# Error Modeling of Fiber Optic Gyroscope Universal Time Measurement
## 2 Analysis Model for FOG Measurements of Earth's Rotation
### Noises in the Measurement Process
#### 2.2.2 Correction of Polar Motion Error  
Using the conservation of angular momentum principle, changes in the rotation of the solid earth can be shown to be caused either by changes in the mass distribution of the solid earth or by torques acting on the solid earth. Such torques can be caused, for example, by the motion of the atmosphere and oceans or by the gravitational effect of the sun, moon, and planets [28].  
Polar motion is due to the movement of the terrestrial material as well as internal material; the earth's rotation axis varies slowly within itself, which causes the position of the earth's instantaneous poles on the ground to constantly move, resulting in the difference between the instantaneous terrestrial system and the conventional terrestrial system. The lunisolar and planetary torques exerted upon the rotating earth are regular and predictable. A standard mathematical model consists of a sum of polynomial and (quasi) harmonic terms. In analyzing the effect of high-frequency variations in the earth's rotation due to polar motion on the FOG measurements, we use the earth rotation model recommended by IERS [25], which corresponds to the parameters given in Tables 8.2 and 8.3 of the IERS Convention 2010.  
IERS observes polar motion using astronomical methods such as VLBI; the EOP 14C04 dataset is available through its official website [29], as shown in Figure 6. The data segment from 11 January to 12 February 2024 (the red line segment) was selected as the reference data for the FOG measurements. The value of 0.1 arcsec at the pole is roughly equivalent to 2 m.  
In order to calculate the effect of polar motion high-frequency signals on FOG observations using the observation equations in the ITRS, it is necessary to take into account the relationship between the polar motion of the earth's instantaneous rotational pole (IRP) and the celestial intermediate pole (CIP) [30]:  
\[m=p+i\frac{\dot{p}}{\Omega_{0}} \tag{11}\]  
Figure 5: Correction of the plumb line variation.  
where \(p\) is the CIP polar motion, denoted by complex numbers as \(p=p_{x}+ip_{y}\), \(p_{x}\) and \(p_{y}\) are the CIP polar motion on the x-axis and y-axis, respectively, \(\arg_{i}(t)\) is a linear combination of six astronomical basic parameters \((l,l^{\prime},F,D,\Omega,\gamma)\). The coefficients a, b, c, and d are obtained from Tabs 8.2a and Tabs 8.2b in IERS Conventions 2010, which, in combination with the conversion relationship, enables the conversion of the CIP polar motion and the IRP polar motion. \(m\) is likewise denoted as complex \(m=m_{1}+im_{2}\), whose corresponding part denotes the IRP polar motion.  
The results from the modeling are shown in Figure 7. It can be seen that the polar motion variations of the earth's instantaneous rotation axis cause a relatively small effect on the FOG measurements, approximately on the order of \(10^{-13}\) rad/s. Its signal may be very small in FOG observations not yet fully measured, but we decided to investigate this signal because giant FOG technology is still under development and the effect of the instantaneous axis of rotation polar motion variation is not negligible.