# Error Modeling of Fiber Optic Gyroscope Universal Time Measurement
## 1 Introduction  
Universal time (UT1) is a linear function of the earth's rotation angle (ERA) and is one of the essential and important parameters in the interconversion between the International Terrestrial Reference Frame (ITRF) and the International Celestial Reference Frame (ICRF). The variation in earth's rotation can be observed mainly via space geodetic techniques, such as very long baseline interferometry (VLBI), global navigation satellite system (GNSS) and other astronomical geometric methods. Since optical gyroscopes based on the Sagnac effect are capable of high-sensitivity and real-time acquisition, as well as having no external reference target and no information radiation to the outside, they are well suited for deployment on the ground to accurately monitor the earth's rotation [1]. UT1 solutions based on optical gyroscopes have become the only direct measurement method apart from the astronomical geometry approach. Optical gyroscopes have been widely used not only in the precise measurement of the angular velocity of earth's rotation [2] and UT1 solution [3] but also in the determination of true north [4], gravity measurement [5] and rotating seismic wave measurements [6]. Three decades ago, with the construction of the laser gyro C-I [7] with an area of 0.748 m\({}^{2}\) by [PERSON] to realize the precise measurement of the angular velocity of earth'srotation, a new scheme was introduced for space geodesy technology. [PERSON] used a FOG with a diameter of 4.25 m and a length of 2.2 km for testing at Wettzell, concluding that the larger experimental fiber optic ring may deliver accurate earth rotation rate measurements, while smaller devices were suitable for strong motion seismology [8]. Prof. [PERSON] conducted experiments at Wettzell, employing an oversized fiber optic ring of wound with a single mode fiber length of 2.2 km, and the earth rotation rate was observed at 400 Hz [1]. It is expected that modifications such as a brighter light source and some enhancements to the electronic circuitry can improve measurement accuracy. [PERSON] used commercial fiber optics to build a giant FOG with an area of 20 km\({}^{2}\) to explore the possibility of geodesy with 2 \(\times\) 10\({}^{-9}\) rad/s accuracy of 1000 s, which demonstrated the feasibility of constructing giant optical rotation sensors [9]. Larger fiber optic ring areas simultaneously bring more errors, such as environmental vibration, temperature variations, anthropogenic influences and other errors, thus failing to achieve the expected results. The G-ring at Wettzell in Germany is the most advanced and highest-resolution large laser gyroscope, and the outstanding stability of the G-ring laser is sufficient to provide the desired sensor resolution in the order of 5 \(\times\) 10\({}^{-13}\) rad/s over at least one month [10]. Although these devices possess the raw sensitivity for such a measurement, they remain limited by long-term geometric instability, detection noise and imperfections in the physical models required to isolate geophysical effects [11]. Hence, the G-ring utilizes three tiltmeters to correct the tilt error of the optical gyro in the north-south direction, taking into account various factors. These in turn have to be corrected for temperature-related effects and for the mass attraction derived from a global weather model. Furthermore, backscatter corrections are considered, subtracting the theoretical diurnal polar motion and the solid earth tides model [12]. [PERSON] combined VLBI with G-ring combination solution to improve the UT1 by 12% compared to using VLBI data only [13]. [PERSON] developed a giant interferometric fiber optic gyroscope (IFOG) prototype with a fiber length of 30 km and achieved a sensitivity of 2 \(\times\) 10\({}^{-10}\) rad/s for 200 s [14]. This giant IFOG underwent long-term testing at the Chinese Academy of Sciences National Time Service Center and solved UT1 with an accuracy of 20 ms at 5 min update rates [15].