## 4 Experimental Study and Discussion
### Further Discussions  
Another issue that has to be made clear is whether the loads on the knee joint have impacts on the effectiveness of the proposed model. There are always loads on the knee joint during most of the cases, such as the situation when a standing position is adopted. Considering that the applied exoskeleton \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & **RMSE (rad)** & **CC** & **Fit** \\ \hline \multirow{2}{*}{S1} & SSM & \(0.0513\pm 0.0079\) & \(0.9935\pm 0.0008\) & \(0.9852\pm 0.0029\) \\  & BPNN & \(0.1217\pm 0.0140\) & \(0.9681\pm 0.0046\) & \(0.9166\pm 0.0097\) \\ \hline \multirow{2}{*}{S2} & SSM & \(0.1017\pm 0.0170\) & \(0.9817\pm 0.0049\) & \(0.9390\pm 0.0186\) \\  & BPNN & \(0.1982\pm 0.0379\) & \(0.9207\pm 0.0117\) & \(0.7962\pm 0.0316\) \\ \hline \multirow{2}{*}{S3} & SSM & \(0.0588\pm 0.0167\) & \(0.9738\pm 0.0189\) & \(0.8891\pm 0.1019\) \\  & BPNN & \(0.1942\pm 0.0603\) & \(0.6699\pm 0.0720\) & \(0.3902\pm 0.0958\) \\ \hline \multirow{2}{*}{S4} & SSM & \(0.0607\pm 0.0206\) & \(0.9704\pm 0.0182\) & \(0.9247\pm 0.0342\) \\  & BPNN & \(0.0938\pm 0.0572\) & \(0.9065\pm 0.0878\) & \(0.8232\pm 0.1502\) \\ \hline \multirow{2}{*}{S5} & SSM & \(0.1093\pm 0.0261\) & \(0.9697\pm 0.0152\) & \(0.9292\pm 0.0312\) \\  & BPNN & \(0.2294\pm 0.0090\) & \(0.8516\pm 0.0149\) & \(0.7083\pm 0.0151\) \\ \hline \multirow{2}{*}{S6} & SSM & \(0.1061\pm 0.0165\) & \(0.9751\pm 0.0045\) & \(0.9309\pm 0.0135\) \\  & BPNN & \(0.1961\pm 0.0283\) & \(0.8838\pm 0.0063\) & \(0.7672\pm 0.0172\) \\ \hline \hline \end{tabular} Note: S1, S2,..., S6 represent the six subjects; RMSE is the root mean square error, CC is the correlation coefficient, Fit is the goodness of fit in terms of NMSE; SSM is the state space model, BPNN is the back propagation neural network.  
\end{table} 
Table 1: Values of RMSE, CC and FIT of different models in terms of joint angle prediction for all the subjects. robot was the combination of a bed and an exoskeleton robot, there would be loads on the knee joint when there was an angle between the bed and the ground during the experiments. Although the bed could not turn to the vertical position because of safety considerations and equipment restrictions, the load impacts on the proposed model could be verified. Thus, to demonstrate that the method did work, not only in the sitting down position, but was also suitable for other applications, the upper part of the bed was risen to about 30 degrees to the ground to find out the load impacts on the effectiveness of the proposed model. A small angle was adopted for safety considerations. Additional experiments were conducted. The resulting CC values were all above 0.95, which were similar to the main parts of the experiments when the sitting down position was adopted. The satisfactory results demonstrated that based on the inputs of extracted EMG features and interactive force, the proposed SSM model was able to predict the joint angle continuously when there were loads on the knee joint. In fact, joint angle learning and prediction has long been a research hotspot. Instead of using GP-based models, traditional neural networks were usually applied [1]. For instance, [PERSON] et al. developed a general state-space model, in which a traditional neural network-based NARX model was integrated with BPNN [4]. They have done a very good job in continuously and accurately estimating the multi-joint movements through the use of a nonlinear filtering algorithm. The CC values of the four predicted angles were 0.95, 0.96, 0.96 and 0.95, which were all close to 1. Compared with their work, we concentrated on the learning and prediction of one joint angle instead of four, and improved the performance, as illustrated in Table 1. It should be recognized that the decrease of the joint angle number needed to be predicted might be one reason for the improvements. There might also be other possible reasons that contributed to the improvements.