## 4 Results Obtained during the Testing of the Redundant Attitude System with Experimental Data  
Once verified all algorithms and software components were included in the proposed inertial redundant attitude system, a global validation software model was conceived in Matlab/Simulink (Figure 8). It puts together the data fusion mechanism for all three redundant clusters of gyros, used on the \(x\), \(y\) and \(z\) axes of the IMU, with the attitude calculation mechanism starting from the fused data provided by each cluster. In the same model, the attitude calculation mechanism takes data from four groups by three gyros disposed on the IMU axes (in each group is one gyro from each redundant cluster), which generates inputs that are then fused. The testing of the integrated system 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 (Figure 9). 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. Our 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. The model in Figure 8 includes three \"Sensors data fusion\" blocks, one for each detection channel, and five \"Attitude\" blocks supplied with signals from the \"Sensors data fusion\" blocks outputs (\"Attitude--fusion\" block supplied with _pf_, _pf_ and _rf_ fused signals, which are the fused values obtained for the angular speed components in body frame \(\omega_{x\_{-}f}=pf\), \(\omega_{y\_{-}f}=qf\), \(\omega_{z\_{-}f}=rf\)), and from the four gyro triads formed with the \(i\)-th sensor in each detection cluster, \(i=1\) to 4 (\"Attitude--gyro 1 in clusters\"--supplied with the measured components of the angular speed in body frame \(\omega_{x\_1}=p1\), \(\omega_{y\_1}=q1\), \(\omega_{z\_1}=r1\), \"Attitude--gyro 2 in clusters\"--supplied with the measured components of the angular speed in the body frame \(\omega_{x\_2}=p2\), \(\omega_{y\_2}=q2\), \(\omega_{z\_2}=r2\), \"Attitude--gyro 3 in clusters\"--supplied with the measured components of the angular speed in the body frame \(\omega_{x\_3}=p3\), \(\omega_{y\_3}=q3\), \(\omega_{z\_3}=r3\), and \"Attitude--gyro 4 in clusters\"--supplied with the measured components of the angular speed in the body frame \(\omega_{x\_4}=p4\), \(\omega_{y\_4}=q4\), \(\omega_{z\_4}=r4\)). Thus, the model allows the evaluation of the attitude starting from the fused signals and from the four gyro triads with perturbed angular speed signals. In the model is also added the reference attitude angles provided by the SDINS/GPS integrated navigator (_phi_--roll, _theta_--pitch, _psi_--yaw). In addition to the six sets of attitude angles included in the output vectors \"roll\", \"pitch\" and \"yaw\", the model in Figure 8 allows the evaluation of the standard deviations for all sensors implied in the detection mechanism, but also for the fused signals obtained from the sensor clusters placed on all three axes of the IMU. For the \(x\)-axis of redundant IMU, the standard deviations of the sensors (\"std1\" \(\div\) \"std4\") and of the fused signal (\"fused signal std\") are stored in the output vector \"p_std\" of the \"Sensors data fusion x\" block; for the \(y\)-axis, the standard deviations of the sensors (\"std1\" \(\div\) \"std4\") and of the fused signal (\"fused signal std\") are stored in the output vector \"q_std\" of the \"Sensors data fusion y\" block, and for the \(z\)-axis, the standard deviations of the sensors (\"std1\" \(\div\) \"std4\") and of the fused signal (\"fused signal std\") are stored in the output vector \"r_std\" of the \"Sensors data fusion z\" block.