This study investigates the possibility of estimating lower-limb joint kinematics and meaningful performance indexes for physiotherapists, during gait on a treadmill based on data collected from a sparse placement of new Visual Inertial Measurement Units (VIMU) and the use of an Extended Kalman Filter (EKF). The proposed EKF takes advantage of the biomechanics of the human body and of the investigated task to reduce sensor inaccuracies. Two state-vector formulations, one based on the use of constant acceleration model and one based on Fourier series, and the tuning of their corresponding parameters were analyzed. The constant acceleration model, due to its inherent inconsistency for human motion, required a cumbersome optimisation process and needed the a-priori knowledge of reference joint trajectories for EKF parameters tuning. On the other hand, the Fourier series formulation could be used without a specific parameters tuning process. In both cases, the average root mean square difference and correlation coefficient between the estimated joint angles and those reconstructed with a reference stereophotogrammetric system was 3.5deg and 0.70, respectively. Moreover, the stride lengths were estimated with a normalized root mean square difference inferior to 2% when using the forward kinematics model receiving as input the estimated joint angles. The popular gait deviation index was also estimated and showed similar results very close to 100, using both the proposed method and the reference stereophotogrammetric system. Such consistency was obtained using only three wireless and affordable VIMU located at the pelvis and both heels and tracked using two affordable RGB cameras. Being further easy-to-use and suitable for applications taking place outside of the laboratory, the proposed method thus represents a good compromise between accurate reference stereophotogrammetric systems and markerless ones for which accuracy is still under debate.

中文翻译：

---

用于步态运动学评估的稀疏视觉惯性测量单元放置


本研究探讨了在跑步机上的步态过程中，根据稀疏放置的新视觉惯性测量单元 (VIMU) 和使用扩展卡尔曼滤波器收集的数据，对物理治疗师估计下肢关节运动学和有意义的性能指数的可能性进行了研究。 EKF）。所提出的 EKF 利用人体的生物力学和所研究的任务来减少传感器的误差。分析了两种状态向量公式，一种基于使用恒定加速度模型，另一种基于傅里叶级数，以及它们相应参数的调整。恒定加速度模型由于其与人体运动固有的不一致性，需要繁琐的优化过程，并且需要参考关节轨迹的先验知识来调整 EKF 参数。另一方面，可以使用傅里叶级数公式而无需特定的参数调整过程。在这两种情况下，估计的关节角度与参考立体摄影测量系统重建的关节角度之间的平均均方根差和相关系数分别为 3.5deg 和 0.70。此外，当使用接收估计关节角度作为输入的正向运动学模型时，步幅长度的估计均方根差小于 2%。使用所提出的方法和参考立体摄影测量系统，还估计了流行的步态偏差指数，并显示出非常接近 100 的相似结果。仅使用位于骨盆和双脚跟的三个无线且经济实惠的 VIMU 即可获得这种一致性，并使用两个经济实惠的 RGB 摄像头进行跟踪。 由于更易于使用并且适合在实验室外进行的应用，因此所提出的方法代表了精确参考立体摄影测量系统和精度仍存在争议的无标​​记系统之间的良好折衷。