Undifferenced and uncombined GNSS time and frequency transfer with integer ambiguity resolution

Precise point positioning (PPP) has been a competitive global navigation satellite system (GNSS) technique for time and frequency transfer. However, the classical PPP is usually based on the ionosphere-free combination of dual-frequency observations, which has limited flexibility in the multi-frequency scenario. More importantly, the unknown integer ambiguities are not restored to the integer nature, making the advantage of high-precision carrier phase observations underutilized. In this contribution, using the undifferenced and uncombined (UDUC) observations, we derive the time and frequency transfer model suitable for multi-constellation and multi-frequency scenarios. Notably, in short- and medium-baseline time and frequency transfer, the ionosphere-fixed and ionosphere-weighted UDUC models are derived, respectively, by making full use of the single-differenced (SD) ionospheric constraints. The proposed model can be applied to short-, medium- and long-baseline time and frequency transfer. The ambiguities are solved in a double-differenced (DD) form and can thus be restored to integers. To verify the feasibility of the model, GPS data from several time laboratories were collected, and the performance of the time and frequency transfer were analyzed with different baseline lengths. The results showed that the ionosphere-fixed and ionosphere-weighted UDUC models with integer ambiguity resolution could improve the frequency stability by 25–60% and 9–30% at an averaging time of several tens of seconds to 1 day for short- and medium-baseline, respectively. Concerning the long-baseline, the UDUC model is 10–25% more stable than PPP for averaging time below a few thousands second and over 1 day.