Estimation and observability analysis of human motion on Lie groups

This article proposes a framework for human-pose estimation from the wearable sensors that rely on a Lie group representation to model the geometry of the human movement. Human body joints are modeled by matrix Lie groups, using special orthogonal groups SO(2) and SO(3) for joint pose and special Euclidean group SE(3) for base-link pose representation. To estimate the human joint pose, velocity, and acceleration, we develop the equations for employing the extended Kalman filter on Lie groups (LG-EKF) to explicitly account for the non-Euclidean geometry of the state space. We present the observability analysis of an arbitrarily long kinematic chain of SO(3) elements based on a differential geometric approach, representing a generalization of kinematic chains of a human body. The observability is investigated for the system using marker position measurements. The proposed algorithm is compared with two competing approaches: 1) the extended Kalman filter (EKF) and 2) unscented KF (UKF) based on the Euler angle parametrization, in both simulations and extensive real-world experiments. The results show that the proposed approach achieves significant improvements over the Euler angle-based filters. It provides more accurate pose estimates, is not sensitive to gimbal lock, and more consistently estimates the covariances.