursive Galerkin Projection Filter" (RGPF) is proposed, and detail solving procedure of n-dimensional state space is given. Due to programming difficulty of calculate multi-dimension matrix multiplication, RGPF has not been used in the system whose state dimension lager than one. In the simulation of one dimension state space, results show that RGPF can obtain the state pdf in finite dimensional function space, and can track the true state, but its root mean square error (RMSE) and stander deviation is larger than Particle Filter.
Common navigation filters are adopted to solve TNSDM in difference way. In order to avoid the divergency phenomenon caused by terrain linearization, interpolation terrain navigation method is proposed, in which Conforming-NNI is used to calculate the water depth from terrain map. Simulation results show that, for same filter, interpolation terrain navigation method can reduce divergency times, estimation error and error range.
Due to high cost of high precision water depth measurement, a scheme that the terrain data in vector nautical charts can used as the data source for terrain navigation cell primary selection is proposed. The relation between terrain parameters and navigation error are analyzed through experiments. Methods of constructing the underwater digital elevation model (DEM) based on vector nautical chart are proposed, and experiment results show that the primary navigation cell can be selected from the nautical charts whose scale is larger than 1:50000.
引文
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