## 7 Experiment  
### Calibration Experiment  
Before this calibration experiment was carried out, the temperature calibration for the FOG-based MWD was implemented from 0 \({}^{\circ}\)C to 150 \({}^{\circ}\)C with the thermostat. It makes it so the remaining errors in the FOG-based MWD have nothing with the temperature. The FOG-based MWD was mounted on the three-axis turntable, as shown in Figure 11. Its performance parameters are listed in Table 4. Then, the calibration experiment was carried out according to the calibration path designed in Table 1. The sensors' data was collected and saved during the calibration experiment.  
Then, the nonlinear EKF was utilized to recognize the error item of ACCs and FOGs. Figure 12 illustrates the estimated results of the nonlinear error coefficients by the nonlinear EKF.The estimated results of the bias error for FOG-based MWD are illustrated in Appendix A. The estimated results of the scale factor error and misalignment error (ACCs) are illustrated in Appendix B. The estimated results of the scale factor error and misalignment error (FOGs) are illustrated in Appendix C.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Items** & **Parameters** \\ \hline Size of mounting surface & \(\Phi\)500 mm \\ \hline Flatness of mounting surface & 0.02 mm \\ \hline Biaxial inclination turning error & \(\leq\)\(\pm\)5\({}^{\prime\prime}\) \\ \hline Non-perpendicularity of the two axes & \(\leq\)\(\pm\)5\({}^{\prime\prime}\) \\ \hline Angular resolution & 0.0001\({}^{\circ}\) \\ \hline Angular measurement accuracy & \(\pm\)5\({}^{\prime\prime}\) \\ \hline Angular Measurement repeatability & \(\pm\)1\({}^{\prime\prime}\) \\ \hline Range of Angular rate & 0.01\({}^{\circ}\)/s\(\sim\)360\({}^{\circ}\)/s \\ \hline \hline \end{tabular}
\end{table}
Table 4: The performance parameter of the three-axis turntable.  
Figure 11: The calibration experiments.  
Based on Figure 12, it can be seen that the nonlinear error coefficients all converged to a stable value at the end of the calibration experiment. The nonlinear error coefficients of the X axial ACC, Y axial ACC, and Z axial ACC are \(29.26\times 10^{-6}\) s/m\({}^{2}\), \(20.81\times 10^{-6}\) s/m\({}^{2}\) and \(-28.39\times 10^{-6}\) s/m\({}^{2}\), respectively. The nonlinear error coefficients of the X axial FOG, Y axial FOG and Z axial FOG are \(33.61\times 10^{-6}\) s/rad, \(-189.25\times 10^{-6}\) s/rad and \(6.54\times 10^{-6}\) s/rad, respectively. The recognition results of all the error items are listed below. With the error coefficients, the nonlinear error model could be established. Thus, the error items could be compensated.  
\[\begin{array}{llll}B_{g}=\left[\begin{array}{cc}1.00&0.58&-1.66\end{array} \right]^{T},\mathbf{K}_{g}=\left[\begin{array}{ccc}186.11&0&0\\ -9818.57&-663.73&0\\ 1878.28&100.67&-632.08\end{array}\right],\mathbf{d}_{g}=\left[\begin{array}{cc}3 3.61&-189.25&6.54\end{array}\right]^{T}\\ \\ B_{a}=\left[\begin{array}{cc}-116.39&-1.74&164.89\end{array}\right]^{T},\mathbf{K }_{a}=\left[\begin{array}{cc}14.77&8280.74&690.50\\ -8397.52&99.64&604.28\\ -996.20&472.14&358.00\end{array}\right],\mathbf{d}_{a}=\left[\begin{array}{cc}2 9.26&20.81&-28.39\end{array}\right]^{T}\\ \\ \end{array}\]