Unbiased Closed-Form GPS Position Estimation

Jonathan Kipling Knight

Abstract:	Presented herein is an unbiased closed form general solution to the classic global navigation satellite system (GNSS) position fix. The new formula builds on the previous closed form solution (Knight, 2015) that was shown to be more than five hundred meters worse than the Maximum Likelihood Estimator (MLE) in normal conditions without corrections. The research found no consistent method of removing the bias since the a-priori value that is needed changes with regards to many variables and needs constant updating. This ends up reducing the value of removing the bias. The research further found that the careful removal of known corrections was adequate for reducing the error in position from 500 meters to 30 meters. The end result will be an in-depth analysis of physics corrections to the pseudorange, including a new formula for tropospheric delay capable of calculations down to the horizon. Real world pseudo-ranges taken from the Operational Support System at Schriever Air Force Base will be used to test the formula accuracy. These pseudo-ranges will be compensated for clock adjustments taken from the actual subframes. Additionally, the space vehicle positions will be calculated from the subframes per the IS-GPS-200 specification. The formula will also be compared to the more widely used solution, the Maximum Likelihood Estimator (MLE). Monte Carlo tests will show that an unsophisticated Matlab implementation was 2-4 times faster than the MLE and about 30-150 times less accurate on average. This formula can be an effective replacement for the Maximum Likelihood Estimator and even Kalman filtering if the accuracy is carefully balanced with the speed improvement.
Published in:	Proceedings of the 28th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2015) September 14 - 18, 2015 Tampa Convention Center Tampa, Florida
Pages:	2766 - 2771
Cite this article:	Knight, Jonathan Kipling, "Unbiased Closed-Form GPS Position Estimation," Proceedings of the 28th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2015), Tampa, Florida, September 2015, pp. 2766-2771.
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