Isolating and Estimating Undifferenced GPS Integer Ambiguities

Paul Collins

Abstract:	The limiting factor in ambiguity resolution using undifferenced GPS observables is not the presence of unknown fractional cycle biases in the phase observations, but the presence of code biases in the estimates of the ambiguities. As parameterised in the ‘standard model’ of undifferenced ionosphere-free pseudoranges and carrier phases, the datum for the station and satellite clock parameters is provided by the pseudoranges. The consequence of this is that the estimated ambiguities contain the time-constant portions of both code and phase biases. To overcome this limitation, a new GPS observation model is presented called the ‘decoupled clock model’. This model rigorously accommodates any synchronisation biases (constant or time-varying) that may occur between common-frequency observables and facilitates the estimation of integer ambiguities without explicit differencing. Application of the decoupled clock model to both the standard model of ionosphere-free code and phase observables and the well known widelanephase/ narrowlane-code combination leads to an extended model, whereby simultaneous resolution of 86cm and 11cm ambiguities is possible in principle. It is stressed that the decoupled clock model is significantly more general than the standard model, requiring no assumption about the stability of code or phase biases. The decoupled model can be applied to both network and single-user processing, where the only limitation in single-user processing is that a separate satellite clock parameter must be provided for each observable used (3 in the case of the extended model presented here). General application of the decoupled clock model may explain some of the remaining issues with GPS processing such as the dayboundary clock jumps identified by the IGS time scale, and, with further development, reduce the convergence time of Precise Point Positioning.
Published in:	Proceedings of the 2008 National Technical Meeting of The Institute of Navigation January 28 - 30, 2008 The Catamaran Resort Hotel San Diego, CA
Pages:	720 - 732
Cite this article:	Collins, Paul, "Isolating and Estimating Undifferenced GPS Integer Ambiguities," Proceedings of the 2008 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2008, pp. 720-732.
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