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    Title: 利用最小一乘法在地籍坐標轉換資料偵錯之研究
    Outlier Detection in Cadastral Coordinate Transformation Using Least Absolute Deviation
    Authors: 林怡君
    Lin, Yi Chun
    Contributors: 林老生
    Lin, Lao Sheng
    林怡君
    Lin, Yi Chun
    Keywords: 地籍坐標轉換
    最小一乘法
    最小二乘法
    資料偵錯
    Cadastral Coordinate Transformation
    Least Absolute Deviation(LAD)
    Least Squares(LS)
    Outlier Detection
    Date: 2012
    Issue Date: 2014-04-01 11:19:58 (UTC+8)
    Abstract: 臺灣現行之地籍坐標系統,依不同的建立時期與地球原子,主要有TWD67(Taiwan Datum 1967)和TWD97(Taiwan Datum 1997)兩種。為了地籍資料管理、操作及運用之便利,常需執行坐標轉換。根據不同需求,有各種不同的坐標轉換方法,通常使用最小二乘法求解坐標轉換參數。然而,最小二乘法計算方便,但僅適用於資料含有偶然誤差的情形。因此,不論使用何種坐標轉換方法,資料本身是否已完全剔除錯誤,對轉換後之坐標精度有一定程度的影響。
    最小一乘法為平差方法之一,其平差結果不易受粗差的影響,故穩健性強。由於最小一乘法之目標函數中,含有絕對值不可直接微分求解的問題,所以限制其實用性;然而,該問題隨著軟體的開發而克服,故目前在參數估計及資料偵錯上皆有良好的成效。因此,本研究之目的為依據最小一乘法之特性,使用此平差方法於地籍坐標轉換中,測試其資料偵錯能力及穩健性。此外,並比較以最小一乘法與常用的最小二乘法坐標轉換後成果之差異、優缺點及適用情形。
    依據研究目的,為檢測地籍坐標資料的品質,以確保地籍坐標轉換的精度,本研究先模擬三個不同大小之實驗區及含不同大小與數量粗差之參考點與檢核點坐標資料,以測試最小一乘法與最小二乘法的穩健性及資料偵錯能力。另一方面,亦使用真實地籍資料,來探討此兩種方法於真實地籍坐標轉換時之資料偵錯能力與適用性。而坐標轉換方法則分別採用四參數及六參數兩種,以比較不同坐標轉換方法與平差方式之成果。
    根據本研究成果顯示,最小一乘法於地籍坐標轉換時,具有不易受粗差影響平差結果之穩健性,以及可由點位殘差中判斷出粗差之位置及大小的偵錯能力。另一方面,最小二乘法平差結果易受粗差的影響,不具有抗差性及偵錯能力。然而,在坐標資料不含有粗差的情形中,最小二乘法之成果則較最小一乘法為佳或相當。因此,為提升地籍坐標轉換之精度,建議未來在執行地籍坐標轉換時,先以最小一乘法執行資料偵錯,待錯誤坐標剔除後,再以最小二乘法求取坐標轉換參數。
    There are two coordinate systems with different geodetic datum in Taiwan region, i.e., TWD67 (Taiwan Datum 1967) and TWD97 (Taiwan Datum 1997). In order to maintain the consistency of cadastral coordinates, it is necessary to transform one coordinate system to another. However, no matter what transformation method was used, the accuracy of the result is highly depended on the data quality. Since the uncertainty about whether outliers exist or not, so the outlier detection of data becomes an important work before coordinate transformation.
    The LAD(Least Absolute Deviation) method was affected by nearly very little or none from outliers. Thus, this method has been successfully used for outlier measurements detection in other fields. Therefore, LAD method was used to detect outliers in cadastral coordinate transformation in this study. This method provides an examination to ensure the quality of cadastral coordinates before converting one coordinate system to another. So, the accuracy of coordinate transformation can be increased. Then, the coordinate transformation results of LAD method and LS (Least Squares) method in the aspects of outlier detection ability and the accuracy of coordinate transformation were compared.
    On one hand, three varied sizes of simulating test areas, which contains different magnitude of outliers, at numbers of reference points and check points were placed, for checking the robustness and outlier detection ability in LAD and LS methods. On the other hand, data of real test areas were also used. Then, results from different coordinate transformation and adjustment methods were compared and analyzed, by using 4 and 6 parameter coordinate transformation respectively.
    The test results show that LAD method is more robust than LS method, and outliers can be detected easily from the residuals of reference points. While LS method is affected by outliers and the outlier detection ability is weaker than LS method. However, if the data contain none outliers, the coordinate transformation results by using LS method is better than LAD method. Therefore, it is suggested to using LAD method firstly. Then, after deleting all the outliers, one can use LS method to calculate coordinate transformation parameters.
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    Description: 碩士
    國立政治大學
    地政研究所
    100257029
    101
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0100257029
    Data Type: thesis
    Appears in Collections:[地政學系] 學位論文

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