## 2 Estimation of Joint Motion Intention Based on sEMG  
### sEMG Signal Pre-Processing  
Aiming at issues such as the noise interference of the original sEMG signal and the sampling rate not being aligned, signal preprocessing was conducted in this study. First, since the sEMG signal was very weak, it needed to be amplified 1000 times after acquisition. In addition, in order to filter out noise signals outside the effective energy band, filtering was required. According to the characteristics of the sEMG signal, the IIR-type Butterworth filter was selected in this study to remove the information outside the frequency band of the sEMG effective energy, and then the ideal frequency domain response curve could be obtained. The filter gain \(G\) (\(\omega\)) is  
\[G^{2}(\omega)=|H(j\omega)|^{2}=\frac{G_{0}^{2}}{1+\left(\frac{\omega}{\omega_ {c}}\right)^{2n}} \tag{1}\]  
where \(n\) is the order of the filter, \(G_{0}\) is the DC gain coefficient, and \(\omega_{c}\) is the cut-off frequency. Relevant parameters are set to complete the filter design. The time-domain waveform and unilateral spectrum of the sEMG signal after filtering are shown in Figure 1. Since the filtering was mainly for frequency interception, the amplitude before and after filtering was basically unchanged, the filtered signal had fewer burrs, the high- and low-frequency signals were basically filtered out, and the signal energy was concentrated within 500 Hz. It can be observed that there was still 50 Hz power frequency interference in the sEMG signal. There are many ways to solve such problems, but relevant information will be lost after removal. Therefore, this study did not manage the power frequency interference. Figure 1: sEMG characteristics with a filter: (**a**) amplitude comparison and (**b**) spectrum comparison. Since the order of magnitude of each eigenvalue was different, in order to ensure the consistent input distribution and speed up the model calculation and convergence speed, the maximum and minimum method was used to complete the normalization process and the eigenvalue \(x_{i}\) was normalized between the values \([-1,1]\) using  
\[x_{i}^{\prime}=-1+\frac{2(x_{i}-x_{\text{min}})}{x_{\text{max}}-x_{\text{min}}} \tag{2}\]  
where \(x_{i}^{\prime}\) is the normalized value and \(x_{\text{max}}\) and \(x_{\text{min}}\) are the maximum and minimum values of the eigenvalues of the normalization process, respectively. The processed signal had redundant information and could not be directly used to identify human motion intentions. In order to further improve the prediction speed, accuracy, robustness, and generalization of the model, it was necessary to convert the original EMG signal into a set of eigenvalues that could clearly represent the physical quantities of joint motion. According to the literature [24], the eigenvalues that have a greater influence on the prediction and the eigenvalues that are not sensitive to electrode offset are selected, and then the feature space is constructed to improve the robustness of the system. The root-mean-square (\(RMS\)) signal wavelength (\(WL\)), zero crossing (\(ZC\)), and attitude acceleration eigenvalues were selected as the eigenvalues of this study, and the mixed vector was formed with attitude angle. 1. The \(RMS\) reflects the validity of the signal, which is expressed as \[RMS=\sqrt{\frac{1}{N}{\sum_{i=1}^{N}{x^{2}(i)}}}\] (3) where \(x(i)\) is the sEMG amplitude sampling sequence and \(N\) is the number of sampling points in the moving sliding window; in this study, \(N\) was 256. 2. The \(WL\) reflects the degree of cumulative change of the sEMG during a period, which is expressed as \[WL=\sum_{i=1}^{N-1}{|x(i+1)-x(i)|}\] (4)
3. The \(ZC\) points are the number of crossings between the amplitude of the sEMG signal and a certain coordinate threshold, which represent an approximate estimation of the frequency domain characteristics as \[ZC=\sum\limits_{i=1}^{N-1}{|\text{sgn}(-x_{i}x_{i+1})|}\cap{|x_{i}-x_{i+1}|} \geq\text{threshold}\] (5) \[\text{sgn}(x)=\left\{