A Study of Using Least Square Support Vector Machine for Three dimensional coordinatesTransformation

目前台灣常用的坐標系統有以下三種：TWD67 ( TAIWAN DATUM 67，1967台灣大地基準)、TWD97 ( TAIWAN DATUM 97，1997台灣大地基準)、WGS84 ( World Geodetic System，1984 )。TWD67坐標系統是以「區域性非地心大地坐標基準」並分「平面坐標」及「高程坐標」兩個子系統，其高程定義是從「大地基準面」起算正高，TWD97坐標系統則是以「全球性地心大地坐標基準」，並以「雙軸橢球體面」起算橢球高，由於TWD67 、TWD97坐標系統所用的基準及橢球體參數不同，同一點位在兩個坐標系統會有不同的坐標值。 本研究將採用最小二乘支持向量機結合三種核函數(lin、poly、RBF)進行TWD97與TWD67間之三維坐標轉換，並與最小二乘法七參數坐標轉換比較。實驗成果顯示，應用最小二乘支持向量機進行三維坐標轉換，可有效降低高程差對三維坐標轉換的影響，並以採用RBF核函數所獲得之成果最佳，轉換精度評估採均方根誤差，E值為：0.016、N值為：0.010、H值為：0.028，遠優於採用最小二乘法七參數坐標轉換之成果，其均方根誤差E值為：0.088、N值為：0.065、H值為：0.035。另由實驗成果顯示，採用最小二乘支持向量機可直接引用投影坐標與椭球高施作三維坐標轉換，其轉換成果，均方根誤差E值為：0.019、N值為：0.013、H值為：0.030，與採用空間直角坐標轉換成果差異不大，根據本文研究成果，將有助於簡化三維坐標轉換計算，省略解算平面直角坐標與空間直角坐標計算過程，達到更省時，省力之效 。At present the Taiwan commonly used coordinates system has following three kinds, TWD67( TAIWAN DATUM 67，Taiwan's Geodetic Datums)、TWD97(TAIWAN DATUM 97，Taiwan's Geodetic Datums)、 WGS84 ( World Geodetic System，1984 )。Taiwan's TWD67 coordinates system is by the regional non-center of earth geodetic coordinates datum, And divides'the place coordinates'and'the elevation coordinates'two sub-systemsIts elevation definition is begins reckoning the orthometric height from 'the earth reduced plane',The TWD97 coordinates system is by'the global center of earth geodetic coordinates datum',And begins reckoning the ellipsoidal height by 'the two axle ellipsoid dignity',Because TWD67 coordinates system and the TWD97 coordinates system uses the datum and the ellipse spheroid parameter is different,The identical spot position can have the different coordinates value in two coordinates systems。 This research will use LSSVM union three kind of functions (lin, poly, RBF) carries on TWD97 and TWD67 the three dimensional coordinates transformation,And compares with the least squares method seven parameter coordinates transformation,The experimental achievement demonstrated that,uses LSSVM to carry on the three dimensional coordinates to transform, but reduces the elevation difference effectively the influence which transforms to the three dimensional coordinates,and uses the RBF function to obtain the achievement to be best,The transformation precision appraised picks the RMSE,the E value is:0.016,the N value is:0.010,the H value is:0.028,Surpasses far uses achievement of the least squares method seven parameter coordinates transformation,its RMSE E value is:0.088,the N value is: 0.065,the H value is:0.035。Demonstrated in addition by the experimental achievement that,uses LSSVM to be possible to quote the projection coordinates and ellipsoidal height makes the three dimensional coordinates transformation,Its transformation achievement, RMSE E value is:0.019, the N value is:0.013,the H value is:0.030,With uses the cartesian coordinates transformation achievement difference not to be big, according to this article research results, will conducive toward favor the simplification three dimensional coordinates transformation computation, the abbreviation resolving projection coordinates and the cartesian coordinates computation process, achieved time-saving, will reduce effort the effect。目錄 誌謝...................................................... i 中文摘要................................................. ii Abstract................................................ iii 目錄..................................................... iv 表目錄................................................... vi 圖目錄.................................................. vii 第一章 緒論................................................1 1-1前言....................................................1 1-2動機與目的..............................................1 1-3文獻回顧......................................... ......2 1-4研究方法................................................3 1-5論文架構................................................4 第二章 理論與基礎..........................................5 2-1台灣常用的坐標系統......................................6 2-1-1 TWD67 坐標系統.......................................6 2-1-2 TWD97 坐標系統.......................................7 2-1-3 TWD67 與TWD97 坐標系統比較..........................10 2-2 坐標系統轉換..........................................11 2-2-1 大地坐標轉換卡式直角坐標-Heiskanen解法..............12 2-2-2 最小二乘法七參數轉換................................14 2-3 最小二乘支持向量機（LSSVM）...........................16 2-3-1 支持向量機..........................................16 2-3-2 最小二乘支持向量機..................................23 2-3-3 參數選擇............................................25 第三章 研究方法...........................................28 3-1研究區介紹.............................................28 3-2研究數據...............................................28 3-3研究步驟...............................................29 3-4研究評估...............................................31 第四章 實驗與成果分析.....................................34 4-1點位資料與處理.........................................34 4-2點位坐標系統轉換-Molodensky Badekas....................35 4-3 點位坐標系統轉換-LSSVM................................41 4-4成果分析...............................................59 第五章 結論與分析.........................................66 5-1結論...................................................66 5-2建議...................................................67 參考文獻........................................................69 附錄 附錄A 驗區域點位共計205個.................................71 附錄B 二維仿射坐標轉換各點位分量差值表....................77 附錄C TWD97(E，N，h)轉換成卡式空間直角坐標(X，Y，Z)對照表.82 附錄D TWD67(E，N，h)轉換成卡式空間直角坐標(X，Y，Z)對照表.8