# Gait Phase Estimation Based on User-Walker Interaction Force
## 5 Discussion
For these subjects, the RMSE of phase estimation provided by the proposed method was lower than that without the adaptive rule and switching mechanism. The switching mechanism improved the estimation accuracy by using two separate states to track the step timing of the two legs. Although the difference in HS estimation error between the proposed method and single AO was significant, the improvement in the estimation accuracy was not very large (reduction by 6.25%). However, over 100 HS misdetections occurred using the conventional AO, whereas most HSs were captured by the proposed method. With a smaller \(\sigma\), the single AO method can achieve fewer misdetections of heel strikes. However, it takes a longer time for the AO to re-synchronize with the input signal when the characteristics of the input signal change. This will eventually deteriorate the estimation accuracy. Although the proposed method successfully detected the HSs, the estimation accuracy was degraded when the orthosis was used. These differences in estimation are likely much larger if the HSs are neglected. The HS estimation error was also compared with offline gait event estimation based on the user-walker interaction force proposed in [10]. This method uses a Butterworth bandpass filter to suppress noise, and the peak timing of the interaction force is considered as the HS instant. Its estimation accuracy was 46.75 \(\pm\) 50.60 ms, outperforming the results of our proposal. However, the HS estimation error of the proposed method in scenario 1 was 54.16 \(\pm\) 53.28 ms, being comparable to the results of [PERSON]'s method. This is a suitable result considering that the results were obtained offline by the method in [10], while the proposed method performs real-time estimation. [PERSON]'s paper does not report any misdetection of HS, but the misdetection of HS is mentioned in other similar research studies [9; 33] while none of them uses the misdetection of HS to evaluate the performance of their estimation methods. The adaptive rule for \(\sigma\) improves not only the estimation performance but also the robustness. Using the proposed method, the number of HS misdetections decreased considerably from 105 to 11. In the few cases in which the proposed method provided HS misdetections, the interaction force did not reflect the change in the gait phase. For example, Figure 10 shows the filtered interaction force for an HS misdetection provided by the proposed method. The HS instant is supposed to coincide with the peak timing of the interaction force, but the peak in the red circle is very small, leading to a failed HS detection. This is a limitation of the proposed method because its results rely on the interaction force. In addition, the gait phase can be indirectly affected by elbow movements or posture changes during walking. If a heel strike is not detected by the proposed method, the AO that kept track of the left steps will turn to track of the right steps while the AO that kept track of the right steps will turn to track of the left steps. It will take several steps for the estimator to re-synchronize with the input signal, which will deteriorate the performance of estimation in a short period. However, the phase estimation error will diminish rapidly during the re-synchronization period. Furthermore, the misdetections barely occur for the proposed method even when the user's knee movement is restricted (11 misdetections for about 3000 steps), and the phase estimation error after the 11 misdetections decreases rapidly due to the choice of a \(\epsilon\) with a large value to increase the converge rate of \(\omega\). Therefore, it is not a big issue for the proposed phase estimation method. Moreover, we will improve the proposed method by making the best use of the interaction force/torque between the walker and a user to determine the left/right heel strikes in real time.