In high-precision global navigation satellite system applications, it is often not possible to simultaneously meet the requirements for fast and reliable integer ambiguity resolution. For a given reliability constraint in form of a user-defined, tolerable probability of an incorrect ambiguity estimate, resolving a subset of ambiguities instead of the full set can be beneficial. We discuss a fixed failure rate implementation of a data-driven, likelihoodratio-based partial ambiguity resolution technique. A key problem in this context is the efficient determination of a scalar that is a model-dependent threshold value. This problem is approached via a conservative functional approximation of the threshold value. The only input parameter of the function is the integer least-squares failure rate of the system model under consideration. Numerically simulated single and combined system GPS/Galileo single baseline cases with single-and dual-frequency measurements are used to analyze the impact of the approximation. The results indicate that the conservative description hardly affects the performance of the algorithm, while the predefined failure rate is not exceeded. Moreover, it is shown that the presented data-driven partial ambiguity resolution approach clearly outperforms a purely model-driven scheme based on the bootstrapping failure rate.
The use of the GLONASS legacy signals for real-time kinematic positioning is considered. Due to the FDMA multiplexing scheme, the conventional CDMA observation model has to be modified to restore the integer estimability of the ambiguities. This modification has a strong impact on positioning capabilities. In particular, the ambiguity resolution performance of this model is clearly weaker than for CDMA systems, so that fast and reliable full ambiguity resolution is usually not feasible for standalone GLONASS, and adding GLONASS data in a multi-GNSS approach can reduce the ambiguity resolution performance of the combined model. Partial ambiguity resolution was demonstrated to be a suitable tool to overcome this weakness (Teunissen in GPS Solut 23(4):100, 2019). We provide an exhaustive formal analysis of the positioning precision and ambiguity resolution capabilities for short, medium, and long baselines in a multi-GNSS environment with GPS, Galileo, BeiDou, QZSS, and GLONASS. Simulations are used to show that with a difference test-based partial ambiguity resolution method, adding GLONASS data improves the positioning performance in all considered cases. Real data from different baselines are used to verify these findings. When using all five available systems, instantaneous centimeter-level positioning is possible on an 88.5 km baseline with the ionosphere weighted model, and on average, only 3.27 epochs are required for a long baseline with the ionosphere float model, thereby enabling near instantaneous solutions.
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