# 100 Picosecond/Sub-10\({}^{-17}\) Level GPS Differential Precise Time and Frequency Transfer
## 1 Introduction  
Time transfer technology is a prerequisite for time synchronization and timing, and high-precision time and frequency transfer technology is particularly important for achieving high-precision time and frequency services. Since the early 1980s, time and frequency transfer based on Global Navigation Satellite Systems (GNSSs) has been widely developed. Satellite one-way time dissemination, as the simplest GNSS time transfer method, provides clock solutions with an accuracy of 20-30 nanoseconds [1]. The Satellite Common View (CV) method provides a relatively high accuracy in short-baseline time comparisons [2]. However, the distance and accuracy of time transfer are limited by the availability of common satellites and the target range measurement [3, 4]. In 2004, [PERSON] et al. [5] proposed the All-in-View (AV) satellite time transfer method as an improvement over the CV method. With AV, time transfer distance is no longer limited by the availability of common satellites [6, 7]. However, both methods use pseudorange, and the pseudorange multipath and noise limit the time and frequency transfer performance, such that only nanosecond-level time transfer can be achieved [8]. Considering that GNSS carrier-phase measurements are two orders of magnitude more accurate than pseudorange measurements, it is possible to further improve timetransfer performance by using phase measurements. [PERSON] et al. [9] first used GPS carrier-phase measurements to validate high-precision time and frequency transfer. As a continuation of the AV method, the Precise Point Positioning (PPP) method uses both pseudorange and carrier-phase measurements for high-precision un-difference time and frequency transfer, and it has been widely promoted in the time community, becoming the main means used by the Bureau International des Poids et Mesures (BIPM) for comparing clocks contributing to International Atomic Time (TAI) techniques [10; 11; 12]. In addition, using carrier-phase differential methods for high-precision time and frequency transfer has become a complementary method. In 2007, [PERSON] et al. [13] directly fixed the single-difference (SD) integer ambiguity by combining AV and CV technology with SD pseudorange and carrier-phase measurements, realizing SD carrier-phase time transfer. This method is suitable for post-processing analysis. In 2008, [PERSON] et al. [14] utilized International GNSS Service (IGS) orbit and clock products to calculate carrier-phase AV and carrier-phase CV clock solutions and realized GPS carrier-phase CV and AV time transfer. In addition, the method based on real-time kinematics (RTK) double difference has also been used to recover high-precision inter-station clock information. [PERSON] et al. [1] proposed a four-dimensional real-time kinematics (4D-RTK) timing method, which further recovered the inter-station SD integer carrier-phase ambiguity based on double-difference observations to obtain relative clock solutions and achieved a precision of better than 0.1 ns on a 21 km baseline for a duration of 1.5 h. What is more, [PERSON] et al. [3] further compared the time difference estimates obtained from the RTK and PPP methods using short baseline links; the STD of the time difference between the two methods was about 0.1 ns. However, while using the carrier phase to improve the precision of clock comparison, the accuracy of time transfer is often overlooked. If the primary focus is on time transfer rather than frequency transfer, the issue of an absolute time difference in carrier-phase time transfer solutions also needs to be solved. Since the carrier phase is ambiguous, only pseudorange can provide the absolute time difference between two stations, so the method using only the carrier phase can only provide frequency transfer results. In order to provide accurate time difference results between two stations, it is necessary to introduce pseudorange to determine receiver clock offset in carrier-phase time transfer.