Smoother-Based 3-D Foot Trajectory Estimation Using Inertial Sensors

<italic>Objective:</italic> Measuring three-dimensional (3-D) foot trajectories with foot-worn inertial measurement units (IMUs) is essential for a variety of applications, such as gait analysis and fall risk assessment. IMU-based foot trajectory is usually reconstructed by double integrating the global coordinate acceleration, in which drifts of signals are accumulated and lead to unbounded error increase. To reduce drift errors, a smoother-based method is proposed in this paper. <italic>Methods:</italic> The smoother-based method not only corrects initial values of integrations, but also smooths integrating processes through a backward update. Both the orientation estimation and the velocity estimation are improved in this concept, which contribute to the improvement of the trajectory estimation. <italic>Results:</italic> The final results are compared with an optical motion capture system as reference. Accuracy is evaluated with ground level walking of nine adult participants, 2302 strides in total. Errors are reduced by 62% on stride length and 44% on stride width of the estimation without our method, with final errors <inline-formula><tex-math notation="LaTeX">$-\text{0.24}\pm \text{1.11}\ \text{cm}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$-\text{0.02}\pm \text{0.95}\ \text{cm}$</tex-math></inline-formula>. <italic>Conclusion/Significance:</italic> Results prove that our method can improve the accuracy of 3-D foot trajectory estimation. Furthermore, this smoother-based method can reduce drift-related errors when estimating trajectories, which will allow it to expand its applications into other IMU-based measurements.