Global Navigation Satellite System Ambiguity Resolution with Constraints from Normal Equations
Publication: Journal of Surveying Engineering
Volume 136, Issue 2
Abstract
Carrier phase ambiguity resolution is the key to precise positioning with a global navigation satellite system (GNSS); therefore, quite a few ambiguity resolution methods have been developed in the past two decades. In this paper, a new ambiguity searching algorithm by treating part of normal equations as constraints is developed. The process starts with the truncation of the terms with respect to the small eigenvalues from the normal equations of a least-squares estimation problem. The remaining normal equations are employed as the constraint equations for the efficient searching of integer ambiguities. In the case of short single baseline rapid GNSS positioning with double differenced phase measurements, there are only three real parameters of the position to be estimated. Therefore three terms of the normal equations should be truncated off due to the fact that there is a large difference between the last three eigenvalues of the normal matrix of the float solution and the others, and then the remaining ambiguities can be trivially solved with three independent ambiguities by means of the remaining normal equations. As a result, only three independent ambiguities are necessarily searched and the searching efficiency is dramatically enhanced. Moreover, a new indicator of minimizing the conditional number of the subsquare matrix of the remaining normal equations is introduced to select three independent ambiguities. Once the correct integer values of the selected three independent ambiguities are applied to solve the remaining ambiguities, the estimated real-valued solutions are very close to their integers, which can be applied as additional strong constraints to further improve the searching efficiency. Finally, two case studies, from real dual-frequency global positioning system (GPS) data of about 10-km baseline and random simulations, respectively, are carried out to demonstrate the efficiency of the new algorithm. The results show that the new algorithm is efficient, especially for the scenarios of high-dimensional ambiguity parameters.
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Acknowledgments
This work was partially supported by the National Natural Science Funds of China (Grant Nos. UNSPECIFIED40674003 and UNSPECIFIED40874016) and partially by Key Laboratory of Advanced Engineering Surveying of SBSM (Grant No. UNSPECIFIEDTJES0809). The writers are very grateful to Prof. Yang Yuanxi from Xi’an Research Institute of Surveying and Mapping and Dr. Xu Peiliang from Kyoto University for his constructive suggestions and comments. Last but not the least, A/Prof. Feng Yanming from Queensland University of Technology, Australia is also appreciated for his thoughtful suggestions.
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Published In
Journal of Surveying Engineering
Volume 136 • Issue 2 • May 2010
Pages: 63 - 71
Copyright
© 2010 ASCE.
History
Received: Feb 13, 2009
Accepted: Aug 4, 2009
Published online: Sep 11, 2009
Published in print: May 2010
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