A mixed multi-frequency precise point positioning strategy based on the combination of BDS-3 and GNSS multi-frequency observations

Due to the traditional fixed model used in precise point positioning (PPP) solutions, multi-frequency and multi-Global Satellite Navigation System (GNSS) observations have not been fully introduced into positioning services. In consideration of the BDS-3 multi-frequency signals and the new development of other GNSS systems, a new multi-frequency and multi-GNSS PPP solution strategy should be proposed to flexibly model and use all observations. In this study, a preliminary mixed multi-frequency PPP solution strategy is analyzed and tested based on a combination of BDS-3 and GNSS observations. First, the multi-frequency observations are combined and their coefficients are rapidly estimated by least squares; then, the inter-system bias parameter and the stochastic model are introduced into the function model; and finally, the mixed PPP solution and its software are developed and verified by three groups of experiments. According to the experimental results of 96 stations and ten-day multi-GNSS experiment observations, it is indicated that the root-mean-square error of positioning and the convergence time are significantly optimized with the aid of additional frequencies, where the accuracy improvements of multi-frequency and multi-GNSS scheme in the east (E), north (N) and up (U) directions can respectively reach up to 23.2%, 13.3% and 23.8% compared with the traditional BDS-3 dual-frequency ionosphere-free (IF) PPP model; and the corresponding convergence time is reduced from 18.54 min to 13.18 min. Meanwhile, from the results of multi-frequency BDS-3 PPP experiments based on 53 stations, it is suggested that a better performance of positioning and convergence can be obtained by the mixed PPP solution, where the position RMS of the E, N and U directions are reduced by 38.2%, 23.9% and 26.3%, and the convergence time is decreased from 23.86 min to 12.43 min for the combined BDS-3 of all observations, compared with the BDS-3-only solution. Furthermore, in the vehicle experiment of multi-frequency kinematics PPP, a convergence process can be found for different scenarios of BDS-3 combination with other observations. Moreover, the residual series are different for each solution, in which reductions of 71.1%, 33.3% and 77.1% in the E, N and U directions, respectively, can be obtained compared with the traditional BDS-3 dual-frequency IF model in kinematics experiments based on multi-GNSS and multi-frequency scenarios. Therefore, it is meaningful to recommend the mixed PPP solution in the GNSS community to fully use multi-frequency and multi-GNSS observations by the adaptive combination of different observations.