座標轉換於測量各大領域中為不可或缺之技術。於大地領域中不同座標系統之轉換以進行歷史圖資之點位資訊比較，於地理資訊系統領域中，整合不同座標系統之圖資使其得以進行圖資之套疊分析，以及攝影測量領域中物空間座標與像空間座標之轉換等等，這些都需要應用座標轉換技術。三度空間座標轉換一般使用Helmert相似轉換或Molodensky轉換，這兩種模型均為非線性模型，通常以迭代方法求解轉換參數。進行迭代運算需要給定合理之初始值，否則解算得到之轉換參數解可能發散或不穩定。本研究使用Cayley轉換將非線性的Molodensky模型轉換為線性模型，因此不必迭代求解，可以直接求得轉換參數。本文將求解過程分為三個步驟:第一步先求尺度參數，第二步求旋轉角度，最後解算平移參數。由於非迭代之座標轉換演算法，其過程中不需要進行線性化且不需要轉換參數的初始值，因此可增進計算效率。此外，本研究也引入 Baarda的粗差偵錯理論，討論三階段非迭代求解和傳統迭代求解方法在偵測粗差行為及其影響的異同。研究結果顯示在粗差偵測上兩種求解方式並無顯著差異。

The coordinate transformation is an indispensable technology in Geomatics and is needed for the transformation beteween different coordinate systems for the comparisons of the history information in Geodesy, the integration of the geospatial information for the overlay analysis in Geographic Information Science, and the spatial transformation between the image and the object spatial systems in Photogrammetry etc. For three-dimensional coordinate transformations, Helmert and the Molodensky models are generally adopted. Those two transformation models are non-linear, and therefore an iterative method isnecessary for the computation of transformation parameters. Reasonable initial values of unknowns including the transformation parameters are essential while solving the nonlinear models by the iterative method. If the initial values of unknowns are not good enough, the solution may become divergent or unstable. In this research, the Cayley transform is adopted to transform the Molodensky model into a linear model. Consequently, the transformation unknown parameters can be solved without iterations. The overall solution processing is divided into three steps in this study. The scale parameter is first calculated. Second, the rotation angles are determined, and in last step the shift parameters are computed. For the non-iterative coordinate transformation algorithm adopted in this research, the transformation parameters can be solved without linearization, iterative calculation and initial values. The gross error detection based on the Baarda theory is introduced. A comparison of our method with the traditional iterative and linearized method is given in error detection. Our result shows that there is no significant differences in the gross error detection between these two methods.

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