Geometry-based cycle slip and data gap repair for multi-GNSS and multi-frequency observations

Carrier phase observations are commonly used in high-precision GNSS positioning applications, such as precise point positioning and real-time kinematic positioning, due to their millimeter precisions. Hence, it is a crucial module to handle cycle slips and short-time signal interruptions when phase observations are involved, which otherwise will lead to a time-consuming re-initialization. With the gradual GNSS modernization, jointly using observations from multi-GNSS and multi-frequency tends to be a hotspot application pattern for high-accuracy positioning. In this contribution, we will present a geometry-based ionosphere-weighted approach to estimate integer cycle slips in an integrated adjustment, which is universally applicable to arbitrary number of frequencies of GNSS systems. Different from the traditional methods, where cycle slips are processed in a satellite-by-satellite mode based on geometry-free combinations, we take full advantage of the mutual correlations between multi-frequency, between satellites and between systems embodied in the receiver coordinate parameters. When it is unable to effectively fix the full set of cycle slips, we further propose to partially fix the subset of cycle slips that can be reliably fixed. Performance of the proposed method is validated by extensive experiments using undifferenced dual/triple-frequency BDS data, dual-frequency GPS data and triple-frequency BDS + dual-frequency GPS data. The results show that the proposed method can effectively fix continuous cycle slips in case of small/large sampling intervals and connect the data gaps up to a few minutes with high success rates.