Accurate and robust orientation estimation using magnetic and inertial measurement units (MIMUs) has been a challenge for many years in long-duration measurements of joint angles and pedestrian dead-reckoning systems and has limited several real-world applications of MIMUs. Thus, this research aimed at developing a full-state Robust Extended Kalman Filter (REKF) for accurate and robust orientation tracking with MIMUs, particularly during long-duration dynamic tasks. First, we structured a novel EKF by including the orientation quaternion, non-gravitational acceleration, gyroscope bias, and magnetic disturbance in the state vector. Next, the a posteriori error covariance matrix equation was modified to build a REKF. We compared the accuracy and robustness of our proposed REKF with four filters from the literature using optimal filter gains. We measured the thigh, shank, and foot orientation of nine participants while performing short- and long-duration tasks using MIMUs and a camera motion-capture system. REKF outperformed the filters from literature significantly (p <; 0.05) in terms of accuracy and robustness for long-duration tasks. For example, for foot MIMU, the median RMSE of (roll, pitch, yaw) were (6.5, 5.5, 7.8) and (22.8, 23.9, 25) deg for REKF and the best filter from the literature, respectively. For short-duration trials, REKF achieved significantly (p <; 0.05) better or similar performance compared to the literature. We concluded that including non-gravitational acceleration, gyroscope bias, and magnetic disturbance in the state vector, as well as using a robust filter structure, is required for accurate and robust orientation tracking, at least in long-duration tasks.

中文翻译：

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使用磁和惯性测量单元在长时间动态任务期间进行方向跟踪的全状态鲁棒扩展卡尔曼滤波器


多年来，使用磁性和惯性测量单元 (MIMU) 进行准确、鲁棒的方向估计一直是关节角度和行人航位推算系统的长期测量中的一个挑战，并且限制了 MIMU 的一些实际应用。因此，本研究旨在开发一种全状态鲁棒扩展卡尔曼滤波器 (REKF)，用于使用 MIMU 进行精确且鲁棒的方向跟踪，特别是在长时间动态任务期间。首先，我们通过在状态向量中包含方向四元数、非重力加速度、陀螺仪偏置和磁扰动来构建新颖的 EKF。接下来，修改后验误差协方差矩阵方程以构建 REKF。我们使用最佳滤波器增益将我们提出的 REKF 与文献中的四个滤波器的准确性和鲁棒性进行了比较。我们使用 MIMU 和相机动作捕捉系统测量了 9 名参与者执行短期和长期任务时的大腿、小腿和脚的方向。在长期任务的准确性和鲁棒性方面，REKF 显着优于文献中的过滤器 (p <; 0.05)。例如，对于脚部 MIMU，REKF 和文献中最佳滤波器的（横滚、俯仰、偏航）的中值 RMSE 分别为 (6.5, 5.5, 7.8) 和 (22.8, 23.9, 25) 度。对于短期试验，与文献相比，REKF 取得了显着 (p <; 0.05) 更好或相似的性能。我们的结论是，至少在长时间任务中，需要在状态向量中包括非重力加速度、陀螺仪偏置和磁扰，以及使用鲁棒的滤波器结构，以实现准确和鲁棒的方向跟踪。