## 4 Results and Discussion
The difference between roll and azimuth is that the azimuth angles for the two methods are all affected by the magnetometer error. However, the black curves indicated that the conventional method gradually deviated from the green curves representing the proposed method at pitch angles greater than 85 degrees. Figure 15c,d show that the maximum value of the azimuth errors of the conventional method exceeds 35 degrees. The azimuth error of the proposed method is approximately 5 degrees at the pitch above 85 degrees. The RMSE curves for the azimuth show that the proposed method is more stable at a pitch above 85 degrees. In this paper, we focus on analyzing the attitude accuracy in the near-vertical station. In Table 3, we conclude the attitude angle error data for pitch angles over 85 degrees. M1 indicates the conventional method, and M2 refers to the near-vertical method proposed in this paper. As for the conventional method, the pitch errors from 85 degrees to 89 degrees  
Figure 14: Comparison of roll errors at different attitudes. (**a**) Roll error at azimuth 330\({}^{\circ}\) and roll 0\({}^{\circ}\). (**b**) Roll error at azimuth 330\({}^{\circ}\) and roll 90\({}^{\circ}\). (**c**) Roll error at azimuth 150\({}^{\circ}\) and roll 90\({}^{\circ}\). (**d**) Roll error at azimuth 150\({}^{\circ}\) and roll 180\({}^{\circ}\). have similar results within \(\pm\)0.2\({}^{\circ}\). The proposed method has a pitch accuracy of \(\pm\)0.1\({}^{\circ}\). The maximum roll errors of the conventional method and the near-vertical optimization algorithm are 28.56\({}^{\circ}\) and 0.73\({}^{\circ}\) at a pitch of 89\({}^{\circ}\), respectively. The azimuth errors of the conventional method and the proposed method are 35.4\({}^{\circ}\) and 6.1\({}^{\circ}\) at a pitch of 89\({}^{\circ}\), respectively. As for the conventional method, the mean roll error and azimuth error for a pitch changing from 87 degrees to 88 degrees grows about 6 degrees and 4 degrees, respectively. The average roll error and azimuth angle error for the conventional method increases approximately 12 degrees and 16 degrees from a pitch of 88 degrees to a pitch of 89 degrees, respectively. The proposed method has the average azimuth errors changing from 5.13\({}^{\circ}\) to 5.7\({}^{\circ}\) as the pitch increases from 85\({}^{\circ}\) to 89\({}^{\circ}\). The average attitude error data reveal that the azimuth and roll angle errors calculated by the conventional method will increase rapidly at a pitch close to 90\({}^{\circ}\). The data of the roll errors and azimuth errors suggest that our proposed near-vertical method based on redundant accelerometers can significantly improve the static measurement accuracy in the near-vertical state. The experimental results show that our proposed method can provide a theoretical basis for the borehole attitude measurement method in near-vertical well sections. Figure 15: Comparison of azimuth errors at different attitudes. (**a**) Azimuth error at azimuth 330\({}^{\circ}\) and roll 0\({}^{\circ}\). (**b**) Azimuth error at azimuth 330\({}^{\circ}\) and roll 90\({}^{\circ}\). (**c**) Azimuth error at azimuth 150\({}^{\circ}\) and roll 90\({}^{\circ}\). (**d**) Azimuth error at azimuth 150\({}^{\circ}\) and roll 180\({}^{\circ}\).