Cycle slip and data gap processing based on the geometry-free, geometry-based, and geometry-fixed methods for different receiver types

Abstract

GNSS precise positioning is based on carrier phase measurements, such as precise point positioning (PPP). However, cycle slips and data gaps in measurements are frequent, which can seriously affect the positioning accuracy. How to appropriately handle the geometric term is an inevitable issue for repairing cycle slips and data gaps. While existing methods have been proposed, there remains a notable research gap in comprehensively understanding how different geometric models interact with various receiver types, particularly under complex conditions such as ionospheric activity and long data gaps. Focusing on the cycle slip and data gap for the different receiver types, this paper systematically and comprehensively studies the geometry-free (GF), geometry-based (GB), and geometry-fixed (GFix) methods through theoretical analysis, designed experiments, and field tests for the first time. In the designed experiments, the minimal detectable cycle slips (MDCs) of these three methods are determined, and their detection capabilities for multiple cycle slips and insensitive cycle slips are discussed. In the field tests, the three methods are used with high-end receiver, low-cost board, and smart phone to investigate their applicability under different conditions. The results show that the accuracy of the GF and GFix methods can reach 1 cycle under good observation conditions with short sampling intervals, but if data gaps occur (e.g., 60 s) the performance of both methods degrades due to atmospheric delays. In addition, they are sensitive to measurement noise and are particularly suited to high-end receivers. The MDC of the GB method is 4 cycles due to the excessive parameters to be estimated. However, the GB method has great potential if constraints and enough redundant measurements are added. This method reduces the impact of measurement noise by least squares, it is recommended for processing data from low-cost boards. For smart phones, due to the complexity of the cycle slips, several methods can be combined for processing. Compared with the results without cycle slip processing, these three methods can improve the 3D root mean square error by 91.3 %, 92.5 %, and 92.0 % respectively with low-cost boards.