## 4 Experimental Results and Analysis
### Analysis of Test Set Results  
In VOIMU, the test set contains twenty-four sets of experiments; the three groups with the best results and the three groups with the worst results are excluded, and nine experimental groups were randomly selected from the remaining test set for index evaluation. Table 2 displays the RBCN-Net evaluation indexes for the nine randomly selected experiments. The trajectory lengths of the nine groups of experiments totaled 1749 m, and the average RMSE and RTE were 2.07 and 1.45%, respectively. It indicates that the errors between the estimated trajectories and the real trajectories are small, all around the meter level, and the trajectory shapes match well. The RMSE and RTE of NO.2 are only 0.763 and 0.561%, which is a difficult positioning accuracy to be achieved by traditional inertial navigation methods [30].  
One more set of experiments was randomly selected among the nine sets for detailed data elaboration. The trajectory length of this experiment is 221.65 m and the time taken is 212.2 s. The raw magnet data of this experiment is shown in Figure 5. With each peak change, the magnetometer data's magnitude varies in a pattern like a wave, and this corresponds to a pedestrian inflection event. In the case of short travel time, the pedestrian attitude obtained by solving the IMU data using the conventional attitude differential equation is closer to the actual attitude [31]. However, as the time increases, the solved heading angle error gradually becomes larger, which eventually makes the solved trajectory  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Validation Set Number** & **Trajectory Length/m** & **RMSE/m** & **RTE** \\ \hline NO.1 & 189 & 1.617 & 1.057\% \\ NO.2 & 156 & 1.405 & 1.005\% \\ NO.3 & 402 & 2.549 & 0.84\% \\ NO.4 & 362 & 2.766 & 1.034\% \\ NO.5 & 112 & 2.336 & 2.346\% \\ NO.6 & 164 & 0.934 & 0.691\% \\ NO.7 & 245 & 1.726 & 1.329\% \\ NO.8 & 338 & 1.918 & 1.514\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Evaluation metrics of the validation set on the model.  
In Figure 7, the starting coordinates are both (0, 0), and the estimated and true end coordinates are \(\widetilde{p}_{end}(-91.32,\,48.81)\) and \(p_{end}(-93.09,\,49.93)\), respectively, with an error of \(2.24\) m between the end coordinates. According to [PERSON]'s first law of motion, the dual integration of the acceleration data is the trajectory length in the ideal case. However, in practice, sensor errors in IMU are unavoidable, and using the direct integration algorithm magnifies the errors exponentially. The estimated and true trajectory lengths of this experiment are \(219.08\) m and \(221.65\) m, respectively, with only \(2.57\) m difference. It indicates that the RBCN-Net completes the learning of dynamic and static error features in the acceleration data. There are some deviations between trajectories in region 1 of Figure 7, however, the trajectories in region 2 almost overlap with small errors, and the deviations are corrected rather than cumulative. The magnitude of the distance error between \(\widetilde{p}_{i}(\widetilde{x}_{i},\widetilde{y}_{i})\) and \(p_{i}(x_{i},y_{i})\) at the same time \(t\) is shown in Figure 8, where the distance error oscillates between \([0,2.5]\), indicating that the RBCN-Net effectively eliminates the inertial navigation system's cumulative error. This experiment has an RMSE of \(1.031\) and an RTE of \(0.603\%\).