# Towards Improved Inertial Navigation by Reducing Errors Using Deep Learning Methodology
## 3 Results
### Experimental Results for the Toy Train  
The experiment with the train was conducted ten times. In each experimental run, the train makes three roundtrips and 60 s along the oval track to obtain better repeatability in data collection. No calibration method such as six-position static test is conducted prior to the experiments. The distance results of the motions and the percentage errors are calculated by using the same methods as with the RC car. Train tracks are drawn using IMU raw data, 10 \(\times\) 10 \(\times\) 1, 6 \(\times\) 6 \(\times\) 1, and 3 \(\times\) 3 \(\times\) 1 CNN, as shown in Figures 7 and 8. As shown in Figure 7, the train track drawn with EPSON IMU raw data (red trajectory) is much more erroneous. Compared with the red trajectory, train tracks by 10 \(\times\) 10 \(\times\) 1 (pink), 6 \(\times\) 6 \(\times\) 1 (green) CNN are much closer to the ground truth. As shown in Figure 8, the train track drawn with TDK IMU raw data (red trajectory) is significantly erroneous. Train tracks by 10 \(\times\) 10 \(\times\) 1 (pink), 6 \(\times\) 6 \(\times\) 1 (green) CNN are much closer to the ground truth. For EPSON M-G364 PD IMU, shown in Tables 8 and 9, 3.21% of the average error percentage is obtained for the CNN with 10 \(\times\) 10 \(\times\) 1 input layer, while 5.84% is obtained for 6 \(\times\) 6 \(\times\) 1 and 12.20% for 3 \(\times\) 3 \(\times\) 1, while the average percentage error for IMU raw data is 44.53%. For TDK ICM-20648 IMU, 12.77% of the average error percentage is obtained for the CNN with 10 \(\times\) 10 \(\times\) 1 input layer, while 6.75% is obtained for 6 \(\times\) 6 \(\times\) 1 and 11.25% for 3 \(\times\) 3 \(\times\) 1 and 42.69% for IMU raw data is 44.53%. Tables 8 and 9, show the more stable distance results and less average percentage errors are obtained for the controlled path. By comparing the average percentage errors between the RC car and the toy train, we find that the distances calculated by using CNN-filtered data are much closer to the ground truth, since fewer average percentage errors are achieved. Furthermore, the network input layer size of 6 \(\times\) 6 \(\times\) 1 is still the best network configuration with the least average percentage error. We achieved up to 38.69% percentage error improvement in the condition of oval motion for TDK ICM-20648 IMU as well. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Trial**} & **Ground Truth** & **IMU Raw Error vs.** & **10 \(\times\) 10 \(\times\) 1 CNN Error** & **6 \(\times\) 6 \(\times\) 1 CNN Error** & **3 \(\times\) 3 \(\times\) 1 CNN Error** \\  & **Distance (m)** & **Ground Truth** & **Vs. Ground Truth** & **vs. Ground Truth** & **vs. Ground Truth** \\ \hline
1 & 2.59 & 3.86\% & 172.59\% & 19.69\% & 18.15\% \\
2 & 2.78 & 87.41\% & 170.14\% & 39.21\% & 42.81\% \\
3 & 2.9 & 113.10\% & 161.03\% & 61.38\% & 47.93\% \\
4 & 2.67 & 88.39\% & 188.76\% & 64.04\% & 72.66\% \\
5 & 2.77 & 61.73\% & 100.00\% & 46.93\% & 24.19\% \\
6 & 2.62 & 152.29\% & 140.46\% & 92.37\% & 121.37\% \\
7 & 2.61 & 124.52\% & 205.75\% & 52.49\% & 90.80\% \\
8 & 2.96 & 137.84\% & 217.91\% & 127.03\% & 125.68\% \\
9 & 2.83 & 100.71\% & 198.23\% & 71.02\% & 59.01\% \\
10 & 2.97 & 78.11\% & 143.77\% & 48.82\% & 59.26\% \\ \hline Average error & & 94.80\% & 169.86\% & 62.30\% & 66.19\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Distance and percentage error results for TDK IMU. Figure 8: Two\(-\)Dimensional Train tracks drawn from TDK IMU raw data, \(10\times 10\times 1\), \(6\times 6\times 1\), and \(3\times 3\times 1\) CNN.