利用加權總體最小二乘法提升二次曲面擬合區域性大地起伏精度之研究－－以台中市為例

A Study of Improving Quadratic Curve Surface Fitting Local Geoid by Weighted Total Least Squares Method-A Case Study of Taichung City

本研究利用台灣台中市現有施測之一等水準點正高與GPS所測得之椭球高進行大地起伏模型擬合。其擬合的方法在傳統上是利用曲面擬合法並通過最小二乘法的方式進行計算出大地起伏值。然而最小二乘法並未考慮到係數矩陣中存在偶然誤差的問題。因此本研究為改善傳統曲面擬合法精度，利用加權總體最小二乘法改進係數矩陣中之誤差，並結合二次多項式曲面擬合法計算出大地起伏值。在通過計算後相互進行比較後，得出精度較高之大地起伏值，結合傳統水準測量控制點位，並藉由改變擬合點位數量建立出較佳的區域性大地起伏模型，本研究顯示該區域模型以可達到1.67cm的高程精度。該區域大地起伏模型不只合乎工程測量規範的標準，也可提供欲建立區域性大地起伏模型的參考。

In this study, we adopt orthometric elevation of first-order leveling data and the ellipsoidal heights that are measured by GPS to fit the local geoid model. Traditionally, the fitting method adopts surface curve fitting method is calculated by least-squares to get the geoid value. Nevertheless, least-squares method can’t deal with the problems which exist in random errors of data in coefficient matrix. Thus, the purpose of this study is to improve the precision of traditional surface curve fitting. We apply weighted total least-squares which also combined with quadratic polynomial surface curve fitting to improve the random errors of data in coefficient matrix and find the local geoid value with better precision. Combining traditional leveling control points with adjustment in number of fitting points, we obtain an ideal optimal local geoid model that is developed into the elevation precision of This study provides not only a fast practical method in getting orthometric elevation but also academic references for a different method to fit the local geoid model.