This paper presents a new constrained optimization-based smoothing algorithm for walking step length estimation using waist-mounted inertial sensors, where the total walking distance is known. The walking trajectory is estimated by double integrating acceleration. Due to sensor noises, the walking step length estimation accuracy degrades as the walking distance becomes longer. To tackle this problem, we introduce a known distance straight-line walking trajectory constraint and a constant speed constraint to the smoothing algorithm. These constraints reduce the walking step estimation accuracy degradation even for long walking distance. Two experiments are conducted to evaluate the pedestrian trajectory and walking step length estimation accuracy. The accuracy of a 20 m walking trajectory estimation has been investigated in the first experiment. This experiment compares the estimated position and velocity with Lidar-based references. The second experiment is to demonstrate the usefulness of the proposed walking step length estimation method. The result shows that the average of mean relative errors is 0.6801% for three different walking speed levels. The proposed method can be applied to generate training data for walking step length estimation without requiring spatial infrastructure.

中文翻译：

---

使用已知总步行距离的腰部惯性传感器估计步行步长

本文提出了一种新的基于约束优化的平滑算法，用于使用腰部安装的惯性传感器进行步行步长估计，其中总步行距离是已知的。步行轨迹通过双积分加速度估计。由于传感器噪声，步行步长估计精度随着步行距离变长而降低。为了解决这个问题，我们在平滑算法中引入了已知距离的直线步行轨迹约束和恒速约束。即使对于长步行距离，这些约束也减少了步行步长估计精度的下降。进行了两个实验来评估行人轨迹和步行步长估计精度。在第一个实验中已经研究了 20 m 步行轨迹估计的准确性。该实验将估计的位置和速度与基于激光雷达的参考进行比较。第二个实验是为了证明所提出的步行步长估计方法的有效性。结果表明，对于三个不同的步行速度水平，平均相对误差的平均值为 0.6801%。所提出的方法可用于生成步行步长估计的训练数据，而无需空间基础设施。