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Formulas for precisely and efficiently estimating the bias and variance of the length measurements
Authors:Shuqiang Xue  Yuanxi Yang  Yamin Dang
Institution:1.School of Geological and Surveying Engineering,Chang’an University,Xi’an,China;2.Institute of Geodesy and Geodynamics,Chinese Academy of Surveying and Mapping,Beijing,China;3.National Key Laboratory for Geo-information Engineering,Xi’an Institute of Surveying,Xi’an,China
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.
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