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    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/119593

    Title: 利用不同目標函數之演算法進行粗差偵測之研究
    The study of using different objective functions with algorithm in gross error detection
    Authors: 張宏嘉
    Chang, Hung-Chia
    Contributors: 甯方璽
    Ning, Fang-Shii
    Chang, Hung-Chia
    Keywords: 粗差定位
    Gross error
    Reverse weight matrix of LAD
    Date: 2018
    Issue Date: 2018-08-27 14:56:28 (UTC+8)
    Abstract: 在測量領域中,最小二乘法為最常被使用的平差方法,然而最小二乘法建立於觀測量僅含有偶然誤差的前提之下,當觀測量含有粗差時,最小二乘法的成果容易受到影響。因此,本研究透利用不同演算法對不同目標函數進行計算,並以統計檢定量分析各方法偵測粗差的能力。
    In the field of surveying, Least Square (LS) methods are often used in adjustment. However, LS built on observations usually show with random errors. If observations have gross errors, the solution of LS will be effected easily. So this study uses different objective functions to calculate with different algorithms, and analyzes the ability of gross errors detection with test statistic.
    The methods in this study are equal weight LS、Iteratively Reweighted LS (IRLS)、Least Absolute Deviation (LAD) and Optimal Weight Matrix (OWM). This study proposes a concept “inverse weight matrix of LAD” to solve the problem that LAD lacks test statistics. And assess the different methods’ results with weight value、 standardized residual and redundant observation component.
    In simulated data, when observations have less redundant observations, OWM and “inverse weight matrix of LAD” have better ability of gross error detection, and them make the gross errors have lower weight value. With more observations, the IRLS has better result. In real data, the posteriori variance will be effected easily, and lead to every methods can’t locate the gross error. However, OWM and “inverse weight matrix of LAD” can enlarge the standardized residual of gross errors and help user to check the observations.
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    Description: 碩士
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0105257032
    Data Type: thesis
    DOI: 10.6814/THE.NCCU.LE.016.2018.A05
    Appears in Collections:[地政學系] 學位論文

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