# Error Modeling of Fiber Optic Gyroscope Universal Time Measurement
## 1 Introduction
The research by this team successfully developed a new type of large-scale fiber optic interferometer, BFOI-1500, with continuous improvement, to achieve a UT1 measurement error within 7 ms [16]. However, the update rate decreased, and the effect of precession and nutation errors in the observation equations was not taken into account. [PERSON] designed and implemented a 2 m diameter, 20.68 km giant FOG [17], with an accuracy of 4 \(\times\) 10\({}^{-11}\) rad/s over an integration time of 30,000 s. Due to the performance advantage of giant FOG, the rotation signal of the surface wave magnitude (MS) 5.5 earthquake 332 km away was measured during system operation. Compared to the many technical challenges and limitations that exist in laser gyroscopes, the FOG has the advantages of being fully solid-state, easy to construct and relatively inexpensive, with the ability to improve the detection's signal-to-noise ratio (SNR) and sensitivity by increasing the number of fiber optic winding turns. However, when the length of the fiber optic ring increases, the noise in the FOG also increases. Therefore, one of the main difficulties of the giant FOG at this point in time is the suppression of errors caused by the environment on the fiber optic ring, which include tilt errors [18; 19], astronomical errors [20], local deformations [21] and others. These noises significantly affect the performance of the FOG, which makes error correction essential to achieve higher-accuracy measurements of the angular velocity of earth's rotation and the UT1 parameter. In order to improve the solution accuracy of the FOG in the field of measuring UT1 and to have the ability to complement the existing astronomical measurements, this paper proposes a theoretical model for error correction based on FOG measurements of UT1. Considering the error in the deviation of the earth's rotation axis caused by the gravitational force of the sun and moon, the error caused by the precession and nutation is corrected, and the observation equations based on the correction of the error in the precession and nutation are established. According to this observation equation, the mapping relationship with UT1 is established by correcting various errors, leading to a final high-precision UT1 solution after the VLBI correction. Through a 14-day measurement experiment, we achieve an RMSE of less than 2.2 ms for the deviation between the FOG solution and EOP 14C04 under a room temperature environment without any vibration isolation and magnetic shielding devices. Compared with the traditional method, the method proposed in this paper shows error variations within a range of 3.57 ms, and the UT1 solution accuracy is relatively improved by 56%. The method proposed in this paper has more obvious advantages than the traditional method, which not only offers a reference for the research of FOG error modeling and correction, but also provides a certain theoretical and experimental basis for the continuous development of the UT1 measurements. As technology progresses, the performance of FOG is expected to improve, alongside iterative refinements to its error correction model. Consequently, the measurement accuracy is anticipated to reach the order of 10\({}^{-13}\) rad/s, with the potential to achieve UT1 measurement precision of 0.1 ms/day. The overall arrangement of this paper is as follows. In Section 2, the FOG observation equation is proposed, and various types of error mechanisms affecting the angular velocity of the earth's rotation with corresponding error correction methods are discussed. In Section 3, an approach to solving the UT1 from FOG measurements is discussed. Section 4 presents several experimental measurements. Finally, the conclusion is given in Section 5.