Equivalence Principle of GPS Algorithms and and Independent Parameterisation Method

Guochang Xu, Yuanxi Yang, Heping Sun, Yunzhong Shen, Qin Zhang, Jianfeng Guo and Ta-Kang Yeh

Abstract:	The equivalence property of the differencing and undifferenced GPS algorithms is outlined theoretically. The by-product of the theory is that a unified GPS data processing method is proposed which may include all undifferenced and differencing algorithms into a unique one and any algorithm can be realised by using a switch. Such equivalence is a soft equivalence and the definition is given. The differencing includes single-, double- and triple-differencing methods, as well as user defined differencing. The equivalence properties of the un-combined and combining GPS data processing algorithms are verified theoretically. The solution vector and the covariance matrix of the solutions are identical regardless of the algorithms adopted. The correct choice of special algorithms will lead to a better and easier dealing of the data and solving of the problem. Such equivalence is an exact one. Two evidences of the singularity of the undifferenced GPS observation models are given to show the need of the study of the parameterisation problem. Then a general method to model the bias parameters independently is proposed through analysis. A geometryfree illustration is given to show the reason of the bias parameterisation. The equivalence of the mixtures of the combining and differencing methods are discussed. Equivalence property of the GPS data processing algorithms is summarized based on the equivalence of the uncombined and combining, undifferenced and differencing algorithms, as well as their mixtures. Conclusions and comments are given.
Published in:	Proceedings of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2007) September 25 - 28, 2007 Fort Worth Convention Center Fort Worth, TX
Pages:	796 - 807
Cite this article:	Xu, Guochang, Yang, Yuanxi, Sun, Heping, Shen, Yunzhong, Zhang, Qin, Guo, Jianfeng, Yeh, Ta-Kang, "Equivalence Principle of GPS Algorithms and and Independent Parameterisation Method," Proceedings of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2007), Fort Worth, TX, September 2007, pp. 796-807.
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