Message Board

Respected readers, authors and reviewers, you can add comments to this page on any questions about the contribution, review,        editing and publication of this journal. We will give you an answer as soon as possible. Thank you for your support!

Name
E-mail
Phone
Title
Content
Verification Code
Turn off MathJax
Article Contents

MAO Zhengyuan, FAN Linna, LI Lin, . Methodological Research on Measuring Distance Uncertainty in Two-Dimensional Space[J]. Geomatics and Information Science of Wuhan University. doi: 10.13203/j.whugis20220131
Citation: MAO Zhengyuan, FAN Linna, LI Lin, . Methodological Research on Measuring Distance Uncertainty in Two-Dimensional Space[J]. Geomatics and Information Science of Wuhan University. doi: 10.13203/j.whugis20220131

Methodological Research on Measuring Distance Uncertainty in Two-Dimensional Space

doi: 10.13203/j.whugis20220131
Funds:

The National Natural Science Foundation of China(40471113, 40871206)

  • Received Date: 2022-03-14
    Available Online: 2022-06-17
  • Objectives:Distances are functions of spatial positions. Precisely revealing the functional relationship which quantitatively embodies the transmission of uncertainty from spatial positions to their distance, a key scientific problem in need of being solved urgently in Geoinformatics, has important theoretical and practical significance. Methods:Aiming at the limitation of presently available solution of the above mentioned problem, under the premise of that the real position corresponding with the observed position of an uncertain point obeys the complete spatial random distribution within the error circle, this article derived the probability distribution function of distance uncertainty and the corresponding density function between a certain point and an uncertain point and between two uncertain points respectively in two-dimensional space. The latter has been employed to explore the transmission law of point uncertainty to distance uncertainty, opening up a new way for studying and solving the problem of distance uncertainty. Results:The results show that for all cases:(1) When the radius of the error circle (corresponding to the point position accuracy) and the observation distance between points change simultaneously, their ratio has a significant positive correlation with distance uncertainty. (2) When the former remains constant, the distance uncertainty has a significant negative correlation with the latter. (3) When the latter remains constant, the distance uncertainty has a significant positive correlation with the former. Conclusions:As far as distance uncertainty of cases containing an uncertain point and the one of those between two uncertain points are concerned, the latter is obviously greater than the former when the radius of the error circle and the observation distance between points are consistent for both of them. Otherwise they are not comparable.
  • [1] EGENHOFER M J, FRANZOSA R D. Point-Set Topological Spatial Relations[J]. International Journal of Geographical Information Systems, 1991, 5(2):161-174
    [2] Chen J, Li C M, Li Z L, et al. A Voronoi-Based 9-Intersection Model for Spatial Relations[J]. International Journal of Geographical Information Science, 2001, 15(3):201-220
    [3] Gil de la Vega P, Ariza-López F J, Mozas-Calvache A T. Models for Positional Accuracy Assessment of Linear Features:2D and 3D Cases[J]. Survey Review, 2016, 48(350):347-360
    [4] Tong X H, Xie H, Liu S J, et al. Uncertainty of Spatial Information and Spatial Analysis[M]//The Geographical Sciences During 1986—2015. Singapore:Springer, 2017:511-522
    [5] Leung Y, Ma J H, Goodchild M F. A General Framework for Error Analysis in Measurement-Based GIS Part 4:Error Analysis in Length and Area Measurements[J]. Journal of Geographical Systems, 2004, 6(4):403-428
    [6] KIIVERI H T. Assessing, Representing and Transmitting Positional Uncertainty in Maps[J]. International Journal of Geographical Information Science, 1997, 11(1):33-52
    [7] Leung Y, Yan J P. A Locational Error Model for Spatial Features[J]. International Journal of Geographical Information Science, 1998, 12(6):607-620
    [8] Xue J, Leung Y, Ma J H. High-Order Taylor Series Expansion Methods for Error Propagation in Geographic Information Systems[J]. Journal of Geographical Systems, 2015, 17(2):187-206
    [9] Xue S Q, Yang Y X, Dang Y M. Formulas for Precisely and Efficiently Estimating the Bias and Variance of the Length Measurements[J]. Journal of Geographical Systems, 2016, 18(4):399-415
    [10] Hanus P, Pęska-Siwik A, Szewczyk R. Spatial Analysis of the Accuracy of the Cadastral Parcel Boundaries[J]. Computers and Electronics in Agriculture, 2018, 144:9-15
    [11] Hanus P, Pęska-Siwik A, Benduch P, et al. Comprehensive Assessment of the Quality of Spatial Data in Records of Parcel Boundaries[J]. Measurement, 2020, 158:107665
    [12] JCGM 101. Evaluation of measurement data-Supplement 1 to the "Guide to the expression of uncertainty in measurement"-Propagation of distributions using a Monte Carlo method[OL]. https://www.bipm.orgdocuments201262071204JCGM_101_2008_E.pdf325dcaad-c15a-407c-1105-8b7f322d651c, 2008
  • 加载中
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Article Metrics

Article views(118) PDF downloads(11) Cited by()

Related
Proportional views

Methodological Research on Measuring Distance Uncertainty in Two-Dimensional Space

doi: 10.13203/j.whugis20220131
Funds:

The National Natural Science Foundation of China(40471113, 40871206)

Abstract: Objectives:Distances are functions of spatial positions. Precisely revealing the functional relationship which quantitatively embodies the transmission of uncertainty from spatial positions to their distance, a key scientific problem in need of being solved urgently in Geoinformatics, has important theoretical and practical significance. Methods:Aiming at the limitation of presently available solution of the above mentioned problem, under the premise of that the real position corresponding with the observed position of an uncertain point obeys the complete spatial random distribution within the error circle, this article derived the probability distribution function of distance uncertainty and the corresponding density function between a certain point and an uncertain point and between two uncertain points respectively in two-dimensional space. The latter has been employed to explore the transmission law of point uncertainty to distance uncertainty, opening up a new way for studying and solving the problem of distance uncertainty. Results:The results show that for all cases:(1) When the radius of the error circle (corresponding to the point position accuracy) and the observation distance between points change simultaneously, their ratio has a significant positive correlation with distance uncertainty. (2) When the former remains constant, the distance uncertainty has a significant negative correlation with the latter. (3) When the latter remains constant, the distance uncertainty has a significant positive correlation with the former. Conclusions:As far as distance uncertainty of cases containing an uncertain point and the one of those between two uncertain points are concerned, the latter is obviously greater than the former when the radius of the error circle and the observation distance between points are consistent for both of them. Otherwise they are not comparable.

MAO Zhengyuan, FAN Linna, LI Lin, . Methodological Research on Measuring Distance Uncertainty in Two-Dimensional Space[J]. Geomatics and Information Science of Wuhan University. doi: 10.13203/j.whugis20220131
Citation: MAO Zhengyuan, FAN Linna, LI Lin, . Methodological Research on Measuring Distance Uncertainty in Two-Dimensional Space[J]. Geomatics and Information Science of Wuhan University. doi: 10.13203/j.whugis20220131
Reference (12)

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return