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

Shuqiang Xue (), Yuanxi Yang and Yamin Dang
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Shuqiang Xue: Chang’an University
Yuanxi Yang: Chang’an University
Yamin Dang: Chinese Academy of Surveying and Mapping

Journal of Geographical Systems, 2016, vol. 18, issue 4, No 5, 399-415

Abstract: 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.

Keywords: Length; Bias correction; Variance estimation; Nonlinear error propagation; C130; Estimation; General (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10109-016-0235-9

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