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首页> 外文期刊>Journal of geographical systems >A general framework for error analysis in measurement-based GIS Part 4: Error analysis in length and area measurements
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A general framework for error analysis in measurement-based GIS Part 4: Error analysis in length and area measurements

机译：基于测量的GIS中误差分析的通用框架，第4部分：长度和面积测量中的误差分析

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摘要

This is the final of a series of four papers on the development of a general framework for error analysis in measurement-based geographic information systems (MBGIS). In this paper, we discuss the error analysis problems in length and area measurements under measurement error (ME) of the defining points. In line with the basic ME model constructed in Part 1 of this series, we formulate the ME models for length and area measurements. For length measurement and perimeter measurement, the approximate laws of error propagation are derived. For area measurement, the exact laws of error propagation are obtained under various conditions. An important result is that area measurement is distributed as a linear combination of independent non-central chi-square variables when the joint ME vectors of vertices coordinates are normal. In addition, we also give a necessary and sufficient condition under which the area measurement estimator is unbiased. As a comparison, the approximate law of error propagation in area measurement is also considered and its approximation is substantiated by numerical experiments.
机译：这是有关基于度量的地理信息系统（MBGIS）中错误分析的通用框架的开发的四篇系列文章的最后一篇。在本文中，我们讨论了在定义点的测量误差（ME）下长度和面积测量中的误差分析问题。根据本系列第1部分中构建的基本ME模型，我们制定了用于长度和面积测量的ME模型。对于长度测量和周长测量，得出误差传播的近似定律。对于面积测量，可以在各种条件下获得误差传播的精确定律。一个重要的结果是，当顶点坐标的联合ME向量为法线时，面积测量值以独立的非中心卡方变量的线性组合分布。另外，我们还给出了一个充分必要的条件，在该条件下面积测量估计量是无偏的。作为比较，还考虑了面积测量中误差传播的近似规律，并通过数值实验证明了其近似性。

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