Functional model modification of precise point positioning considering the time-varying code biases of a receiver

Precise Point Positioning(PPP),initially developed for the analysis of the Global Positing System(GPS)data from a large geodetic network,gradually becomes an effective tool for positioning,timing,remote sensing of atmospheric water vapor,and monitoring of Earth’s ionospheric Total Electron Content(TEC).The previous studies implicitly assumed that the receiver code biases stay constant over time in formulating the functional model of PPP.In this contribution,it is shown this assumption is not always valid and can lead to the degradation of PPP performance,especially for Slant TEC(STEC)retrieval and timing.For this reason,the PPP functional model is modified by taking into account the time-varying receiver code biases of the two frequencies.It is different from the Modified Carrier-to-Code Leveling(MCCL)method which can only obtain the variations of Receiver Differential Code Biases(RDCBs),i.e.,the difference between the two frequencies’code biases.In the Modified PPP(MPPP)model,the temporal variations of the receiver code biases become estimable and their adverse impacts on PPP parameters,such as ambiguity parameters,receiver clock offsets,and ionospheric delays,are mitigated.This is confirmed by undertaking numerical tests based on the real dual-frequency GPS data from a set of global continuously operating reference stations.The results imply that the variations of receiver code biases exhibit a correlation with the ambient temperature.With the modified functional model,an improvement by 42%to 96%is achieved in the Differences of STEC(DSTEC)compared to the original PPP model with regard to the reference values of those derived from the Geometry-Free(GF)carrier phase observations.The medium and long term(1×10^(4) to 1.5×10^(4) s)frequency stability of receiver clocks are also signifi-cantly improved.