坐标转换模型尺度参数的假设检验

徐天河; 杨元喜

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坐标转换模型尺度参数的假设检验

徐天河, 杨元喜

文章导航 > 武汉大学学报 ● 信息科学版 > 2001 > 26(1): 70-74

徐天河, 杨元喜. 坐标转换模型尺度参数的假设检验[J]. 武汉大学学报 ● 信息科学版, 2001, 26(1): 70-74.

引用本文:

徐天河, 杨元喜. 坐标转换模型尺度参数的假设检验[J]. 武汉大学学报 ● 信息科学版, 2001, 26(1): 70-74.

XU Tianhe, YANG Yuanxi. The Hypothesis Testing of Scale Parameter in Coordinate Transformation Model[J]. Geomatics and Information Science of Wuhan University, 2001, 26(1): 70-74.

Citation:

XU Tianhe, YANG Yuanxi. The Hypothesis Testing of Scale Parameter in Coordinate Transformation Model[J]. Geomatics and Information Science of Wuhan University, 2001, 26(1): 70-74.

坐标转换模型尺度参数的假设检验

徐天河¹,
杨元喜²

1 郑州信息工程大学测绘学院, 郑州市陇海中路66号, 450054;
2 西安测绘研究所, 西安市雁塔路中段1号, 710054

基金项目: 国家杰出青年科学基金资助项目(49825107)

详细信息

作者简介:
徐天河,硕士生,现主要从事GPS数据处理与质量控制研究。E-mail:xutianhe@sohu.com

中图分类号: P226.3;P207.1

The Hypothesis Testing of Scale Parameter in Coordinate Transformation Model

XU Tianhe¹,
YANG Yuanxi²

1 Institute of Surveying & Mapping, Information Engineering University of Zhengzhou, 66 Middle Longhai Road, Zhengzhou, China, 450052;
2 Xi'an Research Institute of Surveying & Mapping, 1 Middle Yanta Road, Xi'an, China, 710054

摘要: 介绍了基于空间尺度为各向异性的三尺度参数坐标转换模型及其转化形式,从理论上分析了坐标转换中如何对尺度参数进行选择,给出了坐标转换模型中尺度参数假设检验模型的统一表达形式,构造了相应的检验统计量。该检验模型能对三尺度坐标转换模型、双尺度模型和单尺度模型间的相互转化及尺度参数的显著性等情况进行假设检验。通过该假设检验方法对两算例进行了解算,得出了一些有益的结论。
- 坐标转换 /
- 三尺度坐标转换模型 /
- 线性约束 /
- 假设检验
Abstract: As we know,the Bursa-Wolf coordinate transformation model is generally used in the transformation between two datum systems.This kind of model has a single scale parameter,which implies a hypothesis that the scale space is isotropic.The single scale parameter actually harmonizes the average scale of the three coordinate axis.When the precision of the three coordinate vectors has a large discrepancy,it is not wise to use the single scale parameter coordinate transformation model. Following this fact,we present a coordinate transformation model of three-scale parameters based on the hypothesis that the scale space is isotropic and analyze how to choose the scale parameter in coordinate transformation model theoretically.We also give its special instances, namely, the two-scale and non-scale parameter coordinate transformation models. From the comparison of external and internal precision,we can make a decision on the choice of scale parameter.This method,however,does not provide an objective standard and rule.The reason is that the results of the external and the internal tests do not match each other sometimes,which brings some difficulties to the choosing.In this paper,an united hypothesis testing model of scale parameter is given and the corresponding statistic of testing is constructed.This thinking way comes from the regression testing with linear bound.We can express the three-scale parameter coordinate transformation model as a linear model,and express its special instances such as two-scale parameter,non-scale parameter as linear bounds.Then we can make hypothesis testing on the choice among the coordinate transformation models with one-scale,two-scale,three-scale and non-scale parameter. There are three main steps in this hypothesis testing:①giving the linear bound equation,namely, the hypothesis testing condition; ②constructing the statistic of testing and calculating its value;and ③ giving the significance level and deciding whether the zero hypothesis is accepted or not.Two numerical examples are given and some helpful conclusions are shown in the paper.
- coordinate transformation /
- three-scale parameters coordinate transformation model /
- linear bound /
- hypothesis testing

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坐标转换模型尺度参数的假设检验

徐天河¹,
杨元喜²

1 郑州信息工程大学测绘学院, 郑州市陇海中路66号, 450054;

2 西安测绘研究所, 西安市雁塔路中段1号, 710054

基金项目: 国家杰出青年科学基金资助项目(49825107)

作者简介:
徐天河,硕士生,现主要从事GPS数据处理与质量控制研究。E-mail:xutianhe@sohu.com

收稿日期: 2000-09-10
刊出日期: 2001-01-05

中图分类号: P226.3;P207.1

关键词:

摘要: 介绍了基于空间尺度为各向异性的三尺度参数坐标转换模型及其转化形式,从理论上分析了坐标转换中如何对尺度参数进行选择,给出了坐标转换模型中尺度参数假设检验模型的统一表达形式,构造了相应的检验统计量。该检验模型能对三尺度坐标转换模型、双尺度模型和单尺度模型间的相互转化及尺度参数的显著性等情况进行假设检验。通过该假设检验方法对两算例进行了解算,得出了一些有益的结论。

English Abstract

The Hypothesis Testing of Scale Parameter in Coordinate Transformation Model

XU Tianhe¹,
YANG Yuanxi²

1 Institute of Surveying & Mapping, Information Engineering University of Zhengzhou, 66 Middle Longhai Road, Zhengzhou, China, 450052;

2 Xi'an Research Institute of Surveying & Mapping, 1 Middle Yanta Road, Xi'an, China, 710054

Received Date: 2000-09-10
Publish Date: 2001-01-05

Keywords:

coordinate transformation /
three-scale parameters coordinate transformation model /
linear bound /
hypothesis testing

Abstract: As we know,the Bursa-Wolf coordinate transformation model is generally used in the transformation between two datum systems.This kind of model has a single scale parameter,which implies a hypothesis that the scale space is isotropic.The single scale parameter actually harmonizes the average scale of the three coordinate axis.When the precision of the three coordinate vectors has a large discrepancy,it is not wise to use the single scale parameter coordinate transformation model. Following this fact,we present a coordinate transformation model of three-scale parameters based on the hypothesis that the scale space is isotropic and analyze how to choose the scale parameter in coordinate transformation model theoretically.We also give its special instances, namely, the two-scale and non-scale parameter coordinate transformation models. From the comparison of external and internal precision,we can make a decision on the choice of scale parameter.This method,however,does not provide an objective standard and rule.The reason is that the results of the external and the internal tests do not match each other sometimes,which brings some difficulties to the choosing.In this paper,an united hypothesis testing model of scale parameter is given and the corresponding statistic of testing is constructed.This thinking way comes from the regression testing with linear bound.We can express the three-scale parameter coordinate transformation model as a linear model,and express its special instances such as two-scale parameter,non-scale parameter as linear bounds.Then we can make hypothesis testing on the choice among the coordinate transformation models with one-scale,two-scale,three-scale and non-scale parameter. There are three main steps in this hypothesis testing:①giving the linear bound equation,namely, the hypothesis testing condition; ②constructing the statistic of testing and calculating its value;and ③ giving the significance level and deciding whether the zero hypothesis is accepted or not.Two numerical examples are given and some helpful conclusions are shown in the paper.

徐天河, 杨元喜. 坐标转换模型尺度参数的假设检验[J]. 武汉大学学报 ● 信息科学版, 2001, 26(1): 70-74.

引用本文:

徐天河, 杨元喜. 坐标转换模型尺度参数的假设检验[J]. 武汉大学学报 ● 信息科学版, 2001, 26(1): 70-74.

XU Tianhe, YANG Yuanxi. The Hypothesis Testing of Scale Parameter in Coordinate Transformation Model[J]. Geomatics and Information Science of Wuhan University, 2001, 26(1): 70-74.

Citation:

XU Tianhe, YANG Yuanxi. The Hypothesis Testing of Scale Parameter in Coordinate Transformation Model[J]. Geomatics and Information Science of Wuhan University, 2001, 26(1): 70-74.