## 4 Results Obtained during the Testing of the Redundant Attitude System with Experimental Data
Also, the model provides as outputs the weights (\"w1\" \(\div\) \"w4\") assigned to each sensor in the clusters on the three axes of the IMU. For the \(x\)-axis, the weights are stored in the output vector \"p_w\" of the \"Sensors data fusion x\" block, for the \(y\)-axis are stored in the output vector \"q_w\" of the \"Sensors data fusion y\" block, and for the \(z\)-axis are stored in the output vector \"r_w\" of the \"Sensors data fusion z\" block. Figure 8: Software model for redundant attitude system evaluation with experimental data. A three-minute sequence from an experimentally acquired gyro data set and the fusion results obtained by applying its components on the inputs of the model in Figure 8 (\(p1\div p4\) for the \(x\) detection channel, representing the measurements for \(\omega_{x}\); \(q1\div q4\) for the \(y\) detection channel, representing the measurements for \(\omega_{y}\), and \(r1\div r4\) for the \(z\) detection channel, representing the measurements for \(\omega_{z}\)) are presented in Figure 10.  
The standard deviations of all this data (inputs and fused signals) are shown in Figure 11; in the upper part of the figure, the standard deviations afferent to gyro sensors data are shown, while the lower part depicts the resulting standard deviations for fused signals. Figure 10 shows a reduced noise level in the fused signals comparatively with the experimentally measured data in all three detection channels, confirmed also by the numerical values related to the graphic characteristics of the standard deviations for fused signals presented in Figure 11.  
Figure 8 the attitude solutions provided by the fused signals processing (\"Attitude--fusion\" block), by the reference SDINS/GPS integrated navigator and by the gyro triads formed with the first sensor in each detection cluster data processing (\"Attitude--gyro 1 in clusters\" block) the characteristics in Figure 12 were obtained. The initialization of the \"Attitude\" blocks was realized considering the first values of the attitude angles in the analyzed data sequence provided by the reference SDINS/GPS integrated navigator: initial roll angle = 0.027 degrees, initial pitch angle = 0.051 degrees, and initial pitch angle = 108.103 degrees. Figure 13 presents the graphic results obtained evaluating the roll, pitch and yaw angle deviations (attitude angle errors) between the attitude reference solution (SDINS/GPS navigator solution) and the attitude solutions provided by the proposed redundant attitude system, but also by the non-redundant architecture, which used the information provided by the first gyro in each redundant detection cluster on the IMU axes. The evaluation of the maximum absolute values of these deviations for the proposed system over the analyzed data sequence 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 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. These maximum absolute values of the deviations, but also the characteristics in Figures 12 and 13, 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. Figure 9: Detection unit experimental platform used in the recording of the evaluation data. Figure 10: A sequence from an experimentally acquired gyro data set and the fusion results. Figure 11: Gyro sensors and fused signals standard deviations. Figure 12: Attitude solutions for reference navigator, fused signals (proposed redundant attitude system) and raw signals, obtained for 1 st sensor in each detection cluster. Figure 13: Deviations of the attitude angles from the attitude reference solution.