## 4 Experimental Study and Discussion
### Further Discussions
One reason was that the addition of interactive force in our model would improve the performance of joint angle prediction [30]. The use of nonredundant and redundant sub-vectors of EMG signals were innovative in their study, but the information acquired only from the EMG signals was still limited. The other reason might be the use of GP when the integration of parametric model and non-parametric model of GP would improve the performance [48]. In addition, they also made the comparison between the state space model and the use of NARX model alone. A conclusion was reached that the estimation using the integration of NARX and BPNN over the prediction with the NARX model alone had two improvements: (1) the estimation was closer to the \"true\" angles, and the larger errors have been corrected by the measurement equation; (2) the UKF made the estimation smoother, which would be beneficial for the stable control of the robots. The second conclusion could also be used to explain the differences observed in our experimental results shown in Figure 11 when the fluctuations were only found using BPNN instead of the proposed SSM integrating GP-NARX with BPNN. To take the advantages of GP-based models, [PERSON] et al. also used a GP-NARX model that combined the context of pervious hand movement with instantaneous muscle activity to predict future hand movements [23]. In addition to EMG signals, mechanomyographic (MMG) signals were also used to indicate hand muscle activation in the forearm. Referring to their results, the improvement of fusing MMG with EMG in the GP-NARX model was relatively small. Thus, it was reasonable to only include EMG in the angle prediction model when taking the computational cost into consideration. GP was also used to estimate the ankle angle and torque based on shank angular velocity and angle without information from neural signals [16]. In their study, they showed that it was not necessary to acquire speed determination, gait percent identification, lookup tables, or switching rules to continuously mapping the input to the output. However, all the above studies treated the whole neural control process of human movement as a black-box problem without providing any biomechanical interpretations. In contrast, there are also studies which used [PERSON]'s muscle model to develop the forward dynamics of human neuromuscularsokeletal system for angle prediction [27]. Similar to all the model-based methods, parameter identification, which is very time-consuming, must be done in advance. Thus, the proposedmethod which is a trade-off between engineering application using machine learning techniques and theoretical analysis providing the biomechanical interpretations might be the optimal choice. As stated, one major difference of our method is to bring GP into the state space model. When GP is generally considered equivalent in terms of performance to conventional artificial neural network approaches, it is in fact formally equivalent to a neural network with an infinite number of units in the hidden layer [49]. However, these unique benefits of GP over a standard neural network come at a cost. GP regression is numerically complex and the heavy computational cost is always its major drawback. This leads to the fact that the computational efficiency of the current method seriously limits its adoption in real-time applications. To overcome this limitation, numerous researchers have suggested different sparse approximations, including the subset of data (SoD) approximation, fully independent training conditional (FITC) approximation, and partially independent training conditional (PITC) approximation. One successful application in joint angle prediction can be found in [44] where an online sparse GP algorithm is proposed to learn the human motion intent. In addition, the integration with an evolving system would be another choice [22].