相似轉換之非迭代參數估計法

A Non-Iterative Approach for Solving the Parameters of a Helmert Transformation

樂怡岑(Yi-Tzen Yueh)

指導教授 ： 韓仁毓

國立臺灣大學/工學院/土木工程學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.01627

摘要

不同參考坐標系統之間的轉換是應用空間資訊時常遇見的問題，其中由於線性轉換之型式較為簡易且所引進之參數具有明確之物理意義，在實務上常被廣泛使用，而相似轉換即屬線性轉換之一種，其傳統之求解方式乃是透過轉換前後之坐標值組成觀測量，以最小自乘法求得參數的最佳估值。然而利用最小自乘法求解時，會因為迭代而使解算效率降低，且參數求解時之起始值給定亦是一項問題，此外，於可及性較差之地區難以佈設控制點，若侷限於使用點位坐標作為觀測資訊，將增加轉換參數求解之困難。本研究主要目的為建立一相似轉換的非迭代解法(Non-iterative solution for Helmert Transformations, NIHT)之程序，以提升相似轉換模型參數之解算效率，並建立NIHT法的觀測量加權模式，使其能夠合理處理品質不一的觀測輸入資料，此外並建立轉換參數之精度估計模式。而此方法可延伸應用於使用非點狀之混合控制特徵進行轉換參數解算，因此可廣泛的應用於各類線性轉換問題中。在數值分析中，本研究除了透過模擬資料來驗證本研究方法之正確性，並且利用多測站光達掃瞄點雲套合作業作為應用範例，展示本研究方法於實際空間資訊分析工作之可行性。從實驗成果顯示，本研究所提之NIHT參數估計法可使得線性轉換參數解算過程更具彈性且合理可靠，因此對於空間資訊科學之相關應用工作將有具體助益。

關鍵字

相似轉換 ； 坐標框架轉換 ； 參數求解 ； 非迭代線性轉換參數估計

並列摘要

The Helmert transformation model is of a frequent choice for transforming coordinates between different reference frames due to the fact that it has simple and physically interpretable parameters. The indirect problem (i.e., the parameter estimations) of the Helmert transformation model is usually solved by applying the classical least-squares technique. However, an appropriate set of initial values and iterative computations are required during the parameter estimation process, and the computation may become very inefficient. Besides, only using point coordinates as observables for parameter estimations is very difficult if the target area isn’t reachable for setting control points. In this study, a non-iterative approach for solving the indirect problem of the Helmert Transformation model (NIHT) is proposed to improve the computational efficiency in estimating the transformation parameters, and then a weighted NIHT is developed to deal with the observables of varied levels of quality. Besides, the proposed method is further extended to make use of hybrid control features, including lines, planes and groups of dispersed point clouds. Based on the simulation test results, it is illustrated that the proposed approach is capable of giving a direct and quality parameter solution. Followed by a real case study in which LiDAR point clouds from multiple scanning stations were integrated, it was further concluded that the NIHT technique provides a flexible and reliable solution and will thus benefit related spatial science applications in which linear transformations are involved and to be analyzed.

並列關鍵字

Helmert Transformations ； Frame Transformations ； Parameter Estimations ； Non-Iterative Solution for Linear Transformations

參考文獻

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