# Multi-Condition Constrained Pedestrian Localization Algorithm Based on IMU
As a result, there has been limited in-depth exploration of the single-foot constraint algorithm in subsequent studies. Based on the periodic characteristics of the distance between two feet whilst walking, in 2011, [PERSON] first installed sonar sensing devices between the pedestrian's feet for distance measurement and used the obtained data to correct navigation results [8]. Subsequently, researchers adopted various technologies to measure the distance between the feet, including camera-based vision [9] and ultrasonic sensor techniques [10]. However, these studies all introduced additional equipment beyond the inertial sensors, which may introduce new sources of error. Moreover, such distance measurement methods are susceptible to interference and have a relatively high false detection rate, limiting their practicality. Given that the distance between the feet during walking has a maximum limit, [PERSON] proposed a pedestrian navigation scheme with a dual-feet distance constraint that does not rely on external devices. Study [11] extended the Kalman filter in traditional pedestrian navigation algorithms by introducing inequality constraints. Through comparison of experimental results using different methods, the effectiveness of this approach was confirmed. Then, [PERSON] proposed a dual-feet elliptical motion model [12], which constructed a distance constraint equation between the feet to correct the pedestrian's navigation location. Ultimately, scatter plot results under various algorithms showed a significant reduction in position errors, demonstrating the validity of the model and its algorithm. Inspired by these works, in 2017, [PERSON] et al. proposed a dual-foot ellipsoidal constraint model [13], which reduced the root mean square error of foot position by 41% compared to unconstrained algorithms. In 2019, [PERSON] et al. introduced a dual-foot minimum distance constraint algorithm [14], which, through experimental validation, achieved a positioning accuracy of approximately 0.5% of the walking distance. In 2023, [PERSON] et al. proposed a dual-foot triaxial vector constraint algorithm [15], with experimental results indicating an improvement in positioning accuracy ranging from 49% to 93% in laboratory environments. Compared to traditional pedestrian navigation algorithms, the above dual-feet gait feature-based constraint algorithms demonstrated more significant effectiveness in suppressing pedestrian heading drift. Although extensive research has been conducted on various constraint methods, most existing studies focus on improving the performance of single constraint algorithms, with relatively fewer studies on integrating multiple constraint algorithms to enhance overall navigation performance. Therefore, based on this concept, this article proposes a multi-condition constraint algorithm that innovatively combines the improved zero-velocity correction algorithm, single-foot constraints, and dual-feet constraints. By analyzing pedestrian gait features with biomechanical knowledge, this method optimizes the inherent heading drift problem of inertial sensors using multiple constraint conditions. This significantly improves stability and adaptability without increasing hardware costs or system complexity, thereby making the computed pedestrian navigation trajectory more aligned with the actual walking path and ultimately reducing localization errors.