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Formulas for precisely and efficiently estimating the bias and variance of the length measurements

Author

Listed:
  • Shuqiang Xue

    (Chang’an University
    Chinese Academy of Surveying and Mapping)

  • Yuanxi Yang

    (Chang’an University
    Xi’an Institute of Surveying)

  • Yamin Dang

    (Chinese Academy of Surveying and Mapping)

Abstract

Error analysis in length measurements is an important problem in geographic information system and cartographic operations. The distance between two random points—i.e., the length of a random line segment—may be viewed as a nonlinear mapping of the coordinates of the two points. In real-world applications, an unbiased length statistic may be expected in high-precision contexts, but the variance of the unbiased statistic is of concern in assessing the quality. This paper suggesting the use of a k-order bias correction formula and a nonlinear error propagation approach to the distance equation provides a useful way to describe the length of a line. The study shows that the bias is determined by the relative precision of the random line segment, and that the use of the higher-order bias correction is only needed for short-distance applications.

Suggested Citation

  • Shuqiang Xue & Yuanxi Yang & Yamin Dang, 2016. "Formulas for precisely and efficiently estimating the bias and variance of the length measurements," Journal of Geographical Systems, Springer, vol. 18(4), pages 399-415, October.
    • Handle: RePEc:kap:jgeosy:v:18:y:2016:i:4:d:10.1007_s10109-016-0235-9
    DOI: 10.1007/s10109-016-0235-9
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    References listed on IDEAS

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    1. Michael F. Goodchild, 2004. "A general framework for error analysis in measurement-based GIS," Journal of Geographical Systems, Springer, vol. 6(4), pages 323-324, December.
    2. David Wheeler & Catherine Calder, 2007. "An assessment of coefficient accuracy in linear regression models with spatially varying coefficients," Journal of Geographical Systems, Springer, vol. 9(2), pages 145-166, June.
    3. Tetsuo Kobayashi & Harvey Miller & Walied Othman, 2011. "Analytical methods for error propagation in planar space–time prisms," Journal of Geographical Systems, Springer, vol. 13(4), pages 327-354, December.
    4. Fischer, Manfred M & Nijkamp, Peter, 1992. "Geographic Information Systems and Spatial Analysis," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 26(1), pages 3-17, April.
    5. Jie Xue & Yee Leung & Jiang-Hong Ma, 2015. "High-order Taylor series expansion methods for error propagation in geographic information systems," Journal of Geographical Systems, Springer, vol. 17(2), pages 187-206, April.
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