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

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• 作者：Shuqiang Xue ; Yuanxi Yang ; Yamin Dang
• 关键词：Length ; Bias correction ; Variance estimation ; Nonlinear error propagation
• 刊名：Journal of Geographical Systems
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：18
• 期：4
• 页码：399-415
• 全文大小：872 KB
• 刊物类别：Business and Economics
• 刊物主题：Economics
  Regional Science
  Geographical Information Systems and Cartography
  Computer Applications in Social and Behavioral Sciences
  Landscape, Regional and Urban Planning
  Quantitative Geography
  Simulation and Modeling
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1435-5949
• 卷排序：18

文摘

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.