## 5 Conclusions
All tested situations, as well as the numerical simulations, showed that the data fusion algorithm produced a reduction in the signal noise power approximately proportional to the number of sensors equipping the cluster. Moreover, for the situations when the sensor biases were not compensated, a fused signal was obtained with a reduced bias due to this statistical combination of the sensor signals. The final tests were reserved for the integrated redundant inertial attitude system. Its testing was performed based on a few sets of experimentally acquired inertial data. In this way, a 3D redundant gyro detection unit was manufactured and used together with an SDINS/GPS integrated navigation system on a testing car to record the needed data. The SDINS/GPS provided the reference solution for attitude angles, keeping in mind that it generates this solution by combining Kalman filter data for both GPS and SDINS navigators. The developed 3D redundant gyro detection unit included twelve MEMS gyros, which were disposed in three clusters with four sensors in each of them, allowing the measurement of \(\omega_{x}\), \(\omega_{y}\), \(\omega_{z}\) angular speeds. For a test sequence of 3 min, the evaluation of the maximum absolute values of the roll, pitch and yaw angle deviations between the attitude reference solution (SDINS/GPS navigator solution) and the attitude solution provided by the proposed redundant attitude system found a value of 0.1468 degrees for the roll angle, a value of 0.0487 degrees for the pitch angle, and 0.6558 degrees for the yaw angle. A similar analysis performed for the non-redundant configuration, which used the information provided by the first gyro in each redundant detection cluster on the IMU axes, led to maximum absolute values of 0.5020 degrees for the deviation in the roll angle, 0.0674 degrees for the deviation in the pitch angle, and 1.1603 degrees for the deviation in the yaw angle, showing a low accuracy compared with the redundant configuration. Therefore, the analysis of each component of the proposed redundant attitude system shows promising benefits for their use in future satellite attitude systems or in the estimation of better values for different variables, measured by using sensor networks in redundant linear configurations. More important were the benefits shown by the redundant attitude system as a whole, which proved an important increase in the level of accuracy of attitude angles calculation when the proposed redundant configuration is used, compared to the situation where a non-redundant configuration is used, but also offer a high degree of redundancy in the evaluation of the three-axis attitude solution for small satellites, in terms of roll, pitch, and yaw angles, by using strap-down inertial techniques. [PERSON] proposed, conceived, modeled and tested the data fusion method variant for inertial navigators, and developed, modeled and simulated the attitude algorithm. [PERSON] and [PERSON] integrated software the redundant attitude system and analyzed its behavior with experimentally acquired data. [PERSON] and [PERSON] performed the bench testing of the attitude algorithm. [PERSON] recorded the experimental data needed for the analysis of each component of the proposed redundant attitude system, but also for analysis of the redundant attitude system as a whole. [PERSON] wrote the original draft and [PERSON] revised and edited the final form. All authors have read and agreed to the published version of the manuscript. This work was supported by CNCSIS-UEFISCDI, project PN II-RU, No. 1/28.07.2010, \"High-precision strap-down inertial navigators, based on the connection and adaptive integration of the nano and micro inertial sensors in low cost networks, with a high degree of redundance\", code TE_102/2010. Not applicable. The datasets presented in this article are not readily available because the work was supported by UEFISCDI--Executive Agency for Higher Education, Research, Development and Innovation Funding in Romania, project PN II-RU, No. 1/28.07.2010.