NDLI: Recursive algorithm for fast GNSS orbit fitting

Content Provider	Springer Nature Link
Author	Xue, Shuqiang Yang, Yuanxi
Copyright Year	2014
Abstract	Gaussian elimination is an efficient and numerically stable algorithm for estimating parameters and their precision. However, before estimating the parameters, it is often prudent to perform statistical tests to achieve the best fitting model. We use Gaussian elimination to select the best fitting model among candidate models. A succinct relationship between the weighted sum of squared residuals and the previous one is revealed by a volume formula. For quick parameter estimation and determination of weighted sum of squared residuals, a recursive elimination algorithm is proposed in the context of Gaussian elimination. In order to improve the model selection efficiency, the parameter estimation and the determination of the weighted sum of squared residuals are carried out in parallel using the proposed recursive elimination algorithm in which the improvement at each recursive stage is judged by the Bayesian information criterion. Ultimately, the computational complexity and numerical stability of the recursive elimination proposed are briefly discussed, and a GNSS orbit interpolation example is used to verify the results. It shows that the proposed recursive elimination algorithm inherits the numerical stability of the Gaussian elimination, and this algorithm can be used to examine the gain from the newly introduced parameter, dynamically assess the fitting model, and fix the optimal model efficiently. The optimal fitting model with the lowest information is very close to the real situation verified by checkpoints.
Starting Page	151
Ending Page	157
Page Count	7
File Format	PDF
ISSN	10805370
Journal	GPS Solutions
Volume Number	20
Issue Number	2
e-ISSN	15211886
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-11-14
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Least squares Variance estimation Gaussian elimination Recursive elimination Model selection Statistical test Geophysics/Geodesy Atmospheric Sciences Extraterrestrial Physics, Space Sciences Automotive Engineering Electrical Engineering
Content Type	Text
Resource Type	Article
Subject	Earth and Planetary Sciences

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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