# Gait Phase Estimation Based on User-Walker Interaction Force
## 5 Discussion  
We propose a gait phase estimation method based on AOs and the user-walker interaction force. First, we use a BMFLC to extract the slow oscillation component that reflects walking in the interaction force. Then, we use AOs for phase estimation. In addition, a switching mechanism and a parameter-adaptive rule improve the accuracy and robustness of the AOs under rapid changes in amplitude and frequency of the input gait signal. The switching mechanism allows two AOs to track the frequencies of consecutive steps to account for asymmetric gait. As shown in the simulation, with the increase in the frequency difference between the two legs, the estimation error keeps increasing constantly for the single AO. When the frequencies are 1.4 Hz and 1 Hz, the estimation error reaches 0.7 rad, which is about approximately 10% of a step time (5% of a stride time if the gait is symmetric), while the estimation error is much lower with the proposed switching mechanism. An estimation error of 5% of the gait cycle is not substantial; however, the simulated signal is a pure sinusoidal, while the interaction force contains variations and disturbances, which can deteriorate the estimation accuracy. If the estimation error is over 10% of the gait cycle, it leads to the failure of the control algorithm when the target gait phases are those with short durations, such as the bodyweight acceptance, which lasts for approximately 10% of the gait cycle [30]. By adopting the proposed adaptive rule, parameter \(\sigma\) is adapted based on the difference in estimated frequency \(\omega\) and actual change rate of phase \(\dot{\varphi}\). The proposed adaptive rule considers that the gait phase does not change drastically during walking and is applied when the difference is large, thus maintaining a phase increase of at least \((1-\lambda)\) of the expected frequency. Nevertheless, this method may decelerate the initial AO synchronization when the phase difference between the estimated and true gait phases is large [19; 31]. However, the deterioration of synchronization is suppressed afterward, and there is no substantial influence on the overall estimation accuracy. In the experiments, the phase estimation accuracy of scenario 1 (without knee restriction) was better than that of scenario 2 (with knee restriction) because the interaction force contains more disturbances and variations under the limitations imposed by the knee \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name of Method** & **Gait Phase Estimation Error (RMSE)** & **HS Estimation Error** & **No. HS Misdetections (Ratio *)** \\ \hline AO & 0.774 rad & 54.16 \(\pm\) 53.28 ms & 35 (1.21\%) \\ Proposed method & 0.691 rad & 55.75 \(\pm\) 56.55 ms & 4 (0.14\%) \\ \hline \hline \end{tabular}  
* Percentage for HS misdetections of HSs in all trials.  
\end{table} 
Table 1: Estimation performance when participants walked without knee restriction. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name of Method** & **Gait Phase Estimation Error (RMSE)** & **HS Estimation Error** & **No. HS Misdetections (Ratio *)** \\ \hline AO & 0.889 rad & 80.61 \(\pm\) 70.39 ms & 105 (3.31\%) \\ Proposed method & 0.722 rad & 75.79 \(\pm\) 66.69 ms & 11 (0.35\%) \\ \hline \hline \end{tabular}  
* Percentage for HS misdetections of HSs in all trials.  
\end{table} 
Table 2: Estimation performance when participants walked with knee restriction. orthosis. In fact, a restricted knee movement hampers the coordinative movement of the trunk during walking [32], eventually altering the interaction force during walking. The estimation performance of the proposed method and a single AO is similar without the restriction. As the participants in this study were young and healthy, their gait patterns were symmetric and the interaction force contained few variations and noise, promoting accurate estimation. In contrast, the proposed method showed higher accuracy than AO when the participants walked with a knee orthosis, which elicited asymmetric gait due to the restricted knee movement.