# 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
The tidal components include long-period tidal waves (\(M_{0}\), \(S_{0}\), \(M_{f}\), etc. ), diurnal waves (\(Q_{1}\), \(O_{1}\), \(M_{1}\), \(p_{1}\), \(K_{1}\), etc. ), semidiurnal waves (\(N_{2}\), \(M_{2}\), \(S_{2}\), \(K_{2}\), \(L_{2}\), \(2N_{2}\), etc. ), and one-third diurnal waves, taking into account primarily the influence of the third-order gravitational tidal force. Ocean tide induced deformation can similarly tilt the measurement platform. [PERSON] verified the effect of ocean tides on the Sagnac frequency observed in the G-ring [23]. The oceanic tidal load, although only 9% of the solid earth tidal influence, contributes significantly to the semidiurnal zone [19]. In analyzing the tilt variations caused by the ocean load tide, the earth model under the spherically symmetric approximation was chosen, with the load point selected at the pole position. This enables the Green function result for the tilt variations induced by the ocean load tide on the earth's surface (\(r=R_{0}\)) to be simplified as a function of the cosine latitude only [27]. The effects are divided into geometric deformation of the surface and plumbline change due to variations in the gravitational level of the reference point caused by tides [18], denoted as:  
\[T_{FOG}^{\prime}(\theta)=-\frac{1}{m_{e}}\sum_{n=0}^{\infty}{[-h_{n}^{\prime} +l_{n}^{\prime}]\frac{\partial P_{n}(\cos\theta)}{\partial\theta}} \tag{8}\]  
\[T_{VD}^{\prime}(\theta)=-\frac{1}{m_{e}}\sum_{n=0}^{\infty}{[1+k_{n}^{\prime} -l_{n}^{\prime}]\frac{\partial P_{n}(\cos\theta)}{\partial\theta}} \tag{9}\]  
where \(m_{e}\) is the total mass of the earth, \(h_{n}^{\prime}\), \(l_{n}^{\prime}\), \(k_{n}^{\prime}\) is the load Love number, \(P_{n}(\cos\theta)\) is Legendre polynomials. In addition to tidal influences, local environmental changes around the station also cause slight vibrations or geometrical distortion of the local surface of the station. Since it is generated randomly and cannot be simulated by models, it needs to be detected in real time by using a tiltmeter. The tiltmeter can completely detect the tilt variation of the measurement platform, including those induced by tidal effects, as well as local tilt variation resulting from factors such as groundwater changes and human factors [7]. Although tiltmeter measurement includes tilt data, it also includes data reflecting the local plumbline offset:  
\[\theta_{tilt}=\theta_{Def}+\theta_{VD} \tag{10}\]An optical gyroscope is sensitive only to geometric effects and not to changes in plumbline. Therefore, when the tiltmeter is applied, it is necessary to distinguish between the tilt and the local plumbline offset portion. Gravity-induced plumbline changes are then subtracted from the tiltmeter observations to complete the tilt correction of the FOG. Based on the corresponding conversion relationship in the observation equation of Equation (3), the plumbline offset generated at the observation point under the effect of tides can be converted into the amount of angular velocity affecting the FOG. The result is shown in Figure 5. The unit of data is rad/s, while time is in modified Julian day (MJD).