Abstract
As the signals of Galileo and the global BDS-3 navigation satellite system have been accessible, positioning users can use quad-frequency even five-frequency signals nowadays. With multifrequency signals, one can form some useful combinations to improve the positioning performance, e.g., the widely used extra-wide-lane (EWL)/wide-lane (WL) in triple-frequency cases. For quad-frequency or five-frequency cases, better positioning performance can be expected since additional frequencies are introduced. In this study, we systematically analyse the benefits of Galileo and BDS-3 quad-frequency signals on long-baseline instantaneous positioning. First, the theoretical analysis of EWL/WL ambiguity resolution (AR) and satellite-station range estimation with a single-satellite geometry-free and ionosphere-free model is studied, along with the comparison with triple-frequency cases. Second, using the quad-frequency advantages, an instantaneous decimeter-level positioning model is proposed, where the geometry-free model is adopted for the first two EWL AR and the geometry-based model is adopted for the third WL AR. In the end, the AR and positioning performance are evaluated using real long-baseline date containing Galileo and BDS-3 quad-frequency observations. The results indicate that, with quad-frequency observations, both Galileo and BDS-3 EWL/WL ambiguities can be fixed reliably with a single epoch. Contributed by the resolved EWL/WL ambiguities, instantaneous decimeter-level positioning can be obtained, with the accuracies of 0.116 m/0.126 m/0.351 m in north, east, and up directions, respectively.
Highlights
Chinese BDS-3 has started to provide full operational capability services by July 31, 2020
We mainly test the single-epoch EWL/WL ambiguity resolution (AR) and instantaneous positioning performance using real Galileo and BDS-3 data. e data of a baseline with the length of 104.2 km were collected on May 9, 2020, using the Trimble Alloy receiver in Shanxi Province, China. e data collection lasted for 24 hours with the sampling interval of 10 s
The troposphere delays are directly corrected with the empirical GPT2w model [30], as if the zenith tropospheric delays (ZTD) or relative zenith tropospheric delay (RZTD) is estimated as unknown parameter(s); it will take a long time for convergence due to the correlation with the height component
Summary
Chinese BDS-3 has started to provide full operational capability services by July 31, 2020. At present (September 21, 2020), there are 22 usable Galileo satellites and 29 usable BDS-3 satellites in orbit All these satellites can transmit more than three frequencies for positioning, navigation, and timing (PNT) service, where Galileo transmits signals on five frequencies centered at E1 (1575.42 MHz), E5a (1176.45 MHz), E5b (1207.14 MHz), E5 (1191.795 MHz), and E6 (1278.75 MHz) [1], and BDS-3 transmits signals on five frequencies centered at B1C (1575.42 MHz), B1I (1561.098 MHz), B2a (1176.45 MHz), B2b (1207.14 MHz), and B3I (1268.52 MHz) [2]. Researches about using multifrequency GNSS have been started since the late 1990s, when Forssell et al [5] and Vollath et al [6] first proposed the classical three-frequency ambiguity resolution (TCAR) method. Compared with the early GF models, Vollath [9], Feng and Rizos [10], Hatch [11], Mathematical Problems in Engineering
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