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A general framework for error analysis in measurement-based GIS Part 4: Error analysis in length and area measurements
Authors:Email author" target="_blank">Yee?LeungEmail author  Jiang-Hong?Ma  Michael F?Goodchild
Institution:(1) Department of Geography and Resource Management, Center for Environmental Policy and Resource Management, and Joint Laboratory for Geoinformation Science, The Chinese University of Hong Kong, Hong Kong;(2) Department of Mathematics and Information Science, Changrsquoan University, Xirsquoan, P.R. China;(3) Department of Geography, University of California, Santa Barbara, California, U.S.A
Abstract: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.This project was supported by the earmarked grant CUHK 4362/00H of the Hong Kong Research grant Council.
Keywords:Error propagation  geographic information systems  length and area measurement  measurement error  noncentral chi-square variable
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