A Satellite Selection Algorithm for Achieving High Reliability of Ambiguity Resolution with GPS and Beidou Constellations

Reliability of carrier phase ambiguity resolution (AR) of an integer least-squares (ILS) problem depends on ambiguity success rate (ASR), which in practice can be well approximated by the success probability of integer bootstrapping solutions. With the current GPS constellation, sufficiently high ASR of geometry-based model can only be achievable at certain percentage of time. As a result, high reliability of AR cannot be assured by the single constellation. In the event of dual constellations system (DCS), for example, GPS and Beidou, which provide more satellites in view, users can expect significant performance benefits such as AR reliability and high precision positioning solutions. Simply using all the satellites in view for AR and positioning is a straightforward solution, but does not necessarily lead to high reliability as it is hoped. The paper presents an alternative approach that selects a subset of the visible satellites to achieve a higher reliability performance of the AR solutions in a multi-GNSS environment, instead of using all the satellites. Traditionally, satellite selection algorithms are mostly based on the position dilution of precision (PDOP) in order to meet accuracy requirements. In this contribution, some reliability criteria are introduced for GNSS satellite selection, and a novel satellite selection algorithm for reliable ambiguity resolution (SARA) is developed. The SARA algorithm allows receivers to select a subset of satellites for achieving high ASR such as above 0.99. Numerical results from a simulated dual constellation cases show that with the SARA procedure, the percentages of ASR values in excess of 0.99 and the percentages of ratio-test values passing the threshold 3 are both higher than those directly using all satellites in view, particularly in the case of dual-constellation, the percentages of ASRs (>0.99) and ratio-test values (>3) could be as high as 98.0 and 98.5 % respectively, compared to 18.1 and 25.0 % without satellite selection process. It is also worth noting that the implementation of SARA is simple and the computation time is low, which can be applied in most real-time data processing applications.