GPS/GLONASS Combined Precise Point Positioning with Receiver Clock Modeling

Research has demonstrated that receiver clock modeling can reduce the correlation coefficients among the parameters of receiver clock bias, station height and zenith tropospheric delay. This paper introduces the receiver clock modeling to GPS/GLONASS combined precise point positioning (PPP), aiming to better separate the receiver clock bias and station coordinates and therefore improve positioning accuracy. Firstly, the basic mathematic models including the GPS/GLONASS observation equations, stochastic model, and receiver clock model are briefly introduced. Then datasets from several IGS stations equipped with high-stability atomic clocks are used for kinematic PPP tests. To investigate the performance of PPP, including the positioning accuracy and convergence time, a week of (1–7 January 2014) GPS/GLONASS data retrieved from these IGS stations are processed with different schemes. The results indicate that the positioning accuracy as well as convergence time can benefit from the receiver clock modeling. This is particularly pronounced for the vertical component. Statistic RMSs show that the average improvement of three-dimensional positioning accuracy reaches up to 30%–40%. Sometimes, it even reaches over 60% for specific stations. Compared to the GPS-only PPP, solutions of the GPS/GLONASS combined PPP are much better no matter if the receiver clock offsets are modeled or not, indicating that the positioning accuracy and reliability are significantly improved with the additional GLONASS satellites in the case of insufficient number of GPS satellites or poor geometry conditions. In addition to the receiver clock modeling, the impacts of different inter-system timing bias (ISB) models are investigated. For the case of a sufficient number of satellites with fairly good geometry, the PPP performances are not seriously affected by the ISB model due to the low correlation between the ISB and the other parameters. However, the refinement of ISB model weakens the correlation between coordinates and ISB estimates and finally enhance the PPP performance in the case of poor observation conditions.