## 4 Simulations and Experiments
### Experiments
#### 4.2.2 Experiment Results  
Experiment results include two parts. The first part is static experiment which mainly shows the influence of gyro drift and maneuvering acceleration interference on attitude estimation. The second part is dynamic experiment which mainly shows the advantages of the proposed method in gyro drift and maneuvering acceleration interference restraint and phase compensation. In the experiment, the motion carrier switched between moving state and stationary state and the 3-axis angular attitude are tested for 5 min. In order to show the results clearly and limited by page length, the data were collected for 10 to 15 s.  
In the static experiment, the STD of the corresponding output of accelerometer is shown in Figure 10a and the angular attitude comparison in roll direction is shown in Figure 10c. The STD of the corresponding output of accelerometer is shown in Figure 10b and the angular attitude comparison in pitch direction is shown in Figure 10d. It can be seen from the partial enlarged detail of Figure 10a,b that when the maneuvering acceleration exists, the STD of the accelerometer output data changes greatly and fast. As can be seen from the partial enlarged detail of Figure 10c,d, a cumulative error exists in the angular calculated by the gyro due to the influence of zero drift. The roll and pitch angular attitude drift error reaches 1.649\({}^{\circ}\) and 0.544\({}^{\circ}\) in 9 s, respectively. Due to the adverse effect of maneuvering acceleration on the output signal of accelerometer, there is an obvious error in the angular attitude calculated by DFBGA. The maximum error value of roll and pitch angular attitude reaches 54.53\({}^{\circ}\) and 19.31\({}^{\circ}\), respectively. The signal with such error will seriously affect the performance of the control system. Consequently, it is necessary to adopt the attitude measurement algorithm to suppress maneuvering acceleration. In dynamic experiment, the STD of the corresponding output of accelerometer is shown in Figure 11 and the angular attitude comparison in roll direction is shown in Figure 12. The STD of the corresponding output of accelerometer is shown in Figure 12 and the angular attitude comparison in pitch direction is shown in Figure 12. The angular attitude comparison in yaw direction is shown in Figure 12.  
The angular attitude calculated by DFBGA and SLAIM has the ability to suppress gyro drift and maneuvering acceleration disturbance and there is no obvious noise. However, phase lag error will be introduced in the attitude estimation process based on Kalman filter. The angular attitude calculated by proposed method can restrain the phase lag and smooth the waveform. The proposed method is robust because it can accurately calculate the angular attitude in the presence of gyro drift noise and maneuvering acceleration disturbance. Calculate the RMSE between the 3-axis angular attitude calculated by gyro, DFBGA, DFBGA, and SLAIM, the proposed method and the 3-axis angular attitude calculated by encoder according to Equation (28). Compared with the angular attitude calculated by gyro, the RMSE of the angular attitude calculated by DFBGA and SLAIM in roll, pitch, and yaw attitude decreased 26.84%, 33.53%, and 24.23%, respectively. The RMSE of the angular attitude calculated by the proposed method in roll, pitch, and yaw attitude decreased 44.23%, 49.91%, and 46.21%, respectively. Compared with the angular attitude calculated by DFBGA, the RMSE of the angular attitude calculated by DFBGA and SLAIM in roll, pitch attitude decreased 37.69% and 28.53%, respectively. The RMSE of the angular attitude calculated by the proposed method in roll and pitch attitude decreased 52.50% and 86.84%, respectively. Figure 11: STD of X and Y axes acceleration corresponding to roll angle. Figure 10: Comparison of static experimental results: (**a**) STD of acceleration corresponding to roll attitude. (**b**) STD of acceleration corresponding to pitch attitude.