# A BDGIM-Based Phase-Smoothed Pseudorange Algorithm for BDS-3 High-Precision Time Transfer
## 1 Introduction  
The law of motion and time scales are both characterized by the fundamental physical quantity known as time. High-precision time transfer techniques have been widely used in the fields of communication, power, financial services, autonomous driving, and aerospace, and they are a prerequisite for maintaining synchronization between time-keeping laboratories and time scales in different countries [1, 2]. With the development of Global Navigation Satellite System (GNSS) technology, GNSS-based time transfer techniques have been enhanced. Currently, GNSS-based time transfer methods with pseudorange observations can be included, such as common-view (CV) [3], all-in-view (AV) [4, 5], and two-way satellite time and frequency transfer (TWSTFT) [2] time transfer methods, which have greatly improved the accuracy of time transfer [3, 6, 7]. The aforementioned time transfer techniques have been the subject of extensive scholarly study. In 1980, [PERSON] et al. [1] summarized the GPS time transfer methods and gave a detailed description of the error correction methods involved in time transfer. [PERSON] et al. [8] presented error-processing strategies and the Common GPS GLONASS Time Transfer Standard related to CV time transfer. [PERSON] et al. [9] developed a CV time transfer method using GEO satellites, and it had a time transfer performance comparable to that of TWSTFT. In addition, [PERSON] et al. [10] analyzed the effect of ionospheric delay on CV time transfer. [PERSON] et al. [11] considered the effect of phase ambiguity in CV time transfer, whichgreatly improved time transfer performance. AV time transfer experiments were carried out by [PERSON] et al. [12] utilizing GPS and GLONASS measurements, and the results demonstrated that AV time transfer performed better than CV time transfer. To overcome the drawbacks of the TWSTFT and PPP techniques, [PERSON] et al. [13] combined both for time transfer research. Moreover, [PERSON] et al. [14] investigated the contribution of the Doppler shift to TWSTFT, and the experimental results showed that the effect of the Doppler shift on time transfer is so small that it can be ignored. As is well-known, CV time transfer can determine the difference between the local atomic clock time and the GNSS satellite clock time of two remote stations using the GNSS clock time as a reference. The difference between the two atomic clock times is determined by comparing the two atomic clocks. Within a certain geographical distance, the satellite clock error, orbit error, and atmospheric delay can be eliminated, and the accuracy of remote time transfer improves, which has the benefits of high flexibility, all-weather service, and high accuracy. However, it has obvious disadvantages, as CV time transfer is limited by the geographical distance and the accuracy of pseudorange observations. As the distance between two stations increases, fewer identical satellites can be tracked, and the accuracy of time transfer decreases. With the release of IGS precise products, AV time transfer was formally employed for time comparison between international time laboratories in 2006 [5]. AV time transfer, in contrast to CV time transfer, is not limited by distance; the time difference between two locations may be estimated directly; and the accuracy of AV time transfer is comparable to that of CV time transfer. Unfortunately, however, AV time transfer is relatively dependent on ephemeris. AV time transfer can be negatively affected by satellite orbit errors, clock errors, and atmospheric delays near both stations. Similarly, the accuracy of AV time transfer is also limited by pseudorange observations. In addition to CV and AV time transfer, TWSTFT time transfer, which utilizes the characteristics of satellite signals transmitting and receiving in the same path and opposite direction to improve time transfer performance by eliminating the effects of station position error, satellite error, and atmospheric delay, is also an important means for the current international atomic time TAI calculation.