## 4 Experimental Study and Discussion
### Experimental Results  
To better evaluate the performance of the proposed SSM, different evaluation criteria including the correlation coefficient (CC), root mean square error (RMSE), and the goodness of fit in terms of normalized mean square error (NMSE) are utilized. The goodness of fit in terms of NMSE is abbreviated as FIT in the following. The Pearson CC of predicted values \(\hat{x}\) and actual values \(x\) in terms of the covariance of \(\hat{x}\) and \(x\) is defined as:  
\[cc(\hat{x},x_{k})=\frac{cov(\hat{x},x)}{\sigma_{\hat{x}}\sigma_{x}} \tag{27}\]  
where \(\sigma_{\hat{x}}\) and \(\sigma_{x}\) are the standard deviation of \(\hat{x}\) and \(x\), respectively. The RMSE of predicted values \(\hat{x}\) with actual values \(x\) for \(T\) different predictions is given by:  
\[RMSE=\sqrt{\frac{1}{T}\sum_{1}^{T}(\hat{x}_{k}-x_{k})^{2}} \tag{28}\]  
The cost function of the goodness of fit is chosen as NMSE in our application:  
\[FIT=1-\frac{\|x-\hat{x}\|^{2}}{\|x-mean(x)^{2}\|} \tag{29}\]  
One typical segment of experimental results of Subject 1 (abbreviated as S1) using the proposed SSM is illustrated in Figure 10.  
Referring to Figure 10a, the muscle activation could be well represented by the extracted EMG feature acquired from the energy kernel method. In addition, clear mapping relations could be observed between the interactive force and the joint angle. It also proved the rationality and necessity to include interactive force in the proposed model for the improvement of joint prediction performance. The joint angle and angular velocity prediction performance comparisons between the SSM and their actual values are illustrated in Figure 10b,c. A [PERSON] signed rank test was used to calculate the corresponding \(p\)-value. As can be seen, although there existed local biases, the predicted values of both the angle and angular velocity could approximate their actual values well. Judging from different evaluation criteria, the SSM performances of the angle prediction were as follows: the CC was 0.9944, the RMSE was 0.0433 and the FIT was 0.9881 (\(p<1\times 10^{-3}\)). The SSM prediction performances of the angular velocity were as follows: the CC was 0.9890, the RMSE was 0.0215 and the FIT was 0.9750 (\(p=0.0034\)). It could be found that the prediction performances were satisfactory, which reflected the feasibility and effectiveness of the proposed method. Figure 9: The BPNN for performance comparison with the SSM, where \(\omega_{1,p}\) and \(\omega_{2,p}\) are the weights, \(b_{1,p}\) and \(b_{2,p}\) are the bias values. Different from the BPNN for the measurement model of SSM, the input vector \(x_{k}\) whose dimension is 2 contains the extracted EMG feature and the interactive force, and the output vector \(y_{k}\) whose dimension is 2 contains the joint angle and angular velocity, and 2, 5 and 2 are the numbers of the neurons. The same group of data from S1 was also processed with the traditional BPNN whose structure is illustrated in Figure 9. The joint prediction performance comparison is shown in Figure 11a. It could be found that the angle prediction of BPNN could still approximate the actual joint angle. However, compared with the results acquired from the proposed SSM, performances acquired from BPNN were worse when the CC was 0.9727 (decreased by 2.18%), the FIT was 0.9264 (decreased by 6.24%),  
Figure 10: A typical set of experimental results. (**a**) The raw EMG signals from RF, the extracted energy kernel feature (EK), the interactive force, the actual angle and the predicted angle are listed from top to bottom; (**b**) The results of predicted and actual joint angle; (**c**) The results of predicted and actual joint angular velocity. and the RMSE increased to 0.1077 from 0.0433 (\(p<1\times 10^{-5}\)). Although the overall prediction trend of BPNN was consistent with the actual angle variation when both the FIT and CC were acceptable, visible fluctuations could not be overlooked in Figure 11a.