Models, methods and assessment of four-frequency carrier ambiguity resolution for BeiDou-3 observations
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ORIGINAL ARTICLE
Models, methods and assessment of four‑frequency carrier ambiguity resolution for BeiDou‑3 observations Zhetao Zhang1,2 · Bofeng Li3 · Xiufeng He1 · Zhiteng Zhang3 · Weikai Miao3 Received: 15 January 2020 / Accepted: 10 July 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract One of the most significant advantages of multiple frequencies is that it can improve the success rate of ambiguity resolution, such as the three-frequency carrier ambiguity resolution (TCAR) method. So far, the global BeiDou-3 navigation satellite system already provides four frequencies. Hence, we systematically study the models and methods of four-frequency carrier ambiguity resolution (FCAR) by using real BeiDou-3 data. First, the models of four-frequency linear combinations are given, and the optimal linear combinations are found out based on certain optimal criteria. Second, two typical methods, including geometry-free and geometry-based methods, are studied. In the end, the real BeiDou-3 data are used to evaluate the performance of the FCAR method, where two strategies, i.e., single-epoch and multi-epoch solutions, are both applied. The results indicate that the FCAR method can offer more high-quality virtual signals in quantity and quality than the TCAR method. By using the real BeiDou-3 data with different lengths ranging from 4.9 m to 61.6 km, three high-quality and independent signals can fix the ambiguities instantaneously with an approximately 100% success rate. Then the fourth independent signal can be fixed with high efficiency and success rate. Therefore, the FCAR method is promising in large-scale real-time precise positioning, where the successful ambiguity resolution may take tens of minutes to hours. Keywords BeiDou-3 · Ambiguity resolution · Four frequencies · Linear combination
Introduction Ambiguity resolution is the prerequisite of high-precision Global Navigation Satellite System (GNSS) applications. However, the ambiguities cannot be fixed easily especially when the baseline length is long. At this time, the threefrequency carrier ambiguity resolution (TCAR) method is often adopted if there are three available frequencies. It is desirable to improve the efficiency and accuracy of ambiguity resolution such as in the real-time kinematic positioning (RTK) with large scales or in complex environment. Since the late 1990s, many efforts have concentrated on how to make full use of additional frequency. Forssell et al. * Zhetao Zhang [email protected] 1
School of Earth Sciences and Engineering, Hohai University, Nanjing 211100, China
2
State Key Laboratory of Rail Transit Engineering Informatization (FSDI), Xi’an 710043, China
3
College of Surveying and GeoInformatics, Tongji University, Shanghai 200092, China
(1997) and Vollath et al. (1998) first introduced and studied the methodology of the TCAR method. In fact, the TCAR method allows the application of rounding, bootstrapping or integer least-squares (ILS) search. Since the rounding is easy-to-implement and ef
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