The Study of Applying Surface Fitting to Improve Geometric Geoidal Undulation

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