GPS satellite clock determination in case of inter-frequency clock biases for triple-frequency precise point positioning

Significant time-varying inter-frequency clock biases (IFCBs) within GPS observations prevent the application of the legacy L1/L2 ionosphere-free clock products on L5 signals. Conventional approaches overcoming this problem are to estimate L1/L5 ionosphere-free clocks in addition to their L1/L2 counterparts or to compute IFCBs between the L1/L2 and L1/L5 clocks which are later modeled through a harmonic analysis. In contrast, we start from the undifferenced uncombined GNSS model and propose an alternative approach where a second satellite clock parameter dedicated to the L5 signals is estimated along with the legacy L1/L2 clock. In this manner, we do not need to rely on the correlated L1/L2 and L1/L5 ionosphere-free observables which complicates triple-frequency GPS stochastic models, or account for the unfavorable time-varying hardware biases in undifferenced GPS functional models since they can be absorbed by the L5 clocks. An extra advantage over the ionosphere-free model is that external ionosphere constraints can potentially be introduced to improve PPP. With 27days of triple-frequency GPS data from globally distributed stations, we find that the RMS of the positioning differences between our GPS model and all conventional models is below 1 mm for all east, north and up components, demonstrating the effectiveness of our model in addressing triple-frequency observations and time-varying IFCBs. Moreover, we can combine the L1/L2 and L5 clocks derived from our model to calculate precisely the L1/L5 clocks which in practice only depart from their legacy counterparts by less than 0.006 ns in RMS. Our triple-frequency GPS model proves convenient and efficient in combating time-varying IFCBs and can be generalized to more than three frequency signals for satellite clock determination.