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題名 運用曲面擬合提升幾何法大地起伏值精度之研究
The Study of Applying Surface Fitting to Improve Geometric Geoidal Undulation作者 蔡名曜 貢獻者 甯方璽
蔡名曜關鍵詞 大地起伏
曲面擬合
量子行為粒子群算法
粗差偵測
Geoid Height
Curve Fitting
Quantum-behaved Particle Swarm Optimization
Outlier Detection日期 2013 上傳時間 21-Jul-2014 15:43:49 (UTC+8) 摘要 大地起伏值為正高與橢球高的差異量，如果取得高精度的大地起伏值，可以利用衛星定位測量施測橢球高並計算得到高精度的正高，其成本低廉，可望取代傳統的水準測量。而大地起伏值可以分為幾何法或重力法的大地起伏值，其中幾何法的大地起伏值計算方法簡易且精度高，可以利用曲面擬合方法取得之。但是幾何法的大地起伏值會受到地形起伏的影響，大範圍的曲面擬合會降低其精度。台灣的地形起伏大，難以進行大範圍曲面擬合。於是本研究利用環域方法搜尋待測點位鄰近的水準點參與曲面方程式擬合大地起伏，試圖找到最適合的大地起伏擬合範圍。成果顯示：環域的範圍從10公里至30公里，利用二次曲面方程式擬合大地起伏在台灣平地區域能夠達到預測精度與內部精度同時低於5公分。另外由於衛星定位測量橢球高的誤差較高，需進行資料品質評估並進行粗差偵測。針對粗差偵測提出新的方法，利用最佳化演算法中的量子行為粒子群演算法計算最小二乘平差法中的權矩陣，期望能夠將粗差觀測量的權重降低，達到粗差偵測的效果。成果顯示最佳化權矩陣演算法，能夠將粗差對平差系統的影響量降到最低。本研究建立一套台灣地區的大地起伏擬合作業程序：利用環域搜尋鄰近水準點、曲面方程式及環域範圍選擇與資料的粗差偵測，可獲得高品質的大地起伏。
The geoidal undulation is the difference of ellipsoid height and orthometric height. We can obtain high accuracy of orthometric height by existing high accuracy of geoidal undulation and the ellipsoidal height measuring by GPS. It expected to replace the traditional leveling survey due to the less cost. This study uses buffer method to search the leveling benchmarks around the object point, attempts to find the proper range of fitting geoidal undulation to curve surface. Experimental results shows that it can archive 5cm level on both prediction error and internal precision by fitting geoidal undulation on 2nd curve surface model where the buffer range is from 10 km to 30 km. In this study, also uses the quantum-behaved particle swarm optimization to calculate the weight matrix of least square adjustment, the purpose is to down-weighting the suspicious outlier, and detect the outlier. Experimental results shows that the optimal weight matrix algorithm can reduce the influence of outlier.This study establish a procedure of fitting geoidal undulation: using buffer analysis to search the adjacent leveling benchmark, selecting the proper buffer range and surface equation and detecting outlier in data.參考文獻 一、 中文參考文獻內政部，2001，一等水準點測量作業規範。孔祥元、郭際明、劉宗泉，2001，『大地測量學基礎』，武昌：武漢大 學出版社。台中市政府，2003，九十二年度公共管線資料庫系統建置品質監驗案期末報告書。匡志威、熊琳璞、刘鹏程、戴建清，2010，『大区域 GPS 水准拟合模型研究及应用』，城市勘测，第二卷：78-80.李德仁，1984，利用選擇權迭代法進行粗差定位，武漢測繪學院學報，第一卷。李德仁、袁修孝，2005，誤差處理與可靠性理論，第二版，武漢大學出版社，武昌。李尚訓，2010，『利用支持向量機法推求區域性大地起伏值之研究─以台中地區為例』，國立中興大學土木工程學系碩士論文：臺中。沈昱廷，2011，『以最小二乘支持向量機擬合區域性大地起伏值之研究－以台中地區為例』，國立中興大學土木工程學系碩士論文：臺中。胡明城，2003，『現代大地測量學的理論及其應用』，北京：測繪出版社。陳國華，2004，『整合TWVD2001水準及GPS資料改進台灣區域性大地水準面模式以應用於GPS高程測量』，國立成功大學測量及空間資訊學系博士論文：臺南。陳佳菱，2012，『以粒子群演算法改善傳統二次曲面擬合區域性大地起伏精度之研究』，國立中興大學土木工程學系碩士論文：臺中。趙嘉展、陳松安、甯方璽，2010，『利用衛星測高法與海洋水準法求定台灣海面地形之研究』，測量工程，第五十二卷：5-21簡子淩，2012，『以基因表示規劃法建立區域性大地起伏模型之研究－以台中地區為例』，國立中興大學土木工程學系碩士論文：臺中。黃金維、許宏銳、黃啟訓，2013，『新一代台灣大地水準面模式：防災、監測、高程現代化之應用』，國土測繪與空間資訊，第一卷第一期：57-81。蔡名曜、甯方璽，2013，『利用粒子群演算法與交叉驗證法擬合區域性大地起伏值之研究－以臺中區域為例』，第32屆測量及空間資訊研討會暨第2屆兩岸重力及大地水準面研討會：新竹。二、 外文參考文獻Ardalan, A. A. and Grafarend E. W., 2001, Ellipsoidal geoidal undulations (ellipsoidal Bruns formula): case study, Journal of Geodesy, 75: 544-552.Baarda, W., 1968, A testing procedure for use in geodetic networks. Netherlands Geodetic Commission, New Series, Delft, Netherlands, 2(5).Eberhart, R. C., and Shi, Y., 1998, Comparison between genetic algorithms and particle swarm optimization, Evolutionary Programming VII: 611-616.Efron B., 1983, Estimating the error rate of a prediction rule: improvement on cross-validation. J. Am. Stat. Assoc., 78:316–331Van den Bergh, F., 2001, “An Analysis of Particle Swarm optimizers,” PhD Thesis. University of PretoriaHeiskanen, W. A., and Moritz, H., 1967, Physical Geodesy. , San Francisco: W. H. Freeman and company.Hastie, T., Tibshirani, R., Friedman, J., Hastie, T., Friedman, J., and Tibshirani, R. , 2009, The elements of statistical learning. New York: Springer.Sun, J., Feng, B., and Xu, W. B., 2004, Particle swarm optimization with particles having quantum behavior, in: IEEE Proceedings of Congress on Evolutionary Computation, 2004:325–331.Juhl J., 1984, The "Danish Method" of weight reduction for gross error detection, XVth ISPRS Congress, Volume XXV Part A3:468-472Kubik, K., Weng, W., and Frederiksen, P., 1985, Oh, grosserorors. Cited by Aust. J. Geodesy Photogramm. Surveying, 42:1-18.Kavzoglu, T., and Saka, M. H., 2005, Modelling local GPS/levelling geoid undulations using artificial neural network, Journal of Geodesy, 78: 520-527.Kennedy J., and Eberhart R., 1995, Particle Swarm Optimization, IEEE International of first Conference on Neural Networks, 1995: 167-171.Kohavi R., 1995, A study of cross-validation and bootstrap for accuracy estimation and model selection, International Joint on Artificial Intelligence, Vol. 14, No. 2:1137-1145Lehmann R., 2013, 3 σ-Rule for Outlier Detection from the Viewpoint of Geodetic Adjustment, Journal of Surveying Engineering, 139(4):157-165.Lehmann R., 2013, On the formulation of the alternative hypothesis for geodetic outlier detection, Journal of Geodesy, 87(4):373-386.Meyer, T. H., Roman, D. R., and Zilkoski, D. B., 2006, What DoesHeight Really Mean? Part IV: GPS Orthometric Heighting, Surveying and Land Information Science, Vol. 66, No. 3: 165-183.Schwarz, C. R., and Kok, J. J., 1993, Blunder detection and data snooping in LS and robust adjustments. Journal of surveying engineering, 119(4): 127-136.Sun, J., Xu, W., and Feng, B., 2004, A global search strategy of quantum-behaved particle swarm optimization. In Cybernetics and Intelligent Systems, 2004 IEEE Conference on Vol. 1:111-116.Sun J., Xu W., and Liu J., 2005, Parameter selection of quantum-behaved particle swarm optimization, Advances in Natural Computation,2005: 543-552.Xi, M., Sun, J., and Xu, W., 2008, An improved quantum-behaved particle swarm optimization algorithm with weighted mean best position. Applied Mathematics and Computation, 205(2):751-759.Yetkin, M., Inal, C., and Yigit, C. O., 2011, The Optimal Design of Baseline Configuration in GPS Networks by Using the Particle Swarm Optimisation Algorithm. Survey Review, 43(323):700-712.You R., 2006, Local geoid improvement using GPS and leveling data: case study, Journal of Surveying Engineering, 132:101-107Zilkoski D. B., Carlson E. E., and Smith C. L., 2008, Guidelines for Establishing GPS-Derived Orthometric Heights (NGS-59), NOAA Technical Memorandum NOS NGS 59, National Ocean Service, Nation Geodetic Survey. 描述 碩士
國立政治大學
地政研究所
101257030
102資料來源 http://thesis.lib.nccu.edu.tw/record/#G0101257030 資料類型 thesis dc.contributor.advisor 甯方璽 zh_TW dc.contributor.author (Authors) 蔡名曜 zh_TW dc.creator (作者) 蔡名曜 zh_TW dc.date (日期) 2013 en_US dc.date.accessioned 21-Jul-2014 15:43:49 (UTC+8) - dc.date.available 21-Jul-2014 15:43:49 (UTC+8) - dc.date.issued (上傳時間) 21-Jul-2014 15:43:49 (UTC+8) - dc.identifier (Other Identifiers) G0101257030 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/67632 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 地政研究所 zh_TW dc.description (描述) 101257030 zh_TW dc.description (描述) 102 zh_TW dc.description.abstract (摘要) 大地起伏值為正高與橢球高的差異量，如果取得高精度的大地起伏值，可以利用衛星定位測量施測橢球高並計算得到高精度的正高，其成本低廉，可望取代傳統的水準測量。而大地起伏值可以分為幾何法或重力法的大地起伏值，其中幾何法的大地起伏值計算方法簡易且精度高，可以利用曲面擬合方法取得之。但是幾何法的大地起伏值會受到地形起伏的影響，大範圍的曲面擬合會降低其精度。台灣的地形起伏大，難以進行大範圍曲面擬合。於是本研究利用環域方法搜尋待測點位鄰近的水準點參與曲面方程式擬合大地起伏，試圖找到最適合的大地起伏擬合範圍。成果顯示：環域的範圍從10公里至30公里，利用二次曲面方程式擬合大地起伏在台灣平地區域能夠達到預測精度與內部精度同時低於5公分。另外由於衛星定位測量橢球高的誤差較高，需進行資料品質評估並進行粗差偵測。針對粗差偵測提出新的方法，利用最佳化演算法中的量子行為粒子群演算法計算最小二乘平差法中的權矩陣，期望能夠將粗差觀測量的權重降低，達到粗差偵測的效果。成果顯示最佳化權矩陣演算法，能夠將粗差對平差系統的影響量降到最低。本研究建立一套台灣地區的大地起伏擬合作業程序：利用環域搜尋鄰近水準點、曲面方程式及環域範圍選擇與資料的粗差偵測，可獲得高品質的大地起伏。 zh_TW dc.description.abstract (摘要) The geoidal undulation is the difference of ellipsoid height and orthometric height. We can obtain high accuracy of orthometric height by existing high accuracy of geoidal undulation and the ellipsoidal height measuring by GPS. It expected to replace the traditional leveling survey due to the less cost. This study uses buffer method to search the leveling benchmarks around the object point, attempts to find the proper range of fitting geoidal undulation to curve surface. Experimental results shows that it can archive 5cm level on both prediction error and internal precision by fitting geoidal undulation on 2nd curve surface model where the buffer range is from 10 km to 30 km. In this study, also uses the quantum-behaved particle swarm optimization to calculate the weight matrix of least square adjustment, the purpose is to down-weighting the suspicious outlier, and detect the outlier. Experimental results shows that the optimal weight matrix algorithm can reduce the influence of outlier.This study establish a procedure of fitting geoidal undulation: using buffer analysis to search the adjacent leveling benchmark, selecting the proper buffer range and surface equation and detecting outlier in data. en_US dc.description.tableofcontents 第一章 緒論 1第一節 研究背景 1第二節 研究動機及目的 4第三節 論文架構 5第二章 文獻回顧 7第一節 大地起伏 7第二節 粗差偵測理論 8第三節 粒子群演算法 9第三章 理論基礎 11第一節 大地起伏概念 11第二節 大地起伏值之解算方法 12第三節 粗差偵測原理 15第四節 粒子群演算法原理 21第五節 最佳化權矩陣 26第四章 研究方法 30第一節 研究流程 30第二節 研究資料 31第三節 曲面方程式分析方法 34第四節 曲面擬合範圍分析方法 40第五節 粗差偵測分析方法 45第六節 台灣地區大地起伏擬合作業程序 53第五章 實驗成果 55第一節 曲面方程式初步實驗成果與討論 55第二節 曲面擬合範圍實驗成果與討論 56第三節 粗差偵測分析實驗成果 85第六章 結論與建議 111第一節 結論 111第二節 建議 111參考文獻 113 zh_TW dc.format.extent 10350492 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0101257030 en_US dc.subject (關鍵詞) 大地起伏 zh_TW dc.subject (關鍵詞) 曲面擬合 zh_TW dc.subject (關鍵詞) 量子行為粒子群算法 zh_TW dc.subject (關鍵詞) 粗差偵測 zh_TW dc.subject (關鍵詞) Geoid Height en_US dc.subject (關鍵詞) Curve Fitting en_US dc.subject (關鍵詞) Quantum-behaved Particle Swarm Optimization en_US dc.subject (關鍵詞) Outlier Detection en_US dc.title (題名) 運用曲面擬合提升幾何法大地起伏值精度之研究 zh_TW dc.title (題名) The Study of Applying Surface Fitting to Improve Geometric Geoidal Undulation en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) 一、 中文參考文獻內政部，2001，一等水準點測量作業規範。孔祥元、郭際明、劉宗泉，2001，『大地測量學基礎』，武昌：武漢大 學出版社。台中市政府，2003，九十二年度公共管線資料庫系統建置品質監驗案期末報告書。匡志威、熊琳璞、刘鹏程、戴建清，2010，『大区域 GPS 水准拟合模型研究及应用』，城市勘测，第二卷：78-80.李德仁，1984，利用選擇權迭代法進行粗差定位，武漢測繪學院學報，第一卷。李德仁、袁修孝，2005，誤差處理與可靠性理論，第二版，武漢大學出版社，武昌。李尚訓，2010，『利用支持向量機法推求區域性大地起伏值之研究─以台中地區為例』，國立中興大學土木工程學系碩士論文：臺中。沈昱廷，2011，『以最小二乘支持向量機擬合區域性大地起伏值之研究－以台中地區為例』，國立中興大學土木工程學系碩士論文：臺中。胡明城，2003，『現代大地測量學的理論及其應用』，北京：測繪出版社。陳國華，2004，『整合TWVD2001水準及GPS資料改進台灣區域性大地水準面模式以應用於GPS高程測量』，國立成功大學測量及空間資訊學系博士論文：臺南。陳佳菱，2012，『以粒子群演算法改善傳統二次曲面擬合區域性大地起伏精度之研究』，國立中興大學土木工程學系碩士論文：臺中。趙嘉展、陳松安、甯方璽，2010，『利用衛星測高法與海洋水準法求定台灣海面地形之研究』，測量工程，第五十二卷：5-21簡子淩，2012，『以基因表示規劃法建立區域性大地起伏模型之研究－以台中地區為例』，國立中興大學土木工程學系碩士論文：臺中。黃金維、許宏銳、黃啟訓，2013，『新一代台灣大地水準面模式：防災、監測、高程現代化之應用』，國土測繪與空間資訊，第一卷第一期：57-81。蔡名曜、甯方璽，2013，『利用粒子群演算法與交叉驗證法擬合區域性大地起伏值之研究－以臺中區域為例』，第32屆測量及空間資訊研討會暨第2屆兩岸重力及大地水準面研討會：新竹。二、 外文參考文獻Ardalan, A. A. and Grafarend E. W., 2001, Ellipsoidal geoidal undulations (ellipsoidal Bruns formula): case study, Journal of Geodesy, 75: 544-552.Baarda, W., 1968, A testing procedure for use in geodetic networks. Netherlands Geodetic Commission, New Series, Delft, Netherlands, 2(5).Eberhart, R. C., and Shi, Y., 1998, Comparison between genetic algorithms and particle swarm optimization, Evolutionary Programming VII: 611-616.Efron B., 1983, Estimating the error rate of a prediction rule: improvement on cross-validation. J. Am. Stat. Assoc., 78:316–331Van den Bergh, F., 2001, “An Analysis of Particle Swarm optimizers,” PhD Thesis. University of PretoriaHeiskanen, W. A., and Moritz, H., 1967, Physical Geodesy. , San Francisco: W. H. Freeman and company.Hastie, T., Tibshirani, R., Friedman, J., Hastie, T., Friedman, J., and Tibshirani, R. , 2009, The elements of statistical learning. New York: Springer.Sun, J., Feng, B., and Xu, W. B., 2004, Particle swarm optimization with particles having quantum behavior, in: IEEE Proceedings of Congress on Evolutionary Computation, 2004:325–331.Juhl J., 1984, The "Danish Method" of weight reduction for gross error detection, XVth ISPRS Congress, Volume XXV Part A3:468-472Kubik, K., Weng, W., and Frederiksen, P., 1985, Oh, grosserorors. Cited by Aust. J. Geodesy Photogramm. Surveying, 42:1-18.Kavzoglu, T., and Saka, M. H., 2005, Modelling local GPS/levelling geoid undulations using artificial neural network, Journal of Geodesy, 78: 520-527.Kennedy J., and Eberhart R., 1995, Particle Swarm Optimization, IEEE International of first Conference on Neural Networks, 1995: 167-171.Kohavi R., 1995, A study of cross-validation and bootstrap for accuracy estimation and model selection, International Joint on Artificial Intelligence, Vol. 14, No. 2:1137-1145Lehmann R., 2013, 3 σ-Rule for Outlier Detection from the Viewpoint of Geodetic Adjustment, Journal of Surveying Engineering, 139(4):157-165.Lehmann R., 2013, On the formulation of the alternative hypothesis for geodetic outlier detection, Journal of Geodesy, 87(4):373-386.Meyer, T. H., Roman, D. R., and Zilkoski, D. B., 2006, What DoesHeight Really Mean? Part IV: GPS Orthometric Heighting, Surveying and Land Information Science, Vol. 66, No. 3: 165-183.Schwarz, C. R., and Kok, J. J., 1993, Blunder detection and data snooping in LS and robust adjustments. Journal of surveying engineering, 119(4): 127-136.Sun, J., Xu, W., and Feng, B., 2004, A global search strategy of quantum-behaved particle swarm optimization. In Cybernetics and Intelligent Systems, 2004 IEEE Conference on Vol. 1:111-116.Sun J., Xu W., and Liu J., 2005, Parameter selection of quantum-behaved particle swarm optimization, Advances in Natural Computation,2005: 543-552.Xi, M., Sun, J., and Xu, W., 2008, An improved quantum-behaved particle swarm optimization algorithm with weighted mean best position. Applied Mathematics and Computation, 205(2):751-759.Yetkin, M., Inal, C., and Yigit, C. O., 2011, The Optimal Design of Baseline Configuration in GPS Networks by Using the Particle Swarm Optimisation Algorithm. Survey Review, 43(323):700-712.You R., 2006, Local geoid improvement using GPS and leveling data: case study, Journal of Surveying Engineering, 132:101-107Zilkoski D. B., Carlson E. E., and Smith C. L., 2008, Guidelines for Establishing GPS-Derived Orthometric Heights (NGS-59), NOAA Technical Memorandum NOS NGS 59, National Ocean Service, Nation Geodetic Survey. zh_TW
