# Feature Optimization for Gait Phase Estimation with a Genetic Algorithm and Bayesian Optimization
## 1 Introduction  
Walking and running are essential motions in daily life [1]. Gait motions can be analyzed by gait phases because gait motion is a cyclic movement composed of several gait phases [2]. Therefore, gait phase identification is widely used to evaluate and diagnose gait. Gait phases have been investigated using foot pressure sensors [3] and inertial measurement units (IMUs) [4]. Accordingly, gait phase analysis has been used in several fields, such as rehabilitation [5], diagnosis [6, 7], and assistive robot design [8, 9]. The performance of these applications relies on the gait phase estimation accuracy. Gait phase estimation has been conducted using two different approaches: the discrete and continuous gait phase approaches. In the discrete gait phase approach, the gait event is recognized as one of the discrete gait phases, such as loading response, mid-stance, and terminal stance [10]. These discrete phases are differentiated based on the kinematic characteristics of lower limbs. In the continuous gait phase approach, the gait phase is a motion status that is defined as a value between 0% and 100% of the gait cycle [8]. More specifically, the heel strike of the left (or right) foot matches with 0% and 100%. Other gait events within one cycle correspond to values between 0% and 100%; the gait phase values linearly increase from 0% to 100% over time during one cycle. In practical applications, the discrete gait phase approach has drawbacks when compared with the continuous gait phase approach. First, assigning gait states to discrete gait phases is challenging, especially in transition states between two distinct phases [11]. This gait phase misidentification may provide unreliable gait information, which results in inadequate controls. Furthermore, controls that are determined by the discrete phaseapproach lead to unsmooth controls at transition states because different phases require different controls [12]. Therefore, the continuous gait phase approach is suitable for accurate and precise controls in various applications. Gait phase estimation algorithms can utilize either original time-series signals or statistical features obtained from time-series signals. To obtain these statistical features, the time-series data from two consecutive instants, or times, are segmented. Then, the statistical features (e.g., the mean and standard deviation (SD) of the segmented time-series data) can be calculated. These statistical features are referred to as time-domain (TD) features, and the segmentation length is referred to as the length of the time window (LTW). Estimation models based on the original time-series signals [13; 14; 15; 16; 17] can capture the temporal patterns of such signals. However, complicated neural networks are required to train the temporal patterns from the original time-series data [18]. Moreover, this end-to-end learning approach requires large datasets to achieve high accuracy. TD features can address these issues because the number of features is very small compared to that of the original time-series data. If TD features are used for gait estimation, the temporal characteristics of time-series signals can be represented by a relatively small number of features [19; 20]. The TD features have been proven to obtain high performance with a low computational burden [21]; thus, they have been widely used in gait phase estimation. [PERSON] et al. [22] used a sliding window to obtain several TD features from IMU signals (e.g., mean, variance, minimum, and maximum). Subsequently, the continuous gait phase was estimated via a multi-layer perceptron (MLP), which was trained using the extracted TD features. [PERSON] et al. [23] investigated various gait phase classifiers that used a TD feature set calculated from the angle of the knee and the angular velocity and acceleration of the thigh. [PERSON] et al. [24] introduced several TD feature sets derived from eight IMU datasets.