## 1 Introduction  
Free space laser communication and gravitational wave detection are the focus of current research in space exploration. They must achieve a stable laser beam link between the spacecraft [1; 2]. Due to the small divergence angle of the laser beam and the narrow receiving field of view [3], the optical system terminal must ensure the precise pointing and tracking of the laser beam. In laser communication, the requirement for laser beam stabilization accuracy is in a few microradians, and in gravitational wave detection, the requirement is in a few \(\mathrm{nrad}/\sqrt{\mathrm{Hz}}\)[4]. Spacecraft harmonic vibrations caused by solar array paddle and reaction wheel are the main source of interference in laser beam stability [5]. Measuring the harmonic vibration of a spacecraft can be used for laser beam stabilization control to achieve precise pointing and tracking [6; 7]. Researchers have done a lot of work in improving laser beam pointing and tracking accuracy to improve the stability of the laser beam link in optical systems. For example, [PERSON] et al., proposed a small laser communication structure mounted in a Magnetohydrodynamic Inertial Reference Unit (MIRU). The MIRU provides fine pointing and stabilization [8], where the magnetohydrodynamic angular rate sensor (MHD ARS) provides the MIRU with the precise platform vibration information required for beam stabilization. MHD ARS can effectively measure the harmonic vibration in the kilohertz bandwidth [9], and its accuracy can reach the nanoradian level. At present, MHD ARS has been applied to some high-precision optical system terminals, such as the Relay Mirror Experiment [10], the Advanced Land Observing Satellite [11], and the Mars Laser Communication Demonstration program [12]. MHD ARS can be combined with gyro and star tracker to form the attitude measurement system. It is the main technical development direction of spacecraft harmonic vibration measurement instruments. However, the amplitude of the harmonic vibration of a spacecraft is typically in the range of a few hundred to a few microradians; then, the induced electromotive force generated by the MHD ARS is only on the order of nanovolt. The weak signal must be amplified to be detected. Noise such as sensor noise, errors caused by analog-to-digital (AD) reference voltage fluctuations, and electromagnetic interference will also be amplified, which seriously affects the detection accuracy. [PERSON] et al. [13] presented a correlation function to measure the noise floor of MHD ARS and proposed a method to predict the drift error using the relationship between the noise floor and drift error. [PERSON] et al. [14] presented an improved Wiener filter to fuse MHD ARS and a low frequency measurement system to reduce the measurement error and noise. [PERSON] et al. [15] presented an adaptive Kalman filter to reduce the low frequency bandwidth error and noise of MHD ARS. These methods require accurate mathematical models and noise characteristics. In recent years, an adaptive signal processing method, Empirical Mode Decomposition (EMD) [16; 17], has been widely studied and has been applied in attitude measurement signal denoising [18]. Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is an improvement on EMD by adding adaptive white noise and calculating a unique residual signal to obtain the intrinsic mode functions (IMFs). CEEMDAN can decompose the signal into IMFs from low to high frequencies in sequence and reduce the reconstruction error [19], but the result contains some noisy IMFs and ineffective IMFs. Therefore, the denoising ability is affected. Researchers proposed some methods for determining the IMFs where the effective signals are located and removing noise that may be contained in some IMFs. [PERSON] et al., presented a method of selecting the relevant modes based on the energy content of each mode and the white noise characteristic [20]. However, logarithmic and integral operations are required in this method.