Real-Time Triple-Frequency Cycle Slip Detection and Repair Algorithm Based on the Optimal Fixing Probability

Global Navigation Satellite System (GNSS) is now being speedily expanded to our daily life, but the positioning precision still can hardly meet the demands of many applications, such as approaching landing system on airports. Due to the development of GNSS, triple frequency signals are now available which can contribute to positioning precision. Positioning precision cannot be improved by triple frequency carrier phases until cycle slips are detected and repaired. Traditional cycle slip detection and repair algorithms choose detection combinations with long wavelength, weak ionospheric delay and small combination noise separately. However, these three conditions cannot be satisfied simultaneously. In this paper, these three conditions are not considered separately. On the contrary, the eventual fixing probability of cycle slip is set as the optimal goal to determine the three detection combinations. The combined ionospheric delay and noise in cycles can be regarded as bias and variance respectively. The proposed algorithm has been tested on observations with simulated and real cycle slips. The results show that the proposed algorithm can detect and repair even single cycle slips in real time effectively.