七參數相似轉換為非常重要的一個座標轉換方式，因為它一個非線性模型，所以常以線性化方式進行求解，導致此過程存在一些問題，例如初始值給定不當導致解算過程的法矩陣不穩定、迭代無法收斂等造成解算成果錯誤，或者是其迭代求解的效率問題。
基於上述原因，本研究的目的為採用線性演算法求解七參數相似轉換參數，不需初始值，也沒有迭代過程，可避免以上所提的線性化求解問題。研究中將採用Helmert七參數相似轉換模型並納入的重心概念來進行推導，並且使用卡雷轉換(Cayley Transformation)的方式拆解旋轉矩陣以轉換成線性求解。
本研究將以車載移動式測繪系統(Mobile Mapping System，MMS)應用為例，採用線性演算法進行解算分析。在研究過程裡，模擬MMS所提供之前方定位交會(簡稱前方交會)的成果座標(本研究稱之為模型座標)，並且引入全控點的物空間座標，以線性演算法結合逐一轉換模型平差方式解算模型座標與物空間座標的轉換參數，進一步達成物點在物空間的定位。並於實驗中同時以線性化方式求解相同案例，討論在1.特殊控制點分布(控制點分布於單側情況與兩側控制點連線平行的分布情況)、2.使用不同的模型數的資料以及3.不同量測精度的觀測量資料之情況下，這兩種求解方法的解算成果之差異。
研究顯示，雖然線性演算法結合逐一轉換模型法平差方式，呈現誤差累積的現象，使得在多測站多模型的案例中，成果精度欠佳。但線性演算法的成果有較不受到控制點分布影響的優點，仍值得進一步深入研究。另外，本研究顯示，只要提高控制點的模型座標量測精度，而不必提高所有點的模型座標量測精度，就可以得到相當好的平差成果。
一般說來，七參數相似轉換線性演算法不需要起始值，不需迭代求解，且對於不好的控制點分佈情形仍能得到滿意的成果，因此仍值得繼續研究。

For the usages of seven-parameter transformation problems, the most regular solution is used the linearization approach, which needs to provide the initial values of point coordinates and transformation parameters and also relies on iterations to get approximate numerical solutions. The solutions using the linearization approach may cause the instability of normal matrix and even may result in the divergent solutions. Such problems in linearization have been discussed for a long time. In order to overcome the problems mentioned above, a linear algorithm to solve the seven-parameter transformation problems is proposed in this paper.
In this paper, a linear solution algorithm accompanied with the sequential model adjustment method is introduced, and the capability of this approach is studied for the positioning cases by Mobile Mapping Systems (MMS’s).
In order to evaluate the feasibility of linear solution algorithm, both the linear solution algorithm and the linearization method are researched on the transformation problems between the model coordinates calculated by the forward intersections which normally are used in MMS positioning and spatial coordinates.
For the purposes, three kinds of experiments are designed and discussed: (1) The control points (CPs) distribution, (2) The multi-models and multi-stations, and (3) The measurement precision of the model coordinates and control point coordinates. The experimental results have shown that the influence of CPs distribution to the linearization method is larger than that of linear one. The cases which have the bad CPs distribution may lead to the worse results in the linearization method. Because the so-called sequential model adjustment method was used in the linear algorithm, the accuracy of the results reduced due to the error accumulation, when the number of models increases.
In general, since it does not need the initial values and is not affected by the bad distribution of control points, the linear algorithm to solve seven-parameter transformation problems is still worth furthermore studying.

尤瑞哲(2011)。測量及空間資訊座標系統與轉換。國立成功大學測量及空間資訊學系，台南。
尤瑞哲(2018)。線性七參數相似轉換及應用手稿。國立成功大學測量及空間資訊學系，台南。
王之卓(2007)。攝影測量原理，武漢大學出版社，中國。
史天元，1999。獨立模型中投影中心量測精度探討，航測及遙測學刊，4(1)，第45-52頁，國立交通大學土木工程系。
李育華(2010)。車載移動式製圖系統之系統率定及其直接地理定位之效能分析，國立成功大學測量及空間資訊學系碩士論文，台南。
李育華、江凱偉及饒見有(2010)。測繪車之系統率定及其效能分析，航測及遙測學刊，第十五卷，第3期，第229-242頁。
何維信(1995)。航空攝影測量學，大中國圖書公司，台北。
周千又(2018)。以光束平差法及遮蔽位置估算法改善車載移動式測繪系統在都市地區定位精度之研究，國立成功大學測量及空間資訊學系碩士論文，台南。
林舒葦(2017)。以光束法平差提升地面移動測繪系統精度之研究，國立成功大學測量及空間資訊學系碩士論文，台南。
周適(2013)。七參數座標轉換研究及應用，鐵道勘查，第5期，第7-10頁。
范東明(2001)。非線性最小二乘參數平差迭代算法，測繪學院學報，第18 卷第3 期。
孫小榮、張書畢、徐愛功及趙吉先(2012)。七參數座標轉換模型的適用性分析，測繪科學，第37卷第6期，第37-39頁。
張偉哲(2015)。「臺南市公共設施管線位置調查暨系統建置第五期計畫委託監審案」監審期末報告書定稿版，高苑科技大學，高雄。
黃芸玟、蔡孟倫及江凱偉(2009)。緊耦合與鬆耦合式低成本IMU/GNSS 整合式POS於移動測繪應用之適用性分析，地籍測量，第28卷第4期，第1-16頁。
Awange, J.L., Fukuda, Y, and Grafarend, E.K.(2004). Exact solution of the nonlinear 7 parameter datum transformation by Groebner basis. Bolletiino di Geodesia Science Affini-N.1., pp.1-10.
Awange, J.L., Grafarend, E.W.(2002). Linearizaed Least Squares and nonlinear Guass-Jacobi combinatorial algorithm applied to the 7-parameter datum transformation C_7 (3) problem. Zeitschrift für Geodäsie, Geoinformation und Landmanagement.,127.Jg.2, pp.109-116 .
Awange, J.L.and Grafarend, E.W.(2003). Nonlinear analysis of the three-dimensional datum transformation conformal groupC_7 (3). Journal of Geodesy., Vol. 77, pp.66-76.
Deakin, R.E.(2006). A note on the Bursa-Wolf and Molodensky-Badekas Transformations. School of Mathematical & Geospatial Sciences, RMIT University, Australia.
Ellum, C.M.K.(2001). The Development of a backpack Mobile Mapping System. Department of Geomatics Engineering, University of Calgary, Canada.
Ellum, C. and Sheimy, N.E.(2002). Land-Based Mobile Mapping Systems. Photogrammetric Engineering & Remote Sensing., January 2002, 68(1), pp.13-28.
Hashemi, A., Kalantari, M., and Kasser, M.(2013). Direct Solution of the 7 parameters transformation problem. Applied Mathematics and Information Sciences., Vol. 7, No. 4, pp. 1375-1382.
Hassan, T., Ellum, C., Nassar, S., W., Cheng, and Sheimy, N.E.(2006). Photogrammetric Bridging of GNSS/INS in Urban Centers for Mobile Mapping Applications. ION GNSS 19th International Technical Meeting of the Satellite Division, September 2006, pp.604-610.
Hide, C, and Moore, T.(2005). GPS and Low Cost INS Integration for
Positioning in the Urban Environment. Institute of Engineering Surveying and Space Geodesy, University of Nottingham, U.K..
Kutoglu, H.S., Mekik, C. ,and Akcin, H.(2002). A Comparison of Two Well Known Models for 7-Parameter Transformation. The Australian Surveyor., Vol.47, No.1, pp.24-30.
Rau,J.Y., Habib, A.F., Ana P. Kersting, A.P., Chiang,K.W., Bang K.I., Tseng,Y.H., and Li,Y.H.(2011). Direct Sensor Orientation of a Land-Based Mobile Mapping System. Sensors, 11(7), pp. 7243-7261.
Tao, C.V.(2000). Mobile Mapping Technology for Road Network Data Acquisition. Department of Geomatics Engineering, The University of Calgary, Canada.
Závoti, J. and Fritsch, D.(2011). A first attempt at a new algebraic solution of the exterior orientation of Photogrammetry. Acta Geod. Geoph. Hung., Vol. 46(3), pp.317-325.
Závoti, J.(2012). A simple proof of the solutions of the Helmert and the overdetermined nonlinear 7-parameter datum transformation. Acta Geod. Geoph. Hung., Vol. 47(4), pp. 453–464.