## 5 Experimental Verification
### The Virtual Velocity Loop with the FDOB  
Figure 11 presents the time-domain waves of the virtual gyro in different frequencies and we also present a group of signals of the fiber-optic gyro (FOG) (XW-FG70-20, Starneto, Beijing, China) as a comparison. The signal of the virtual gyro has a negligible phase lag and is very close to the real FOG's. It means the frequency-domain fusion is much better than the time-fusion fusion in Reference [14], which would lead to the signal's big phase lag at a relatively high frequency. Figure 12 shows the open-loop bode responses of the velocity from the FOG and virtual gyro. The identified transfer functions are as Equations (32) and (33). Their models are the same but the parameters are somewhat different.  
Figure 11: Time-domain wave of the FOG and virtual gyro. (**a**) \(1\,\mathrm{Hz}\) sine wave, (**b**) \(10\,\mathrm{Hz}\) sine wave, (**c**) \(50\,\mathrm{Hz}\) sine wave.  
Figure 10: The improvement of DS brought by EDOB and FDOB.  
\[\widetilde{G}_{v}(s)=\frac{2.3s}{0.0072s^{2}+0.0202s+1}\cdot\frac{1}{0.0005s+1} \tag{32}\]  
\[\widetilde{F}_{v}(s)=\frac{1.8s}{0.000489s^{2}+0.02873s+1}\cdot\frac{1}{0.0004s+1} \tag{33}\]  
From the open-loop transfer functions, although the resonant frequency and damping coefficient of the virtual gyro has changed, its bandwidth is very high and fits the closed-loop feedback control. Now, the ADLC feedback control has turned to be the TLC structure. \(C_{a}\) and \(C_{f}\) could be the same as the previous design. Since the inner acceleration loop has improved the platform's characteristics, we can both use a low-pass filter as the velocity controller \(C_{v}\) and the position controller \(C_{p}\).  
\[C_{v}=0.15\cdot\frac{1}{1+0.00077s},\ C_{p}=12\cdot\frac{1}{1+0.0005s} \tag{34}\]  
Figure 13 shows the comparison of the DS with different fusion methods. Compared with the ADLC method enhanced by FDOB, the introduction of the virtual velocity loop with the time-domain fusion method in Reference [14] can enhance the low-frequency DS a little but the medium-frequency DS would decrease because of the CCD's time delay. However, the virtual velocity loop based on the frequency-domain fusion could apparently improve the low- and medium- frequency DS. Although the virtual velocity loop cannot enhance the high-frequency DS, it does not matter because it commonly relies on the mechanical design. In total, after fusing the sensors' data twice, the performance of the sensors has been fully utilized and we have obtained a satisfied system with extremely strong DS.  
Figure 14 presents the DS's comparison of the proposed method and Reference [14]. Figure 15 displays the residual stabilization errors of the two methods in different frequencies. Obviously, whether in frequency domain or time domain, the promotion is very big and could reach 10 dB in low and medium frequency, which means we have succeeded in further enhancing the system's DS.  
Figure 12: The open-loop bode responses of the velocity. (**a**) \(\widetilde{G}_{v}\) based on the FOG; (**b**) \(\widetilde{F}_{v}\) based on the virtual gyro.  
Figure 14: The DS’s comparison of Reference [14] and the proposed way.  
Figure 13: The comparison of DS with time-domain and frequency-main fusion methods.  
Figure 15: The residual stabilization errors in different frequencies.