# Error Modeling of Fiber Optic Gyroscope Universal Time Measurement
## 4 Measurement Experiment
High noise above 1 Hz shows up as 1/f noise in the Allan variance because the slope of the Allan deviation is clearly equal to 1 for frequencies above 1 Hz. Figure 11: Time series of several days of raw measurement data. Figure 12: (a) Allan deviation curves and (b) PSD analysis of FOG for several days. Three experiments were conducted in January-February 2024 for three different periods of the FOG measurements. The FOG and tiltmeter collected 1 day of data per day, both with a sampling frequency of 10 Hz. Continuous uninterrupted measurements were taken during the acquisition time period and saved to the computer for solution. The gold standard in this regard is the VLBI technique, which has a measured UT1 error of 0.015 ms. The UT1 results from the FOG solution were compared with the EOP 14C04 data released by IERS in the same period. The errors in the three experimental results are shown in Figure 13.  
The results of the three experiments, compared with the standard values published by IERS, are shown in Figure 13. Figure 13a,c show the short-term experiments in which the VLBI observations of the first two days were used to calibrate the parameters of the FOG; hence, the errors of the two previous days were not included in the calculation of the errors. As the measurement time increases due to effects such as the drift of the FOG, the error gradually increases, though it remains very small. In the long-term experiment in Figure 13b, the traditional algorithm is compared. Over a period of 14 days, it is observed that the traditional algorithm has basically the same trend as the UT1-UTC provided by IERS in the short-term time, but with the increase in time, the error gradually accumulates, leading to an increase in the drift of the last two days. The method used in this paper, on the other hand, is consistent with the results provided by IERS for a period of 14 days, which proves the feasibility of this paper's method. Figure 13: (**a**) Results of the UT1–UTC solution for Experiment 1 (11–15 January 2024). Shown are the estimates from VLBI only (red) and from the combinations of VLBI and FOG data (blue). (**b**) Results of the UT1–UTC solution for Experiment 2 (24 January–6 February 2024). The yellow line is the traditional method. (**c**) Results of the UT1–UTC solution for Experiment 3 (8–12 February 2024). Note that the y-axis scales are different. Table 1 summarizes the results of the comparison between the UT1 solution from FOG and the IERS EOP 14C04 standard data for the three experiments, where STD, RMSE, MAE represent Standard Deviation, Root Mean Square Error, Mean Absolute Error, respectively. The results show that the FOG data are in excellent agreement with the independent measurements by VLBI, with the RMSE and MAE during the 5-day measurement period of Experiment 1 and Experiment 3 both less than 0.9 ms. In the 14-day experiment with continuous measurement period in Experiment 2, the maximum error is 3.57 ms, and both the RMSE and MAE are less than 2.2 ms. In Experiment 2, using the error correction method used in [16] (as shown in Figure 13b; yellow curve is the traditional method), the calculated error variation is within 8.19 ms. In comparison, using the method proposed in this paper, the error variation of the solution is within 3.57 ms. The relative improvement of the UT1 solution accuracy is 56%, which shows its potential in UT1 long-period observation.