Rapid and Reliable Integer Ambiguity Resolution in BDS-3 and Galileo Penta-Frequency Observations over Long Baselines

Penta-frequency signals of BDS-3 and Galileo have the potential to provide a greater number of signal combinations with varying characteristics, which can enable accurate ambiguity resolution within a range of tens to hundreds of kilometers. Nonetheless, this potential has yet to be fully realized. To address this issue, we propose a five-frequency carrier ambiguity resolution (FiCAR) method that utilizes ionosphere-reduced (IR) combinations of extra wide-lane (EWL), wide-lane (WL), and narrow-lane (NL) signals from BDS-3 and Galileo for stepwise ambiguity resolution (AR). Firstly, we select the EWL, WL, and NL combined signals with low noise and small ionospheric scale factor characteristics and use Kalman filtering to estimate the tropospheric wet delay while disregarding the residual ionospheric errors of the IR combinations. This method does not require the estimation of ionospheric delay, reducing the number of estimated parameters and enabling high-precision real-time kinematic (RTK) positioning over baselines ranging from several hundred to thousands of kilometers. Thirdly, based on the FiCAR method, we propose a modified FiCAR (MFiCAR) method in which the PAR strategy of NL is further optimized, effectively enhancing the timeliness and reliability of long baseline RTK positioning. To validate our approach, we conducted experiments on four baselines containing BDS-3 and Galileo penta-frequency signals, with baseline lengths ranging from 151 to 1946 kilometers. The experimental results demonstrate that the geometry-based ionosphere-reduced FiCAR and MFiCAR methods can instantly fix the EWL and WL signals, providing positioning services at the sub-meter level and effectively enhancing the positioning accuracy of float solutions. Additionally, the MFiCAR method can improve the NL ambiguity fix rate on longer baselines, with fix rates of 99.17%, 98.82%, 95.89%, and 88.96% for the four baselines, respectively.