政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/65095

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/65095

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Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/65095

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.
Reference:	一、中文參考文獻王文峰，2006，「基於LINGO的最小一乘線性回歸的參數估計」，『貴州財經學院學報』，6：106-108。王奕鈞，2006，「神經網路應用於地籍坐標轉換之研究」，國立政治大學地政學系碩士論文：臺北。王福昌、胡順田、張艷芳，2007，「最小一乘回歸係數估計及其MATLAB實現」，『防災科技學院學報』，9（4）。方述誠，1993，「線性優化及擴展—理論與演算法」，『數學傳播』，17（1）。方述誠、S. 普森普拉，1994，『線性優化及擴展—理論與演算法』，北京：科學出版社。肖建華、楊緯隆、李軍，2006，「基於Matlab的最小一乘回歸的線性規劃實現」，『五邑大學學報（自然科學版）』，20（1）。何維信，2009，『測量學』第六版，臺北：宏泰出版社。李哲仁，2001，「完全最小二乘法平差於坐標轉換之研究」，國立成功大學測量工程學系碩士論文：台南。吳孟旭，2008，「應於VRS-RTK技術於圖根點重測時坐標轉換之探討-以彰化縣市地區為例」，國立中興大學土木工程學系測量資訊組碩士學位論文：台中。吳亞翰，2009，「藉由附有面積限制條件的坐標轉換以提升圖解區土地複丈效率之研究」，國立中興大學土木工程學系碩士學位論文：台中。林老生，2012，「e-GPS水準測量精度研究」，『臺灣土地研究』，15（2）：35-58。岳東杰、黃騰，1999，「GPS高程的抗差擬合推估」，『河海大學學報』，27（6）：90-93。梁勇、郭祿光、樊功瑜，1990，「穩健估計在測量平差中的應用」，『同濟大學學報』，18（4）：467-474。章棟恩、馬玉蘭、徐美萍、李雙，2008，『MATLAB高等數學實驗』，北京：電子工業出版社。陳世平，2003，「數值法辦理圖解地籍圖數化區之土地複丈作業研究--以農地重測區為例」，逢甲大學土地管理學系碩士在職專班碩士論文：台中。張裕民，1993，「以穩健推估法進行測量平差之研究」，四海學報，8：33-50。許皓寧，2003，「臺北市地籍資料TWD67與TWD97坐標轉換之比較研究」，國立中興大學土木工程學系碩士論文：台中。馮守平、石澤、鄧瑾，2008，「一元線性回歸模型中參數估計的幾種方法比較」，『統計與決策』，24：152-153。楊鳳芸、張旭東，2005，「採用抗差推估法剔除GPS高程數據粗差」，『測繪通報』，10：9-11。臺北市政府地政處測量大隊，2004，「臺北市TWD67地籍坐標系統轉換為TWD97坐標系統作業總報告」。溫豐文，2012，『土地法』修訂版，臺北：三民書局。鄭彩堂，2002，「以限制條件及附加參數法轉助圖解區土地複丈之研究」，國立中興大學土木工程學系碩士論文：台中。顧樂民，2011，「曲線擬合的最小一乘法」，『同濟大學學報（自然科學版），39（9）。二、外文參考文獻 Bektas, S. and Y. Sisman, 2010, “The comparison of L1 and L2-norm minimization methods”, International Journal of the Physical Sciences, 5 (11): 1721-1727. Bidabad, B. (2005, January). L1 Norm Based Data Analysis and Related Methods (1632-1989), on the World Wide Web: http://www.bidabad.com/doc/l1-article1.pdf. Calitz, M. F. and H. Rüther, 1996, “Least Absolute Deviation (LAD) image matching”, ISPRS Journal of Photogrammetry & Remote Sensing, 51: 223-229. Chen, K., Z. Ying, H. Zhang and L. Zhao, 2006, “Analysis of least absolute deviation”, Oxford Journals, Life Sciences & Mathematics & Physical Sciences, Biometrika, 95 (1): 107-122. Dasgupta, M. and SK Mishra, (2007, November). Least absolute deviation estimation of linear econometric models: A literature review, Munich Personal RePEc Archive, 7 (1781), on the World Wide Web: http://mpra.ub.uni-muenchen.de/1781/. Fang, S. C. and S. Puthenpura, 1993, “Linear Optimization and Extensions - Theory and Algorithms”, Prentice Hall, Inc. , Federal Geographic Data Committee (FGDC), 1998, “Geospatial Positioning Accuracy Standards Part 3. National Standard for Special Data Accuracy”, Washington, D.C: 1-28. Fu, H., M. K. Ng, M. Nikolova and J. L. Barlow, 2004, “Efficient Minimization Methods of Mixed L2-L1 and L1-L1 Norms for Image Restoration”, Siam Journal On Scientific Computing, Report CMLA No 2004-14. Ghilani, C. D. and P. R. Wolf, 2010, “Adjustment Computations: Spatial Data Analysis”, 5th Edition, John Wiley & Sons, Inc. Khodabandeh, A. and A. R. Amiri-Simkooei, 2011, “Recursive algorithm for l1 norm estimation in linear models”, Journal of Surveying Engineering, 137 (1): 1-8. Kuzmanovi´c, I., K. Sabo, R. Scitovski, and I. Vazler, 2009, “The best least absolute deviation linear regression: properties and two efficient methods”, Aplimat - Journal of Applied Mathematics, 2 (3): 227-240. Li, Y. and G. R. Arce, 2004, “A Maximum Likelihood Approach to Least Absolute Deviation Regression”, EURASIP Journal on Applied Signal Processing, Hindawi Publishing Corporation, 12: 1762–1769. Neuman, E. (2013, March). Tutorial 6: Linear Programming with MATLAB, on the World Wide Web: http://www.math.siu.edu/matlab/tutorial6.pdf. Nobakhti, A., Wang H. and Chai T., 2009, “Algorithm for very fast computation of Least Absolute Value regression”, American Control Conference, Hyatt Regency Riverfront, St. Louis, MO, USA, June 10-12. Pfeil, W. A., 2006, “Statistical teaching aids”, Project Number: JP-0501. Sisman, Y., 2011, “Parameter estimation and outlier detection with different estimation methods”, Scientific Research and Essays, 6 (7): 1620-1626. Soliman, S. A., S. Persaud, K. EI-Nagar and M. E. EI-Hawary, 1997, “Application of least absolute value parameter estimation based on linear programming to shorbterm load forecasting”, International Journal of Electrical Power & Energy Systems, 19 (3): 209-216. Wolf, P. R. and B. A. Dewitt, 2004,”Elements of Photogrammetry: with Application in GIS”, 3rd edition, McGraw-Hill. Yetkin, M. and C. Inal, 2011, “L1 Norm Minimization in GPS Networks”, Survey Review, 43, 323: 523-532. 三、網頁參考文獻國土資訊系統─土地基本資料庫全球資訊網，取用日期2012年12月，http://law.moj.gov.tw/LawClass/LawAll.aspx?PCode=D0060053。全國法規資料庫（地籍測量實施規則），取用日期2012年12月，http://law.moj.gov.tw/LawClass/LawAll.aspx?PCode=D0060053。內政部地政司衛星測量中心，取用日期2013年6月，http://www.gps.moi.gov.tw/SSCenter/Introduce/InfoPage.aspx。國家圖書館臺灣鄉土書目資料庫，取用日期2013年8月，http://localdoc.ncl.edu.tw/tmld/browse_map.jsp?map=2001。 Math Works. Retrieved May 17, 2013 on the World Wide Web: http://www.mathworks.com/.
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:	[Department of Land Economics] Theses

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