# Towards Improved Inertial Navigation by Reducing Errors Using Deep Learning Methodology
## 3 Results
### Train and Test for Experimental Results  
After the training and test data are collected, the data are divided into three small step sizes that contain 100, 36, and 9 data points each. To fit each step size of the data, we set different sizes of input layer for the CNN. In other words, we set input layer size of \(10\times 10\times 1\) when feeding data with a step size of 100, size 6 \(\times\) 6 \(\times\) 1 for a step size of 36, and 3 \(\times\) 3 \(\times\) 1 for a step size of 9. Table 2 demonstrates the experimental results with different test accuracies by using acceleration data collected from EPSON M-G364 PD IMU. From the table, 92.67% test accuracy is obtained with network configurations of  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Epson** & **TDK** \\ \hline Gyroscope & & \\ Bias & \(\pm\)0.1 deg/s & \(\pm\)5 deg/s \\ Scale Factor & 0.00375 deg/s & 16.4 deg/s \\ Temperature Coefficient & \(\pm\)0.0005 deg/s/\({}^{\circ}\)C & \(\pm\)0.05 deg/s/\({}^{\circ}\)C \\ Noise Density & 0.002 deg/s/\(\sqrt{\mathrm{Hz}}\) & 0.015 deg/s/\(\sqrt{\mathrm{Hz}}\) \\ Angular Random Walk & 0.09 deg/\(\sqrt{\mathrm{Hz}}\) & 0.9 deg/\(\sqrt{\mathrm{Hz}}\) \\ Accelerometer & & \\ Bias & \(\pm\)5 mG & \(\pm\)25 mG \\ Scale Factor & 0.125 mG & 2.048 mG \\ Temperature Coefficient & \(\pm\)0.02 mG/\({}^{\circ}\)C & \(\pm\)0.80 deg/s\({}^{\circ}\)C \\ Noise Density & 0.06 mG/\(\sqrt{\mathrm{Hz}}\) & 0.23 mG/\(\sqrt{\mathrm{Hz}}\) \\ Velocity Random Walk & 0.025 (m/s)/\(\sqrt{\mathrm{Hz}}\) & 0.13 (m/s)/\(\sqrt{\mathrm{Hz}}\) \\ Output Data Rate & Up to 2 kHz & Up to 1 kHz \\ \hline \hline \end{tabular}
\end{table}
Table 1: Specifications EPSON and TDK IMUs.  
Figure 5: Collections of acceleration and angular velocity levels: (**a**) 121 acceleration levels collected from IMU; (**b**) 91 angular velocity levels collected from IMU.  
\(10\times 10\times 1\) input size. Test accuracy decreases to 80.95% when reducing the input data size to \(3\times 3\times 1\). Table 3 lists the experimental results with testing accuracies by using data collected from TDK ICM-20648 IMU. From the results in Table 3, TDK ICM-20648 IMU achieves relatively higher test accuracy for the \(10\times 10\times 1\) input layer size, while \(3\times 3\times 1\) has the lowest test accuracy. When comparing the test accuracies with the same input size of each network, TDK ICM-20648 IMU data shares similar test accuracies but requires more training epochs. The reason for such trends of test accuracies is that the smaller the input-size of the network, the less information in each step size is available to the network for training. By comparing the test accuracies with validation accuracies, the CNN with \(6\times 6\times 1\) is considered a well-fitted model since both accuracies are closed with each other, while CNNs with \(10\times 10\times 1\) and \(3\times 3\times 1\) are over fitted since the test accuracies are less than validation.  
Tables 4 and 5 demonstrate all experimental results with different test accuracies by using angular velocity data collected from IMU units. From the table, up to 98.90% test accuracy is obtained with network configurations of \(10\times 10\times 1\) input size. Test accuracies decrease much less than those test accuracies for acceleration. Most of the test accuracies for angular velocities are more than 90%, while some of the test accuracies for accelerations are less than 90% for accelerations.