# Estimation of Stride Length, Foot Clearance, and Foot Progression Angle Using UWB Sensors
## 1 Introduction  
Gait analysis assesses and measures the temporal and spatial characteristics of the body during motion. Gait characteristics data can be used as diagnostic parameters for various adult diseases, resulting in numerous clinical researchers focusing on developing technologies for measuring gait characteristics [1; 2]. Among gait parameters, stride length (SL), gait speed (GS), and foot clearance (FC) are used to determine the risk of falling [3; 4; 5]. In addition, the foot progression angle (FPA) could be applied to examine the characteristics of the load applied to the knee joint while assessing degenerative arthritis [6; 7; 8; 9]. Clinicians have reported that the gait asymmetry problem caused by slow GS [10] or low FC [11; 12] could be improved through visual biofeedback. In addition, a study that fed the FPA to a subject walking on a treadmill confirmed that the subject improved the FPA on their own [13]. However, these studies were inapplicable in their daily life because they were mostly conducted in experimental environments that used motion capture systems (MCSs). Therefore, numerous studies have analyzed gait parameters using wearable devices. An inertial measurement unit (IMU) is commonly used for gait analysis with wearable devices. The SL [14; 15; 16], GS [17; 18], gait phase [19; 20; 21], joint angle [22; 23], and FC [24; 25; 26] can be estimated using these devices. The IMU can also be used simultaneously with an ultrasonic sensor to measure the step length and stride width [27]. The disadvantage of using an IMU is the drift phenomenon, which is the occurrence of a cumulative error during speed acquisition by integrating acceleration data. Therefore, researchers conducting mobile gait analysis have improved the accuracy by applying the zero-velocity update (ZUPT) method [28], which corrects the sensor measurement by constraining the speed to zero if the sensor is determined to be at rest owing to theset threshold value. However, although ZUPT may be effective under circumstances of a short activity time and repeated state of rest, it does not function when: (1) the stance phase only occurs for a very short period, such as while fast walking or running; and (2) the sensor used to detect zero velocity is affected by noise and the drift is not adequately corrected [29; 30; 31]. Ultra-wideband (UWB) is an alternative to the IMU with the abovementioned problems. UWB sensors determine distance using the time-of-flight (TOF) between two UWB sensors based on the reception and transmission of radio signals, making it highly advantageous compared with IMU because of its capability to measure distances directly. UWB technology has mainly been used to track locations within indoor spaces using fixed UWB anchor [32; 33]. However, as the power consumption of UWB is reduced [34] and the measurement accuracy is increased [35] owing to recent technological developments, the utilization of UWB for gait parameter analysis, such as tracking the joint angle [36; 37] and measuring the SL [38], is increasing. The limitations of previous studies using UWB sensors are as follows: (1) since the signal receiver is installed in a fixed location, such as a wall or tripod, it can only operate within a designated place; and (2) gait analysis is possible only in the double stance phase. To overcome these limitations, this study proposes a UWB sensor system (Figure 1) that tracks foot trajectory using four UWB sensors installed on each foot to analyze gait characteristics. First, the trilateration method was applied, which involved simultaneously applying the distance data acquired from each UWB sensor to determine the overlapping location and estimate the actual distance between the sensors. However, the distance data provided by the UWB sensors had errors owing to variations in the antenna direction. Therefore, the variation in the strength of the received sensor signals was considered to compensate for this error.