Global navigation satellite system (GNSS) real-time kinematic (RTK) normally takes advantage of a common-frequency (CF) model, in which, the frequency bands in use are assumed to be the same across all satellites visible to two receivers. This assumption discards satellites whose frequency bands differ from the majority of satellites, thereby weakening the CF model. In this contribution, we present a mixed-frequency (MF) RTK model that considers all satellites whose frequency bands may vary from each other. Due to the new rank deficiencies in the MF RTK model, the formulation of the MF RTK model needs to choose a set of unknown parameters as an S-basis based on S-system theory. The formulated MF model is generally more applicable than the CF model, particularly for the BeiDou navigation satellite system (BDS) since its second-generation (BDS2) satellites broadcast B1I, B2I, and B3I signals and its third-generation (BDS3) satellites broadcast B1I, B3I, B1C, B2a, and B2b signals. To verify, we collected BDS data at a static station and a kinematic vehicle which are a zero-baseline and an approximate 10 km baseline, respectively, to test the MF model and compared it with three CF models employing BDS2 B1I+B2I+B3I (CF1), BDS3 B1I+B3I+B1C+B2a+B2b (CF2) and BDS B1I+B3I (CF3). Both static and kinematic results show that the MF model outperforms the three CF models regarding the integer ambiguity resolution time-to-first-fix and positioning accuracy. The MF model can obtain the most accuracy positioning with 0.094/0.081/0.230 in the static test and 5.49, 6.30, and 9.54 in the kinematic test, respectively. Which compared with the traditional CF model which utilized all BDS satellites (CF3), the MF model obtain improvements of 21.7%, 19.0%, and 11.5% in the east, north, and up components in the static test and 52.7%, 57.6%, and 58.4% in the kinematic test, respectively.

Mixed-frequency (MF),Real-time kinematic (RTK),Single differenced (SD),Integer ambiguity resolution (IAR),BeiDou navigation satellite system (BDS)