## 1 Introduction
The singular value decomposition method primarily depends on the correspondence between the information of the signal and the singular value of the reconstruction matrix. The signal component corresponding to the noise is a smaller singular value. By retaining the larger singular values first, the optimal approximation of the original signal can be obtained, and the influence of the noise can be eliminated [15]. However, there are two critical issues to be solved: the first issue is how to determine the effective rank order of the reconstruction matrix, and the second issue is how to determine the number of rows and columns in the reconstruction matrix--which restricts the applications of this method [16]. Recently, the EMD method was introduced for analyzing signals from nonlinear, nonstationary processes, which can adaptively decompose the non-stationary signal into a series of intrinsic mode functions (IMFs), and the decomposed into components containing local characteristic signals of different time scales of the source signal [17]. The EMD de-noising method reduces the influence of noise by eliminating a certain number of low-order IMFs with relatively high frequencies [18]. However, the IMFs decomposed using the EMD method have a mode mixing problem that causes the decomposed IMFs to contain useful components and noise--especially under dynamic conditions. This may cause a loss of precision when using the EMD de-noising method [19]. The ensemble empirical mode decomposition (EEMD) method is an improvement based on the EMDmethod and uses the EMD method as its core, inheriting the advantages of the EMD method [20]. The EEMD method repeatedly decomposes the original signal with added white noise into a series of IMFs and further calculates the ensemble of IMFs to alleviate mode mixing, which has been widely used in the field of signal de-noising [21; 22]. However, the EEMD method is affected by parameters such as the amplitude of added noise and the number of ensemble trials [23]. Moreover, although the EMD and EEMD methods can effectively reduce the influence of the periodic noise [22], it is difficult to reduce the influence of the instantaneous noise, such as the instantaneous vibrations of the equipment itself caused by passing vehicles with a different speed and weight in this study. Unlike the above signal de-noising methods used to reduce the influence of noise from single time-series data individually, the blind source separation (BSS) technique can separate multiple source signals acquired in the same time domain by multiple sensors without any prior information--even when the mixed model of different signals is unknown [24]. BSS has been successfully applied in the fields of wireless communication, image processing, speech signal processing, and biomedical signal processing [25]. The second-order blind identification (SOBI) method is a relatively robust blind source separation method that uses second-order statistics of the sample data (correlation matrix with different time delays) and the source signal time sequence structure feature to achieve blind separation of the source signals [26]. In recent years, the SOBI method has successfully been applied in the fields of signal processing and mechanical fault detection [27; 28]. In this study, we used a new type of ground-based microwave interferometry technology, which uses multi-set time-series displacements of monitored targets in bridges in the same time domain with a distance resolution of up to 0.5 m, using GBSAR. The obtained time-series displacements of the adjacent monitoring points have the same noise information, especially for the noise of the instantaneous vibrations of the equipment itself caused by passing vehicles with a different speed and weight. Generally, the obtained dynamic deflection signal of bridges using GBSAR is a complicated non-stationary time-series displacement that mixes the useful signal with noise.