Optimal Success/Error Rate and Its Calculation in Resolution of Integer Ambiguities in Carrier Phase Positioning of Global Positioning System (GPS) and Global Navigation Satellite System (GNSS)

K. Kondo

Abstract:	This study explores the non-conditionally and conditionally statistical optimal decisions for the fixed sample resolution of integer ambiguities in carrier phase positioning of the Global Positioning System (GPS) and the global navigation satellite system (GNSS) based on the formulation of Bayesian statistics and proposes semi-analytical formulas to calculate their optimized success and error rates, which are derived from the decompositions of a high-dimensional integration of the error probability distribution in the domain of a polytope to one-dimensional ones. The formulas' accuracy is demonstrated by comparison with the solutions of an accelerated numerical Monte Carlo integration under the condition that the solutions have an extremely high success rate and extremely low error rate. This study also describes the formulas' application to the integer ambiguity resolution problem and derives the conditions under which an extremely high success rate and low error rate can be simultaneously achieved. These conditions include a large number of visible satellites, accurate prediction of ionospheric delay, and the use of multiple carrier frequencies.
Published in:	Proceedings of the 59th Annual Meeting of The Institute of Navigation and CIGTF 22nd Guidance Test Symposium (2003) June 23 - 25, 2003 Hyatt Regency Hotel Albuquerque, NM
Pages:	176 - 187
Cite this article:	Kondo, K., "Optimal Success/Error Rate and Its Calculation in Resolution of Integer Ambiguities in Carrier Phase Positioning of Global Positioning System (GPS) and Global Navigation Satellite System (GNSS)," Proceedings of the 59th Annual Meeting of The Institute of Navigation and CIGTF 22nd Guidance Test Symposium (2003), Albuquerque, NM, June 2003, pp. 176-187.
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