**3. Results**

In this section, di fferent kinds of estimation methods for the estimation of the knee from the sEMG signals were compared to investigate whether the sample size and the previous sEMG signals would a ffect the performance of the estimation. All of the data processing was done on the software of MATLAB R2016b. In order to avoid the influence of the processor on the computation time, all the execution time in our study is relative.

### *3.1. The Results of Di*ff*erent Sample Size*

Di fferent sample sizes from 1 GD to 60 GDs were utilized for RFPCA and BPPCA to predict the knee joint angle.

Partial results of Subject 1 for estimation are shown in Figure 6. It can be seen that, as *Ss* increases, the estimations of BPPCA and RFPCA are close to the EV. However, the estimation results of RFPCA are always closer to the EV and more robust than BPPCA.

**Figure 6.** Partial results for estimation with di fferent sample sizes of Subject 1.

The relative execution time (the execution time of each calculation processed against the longest computation among all of the sample size results), and the evaluation metric for the estimation with di fferent methods and di fferent subjects, are depicted in Figure 7. As the sample size increases, so does the execution time. Compared to the increase in time using BPPCA, RFPCA appears more e fficient for the training, as it is less time consuming. Although the value of *R* decreases and the error decreases with the larger sample size from 1 to 10 GDs, both of the methods have no significant changes after *Ss* = 20. When *Ss* ≥ 30, the *R* of BPPCA is slightly smaller than RFPCA, with a longer execution time.

**Figure 7.** The relative execution time and *R* for the estimation with di fferent *Ss*.

### *3.2. The Results of Di*ff*erent Previous sEMG Input*

In the process of training, different previous sEMG signals were used, and the result of relative execution time and the evaluation metric are shown in Figure 8. As the attributes of input *Xt* increase, the execution time of the different methods also increases, and this is more pronounced for BPPCA. RFPCA is much smaller, which is conducive to the application of myoelectric control. For the results of *R*, the estimation errors of different methods are various. The BPPCA results are much larger than RFPCA, and the method is insensitive to the input dimension when *n* is larger than approximately 7. The results of RFPCA seem to increase when *n* is bigger than 2. The results of *R* also show that BPPCA has larger standard deviations than RFPCA.

**Figure 8.** The relative execution time and *R* for the estimation with different previous input.

The estimation results of all six subjects using various methods when *n* = 2 are shown in Figure 9. From the figure, it is clear that the EV tracking errors of RFPCA are much smaller than BPPCA.

**Figure 9.** The estimation results of different models from different subjects when *n* = 2.

Furthermore, the evaluation metric *R* of different models for different subjects when *n* = 2 is depicted in Figure 10. The *R* of RFPCA is almost 5◦, while the BPPCA has a poor prediction ability of the knee angle estimation, showing a large variation between different subjects, with errors ranging between 7◦ to 25◦.

**Figure 10.** The evaluation metric of different models for different subjects when *n* = 2.
