Integer ambiguity resolution and precise positioning for tight integration of BDS-3, GPS, GALILEO, and QZSS overlapping frequencies signals

The loose integration positioning is typically applied for multi-frequency, multi-GNSS observations where the individual reference satellite is assigned for each system. BeiDou-3 navigation satellite system (BDS-3) broadcasts overlapping frequencies with other GNSS systems to enhance their interoperability, which allows us to set up the tight integration with a unique reference satellite for all systems with the same frequency. Although the unknown differential inter-system bias (DISB) parameters as the same number of increased observations are introduced epoch by epoch in tight integration, the stability of DISB can enhance the model strength and then improve the positioning performance. This paper intends to comprehensively study the tight integration to show its superiority for integer ambiguity resolution and precise positioning, compared to the loose integration. We first formulate the mathematical models for the loose and tight integrations, followed by the mathematical definition of DISB-float and -fixed tight integration models, respectively. The analysis of a two-day static datasets indicates the temporal stability of DISB and thus the feasibility of correcting DISB in tight integration. The static and kinematic positioning experiments show that the tight integration can significantly improve ambiguity resolution and positioning accuracy. Especially in harsh environments, with a given threshold of 3 for ratio-test, the ambiguity fix-rate is improved from 36.0 to 99.6% and from 13.1 to 26.6% and the positioning precision is improved by 98.8% and 31.3% for static and kinematic situations, respectively.