## 4 Analysis of the Experimental Results
### Inclined-Sumping Running Positioning Experiments
#### 4.2.2 Analysis of Positioning Results  
The positioning results of Schemes 5-10 are shown in Figure 10. The blue points represent the shearer position estimated by the positioning system, and the gray grid lines are the actual trajectories. It can be clearly seen from the figure that the estimated points can accurately reflect the trajectory of the shearer running, including straight line running, inclined-sumping running, and straight line running after sumping. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Scheme**} & **Heading Angle in Curved Section (\({}^{\circ}\))** & **Angle Error in Curved Section (\({}^{\circ}\))** & **Heading Angle at the Endpoint (\({}^{\circ}\))** & **Angle Error at the Endpoint (\({}^{\circ}\))** \\ \hline No. 5 & \(-\)4.96 & 0.04 & \(-\)0.23 & 0.23 \\ No. 6 & \(-\)4.49 & 0.51 & \(-\)2.82 & 2.82 \\ No. 7 & \(-\)4.53 & 0.47 & 1.76 & 1.76 \\ No. 8 & \(-\)3.62 & 1.38 & \(-\)0.55 & 0.55 \\ No. 9 & \(-\)3. In the straight line running section, the estimated points are distributed around a straight line, reflecting the straight line running characteristics of the shearer, and the absolute value of the error is small. When the shearer is running in the curved section, the estimated points can reflect the position and angle of the turning movement. When the shearer turns, the error between the estimated points and the actual trajectory becomes larger, but the trend of the estimated points can still reflect the shape of the scraper conveyor. After the shearer exits the turning section, the error of the estimated points is larger than that of the initial straight line running section, mainly because the inertial navigation instrument fails to compensate completely. The pulse data output from the odometer for the above six experimental schemes is given in Table 5. It can be seen from the table that the error between the measurement result of the odometer and the actual running distance is small, and thus the odometer is an effective device for measuring the running distance and has very high reliability. Taking Schemes 5 and 6 as examples, comparing the positioning results of different running times of the same trajectory, the following rules are followed. The longer the running time, the larger the positioning error, including the distance error and the angular offset error. The positive and negative of the distance error and the angle error are random  
Figure 10: Results of the inclined-sumping running positioning experiments. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scheme** & **Number of Signals** & **Running Distance (cm)** & **Displacement Error (cm)** \\ \hline No. 5 & 605 & 199.47 & 0.53 \\ No. 6 & 604 & 199.14 & 0.86 \\ No. 7 & 604 & 199.14 & 0.86 \\ No. 8 & 605 & 199.47 & 0.53 \\ No. 9 & 605 & 199.47 & 0.53 \\ No. 10 & 604 & 199.14 & 0.86 \\ Average value & 604.5 & 199.305 & 0.695 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Pulse data output from the Hall sensor. and have nothing to do with the length of the running time. This is because the drift of the inertial instrument and the zero offset of the instrument is different after each startup or operation for a period of time. We know from other studies that the zero offset of inertial instruments will be affected by temperature and vibration [45; 46], an effect which is shown by certain characteristics. But the use of threshold filtering and constant compensation cannot completely eliminate this error. Further research should be done on the filtering method of inertial instruments in future research. From the above experiments, the following can be concluded:  
1. Compared with the current shearer positioning technology, the shearer positioning system in this paper can not only accurately describe the shape of the scraper conveyor, but also provide information such as the sumping position and angle and length of the shearer and can achieve higher precision positioning of the shearer;
2. The random error of inertial navigation instruments cannot be completely eliminated.