A New Method for Partial Ambiguity Resolution

David G. Lawrence

Abstract:	Traditional GNSS RTK processing typically requires a step of cycle ambiguity resolution to achieve the positioning accuracy potentially achievable from the high precision carrier phase measurements. However, during marginal multipath or atmospheric conditions and over longer baselines, it is often difficult to resolve the cycle ambiguities for all satellites on all frequencies. Early RTK algorithms either resolved all double difference cycle ambiguities or did not leverage the integer nature of the ambiguities at all. RTK solutions were either “fixed” (if all integers were resolved) or “float” (if all integers were treated as floating, non-integer biases). Many applications have accuracy requirements between what is provided by fixed and float solutions, but with only those two options available, such applications have to wait for RTK fixed status. Therefore, there is a need for a solution that provides the high availability of RTK float and some of the accuracy improvements offered by rounding all of the cycle ambiguities. Existing partial ambiguity resolution techniques attempt to round fewer integers than the total number of unknown ambiguities to provide such a solution. However, because the common approaches to partial ambiguity resolution put artificial constraints on the results, they may exclude better results. The focus of this research was to explore new ways to leverage the integer nature of the cycle ambiguities when the full set cannot be fixed reliably. A method is proposed to find a general linear combination of the ambiguities that is invariant to ambiguity parameterization. This linear combination is sometimes equivalent to the result of existing methods, but in many cases, it will be shown to provide higher order constraints than existing methods. For a given probability of correctly constraining a linear combination of integers, the new method finds a linear combination that results in the smallest position covariance. Under certain conditions, the new method may require an unacceptable computational load. Modifications are proposed to improve computational efficiency in such cases. Simulation results of the new technique are presented and compared with traditional partial fixing results. Two and three frequencies systems are simulated with various levels of ionosphere, troposphere, and multipath errors. Statistical improvements of the new method are demonstrated under a variety of conditions.
Published in:	Proceedings of the 2009 International Technical Meeting of The Institute of Navigation January 26 - 28, 2009 Disney's Paradise Pier Hotel Anaheim, CA
Pages:	652 - 663
Cite this article:	Lawrence, David G., "A New Method for Partial Ambiguity Resolution," Proceedings of the 2009 International Technical Meeting of The Institute of Navigation, Anaheim, CA, January 2009, pp. 652-663.
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