GNSS is now being speedily expanded to our daily life, but the positioning precision still can hardly meet the demands of many high-precision applications, such as approaching landing system on airports. Due to the development of GNSS, quadruple-frequency signals are now available in China’s BeiDou Navigation Satellite System (BDS) and the European Galileo system, which can contribute to positioning precision. Positioning precision can not be improved obviously by quadruple-frequency carrier phases until cycle slips are detected and repaired. A method using four linear combinations to detect and repair quadruplefrequency cycle slips is proposed in the paper. The choices of the four linear combinations are conducted in cascaded steps in accordance to the cycle slip fixing probability. When the four detection combinations are determined, cycle slips on original carrier phase observations can be uniquely determined. The proposed algorithm has been tested on real 30-second quadruple-frequency static observations of BDS and Galileo and on real 0.05-second quadruple-frequency kinematic observations of BDS and Galileo. Simulated and real cycle slips are tested. The results show that the proposed algorithm can detect and repair cycle slips even for one cycle effectively.

Introduction

With the completion of the experimental and regional phases, China’s BeiDou Navigation Satellite System (BDS) is being speedily expanded to a global and multifunctional satellite navigation system, BDS-3 [1]. To ensure the smooth transition from BDS-2 to BDS-3, B1I and B3I will continue to be broadcast while B2I will not be retained [2]. At the same time, two new OS (open service) signals, i.e. B1C and B2a, will be broadcast by the BDS-3 satellites [3], [4]. Those four signals are broadcast on four frequencies and can be received by BDS users. In addition, the European Galileo system has broadcasted quadruple-frequency signals, i.e. E1, E5a, E5b and E6, and several researches have been done based on Galileo quadruple-frequency signals [5], [6]. Carrier phase measurements are the important observations for highly accurate positioning because of their high accuracy. Multi-frequency signals can form more linear combinations with small combined noise, small ionospheric delay and long wavelength compared with single-frequency signal, and multi-frequency signals are used in many high precise applications, such as approaching landing system and geodetic measurement applications [7]–[۱۸].