## 5 Conclusions  
In this paper, an autocorrelation-based CEEMDAN-WTD algorithm is proposed to denoise the static and dynamic signals of the MHD ARS. Firstly, CEEMDAN was used to decompose noisy signal and obtain IMFs, and the autocorrelation of each mode was used to determine the relevant modes. Compared with conventional CEEMDAN, this step could remove ineffective modes in low-frequency and noise IMFs in high-frequency. Then, the autocorrelation of each wavelet coefficient sequence was used to adjust the wavelet threshold. Compared with conventional WTD, this step could remove more noise and retain weak signals. Meanwhile an improved thresholding function was proposed to overcome additional oscillation and reconstruction error in the conventional WTD. Finally, the denoised signal was obtained by combining the denoised relevant modes. Compared with the conventional method, the proposed method could achieve a better denoising effect.  
In the static test, the proposed method outperformed the conventional methods. The quantization noise, angle random walk, and bias instability were effectively reduced. In dynamic test, the proposed method improved the SNR and reduced the RMSE more than conventional methods. The denoised signal produced by the proposed method was smoother. As the rate decreased, the effect of noise on the relevant modes increased, the improved threshold and thresholding function achieved a better denoising effect. The tests verified the effectiveness of the proposed method for denoising the angular vibration signal measured by MHD ARS. The proposed method has good prospects in laser communication, gravitational wave detection, and others. Future work is needed to verify the denoising of the angle vibration signals in the three axes and implement it in hardware.  
Conceptualization, Y.S.; methodology, Y.S., C.M. and J.H.; validation, Y.S.; data curation, Y.S., X.W., Y.W. and Z.J. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Methods** & **Angular Rate (\({}^{\circ}\)/s)** & **RMSE** & **SNR (dB)** & **SNR Gain (\%)** \\ \hline \multirow{3}{*}{Noisy MHD ARS signal} & 0.180, 0.090, 0.054 & 1.912 \(\times\) 10\({}^{-3}\) & 30.7586 & - \\  & 0.135, 0.072, 0.046 & 1.718 \(\times\) 10\({}^{-3}\) & 29.3816 & - \\  & 0.090, 0.054, 0.027 & 1.306 \(\times\) 10\({}^{-3}\) & 28.3960 & - \\ \hline \multirow{3}{*}{CEEMDAN} & 0.180, 0.090, 0.054 & 1.740 \(\times\) 10\({}^{-3}\) & 31.5782 & 2.66 \\  & 0.135, 0.072, 0.046 & 1.457 \(\times\) 10\({}^{-3}\) & 30.8117 & 4.87 \\  & 0.090, 0.054, 0.027 & 1.009 \(\times\) 10\({}^{-3}\) & 30.6355 & 7.89 \\ \hline \multirow{3}{*}{CEEMDAN-Soft Thresholding} & 0.180, 0.090, 0.054 & 1.435 \(\times\) 10\({}^{-3}\) & 33.2485 & 8.09 \\  & 0.135, 0.072, 0.046 & 1.211 \(\times\) 10\({}^{-3}\) & 32.4143 & 10.32 \\  & 0.090, 0.054, 0.027 & 8.126 \(\times\) 10\({}^{-4}\) & 32.5149 & 14.51 \\ \hline \multirow{3}{*}{CEEMDAN-Hard Thresholding} & 0.180, 0.090, 0.054 & 1.683 \(\times\) 10\({}^{-3}\) & 31.8686 & 3.61 \\  & 0.135, 0.072, 0.046 & 1.418 \(\times\) 10\({}^{-3}\) & 31.0493 & 5.68 \\  & 0.090, 0.054, 0.027 & 9.795 \(\times\) 10\({}^{-4}\) & 30.8916 & 8.79 \\ \hline \multirow{3}{*}{Proposed Method} & 0.180, 0.090, 0.054 & 1.329 \(\times\) 10\({}^{-3}\) & 33.9170 & 10.27 \\  & 0.135, 0.072, 0.046 & 1.091 \(\times\) 10\({}^{-3}\) & 33.3205 & 13.41 \\ \cline{1-1}  & 0.090, 0.054, 0.027 & 7.618 \(\times\) 10\({}^{-4}\) & 33.0754 & 16.48 \\ \hline \hline \end{tabular}
\end{table}
Table 5: RMSE and SNR results of MHD ARS mixed-frequency signals.  
**Funding:** This work was supported in part by National Key R&D Program of China, Gravitational Wave Detection Project No. 2022 YFC2203800.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.