# Performance Enhancement of Consumer-Grade MEMS Sensors through Geometrical Redundancy
## 5 Experimental Results
### Attitude and Position  
Once the best entries for the process noise covariance matrix are determined, the performance of the prototype has been assessed by a real navigation condition carried out \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Range Values**} & \multicolumn{2}{c}{**Gyroscopes**} & \multicolumn{2}{c}{**Accelerometers**} \\ \cline{2-5}  & **BI** & **ARW** & **BI** & **VRW** \\
**[min-max]** & **[\({}^{\circ}\)/h]** & **[\({}^{\circ}\)/\(\sqrt{\mathbf{h}}\)]** & **[mg]** & **[m/s/\(\sqrt{\mathbf{h}}\)]** \\ \hline X-Axis & 5.7–73 & 0.21–0.25 & 0.05–0.08 & 0.04–0.07 \\ \hline Y-Axis & 5.1–25 & 0.21–0.37 & 0.05–0.09 & 0.05–0.07 \\ \hline Z-Axis & 3–15 & 0.24–0.36 & 0.05–0.1 & 0.04–0.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Variation interval, for each sensing axis, of accelerometer and gyroscope errors affecting the inertial sensors involved in the realized prototype. Figure 10: Allan deviation of gyros, axis \(z\): single SensorTile vs. prototype. Figure 9: Allan deviation of accelerometers, axis \(z\): single SensorTile vs. prototype. on the terrestrial vehicle. In particular, both prototype and reference IMU have experienced an urban path whose GNSS positions, acquired with a sampling period equal to 1s, are shown in Figure 11. According to the proposed method, the measurement setup has been held in stationary conditions for about 60 s to accomplish the ZUPT stage, mandated to the initial bias estimation. Successive GNSS outputs, in terms of position and velocity, have been exploited in the correction stage of the Kalman filter to finely estimate sensor parameters, thus allowing a metrological behavior of the prototype very close to the tactical-grade reference IMU. The first test aimed at assessing the improvement in attitude and position estimation granted by the redundant configuration; for this set of tests, all the available position and speed values of the GNSS have been considered. Heading, pitch and roll provided by both prototype and single SensorTileTM have been compared with the attitude estimates granted by the STIM300; in particular, results shown in Figure 12 are associated with the heading angle, i.e., the one most difficult to be estimated due to observability issues [38; 39]. Even though the prototype outputs appeared to be slower to converge with respect to the reference IMU, it is worth noting the remarkable concurrence experienced for time intervals greater than 400 s. In particular, in the route section referred to as straight in Figure 11, average differences between prototype and STIM300 angle estimates results as low as 0.025 rad have been encountered. On the contrary, heading estimates obtained by means of a single SensorTileTM have proven unreliable and very different from the reference values. Figure 11: Nominal car route travelled in tests for position and attitude estimation. Moreover, with the aim of observing the benefits introduced by the redundancy, the results of the initial leveling procedure described in [5] are shown in Table 5. In particular, the acceleration measures of both single SensorTiles and prototype have been acquired upon an observation interval of 60 s in a stationary condition, and mean values as well as experimental standard deviations of estimated pitch and roll angles have been evaluated highlight the improvement granted by the proposed method. Similar results have also been experienced in tests conducted for position and velocity; for the sake of brevity, the position is only presented in the following. Comparison between the positions estimated through the redundant configuration and those granted by the STIM300 is shown in Figure 13; in particular, the improvement brought by the application of the ZUPT filter can be appreciated in Figure 13. To better appreciate the performance enhancement assured by the realized prototype, a detail of the traveled path is reported in Figure 14, where the considered comparison has also involved the positions estimated by means of a single SensorTileTM.