[1]郭同德,贾军国..误差椭球的性质及其在置信域问题中的应用[J].郑州大学学报(工学版),2006,27(03):116-118.[doi:10.3969/j.issn.1671-6833.2006.03.029]
　GUO Tongde,Jia Junguo.The nature of error ellipsoids and their application to confidence domain problems[J].Journal of Zhengzhou University (Engineering Science),2006,27(03):116-118.[doi:10.3969/j.issn.1671-6833.2006.03.029]
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误差椭球的性质及其在置信域问题中的应用()
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《郑州大学学报(工学版)》[ISSN:1671-6833/CN:41-1339/T]

卷:
27卷
期数:
2006年03期
页码:
116-118
栏目:
出版日期:
1900-01-01

文章信息/Info

Title:

The nature of error ellipsoids and their application to confidence domain problems
作者:
郭同德; 贾军国.
郑州大学环境与水利学院,河南,郑州,450002, 西安交通大学理学院,陕西,西安,710000;郑州大学数学系,河南,郑州,450052
Author(s):
GUO Tongde; Jia Junguo
关键词:
误差椭球;  置信域;  概率分布;  多元分析
Keywords:
DOI:
10.3969/j.issn.1671-6833.2006.03.029
文献标志码:
A
摘要:
研究了空间点定位误差的误差椭球的性质和空间点误差的表示.以概率论和多元分析为工具,证明空间点误差落入椭球内的概率可以由标准正态分布的分布函数和密度函数表示;证明了空间点误差可以沿误差椭球主轴方向分解为3个独立的分量,并给出了分解方法和算例;证明点误差落在误差椭球一侧内的概率为常数,该常数与切点坐标无关且可以由标准正态分布函数表示;讨论了点误差的可视化表达问题,为空间点建立了椭球形及长方体形置信域,并给出了置信水平的计算公式.
Abstract:
The properties of the error ellipsoids and the representation of spatial point errors were studied. Using probability theory and multivariate analysis as tools, it is proved that the probability of the spatial point error falling into the ellipsoid can be represented by the distribution function and density function of the standard normal distribution. It is proved that the spatial point error can be decomposed into three independent components along the direction of the error ellipsoid main axis, and the decomposition method and example are given. The probability of proving that the point error falls within one side of the error ellipsoid is a constant, which is independent of the tangent point coordinates and can be represented by the standard normal distribution function; The visual expression of point error is discussed, ellipsoid and cuboid confidence domains are established for spatial points, and the calculation formula of confidence level is given.

更新日期/Last Update: 1900-01-01