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A general framework for error analysis in measurement-based GIS Part 4: Error analysis in length and area measurements

Author

Listed:
  • Yee Leung
  • Jiang-Hong Ma
  • Michael F. Goodchild

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. Copyright Springer-Verlag Berlin Heidelberg 2004

Suggested Citation

  • Yee Leung & Jiang-Hong Ma & Michael F. Goodchild, 2004. "A general framework for error analysis in measurement-based GIS Part 4: Error analysis in length and area measurements," Journal of Geographical Systems, Springer, vol. 6(4), pages 403-428, December.
    • Handle: RePEc:kap:jgeosy:v:6:y:2004:i:4:p:403-428
    DOI: 10.1007/s10109-004-0144-1
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    More about this item

    Keywords

    Error propagation; geographic information systems; length and area measurement; measurement error; noncentral chi-square variable; C10; C31;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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