Ambiguity Recovery Using the Triple-Differenced Carrier Phase Type Approach for Long-Range GPS Kinematic Positioning

Precise, long-range GPS kinematic positioning to centimeter accuracy requires that carrier phase ambiguities be resolved correctly during an initialization period, and subsequently to recover the “lost" ambiguities in the event of a cycle slip. Furthermore, to maximize navigational efficiency, ambiguity resolution and carrier phase-based positioning need to be carried out in real-time. Due to the presence of the ionospheric signal delay, satellite orbit errors, and the tropospheric delay, so-called absolute ambiguity resolution “on-the-fly” for long-range applications becomes very difficult, and largely impossible. However, all of these errors exhibit a high degree of spatial and temporal correlation. In the case of short-range ambiguity resolution, because of the high spatial correlation, their effect can be neglected, but their influence will dramatically increase as the baseline length increases. On the other hand, between discrete trajectory epochs, they will still exhibit a large degree of similarity for short time spans. In this article, a method is described in which similar triple-differenced observables formed between one epoch with unknown ambiguities and another epoch with fixed ambiguities can be used to derive relative ambiguity values, which are ordinarily equal to zero (or to the number of cycles that have slipped when loss-of-lock occurred). Because of the temporal correlation characteristics of the error sources, the cycle slips can be recovered using the proposed methodology. In order to test the performance of this algorithm an experiment involving the precise positioning of an aircraft, over distances ranging from a few hundred meters up to 700 kilometres, was carried out. The results indicate that the proposed technique can successfully resolve relative ambiguities (or cycle slips) over long distances in an efficient manner that can be implemented in real-time.