Models, methods and assessment of four-frequency carrier ambiguity resolution for BeiDou-3 observations

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.