Multi-Kernel Correntropy Smoother for 6D Foot Motion Tracking With Inertial Sensors

Accurate foot orientation and trajectory estimation are pivotal for advanced gait analysis, yet achieving this with inertial measurement units (IMUs) remains challenging due to their susceptibility to external acceleration, magnetic disturbances, and unbounded position errors. To address these limitations, we propose a multi-kernel correntropy smoother, which effectively mitigates unknown disturbances and enhances orientation accuracy. Furthermore, while the conventional zero-velocity update (ZUPT) method has been widely adopted in IMUs, the impact of incorporating position constraints has been largely overlooked. This paper demonstrates that by incorporating a single loop closure, the maximum positioning error can be reduced by up to 75%, with further reductions achievable through multiple position constraints. Comprehensive theoretical analysis and extensive experimental validation confirm the superior performance of the proposed methods. Note to Practitioners—This paper aims to enhance 6D foot motion tracking accuracy for foot-mounted IMUs. A hierarchical orientation and position estimation scheme are deployed. Specifically, a robust Kalman smoother for orientation, leveraging multi-kernel correntropy, is designed to mitigate the effects of free acceleration and indoor magnetic disturbances. Additionally, a special forward-backward Kalman smoother for position estimation is designed to accommodate zero velocity and loop closure constraints. Our results underscore the importance of disturbance rejection in orientation estimation and the velocity and position constraints in trajectory estimation, offering insights that may inspire broader applications of IMUs.