利用穩健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－－以舊台中市為例

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

如何利用GNSS測量資料處理取得較合理的點位高程精度為本研究所探討的課題。本研究採用台灣舊台中市的一等水準點的正高資料與GNSS所測得橢球高進行擬合，擬合的方法採用傳統的方法，利用最小二乘法搭配曲面擬合法進而建立大地起伏模型。但由於最小二乘法計算值中，並未考慮到係數矩陣與觀測向量中所存在的偶然誤差等問題，故採用穩健加權總體最小二乘法計算，解決這些因素。本研究乃利用穩健加權總體最小二乘法結合二次曲面擬合法，改進傳統方法中未考慮到係數向量與觀測向量的協因數矩陣，並分析此模型的解法，以提高點位高程精度。本研究所得之高程精度可達到±1.401cm。此方法不僅合乎工程測量規範的高程精度要求標準，在學術上也可以提供建立區域性大地起伏的研究。

The objective of this study involved using global navigation satellite system (GNSS) data to achieve reasonable point height accuracy. In this study, the orthometric heights of benchmarks were obtained from first order leveling of Taichung city and GNSS measurements of ellipsoid heights underwent fitting. A traditional fitting method was adopted, in which geoid height was built using generalized least squares combined with a curved surface fitting method. However, because generalized least square calculations do not take into consideration random errors that exist in coefficient matrices and observation vectors, weighted total generalized least square-based calculations were performed to solve these problems. In this study, the combination of weighted total generalized least squares and the quadratic curved surface fitting method improved on the traditional method by considering the covariance matrices of coefficient vectors and observation vectors. The solutions of the new model were subsequently analyzed, elevating point height accuracy to 1.401 cm. The new method satisfies height accuracy requirements demanded in engineering surveys and provides valuable information for regional geoid height research.