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.

中文翻译：

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北斗3号观测资料四频载波歧义分辨率的模型，方法及评估。

多频率最显着的优点之一是它可以提高歧义度解决的成功率，例如三频载波歧义度解决方案（TCAR）。到目前为止，全球北斗三号导航卫星系统已经提供了四个频率。因此，我们利用真实的北斗3资料系统地研究了四频载波模糊度解析（FCAR）的模型和方法。首先，给出了四频线性组合的模型，并根据某些最优准则找出了最优线性组合。其次，研究了两种典型方法，包括无几何方法和基于几何的方法。最后，使用真实的BeiDou-3数据评估FCAR方法的性能，同时应用了两种策略，即单周期和多周期解决方案。结果表明，与TCAR方法相比，FCAR方法可以在数量和质量上提供更多高质量的虚拟信号。通过使用长度范围从4.9 m到61.6 km的真实BeiDou-3数据，三个高质量且独立的信号可以立即修复歧义，成功率约为100％。然后，可以以高效率和成功率来固定第四独立信号。因此，FCAR方法在大规模实时精确定位方面很有希望，因为成功的模糊度解析可能需要数十分钟到几小时。三个高质量且独立的信号可以立即消除歧义，成功率约为100％。然后，可以以高效率和成功率来固定第四独立信号。因此，FCAR方法在大规模实时精确定位方面很有希望，因为成功的模糊度解析可能需要数十分钟到几小时。三个高质量且独立的信号可以立即消除歧义，成功率约为100％。然后，可以以高效率和成功率来固定第四独立信号。因此，FCAR方法在大规模实时精确定位方面很有希望，因为成功的模糊度解析可能需要数十分钟到几小时。