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High-order Taylor series expansion methods for error propagation in geographic information systems

Author

Listed:
  • Jie Xue
  • Yee Leung
  • Jiang-Hong Ma

Abstract

The quality of modeling results in GIS operations depends on how well we can track error propagating from inputs to outputs. Monte Carlo simulation, moment design and Taylor series expansion have been employed to study error propagation over the years. Among them, first-order Taylor series expansion is popular because error propagation can be analytically studied. Because most operations in GIS are nonlinear, first-order Taylor series expansion generally cannot meet practical needs, and higher-order approximation is thus necessary. In this paper, we employ Taylor series expansion methods of different orders to investigate error propagation when the random error vectors are normally and independently or dependently distributed. We also extend these methods to situations involving multi-dimensional output vectors. We employ these methods to examine length measurement of linear segments, perimeter of polygons and intersections of two line segments basic in GIS operations. Simulation experiments indicate that the fifth-order Taylor series expansion method is most accurate compared with the first-order and third-order method. Compared with the third-order expansion; however, it can only slightly improve the accuracy, but on the expense of substantially increasing the number of partial derivatives that need to be calculated. Striking a balance between accuracy and complexity, the third-order Taylor series expansion method appears to be a more appropriate choice for practical applications. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
  • Handle: RePEc:kap:jgeosy:v:17:y:2015:i:2:p:187-206
    DOI: 10.1007/s10109-014-0207-x
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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. 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.
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    Citations

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    Cited by:

    1. 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.
    2. Sajjad Eghdamirad & Fiona Johnson & Ashish Sharma, 2017. "Using second-order approximation to incorporate GCM uncertainty in climate change impact assessments," Climatic Change, Springer, vol. 142(1), pages 37-52, May.

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    More about this item

    Keywords

    Error propagation; Geographic information system; Taylor series expansion method; Length measurement; Intersection operation; C10; C63;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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