WO2023159420A1 - Distance and direction relation uncertainty measurement method - Google Patents
Distance and direction relation uncertainty measurement method Download PDFInfo
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- WO2023159420A1 WO2023159420A1 PCT/CN2022/077657 CN2022077657W WO2023159420A1 WO 2023159420 A1 WO2023159420 A1 WO 2023159420A1 CN 2022077657 W CN2022077657 W CN 2022077657W WO 2023159420 A1 WO2023159420 A1 WO 2023159420A1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
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- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
- G06T17/05—Geographic models
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- the present invention relates to the field of surveying and mapping and geographic information science (attributed by subject) and geospatial data consistency verification and control, land resource management and law enforcement, surface change detection and urban and rural planning and other related topics and fields (attributed by application), specifically It is a measurement method for the uncertainty of the relationship between distance and direction caused by the uncertainty of point information.
- the spatial location information recorded in the geospatial database is uncertain.
- the spatial relationship can be intuitively understood as a function of the spatial position.
- a definite spatial position leads to a definite spatial relationship, while an uncertain spatial position leads to an uncertain spatial relationship.
- the uncertainty of spatial relationship can be regarded as the uncertainty of spatial position via the Transfer of functional relations. How to scientifically and reasonably measure this uncertainty is crucial for improving the quality and efficiency of geospatial data processing and analysis, improving the consistency verification and control of geospatial data, land resource management and law enforcement, surface change detection and urban and rural planning, etc.
- Spatial relationship includes distance relationship, direction relationship, topological relationship, etc.
- This patent focuses on the measurement method of the uncertainty of distance and direction relationship caused by point uncertainty. Previous research on this problem is less, and the research results have not yet fully revealed the functional relationship from the uncertainty of point information to the uncertainty of the relationship between distance and direction. At present, there is no good solution in the industry.
- the invention provides a measurement method for the uncertainty of distance and direction relationship information caused by the uncertainty of point information, and reveals the point position uncertainty by establishing a quantitative model of point position uncertainty, distance relationship between points, and direction relationship uncertainty.
- the functional relationship of information uncertainty to the transmission of distance and direction information uncertainty is scientific, reasonable, practical and efficient.
- the present invention includes:
- the possible range of the actual position of the uncertain point is described by an error circle with its observed position as the center; when the application involved is a three-dimensional space, The possible range of the actual position of the uncertain point is described by an error sphere with its observed position as the center of the sphere; An error hypersphere description with its observation position as the center of the hypersphere.
- z is a random variable, which represents the possible value of the distance between a definite point and an uncertain point
- g 1 (z) is the density function of the random variable z
- x (x>0) is the definite point and the uncertain point
- the distance between the observation positions, r(0 ⁇ r ⁇ x) is the radius of the error circle
- t is the integral variable
- t 1 and t 2 are the upper and lower limits of the integral interval corresponding to the integral variable
- u (zcost-x,zsint)
- k(u) represents the distribution density function that the actual position of the uncertain point appears in the corresponding error circle, which describes the nature of the uncertain point, and k(u) is commonly used
- the analytical expression is as follows:
- formula (1) and its variables are expanded into corresponding forms based on the relevant knowledge of spherical trigonometry, three-dimensional analytic geometry and multi-dimensional vector.
- z is a random variable, indicating the possible value of the distance between two uncertain points
- g 2 (z) is the density function of the random variable z
- L is the distance between the observation positions of two uncertain points
- r (0 ⁇ r ⁇ L) is the radius of the error circle
- x is the distance from the first uncertain point to the observation position of the second uncertain point
- ⁇ 1 (z) max(zr,Lr)
- t is the integral variable
- t 3 , t 4 , t 5 , t 6 are the upper and lower limits of the integral interval corresponding to the integral variable
- (2)-(7) the formula (8) and its variables are respectively expanded into corresponding forms according to the relevant knowledge of spherical trigonometry, solid analytic geometry and multi-dimensional vector
- f 1 ( ⁇ ) is the density function of the random variable ⁇
- x(x>0) is the distance between the observation positions of the fixed point and the uncertain point
- r(0 ⁇ r ⁇ x) is the radius of the error circle
- t is the integral variable
- t 7 , t 8 are the upper and lower limits of the integral interval corresponding to the integral variable
- f 2 ( ⁇ ) is the density function of the random variable ⁇
- L is half of the observation distance between two uncertain points
- r (0 ⁇ r ⁇ L) is the radius of the error circle
- a, x are the integral variables
- x 1 , x 2 , x 3 , x 4 are the upper and lower limits of the integral interval corresponding to the integral variable x
- the beneficial effect of the present invention is that it provides more scientific, reasonable, practical and efficient measurement indicators for related topics such as geospatial data consistency verification and control, and also provides a basis for the design of land resource management and law enforcement, surface change detection and urban and rural planning and other related fields.
- the solutions to various problems involving the uncertainty of the relationship between spatial distance and direction provide a more solid theoretical foundation and more robust technical support.
Abstract
The present invention provides a measurement method for measuring distance and direction relationship information uncertainty caused by point position information uncertainty. The present invention comprises: a method for measuring distance and direction relationship uncertainty between a point of certainty and an uncertain point or between two uncertain points when the actual position of the uncertain point obeys, within an error circle/error ball/error hypersphere centred on an observation position of the uncertain point, a distribution delineated by a function taking the position as an independent variable. The present invention discloses a function relationship of transmission of point position information uncertainty to distance and direction information uncertainty caused by point position information uncertainty, provides more scientific, reasonable, practical and efficient measurement indexes for geographic space data consistency verification and control, and provides a more solid theoretical basis and more robust technical support for designing solutions of various problems in the related fields of land resource management and law enforcement, surface change detection and urban and rural planning and the like.
Description
本发明涉及测绘与地理信息科学领域(按学科归属)以及地理空间数据一致性校验与控制、土地资源管理与执法、地表变化检测与城乡规划等相关专题、领域(按应用归属)，具体说是因点位信息不确定性导致的距离与方向关系不确定性的测度方法。The present invention relates to the field of surveying and mapping and geographic information science (attributed by subject) and geospatial data consistency verification and control, land resource management and law enforcement, surface change detection and urban and rural planning and other related topics and fields (attributed by application), specifically It is a measurement method for the uncertainty of the relationship between distance and direction caused by the uncertainty of point information.
受空间信息获取、处理与分析过程中各种不利因素的影响，地理空间数据库中记录的空间位置信息具有不确定性。空间关系可以直观地理解为空间位置的函数，确定的空间位置得到确定的空间关系，不确定的空间位置则导致不确定的空间关系，空间关系不确定性可视为空间位置不确定性经由该函数关系的传递。如何科学合理地测度这种不确定性对于提升地理空间数据处理和分析的质量与效率，提高地理空间数据一致性校验与控制、土地资源管理与执法、地表变化检测与城乡规划等相关专题、领域的研究和应用水平具有重要意义，是测绘与地理信息领域需要重点研究与解决的关键技术问题。空间关系包括距离关系、方向关系、拓扑关系等，本专利关注因点位不确定性导致的距离与方向关系不确定性的测度方法。前人针对该问题展开的研究较少，已经取得的研究成果尚未彻底揭示从点位信息不确定性向奌间距离与方向关系信息不确定性传递的函数关系，目前业界尚无好的解决方案。Affected by various unfavorable factors in the process of spatial information acquisition, processing and analysis, the spatial location information recorded in the geospatial database is uncertain. The spatial relationship can be intuitively understood as a function of the spatial position. A definite spatial position leads to a definite spatial relationship, while an uncertain spatial position leads to an uncertain spatial relationship. The uncertainty of spatial relationship can be regarded as the uncertainty of spatial position via the Transfer of functional relations. How to scientifically and reasonably measure this uncertainty is crucial for improving the quality and efficiency of geospatial data processing and analysis, improving the consistency verification and control of geospatial data, land resource management and law enforcement, surface change detection and urban and rural planning, etc. The level of research and application in the field is of great significance, and it is a key technical issue that needs to be researched and solved in the field of surveying, mapping and geographic information. Spatial relationship includes distance relationship, direction relationship, topological relationship, etc. This patent focuses on the measurement method of the uncertainty of distance and direction relationship caused by point uncertainty. Previous research on this problem is less, and the research results have not yet fully revealed the functional relationship from the uncertainty of point information to the uncertainty of the relationship between distance and direction. At present, there is no good solution in the industry.
发明内容Contents of the invention
本发明提供了因点位信息不确定性导致的距离与方向关系信息不确定性的测度方法，通过建立点位不确定性与点间距离关系、方向关系不确定性的定量模型，揭示点位信息不确定性向其导致的距离与方向信息不确定性传递的函数关系，科学合理、实用高效。The invention provides a measurement method for the uncertainty of distance and direction relationship information caused by the uncertainty of point information, and reveals the point position uncertainty by establishing a quantitative model of point position uncertainty, distance relationship between points, and direction relationship uncertainty. The functional relationship of information uncertainty to the transmission of distance and direction information uncertainty is scientific, reasonable, practical and efficient.
本发明包含：The present invention includes:
(1)当不确定点实际位置出现的可能性在以其观测位置为圆心/球心/超球心的误差圆/误差球/误差超球内服从以位置为自变量的密度函数所刻画的分布时，一个确定点与一个不确定点间的距离不确定性模型；(1) When the possibility of the actual position of the uncertain point is described by the density function with the position as the independent variable in the error circle/error sphere/error hypersphere with its observed position as the center/sphere center/hypersphere center When distributed, the distance uncertainty model between a certain point and an uncertain point;
(2)当不确定点实际位置出现的可能性在以其观测位置为圆心/球心/超球心的误差圆/误差球/误差超球内服从以位置为自变量的密度函数所刻画的分布时，两个不确定点间的距离不确定性模型；(2) When the possibility of the actual position of the uncertain point is described by the density function with the position as the independent variable in the error circle/error sphere/error hypersphere with its observed position as the center/sphere center/hypersphere center When distributed, the distance uncertainty model between two uncertain points;
(3)当不确定点实际位置出现的可能性在以其观测位置为圆心/球心/超球心的误差圆/误差球/误差超球内服从以位置为自变量的密度函数所刻画的分布时，一个确定点与一个不确 定点间的方向不确定性模型；(3) When the possibility of the actual position of the uncertain point is described by the density function with the position as the independent variable in the error circle/error sphere/error hypersphere with its observed position as the center/sphere center/hypersphere center When distributed, the directional uncertainty model between a certain point and an uncertain point;
(4)当不确定点实际位置出现的可能性在以其观测位置为圆心/球心/超球心的误差圆/误差球/误差超球内服从以位置为自变量的密度函数所刻画的分布时，两个不确定点间的方向不确定性模型。(4) When the possibility of the actual position of the uncertain point is described by the density function with the position as the independent variable in the error circle/error sphere/error hypersphere with its observed position as the center/sphere center/hypersphere center The directional uncertainty model between two uncertain points when distributed.
当涉及的应用场合为二维平面空间或二维球面空间时，所述不确定点实际位置可能出现的范围用以其观测位置为圆心的误差圆描述；当涉及的应用场合为三维空间时，所述不确定点实际位置可能出现的范围用以其观测位置为球心的误差球描述；当涉及的应用场合为超过三维的高维空间时，所述不确定点实际位置可能出现的范围用以其观测位置为超球心的误差超球描述。When the application involved is a two-dimensional plane space or a two-dimensional spherical space, the possible range of the actual position of the uncertain point is described by an error circle with its observed position as the center; when the application involved is a three-dimensional space, The possible range of the actual position of the uncertain point is described by an error sphere with its observed position as the center of the sphere; An error hypersphere description with its observation position as the center of the hypersphere.
当涉及的应用场合为二维平面空间时，所述一个确定点与一个不确定点间的距离不确定性模型为When the application involved is a two-dimensional plane space, the distance uncertainty model between a definite point and an uncertain point is
式中，z为随机变量，表示确定点与不确定点间的距离可能取到的值，g
1(z)为随机变量z的密度函数；x(x>0)为确定点与不确定点观测位置间的距离，r(0<r<x)为误差圆半径；t为积分变量，t
1,t
2为与该积分变量对应的积分区间上下限，且
In the formula, z is a random variable, which represents the possible value of the distance between a definite point and an uncertain point, g 1 (z) is the density function of the random variable z; x (x>0) is the definite point and the uncertain point The distance between the observation positions, r(0<r<x) is the radius of the error circle; t is the integral variable, t 1 and t 2 are the upper and lower limits of the integral interval corresponding to the integral variable, and
u＝(zcost-x,zsint)，k(u)表示不确定点的实际位置出现在对应的误差圆内各处所服从的分布密度函数，刻画了不确定点的性质，k(u)常用的解析表达式如下：u=(zcost-x,zsint), k(u) represents the distribution density function that the actual position of the uncertain point appears in the corresponding error circle, which describes the nature of the uncertain point, and k(u) is commonly used The analytical expression is as follows:
k(u)＝1 (2)k(u)=1 (2)
k(u)＝(1-u
Tu)
2， (5)
k(u)=(1-u T u) 2 , (5)
当涉及的应用场合为二维曲面空间、三维或三维以上的空间时，公式(1)及其中各变量分别依据球面三角、立体解析几何和多维矢量方面的相关知识拓展为对应的形式。When the application involved is two-dimensional surface space, three-dimensional or more than three-dimensional space, formula (1) and its variables are expanded into corresponding forms based on the relevant knowledge of spherical trigonometry, three-dimensional analytic geometry and multi-dimensional vector.
当涉及的应用场合为二维平面空间时，所述的两个不确定点间的距离不确定性模型为When the application involved is a two-dimensional plane space, the distance uncertainty model between the two uncertain points is
式中，z为随机变量，表示两个不确定点间的距离可能取到的值，g
2(z)为随机变量z的密度函数；L为两个不确定点观测位置间的距离，r(0<r<L)为误差圆半径；x为第一个不确定点到第二个不确定点观测位置的距离；ρ
1(z)＝max(z-r,L-r),ρ
2(z)＝min(z+r,L+r)分别为积分区间上下限表达式；t为积分变量，t
3,t
4,t
5,t
6为与该积分变量对应的积分区间上下限，且
In the formula, z is a random variable, indicating the possible value of the distance between two uncertain points, g 2 (z) is the density function of the random variable z; L is the distance between the observation positions of two uncertain points, r (0<r<L) is the radius of the error circle; x is the distance from the first uncertain point to the observation position of the second uncertain point; ρ 1 (z)=max(zr,Lr), ρ 2 (z) ＝min(z+r, L+r) are expressions of the upper and lower limits of the integral interval respectively; t is the integral variable, t 3 , t 4 , t 5 , t 6 are the upper and lower limits of the integral interval corresponding to the integral variable, and
u
1＝(xcost,xsint)，u
2＝(zcost-x,zsint)，k(u)表示不确定点的实际位置出现在对应的误差圆内各处所服从的分布密度函数，刻画了不确定点的性质，其常用的解析表达式同(2)-(7)式。当涉及的应用场合为二维曲面空间、三维或三维以上的空间时，公式(8)及其中各变量分别依据球面三角、立体解析几何和多维矢量方面的相关知识拓展为对应的形式
u 1 ＝(xcost,xsint), u 2 ＝(zcost-x,zsint), k(u) represents the distribution density function that the actual position of the uncertain point appears in the corresponding error circle, and it describes the uncertainty The nature of the point, its commonly used analytical expressions are the same as (2)-(7). When the application involved is two-dimensional surface space, three-dimensional or more than three-dimensional space, the formula (8) and its variables are respectively expanded into corresponding forms according to the relevant knowledge of spherical trigonometry, solid analytic geometry and multi-dimensional vector
当涉及的应用场合为二维平面空间时，所述一个确定点与一个不确定点间的方向不确定性模型为When the application involved is a two-dimensional plane space, the directional uncertainty model between a definite point and an uncertain point is
式中，
为随机变量，表示确定点与不确定点间的方向角可能取到的值，f
1(θ)为随机变量θ的密度函数；x(x>0)为确定点与不确定点观测位置间的距离，r(0<r<x)为误差圆半径；t为积分变量，t
7,t
8为与该积分变量对应的积分区间上下限，且
In the formula, is a random variable, indicating the possible value of the direction angle between the fixed point and the uncertain point, f 1 (θ) is the density function of the random variable θ; x(x>0) is the distance between the observation positions of the fixed point and the uncertain point , r(0<r<x) is the radius of the error circle; t is the integral variable, t 7 , t 8 are the upper and lower limits of the integral interval corresponding to the integral variable, and
u＝(t,(t+x)tgθ)，k(u)表示不确定点的实际位置出现在对应的误差圆内各处所服从的分布密度函数，刻画了不确定点的性质，其常用的解析表达式同(2)-(7)式。当涉及的应用场合为二维曲面空间、三维或三维以上的空间时，公式(9)及其中各变量分别依据球面三角、立 体解析几何和多维矢量方面的相关知识拓展为对应的形式u=(t,(t+x)tgθ), k(u) represents the distribution density function that the actual position of the uncertain point appears in the corresponding error circle, which describes the nature of the uncertain point, and its commonly used The analytical expression is the same as (2)-(7). When the application involved is two-dimensional surface space, three-dimensional or more than three-dimensional space, the formula (9) and its variables are respectively expanded to the corresponding form based on the relevant knowledge of spherical trigonometry, solid analytic geometry and multi-dimensional vector
当涉及的应用场合为二维平面空间时，所述两个不确定点间的方向不确定性模型为When the application involved is a two-dimensional plane space, the directional uncertainty model between the two uncertain points is
式中，
为随机变量，表示两个不确定点间的方向角可能取到的值，f
2(θ)为随机变量θ的密度函数；L为两个不确定点间观测距离的二分之一，r(0<r<L)为误差圆半径；a,x为积分变量，x
1,x
2,x
3,x
4为与积分变量x对应的积分区间上下限，且
In the formula, is a random variable, indicating the possible value of the direction angle between two uncertain points, f 2 (θ) is the density function of the random variable θ; L is half of the observation distance between two uncertain points, r (0<r<L) is the radius of the error circle; a, x are the integral variables, x 1 , x 2 , x 3 , x 4 are the upper and lower limits of the integral interval corresponding to the integral variable x, and
为被积函数；u＝(x,xtgθ+a)，k(u)表示不确定点的实际位置出现在对应的误差圆内各处所服从的分布密度函数，刻画了不确定点的性质，其常用的解析表达式同(2)-(7)式。当涉及的应用场合为二维曲面空间、三维或三维以上的空间时，公式(10)及其中各变量分别依据球面三角、立体解析几何和多维矢量方面的相关知识拓展为对应的形式。is the integrand; u=(x, xtgθ+a), k(u) represents the distribution density function that the actual position of the uncertain point appears in the corresponding error circle, and describes the nature of the uncertain point, its Commonly used analytical expressions are the same as (2)-(7). When the application involved is two-dimensional surface space, three-dimensional or more than three-dimensional space, the formula (10) and its variables are respectively expanded into corresponding forms based on the relevant knowledge of spherical trigonometry, solid analytic geometry and multi-dimensional vector.
本发明的有益效果是：为地理空间数据一致性校验与控制等相关专题提供了更加科学合理、实用高效的测度指标，也为设计土地资源管理与执法、地表变化检测与城乡规划等相关领域中涉及空间距离与方向关系不确定性的各类问题的解决方案提供了更加坚实的理论基础与更加鲁棒的技术支撑。The beneficial effect of the present invention is that it provides more scientific, reasonable, practical and efficient measurement indicators for related topics such as geospatial data consistency verification and control, and also provides a basis for the design of land resource management and law enforcement, surface change detection and urban and rural planning and other related fields. The solutions to various problems involving the uncertainty of the relationship between spatial distance and direction provide a more solid theoretical foundation and more robust technical support.
根据具体应用的需求，选择不确定点实际位置服从的分布密度函数k(u)，采用本专利所提供的公式(1)、(8)、(9)与(10)计算得到反映距离与方向关系不确定性的密度函数g
1(z)、g
2(z)与f
1(θ)、f
2(θ)，再与由实际采集的数据集计算得到的同一指标比对即可。
According to the needs of specific applications, select the distribution density function k(u) that the actual position of the uncertain point obeys, and use the formulas (1), (8), (9) and (10) provided by this patent to calculate the reflected distance and direction The density functions g 1 (z), g 2 (z) and f 1 (θ) and f 2 (θ) of the relationship uncertainty can be compared with the same index calculated from the actual collected data set.
Claims (5)
- 距离与方向关系不确定性测度方法，其特征在于包括：The method for measuring the uncertainty of the relationship between distance and direction is characterized in that it includes:①当不确定点实际位置出现的可能性在以其观测位置为圆心/球心/超球心的误差圆/误差球/误差超球内服从以位置为自变量的函数所刻画的分布时，一个确定点与一个不确定点间的距离不确定性模型；①When the possibility of the actual position of the uncertain point obeys the distribution described by the function of the position as the independent variable in the error circle/error sphere/error hypersphere with its observed position as the center/sphere center/hypersphere center, An uncertainty model of the distance between a certain point and an uncertain point;②当不确定点实际位置出现的可能性在以其观测位置为圆心/球心/超球心的误差圆/误差球/误差超球内服从以位置为自变量的函数所刻画的分布时，两个不确定点间的距离不确定性模型；②When the possibility of the actual position of the uncertain point obeys the distribution described by the function of the position as the independent variable in the error circle/error sphere/error hypersphere with its observed position as the center/sphere center/hypersphere center, The distance uncertainty model between two uncertain points;③当不确定点实际位置出现的可能性在以其观测位置为圆心/球心/超球心的误差圆/误差球/误差超球内服从以位置为自变量的函数所刻画的分布时，一个确定点与一个不确定点间的方向不确定性模型；③When the possibility of the actual position of the uncertain point obeys the distribution described by the function of the position as the independent variable in the error circle/error sphere/error hypersphere with its observed position as the center/sphere center/hypersphere center, A directional uncertainty model between a certain point and an uncertain point;④当不确定点实际位置出现的可能性在以其观测位置为圆心/球心/超球心的误差圆/误差球/误差超球内服从以位置为自变量的函数所刻画的分布时，两个不确定点间的方向不确定性模型；④When the possibility of the actual position of the uncertain point obeys the distribution described by the function of the position as the independent variable in the error circle/error sphere/error hypersphere with its observed position as the center/sphere center/hypersphere center, A directional uncertainty model between two uncertain points;当涉及的应用场合为二维平面空间或二维球面空间时，不确定点实际位置可能出现的范围用以其观测位置为圆心的误差圆描述；当涉及的应用场合为三维空间时，不确定点实际位置可能出现的范围用以其观测位置为球心的误差球描述；当涉及的应用场合为超过三维的高维空间时，不确定点实际位置可能出现的范围用以其观测位置为超球心的误差超球描述。When the application involved is a two-dimensional plane space or a two-dimensional spherical space, the possible range of the actual position of the uncertain point is described by an error circle with its observed position as the center; when the application involved is a three-dimensional space, the uncertain The possible range of the actual position of a point is described by an error sphere with its observed position as the center of the sphere; when the application involved is a high-dimensional space beyond three dimensions, the possible range of the actual position of an uncertain point is described by its observed position as the hypersphere. The error hypersphere description of the center of the sphere.
- 根据权利要求1所述的距离与方向关系不确定性测度方法，其特征在于：当涉及的应用场合为二维平面空间时，所述一个确定点与一个不确定点间的距离不确定性模型为The method for measuring the uncertainty of the relationship between distance and direction according to claim 1, characterized in that: when the application involved is a two-dimensional plane space, the distance uncertainty model between the one definite point and one uncertain point for
式中，z为随机变量，表示确定点与不确定点间的距离可能取到的值，g 1(z)为随机变量z的密度函数；x为确定点与不确定点观测位置间的距离，r是以不确定点观测位置为圆心的误差圆半径；t为积分变量，t 1,t 2为与该积分变量对应的积分区间上下限，且 In the formula, z is a random variable, which represents the possible value of the distance between the fixed point and the uncertain point, g 1 (z) is the density function of the random variable z; x is the distance between the observation positions of the fixed point and the uncertain point , r is the radius of the error circle whose center is the observation position of the uncertain point; t is the integral variable, t 1 , t 2 are the upper and lower limits of the integral interval corresponding to the integral variable, and
u＝(zcost-x,zsint)，k(u)表示不确定点的实际位置出现在对应的误差圆内各处所服从的分布密度函数，刻画了不确定点的性质，当涉及的应用场合为二维曲面空间、三维或三维以上的空间时，公式(1)右侧的表达式及其中涉及的各变量分别拓展为对应的形式。u=(zcost-x,zsint), k(u) represents the distribution density function that the actual position of the uncertain point appears in the corresponding error circle, which describes the nature of the uncertain point. When the application involved is For two-dimensional surface space, three-dimensional or more than three-dimensional space, the expression on the right side of formula (1) and the variables involved in it are respectively expanded into corresponding forms. - 根据权利要求1所述的距离与方向关系不确定性测度方法，其特征在于：当涉及的应用场 合为二维平面空间时，所述的两个不确定点间的距离不确定性模型为The distance and direction relation uncertainty measurement method according to claim 1 is characterized in that: when the application involved is a two-dimensional plane space, the distance uncertainty model between the two uncertain points is
式中，z为随机变量，表示两个不确定点间的距离可能取到的值，g 2(z)为随机变量z的密度函数；L为两个不确定点观测位置间距离的二分之一，r为误差圆半径，x为第一个不确定点到第二个不确定点观测位置的距离；ρ 1(z)＝max(z-r,L-r),ρ 2(z)＝min(z+r,L+r)分别为积分区间上下限表达式；t为积分变量，t 3,t 4,t 5,t 6为与该积分变量对应的积分区间上下限，且 In the formula, z is a random variable, indicating the possible value of the distance between two uncertain points, g 2 (z) is the density function of the random variable z; L is the dichotomy of the distance between the observation positions of two uncertain points One of them, r is the radius of the error circle, x is the distance from the first uncertain point to the observation position of the second uncertain point; ρ 1 (z)=max(zr,Lr), ρ 2 (z)=min( z+r, L+r) are expressions of the upper and lower limits of the integral interval respectively; t is the integral variable, t 3 , t 4 , t 5 , t 6 are the upper and lower limits of the integral interval corresponding to the integral variable, and
u 1＝(xcost,xsint)，u 2＝(zcost-x,zsint)，k(u)表示不确定点的实际位置出现在对应的误差圆内各处所服从的分布密度函数，刻画了不确定点的性质，当涉及的应用场合为二维曲面空间、三维或三维以上的空间时，公式(2)右侧的表达式及其中涉及的各变量分别拓展为对应的形式。 u 1 ＝(xcost,xsint), u 2 ＝(zcost-x,zsint), k(u) represents the distribution density function that the actual position of the uncertain point appears in the corresponding error circle, and it describes the uncertainty The properties of points, when the application involved is two-dimensional surface space, three-dimensional or more than three-dimensional space, the expression on the right side of formula (2) and the variables involved in it are respectively expanded into corresponding forms. - 根据权利要求1所述的距离与方向关系不确定性测度方法，其特征在于：当涉及的应用场合为二维平面空间时，所述一个确定点与一个不确定点间的方向不确定性模型为The method for measuring the uncertainty of the relationship between distance and direction according to claim 1, characterized in that: when the application involved is a two-dimensional plane space, the direction uncertainty model between the one definite point and one uncertain point for
式中，θ为随机变量，表示确定点与不确定点间的方向角可能取到的值，f 1(θ)为随机变量θ的密度函数；x为确定点与不确定点观测位置间的距离，r为误差圆半径；t为积分变量，t 7,t 8为与该积分变量对应的积分区间上下限，且 In the formula, θ is a random variable, indicating the possible value of the direction angle between the fixed point and the uncertain point, f 1 (θ) is the density function of the random variable θ; x is the distance between the fixed point and the uncertain point. distance, r is the radius of the error circle; t is the integral variable, t 7 and t 8 are the upper and lower limits of the integral interval corresponding to the integral variable, and
u＝(t,(t+x)tgθ)，k(u)表示不确定点的实际位置出现在对应的误差圆内各处所服从的分布密度函数，刻画了不确定点的性质，当涉及的应用场合为二维曲面空间、三维或三维以上的空间时，公式(3)右侧的表达式及其中涉及的各变量分别拓展为对应的形式。u=(t,(t+x)tgθ), k(u) represents the distribution density function that the actual position of the uncertain point appears in the corresponding error circle, which describes the nature of the uncertain point. When the application occasion is two-dimensional surface space, three-dimensional or more than three-dimensional space, the expression on the right side of formula (3) and the variables involved in it are respectively expanded into corresponding forms. - 根据权利要求1所述的距离与方向关系不确定性测度方法，其特征在于：当涉及的应用场合为二维平面空间时，所述两个不确定点间的方向不确定性模型为According to the method for measuring the uncertainty of the relationship between distance and direction according to claim 1, it is characterized in that: when the application involved is a two-dimensional plane space, the direction uncertainty model between the two uncertain points is:
式中，θ为随机变量，表示两个不确定点间的方向角可能取到的In the formula, θ is a random variable, which represents the possible orientation angle between two uncertain points值，f 2(θ)为随机变量θ的密度函数；L为两个不确定点观测位置间距离的二分之一，r为误差圆半径；a,x为积分变量，x 1,x 2,x 3,x 4为与积分变量x对应的积分区间上下限，且 value, f 2 (θ) is the density function of the random variable θ; L is one-half of the distance between the observation positions of two uncertain points, r is the radius of the error circle; a, x are integral variables, x 1 , x 2 , x 3 , x 4 are the upper and lower limits of the integral interval corresponding to the integral variable x, and
为被积函数；u＝(x,xtgθ+a)，k(u)表示不确定点的实际位置出现在对应的误差圆内各处所服从的分布密度函数，刻画了不确定点的性质，当涉及的应用场合为二维曲面空间、三维或三维以上的空间时，公式(4)右侧的表达式及其中涉及的各变量分别拓展为对应的形式。is the integrand; u=(x,xtgθ+a), k(u) represents the distribution density function that the actual position of the uncertain point appears in the corresponding error circle, and describes the nature of the uncertain point. When When the application involved is a two-dimensional surface space, three-dimensional or more than three-dimensional space, the expression on the right side of formula (4) and the variables involved in it are respectively expanded into corresponding forms.
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