Improving undifferenced precise satellite clock estimation with BDS-3 quad-frequency B1I/B3I/B1C/B2a observations for precise point positioning

Estimates of satellite clock offsets typically employ dual-frequency undifferenced (UD) ionospheric-free (IF) observations from global network. The third-generation BeiDou Navigation Satellite System (BDS-3) can transmit B1I (1561.098 MHz), B3I (1268.52 MHz), B1C (1575.42 MHz), B2a (1176.45 MHz), B2b (1207.14 MHz) and B2ab (1191.795 MHz) signals. To make full use of the advantage of BDS-3 multi-frequency signals and improve BDS-3 service performance, we present some new quad-frequency satellite clock estimation techniques using B1I/B3I/B1C/B2a signals, which are QFIF0 model combining B1I/B3I and B1C/B2a IF observables, QFIF1 model combining the B1I/B3I, B3I/B1C and B1I/B2a IF observables, QFIF2 model combining B1I/B3I and B1I/B3I/B1C/B2a IF observables, and quad-frequency uncombined QFUC model, respectively. These new techniques only improve the performance of satellite clock estimation by fully utilizing the BDS-3 multi-frequency observations on the premise of ensuring the dual-frequency IF datum but also obtain the corresponding inter-frequency clock bias (IFCB) simultaneously. The quad-frequency satellite clock offsets are evaluated in terms of the clock offset precision, the modified Allan deviation (MDEV) and precise point positioning (PPP) performances. The new methods can improve the performances of the estimated clock offsets compared with the traditional dual-frequency IF model. The precision for the estimated clock offsets using quad-frequency satellite clock estimation models can be improved by 13–26% in terms of standard deviation (STD). The improvement of frequency stability ranges from 0 to 24%, especially for the short-term stability, which can reach 12% and 24% for B1I/B3I and B1C/B2a clock offsets, respectively. Similarly, the corresponding PPP performance has also been better improved with respect to those of using traditional dual-frequency IF clock offsets. Thus, the proposed quad-frequency satellite clock estimation techniques can be well applied into precise satellite clock estimation.