# Towards Improved Inertial Navigation by Reducing Errors Using Deep Learning Methodology
## 5 Conclusions  
This paper examined the extended design of an error-reduction method for MEMS IMUs. Compared with traditional error-removal processes, our approach succeeded in removing errors from various grades of IMUs applicable to consumer and industrial applications. We achieved a test accuracy of 92.67% in correctly identifying the accelerometers for the high-grade IMU and 91.61% for the low-grade IMU. Meanwhile we achieved a test accuracy of 98.90% in the high-grade IMU's gyroscopes and 97.93% in the low-grade IMU's gyroscopes. In addition, we achieved up to 32.5% percentage error improvement in the condition of straight-path motion and up to 38.69% percentage error improvement in the condition of oval motion compared with the ground truth. This study shows that CNNs are capable of reducing both systematic and stochastic errors for the IMUs without the aid of external measurement sources such as GNSS over short time durations. Furthermore, the results of this study could be implemented in an ultra-low power hardware to remove the errors of IMUs in real time.  
Conceptualization, H.C., T.M.T. and V.P.C.; methodology, H.C., T.M.T. and V.P.C.; software, H.C.; validation, H.C.; formal analysis, H.C. and V.P.C.; investigation, H.C. and V.P.C.; resources, T.M.T. and V.P.C.; data curation, H.C.; visualization, H.C.; supervision, V.P.C.; project administration, V.P.C.; writing--original draft preparation, H.C.; writing--review and editing, T.M.T. and V.P.C. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Trial** & \begin{tabular}{c} **Ground Truth** \\ **Distance (m)** \\ \end{tabular} & \begin{tabular}{c} **IMU Raw Error vs.** \\ **Ground Truth** \\ \end{tabular} & \begin{tabular}{c} **10 \(\times\) 10 \(\times\) 1 CNN Error** \\ **vs. Ground Truth** \\ \end{tabular} & \
\begin{tabular}{c} **6 \(\times\) 6 \(\times\) 1 CNN Error** \\ **vs. Ground Truth** \\ \end{tabular} &
\begin{tabular}{c} **3 \(\times\) 3 \(\times\) 1 CNN Error** \\ **vs. Ground Truth** \\ \end{tabular} \\ \hline
1 & 15.89 & 48.52\% & 16.43\% & 11.77\% & 13.78\% \\
2 & 15.92 & 43.22\% & 11.56\% & 7.79\% & 12.19\% \\
3 & 16.20 & 40.25\% & 12.84\% & 5.74\% & 7.53\% \\
4 & 15.22 & 45.73\% & 18.00\% & 7.10\% & 8.94\% \\
5 & 15.91 & 41.04\% & 13.45\% & 10.25\% & 13.95\% \\
6 & 16.15 & 35.05\% & 10.90\% & 3.34\% & 10.65\% \\
7 & 15.78 & 43.85\% & 9.82\% & 1.77\% & 13.05\% \\
8 & 16.22 & 40.14\% & 12.33\% & 6.84\% & 8.57\% \\
9 & 15.76 & 44.42\% & 11.48\% & 6.41\% & 12.31\% \\
10 & 15.68 & 44.71\% & 10.84\% & 6.51\% & 11.54\% \\ \hline Average error & & 42.69\% & 12.77\% & 6.75\% & 11.25\% \\ \hline \hline \end{tabular}
\end{table}
Table 9: Distance and percentage error results for TDK IMU.  
**Funding:** This research was funded by the School of Engineering at University of Dayton.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Research data presented in this article are available on request from the corresponding author with appropriate justification.  
**Acknowledgments:** The authors would like to thank [PERSON] for her help with explaining IMU mechanization and calibration methods.  
**Conflicts of Interest:** The authors declare no conflict of interest.