New Algorithm of GPS Rapid Positioning Based on Double- -Type Ridge Estimation
Publication: Journal of Surveying Engineering
Volume 133, Issue 4
Abstract
In this paper, a new algorithm is employed in global positioning system (GPS) rapid positioning using several-epoch single-frequency phase data. First, we define the double- -type ridge estimator (DKRE) based on the structure characteristics of multicollinearities of the normal equations matrix in the double-difference (DD) model, and prove when the DKRE is not worse than the least-squares estimator (LSE) in the sense of a reduced MSEM. Taking into account how the ridge parameter in the ordinary ridge estimator is confirmed based on the generalized ridge estimator (GRE), we propose a method of estimating two ridge parameters for the DKRE. Second, we improve the LAMBDA method through replacing the cofactor matrix computed by the LSE with the cofactor matrix computed by the DKRE. The ambiguities-fixed solution is found by the sequential LSE. A theorem stating that the success rate of the improved LAMBDA method is bigger than the original LAMBDA method is given. Finally, through the GPS positioning tests, it is shown that the present method is highly efficient and reliable, and some very valuable conclusions are obtained by analyzing the computation results.
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Acknowledgments
The writers wish to thank the editor and referee for helpful suggestions which improved the quality of the paper. This work is supported jointly by National Science Foundation of China (Grant No. NSFC40474007), National Splendid Youth Science Foundation of China (Grant Nos. UNSPECIFIED40125013, UNSPECIFIED49825107), “Basic Geographic Information and Digital Technique” Task of Important Laboratory of Shandong Province (Grant No. UNSPECIFIEDSD040202), and Henan Province Nature Science Foundation of China (Grant No. NSFC0511010100).
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Information & Authors
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Published In
Journal of Surveying Engineering
Volume 133 • Issue 4 • November 2007
Pages: 173 - 178
Copyright
© 2007 ASCE.
History
Received: May 26, 2006
Accepted: Jan 23, 2007
Published online: Nov 1, 2007
Published in print: Nov 2007
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