# Error Modeling of Fiber Optic Gyroscope Universal Time Measurement
## 2 Analysis Model for FOG Measurements of Earth's Rotation
### Noises in the Measurement Process  
#### 2.2.1 Correction of Orientation Error  
Due to the gravitational forces exerted by the sun, moon and external planets, relative angular momentum is generated with respect to the rotating reference frame, leading to periodic deformation of the earth's surface and sea surface variations. These forces influence the earth's inertia tensor and result in perturbations of the earth's rotation vector. Axial perturbations affect the rotation rate and can be quantified as changes in increments to UT1. The primary effects on FOG are manifested in solid tides, and oceanic tidal effects. In addition to tidal effects, there are localized non-tidal surface effects, such as earthquakes, changes in station latitude as well as anthropogenic disturbances. FOG is highly sensitive to the earth's instantaneous rotation pole (IRP); all of the above effects will lead to the tilt of the normal direction of the fiber optic ring measurement plane, leading to a change in the inner product between the FOG normal vector and the earth's rotation axis. The resulting effect on the raw data output from the FOG, as well as the influence of the tilt on the earth's angular velocity, can be expressed as:  
\[\Omega=\Omega_{0}\sin(\varphi_{0}+dT_{ns})\cos dT_{ew} \tag{5}\]  
where \(\varphi_{0}\) is the latitude of the measurement point, and \(dT_{ns}\) and \(dT_{ew}\) represent small angle changes in the northward and eastward directions, respectively. The northward component is much larger than the eastward component, which is negligible. Taking the FOG as an example, the latitude where the station is located is 40.24\({}^{\circ}\) N, and the measurement platform produces a change in the tilt angle of 100 nrad (20 mas) in the north-south direction, which will result in a corresponding angular velocity measurement error of about 10\({}^{-12}\) rad/s. In contrast, the same change in the east-west direction will only increase by 10\({}^{-18}\) rad/s. Angular velocity error variations in the east-west direction have a negligible effect on the FOG signal, except for strong seismic motions. The influence of tidal effect mainly includes solid tides and oceanic tides [1], where the periodic deformation results in tilt variation of the FOG measurement platform. The tidal displacement caused by the earth's external gravitational tide force contains the coupling of spherical and annular displacement fields of adjacent orders, while the annular displacement field has no effect on the role of the north-south direction tilt [26]. Since the  
Figure 4: G-ring and FOG are presented in Allan deviation curves with respect to the approximate magnitude and frequency range of known geophysical excitations. coupling term has a weak effect on the solid tide Love number and a limited effect on the tilt variation of the measurement platform, a spherically symmetric approximation can be taken to simplify the analysis. The tilt variation of the measurement platform in the north-south direction [18] under the influence of the solid tide is given by:  
\[T_{FOG}=(h_{0}-l_{0})\frac{\Phi_{nm}(a)}{ag_{0}}\frac{\partial Y_{n}^{m}(\theta,\lambda)}{\partial\theta} \tag{6}\]  
This variation is mainly generated by the surface deformation and the overall north-south displacement of the station [19], which leads to the inclination of the measurement platform. Additionally, under the influence of the gravitational tidal force, the local plumb line at the location of the station is also deflected, with the north-south component [18] expressed as:  
\[T_{VD}=-(1+k_{0}-l_{0})\frac{\Phi_{nm}(a)}{ag_{0}}\frac{\partial Y_{n}^{m}( \theta,\lambda)}{\partial\theta} \tag{7}\]  
where \(h_{0}\), \(l_{0}\) and \(k_{0}\) are tidal Love numbers of a degree 0, \(\Phi_{nm}(a)Y_{n}^{m}\) represents the external tide generating potential, \(Y_{n}^{m}\) is the spherical harmonic function, \(a\) is the geocentric radius of the observation point, and \(g_{0}\) is the equatorial mean gravity value (for more details, see [18,19]).