## 4 Experimental Platform and Result Analysis
### Dynamic Test Analysis
\[RMSE=\sqrt{\frac{1}{N}\sum_{k=1}^{N}(x(k)-\overline{x}(k))^{2}} \tag{22}\]  
\[SNR=10\lg\left(\frac{P_{S}}{P_{N}}\right) \tag{23}\]  
where \(x(k)\) is the true vibration signal of the turntable, \(\overline{x}(k)\) is the denoised signal. \(P_{S}\) is the signal power, and \(P_{N}\) is the noise power. In Tables 2-4, the RMSE and SNR of vibrations of different angular rates at three frequencies are shown. The RMSE is reduced by 46.58%, and the SNR is improved by 32.75% for the 0.025\({}^{\circ}\)/s signal at 15 Hz. The proposed method has the lowest RMSE and the highest percentage of SNR gain for different rates of angular vibration signals at each frequency. It is observed that as the rate decreases, the percentage of SNR gain increases in the improved algorithm. This is because as the rate decreases, the effect of noise on the relevant modes increases. The improved threshold and thresholding function can be used to better advantage. The harmonic vibration of a spacecraft has high-frequency with low amplitude and low-frequency with high amplitude characteristics [37; 38]. To further verify the effectiveness of the proposed method in denoising the MHD ARS dynamic signal, we acquired mixed-frequency angular vibration signals with different amplitudes at 5 Hz, 10 Hz, and 15 Hz. Figure 12: \(R_{RMS}\) of the IMFs of the 0.100\({}^{\circ}\)/s signal at 15 Hz. As shown in Figure 13, the mixed-frequency signal with high amplitude consists of the high amplitude of each frequency. At 5 Hz, the amplitudes of the angular vibrations are 100 \(\upmu\)rad, 75 \(\upmu\)rad, and 50 \(\upmu\)rad, the corresponding angular rates are 0.180\({}^{\circ}\)/s, 0.135\({}^{\circ}\)/s, and 0.090\({}^{\circ}\)/s. At 10 Hz, the amplitudes of the angular vibrations are 25 \(\upmu\)rad, 20 \(\upmu\)rad, and 15 \(\upmu\)rad, the corresponding angular rates are 0.090\({}^{\circ}\)/s, 0.072\({}^{\circ}\)/s, and 0.054\({}^{\circ}\)/s. At 15 Hz, the amplitudes of the angular vibrations are 10 \(\upmu\)rad, 8.5 \(\upmu\)rad, and 5 \(\upmu\)rad, the corresponding angular rates are 0.054\({}^{\circ}\)/s, 0.046\({}^{\circ}\)/s, and 0.027\({}^{\circ}\)/s. The proposed method has a smoother denoising effect on the mixed-frequency signal with a high amplitude, as shown in Figure 13. Figures 14 and 15 show the IMFs of the mixed-frequency signal with a high amplitude and the \(R_{RMS}\) of the relevant modes. The signal is decomposed into multiple modes. Mode mixing occurs in the relevant modes, as shown in Figure 14, which results in a larger magnitude of IM8 than the other relevant modes. Noise in the relevant mode IMF6 can be observed. Figure 13: Denoising results of MHD ARS mixed-frequency signal with high amplitude. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Methods** & **Angular Rate (\({}^{\circ}\)/s)** & **RMSE** & **SNR (dB)** & **SNR Gain (\%)** \\ \hline \multirow{4}{*}{Noisy MHD ARS signal} & 0.100 & \(1.615\times 10^{-3}\) & 25.8416 & - \\  & 0.050 & \(1.717\times 10^{-3}\) & 19.2888 & - \\  & 0.025 & \(1.165\times 10^{-3}\) & 16.6340 & - \\ \hline \multirow{4}{*}{CEEMDAN} & 0.100 & \(1.419\times 10^{-3}\) & 26.9644 & 4.34 \\  & 0.050 & \(1.140\times 10^{-3}\) & 22.8417 & 18.42 \\  & 0.025 & \(8.549\times 10^{-4}\) & 19.3249 & 15.64 \\ \hline \multirow{4}{*}{CEEMDAN-Soft Thresholding} & 0.100 & \(1.294\times 10^{-3}\) & 27.7629 & 7.43 \\  & 0.050 & \(1.140\times 10^{-3}\) & 22.8421 & 18.42 \\  & 0.025 & \(8.548\times 10^{-4}\) & 19.3252 & 16.18 \\ \hline \multirow{4}{*}{CEEMDAN-Hard Thresholding} & 0.100 & \(1.405\times 10^{-3}\) & 27.0507 & 4.68 \\  & 0.050 & \(1.131\times 10^{-3}\) & 22.9154 & 18.80 \\  & 0.025 & \(8.507\times 10^{-4}\) & 19.3676 & 16.43 \\ \hline \multirow{4}{*}{Proposed Method} & 0.100 & \(1.198\times 10^{-3}\) & 28.4383 & 10.05 \\  & 0.050 & \(8.862\times 10^{-4}\) & 25.0325 & 29.78 \\ \cline{1-1}  & 0.025 & \(6.224\times 10^{-4}\) & 22.0809 & 32.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: RMSE and SNR results of MHD ARS signals at 15 Hz. 16.48% for mixed-frequency signals with a high amplitude.