# Bio-Inspired Real-Time Prediction of Human Locomotion for Exoskeletal Robot Control
## 4 Implementation and Assessment
### Parameter Selection for Takens' Reconstruction-Based Methods  
For [PERSON] reconstruction-based methods common parameters were evaluated, including the history data length, embedding vector length, and the number of weighted best matching vectors. A group of basic parameters are listed in Table 2. During the evaluation the evaluated parameters were taken as variables while others were fixed.  
Only the left hip data were shown in the following paragraphs because the four joints results exhibited the same varying patterns which meant the ruling laws were the same for different methods.  
Theoretically, a longer history is beneficial and Figure 8 gave the proof with continuous escalation of \(PR\)s. A steep rise ended at the value of 360, which was the chosen value in Table 2. The history data length had limited influence on \(SF\)s after 360, because a longer history could not generate better historical embedding vectors.  
The length of embedding vectors represents the orders of the reconstructed system. Excessive higher order might cause overfitting, which reduces the prediction accuracy and increases unnecessary computational expense. Gaussian weightings mitigate the problem by reducing the influence of the history data far away and the offset correction and feedback scheme also provide powerful fixation. Figure 9 proved the analysis. For the \(SF\) values, the expending of embedding vectors could improve them more or less for all methods. Thus, considering that a length of 20 is not an burden to the embedded system and it has limited influence on most of the improved methods, the embedded vector length was chosen to be 20.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Parameter Name** & **Symbol** & **Value** & **Variation Range** & **Variable** \\ \hline History data length & \(l\) & 360 & 200–400 & Yes \\ Embedding vector length & \(p\) & 20 & 6–20 & Yes \\ Number of weighted best matching vectors & \(M\) & 5 & 1–8 & Yes \\ Prediction horizon & \(k\) & 5 & / & No \\ \hline \hline \end{tabular}
\end{table}
Table 2: Basic parameters for parameter evaluation.  
As shown in Figure 10, when the weighted best matching vector number increased, the \(PR\)s of different methods rose to the highest at 5 and the trend then descended afterwards. Meanwhile, for the \(FS\)s after 5, they also entered an slow falling state. This was reasonable because the matched vector quality degraded when the number increased to a certain level, and their weighting values fell quickly. At the same time, the increasing number of weighted history embedding vectors worked as a smoother by averaging down the oscillations.  
Figure 8: Influence of history data length used in embedding vector generation (left hip joint data in the sagittal plane). \(SF\): smoothness factor; \(PR\): prediction ratio.  
Figure 9: Influence of embedding vector length (left hip joint data in the sagittal plane).  
Surprisingly, most newly-introduced Takens' reconstruction-based methods exhibited robust performance with parameter variation. Thus, the parameter robustness of the newly introduced methods was discovered.  
Summarizing the previous analysis, the basic parameters are selected with enough confidence, and could be applied to algorithm performance assessment.