Estimation and Observability Analysis of Human Motion on Lie Groups

Area of Science:

• Robotics and Biomechanics
• Sensor Fusion and State Estimation
• Computational Geometry

Background:

• Accurate human pose estimation is crucial for applications like biomechanics and human-computer interaction.
• Traditional methods using Euler angles struggle with singularities like gimbal lock and non-Euclidean state spaces.
• Modeling human movement geometry requires advanced mathematical frameworks.

Purpose of the Study:

• To propose a novel framework for human pose estimation using wearable sensors.
• To leverage Lie group theory for modeling the non-Euclidean geometry of human movement.
• To develop an advanced filtering technique for improved pose, velocity, and acceleration estimation.

Main Methods:

• Modeling human body joints using matrix Lie groups (SO(2), SO(3)) and base-link pose with SE(3).
• Developing the Lie group extended Kalman filter (LG-EKF) for state estimation on non-Euclidean manifolds.
• Conducting observability analysis of kinematic chains using differential geometry and marker position measurements.

Main Results:

• The LG-EKF demonstrates significant improvements over traditional Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) methods.
• The proposed approach provides more accurate human pose estimates.
• The LG-EKF is robust to gimbal lock and offers more consistent covariance estimation.

Conclusions:

• The Lie group-based framework offers a superior approach to human pose estimation from wearable sensors.
• LG-EKF effectively handles the non-Euclidean geometry inherent in human movement.
• This method enhances accuracy, stability, and reliability in pose tracking applications.