## 4 Analysis of the Experimental Results  
### Straight-Line Running Positioning Experiments  
In the straight line running positioning experiment, we deployed four schemes according to different running times (37, 28, 22, and 12 s, respectively). According to Formula 4, we can get the positioning results of the shearer, but we need to process the experimental data through the Kalman filter in 3.3 firstly, and zero bias compensation and 10-point smoothing preprocessing are also used to process the experimental data. Figure 7 shows a comparison of the shearer coordinate distribution obtained by using the original data and after error compensation. During the experiment, the odometer received a pulse signal output from the Hall sensor, and each pulse represented a distance of 0.3297 cm. The pulse data output from the odometer for the above four experimental schemes is given in Table 1. Because the shearer undergoes linear motion during the experiment, the trajectory equation of the shearer is Y = 0 (0 \(\leq\) X \(\leq\) 2). The positioning errors of the final point under different motion times are listed in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scheme** & **Number of Signals** & **Running Distance (cm)** & **Displacement Error (cm)** \\ \hline No. 1 & 601 & 198.15 & 1.85 \\ No. 2 & 604 & 199.14 & 0.86 \\ No. 3 & 603 & 198.81 & 1.19 \\ No. 4 & 603 & 198.81 & 1.19 \\ Average value & 602.75 & 198.73 & 1.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Pulse data output from the Hall sensor. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scheme** & **Endpoint Coordinates** & **Running Distance Error (cm)** & **Angle Error (\({}^{\circ}\))** \\ \hline No. 1 & (2.03,\(-\)0.01) & 3 & \(-\)0.04 \\ No. 2 & (1.89,\(-\)0.01) & 11 & \(-\)0.25 \\ No. 3 & (2.04,0.01) & 4 & 0.02 \\ No. 4 & (1.95,\(-\)0.01) & 5 & \(-\)0.03 \\ Average value & — & 5.8 & 0.085 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Error statistics from the straight line running positioning experiment. Through the straight line running positioning experiment, the following can be concluded:  
1. The estimated points of the integral calculation after error compensation accurately reflect the linear operation characteristics of the shearer. By comparing the positioning results obtained before and after compensation, it can be seen that, after 10-point smoothing preprocessing, zero bias compensation, and Kalman filter compensation of the output gyroscope and accelerometer data, the validity of the data increases greatly, and the error is significantly reduced. The position of the shearer estimated by the positioning system surrounds the actual trajectory;
2. The error of the position point on the X axis is greater than that on the Y axis. The maximum error measured along the direction of the shearer movement is 0.11 m. Therefore, there is an error in measuring the displacement of the shearer by relying solely on the accelerometer. The error is mainly related to the working principle of the instrument. The data measured by the accelerometer needs to be integrated twice to obtain the distance information. In practice, the map-matching technique can be used for correction;
3. The displacement accuracy measured by the odometer is higher than that of the accelerometer. The displacement measured by the odometer is less than the actual displacement. The main reason for this error is the slip between the walking wheel and the track. Moreover, slip is less likely to occur on the chainless shearer, so the odometer has higher reliability and can correct the acceleration integral result;  
Figure 7: Comparison of the shearer coordinate distribution obtained by original data and error compensation. 4. The number of isolated points is proportional to the running time. By comparing the four experimental schemes, it can be found that the longer the running time, the greater the number of isolated points and the greater the absolute value of the discrete quantities.