# Towards Improved Inertial Navigation by Reducing Errors Using Deep Learning Methodology
## 3 Results
### Experimental Results for the Remote-Control (RC) Car  
The experiment with the RC car is repeated ten times and the IMU data are collected from both the ESPON and TDK IMUs. For each run, the RC car takes around 3.5 s along the straight path. For both the ESPON and TDK IMU, no calibration method such as a six-position static test is conducted prior to the experiments. Ground truth distances are measured by using a tape ruler. The error bars are the differences between computed distances and ground truths. IMU raw distances are computed by integrating the raw acceleration data collected from IMU. The other distances are computed by using the filtered acceleration data from the CNN algorithms. Tables 6 and 7 demonstrate all experimental results with ground truth distances and error percentages.  
For the EPSON M-G364 PD IMU, an average error of 14.17% is obtained for the CNN with 10 \(\times\) 10 \(\times\) 1 input layer, while 28.33% is obtained for 6 \(\times\) 6 \(\times\) 1 and 30.83% for 3 \(\times\) 3 \(\times\) 1. The error percentages are computed by comparing with the ground truth distances which are measured by using tape ruler. From the results of average error percentages, the CNN with the 10 \(\times\) 10 \(\times\) 1 input layer achieves the highest performance of error reduction. For the TDK ICM-20648 IMU, larger average error percentages are obtained for each CNN. Especially, the CNN with 10 \(\times\) 10 \(\times\) 1 shows the average percentage error up to 169.86%, where the distance results are far more off than the ground truth. For the CNN with  
\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 & 2.74 & 22.26\% & 12.04\% & 23.36\% & 23.36\% \\
2 & 2.18 & 27.52\% & 0.92\% & 31.19\% & 31.65\% \\
3 & 1.28 & 15.63\% & 24.22\% & 2.34\% & 15.63\% \\
4 & 2.15 & 33.02\% & 13.49\% & 27.91\% & 31.63\% \\
5 & 2.02 & 103.47\% & 38.12\% & 55.45\% & 70.30\% \\
6 & 1.78 & 37.08\% & 3.93\% & 48.31\% & 41.01\% \\
7 & 3.21 & 3.43\% & 3.74\% & 9.97\% & 6.23\% \\
8 & 3.39 & 48.67\% & 21.53\% & 50.74\% & 57.82\% \\
9 & 2.25 & 10.67\% & 14.67\% & 1.78\% & 1.78\% \\
10 & 2.11 & 22.27\% & 9.00\% & 32.23\% & 28.91\% \\ \hline Average error & & 32.40\% & 14.17\% & 28.33\% & 30.83\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Distance and percentage error results for EPSON IMU.  
Figure 6: Experimental setups. (**a**) Application of the remote-control car. (**b**) Application of the toy train and track.  
6 \(\times\) 6 \(\times\) 1, we obtained the better average percentage of 62.30% while the 3 \(\times\) 3 \(\times\) 1 CNN obtains 66.19%. For TDK ICM-20648 IMU, the results show that the CNN with the input layer of 6 \(\times\) 6 \(\times\) 1 is the most optimized option, as there are more dynamic and systematic errors contained in the data collected from TDK IMU. In conclusion, we believe that the most optimized input-layer size for CNN is that of 6 \(\times\) 6 \(\times\) 1, as it is best suited for many general applications. We achieved up to 32.5% percentage error improvement in the condition of straight-path motion for TDK ICM-20648 IMU.