隨著科技的日趨進步，將近半個世紀的努力，全球定位系統（Global Positioning System, GPS）的技術日漸成熟，人們及各類交通工具的蹤跡，將可輕易經由此系統而得到。本論文指在採用由GPS衛星所發送出之C/A碼，利用一般常用的最小平方法(Least-squares method)及目前廣泛應用於類神經網路訓練之拉凡格式演算法(Levenberg-Marquardt algorithm)於求解GPS虛擬距離及差分定位（Differential GPS, DGPS）位置解中精度之研究。而經過一連串靜態及動態實驗及分析，在本研究中驗證拉凡格式法其快速收斂及甚少的疊代次數之優點，而拉凡格式法所解之位置精度可到達約10公尺，其精度亦相當於修改過後的最小平方法之解，在經過DGPS修正誤差後，其位置精度更可達到約2～3公尺。此結果更進一步說明該新方法具有與最小平方法並駕齊驅之潛力。

　　In recent year, owing to the maturity of Satellite technology and Global Positioning System (GPS), the precise positioning potential of GPS has been the primary sensor for navigation and control of a vehicle. This thesis emphasizes that the concept of processing the raw data emitting from GPS satellite by Least-squares method, and new method, Levenberg-Marquardt algorithm widely used in neural network training, in GPS and DGPS. In this study, the advantage of applying Levernberg-Marquardt algorithm is that it converges in much less iteration times without divergence in both static and dynamic condition. As the result of experiments, solving GPS position by Levernberg-Marquardt algorithm can achieve the accuracy around 10 meters. After post processing DGPS, the position accuracy even can achieve 2~3-meter level and this result explain that the new algorithm is the other choice comparing to the Least-squares method.

References
[1] Gilbert Strang and Kai Borre, “Linear algebra, geodesy, and GPS”, Wellesley-Cambridge Press, Wellesley, MA, 1997.
[2] Huang, S. H., “The Study of Real-Time DGPS Navigation Accuracy during Approach and Landing of an Ultralight Vehicle”, Institute of Aeronautics and Astronautics, National Cheng Kung University, Master Thesis, 2002
[3] Technical University of Catalonia, http://maite152.upc.es
[4] University of California, http://math.ucr.edu
[5] Natural Resources Canada, http://www.geod.nrcan.gc.ca
[6] Marquardt, D.W., “An algorithm for least-squares estimation of nonlinear parameters.” Journal of the Society for Industrial and Applied Mathematics, pp.431–441, 1963.
[7] Hagan, M. T. and Menhaj, M., “Training feedforward networks with the Marquardt algorithm”, IEEE Transactions on Neural Networks, vol. 5, no. 6, pp.989- 993, 1994.
[8] Wilamowski, Iplikci, Kayank, and Onder, “An Algorithm for Fast Convergence in Training Neural Networks”, International Joint Conference on Neural Networks (IJCNN'01), pp.1778-1782, Washington DC, 2001.
[9] Wilamowski, Chen, and Malinowski, “Efficient algorithm for training neural networks with one hidden layer”, International Joint Conference on Neural Networks (IJCNN'99), pp.1725-1728, Washington, DC, 1999.
[10] 陳威昇，”類神經網路訓練程序之些許建議”，碩士論文，國立成功大學航太工程研究所，2003。
[11] Sung, D. U., Oh, J. H., Kim, C. G., and Hong, C. S., “Impact monitoring of smart composite laminates using neural network and wavelet analysis”, Journal of Intelligent Material Systems and Structures. Vol. 11, no. 3, pp.180-190, 2000.
[12] Doicu, A. Schreier, F. and Hess, M. “Iterative regularization methods for atmospheric remote sensing”, Journal of Quantitative Spectroscopy & Radiative Transfer (0022-4073), vol.83, no.1, p.47-61, 2004.
[13] Goettsche, F. M. and Olesen, F. S., “Modelling of diurnal cycles of brightness temperature extracted from METEOSAT data”, Remote Sensing of Environment. Vol. 76, no.3, pp.337-348., 2001.
[14] Shih, S. E., Ding, K. H., Nghiem, S. V., Hsu, C. C., Kong, A. A., and Jordan, A. K., “Thin saline ice thickness retrieval using time-series C-band polarimetric radar measurements”, IEEE Transactions on Geoscience and Remote Sensing. Vol.36, pt.1, no.5, pp.1589-1598., 1998.
[15] Bradford W. Parkinson, James J. Spilker Jr., “Global Positioning System: Theory and Applications”, American Institute of Aeronautics and Astronautics, Washington, DC, 1995.
[16] W. de Gruyter, “Satellite geodesy: foundations, methods, and applications”, W. de Gruyter, Berlin, 1993.
[17] Dept. of Earth & Atmospheric Sciences Purdue University, http://www.eas.purdue.edu/~calais/
[18] Guan, W.L., “The development and application of DGPS technique in estimating longitudinal aerodynamic parameters for RPV and Ultralight Airplane”, Institute of Aeronautics and Astronautics, National Cheng Kung University, Ph.D. Dissertation, 1998.
[19] Christian Altmayer, “Accuracy Improvements of Pseudolite Systems -First Results”, ION NTM, Long Beach, 2001.
[20] William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery, “Numerical Recipes in C: The Art of Scientific Computing Second Edition”, Cambridge University Press, 1992.
[21] Borse, G.. J., “Numerical methods with MATLAB: a resource for scientists and engineers”, Boston, PWS Publishing, 1997.
[22] Ashtech of Thales groups, “G12TM GPS Board & Sensor Reference Manual”, http://www.ashtech.com/en/