Attitude Estimation on SO(3) Using MARG Data: A Lie Group Kalman Filter Approach
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This paper presents a Lie Group Extended Kalman Filter (LGEKF) for attitude estimation, formulated directly on the special orthogonal group SO(3), to preserve the geometric properties of 3D rotations. Unlike conventional methods that suffer from singularities or normalization issues, our approach leverages an exponential map to propagate rotations and fuses the Magnetometer, Accelerometer, Rate Gyroscope (MARG) sensor data while respecting the manifold structure of the SO(3). Using a dynamically challenging helical trajectory with realistic sensor noise and biases, we demonstrate that the LGEKF significantly outperforms the standard Extended Kalman Filter (EKF), reducing Root Mean Square (RMS) errors by 26.7% in yaw (0.44° vs. 0.60°), 99.48% in pitch (0.007° vs. 1.34°), and 99.84% in roll (0.008° vs. 5.15°). The covariance propagation of the filter remained stable even during aggressive maneuvers, reflecting its robustness in highly dynamic scenarios. The simulation results highlight the superiority of the LGEKF in drift mitigation and estimation efficiency, making it ideal for real-time applications in autonomous navigation vehicles in underwater environments and other Global Positioning System (GPS)-denied environments.
Abstract
This paper presents a Lie Group Extended Kalman Filter (LGEKF) for attitude estimation, formulated directly on the special orthogonal group SO(3), to preserve the geometric properties of 3D rotations. Unlike conventional methods that suffer from singularities or normalization issues, our approach leverages an exponential map to propagate rotations and fuses the Magnetometer, Accelerometer, Rate Gyroscope (MARG) sensor data while respecting the manifold structure of the SO(3). Using a dynamically challenging helical trajectory with realistic sensor noise and biases, we demonstrate that the LGEKF significantly outperforms the standard Extended Kalman Filter (EKF), reducing Root Mean Square (RMS) errors by 26.7% in yaw (0.44° vs. 0.60°), 99.48% in pitch (0.007° vs. 1.34°), and 99.84% in roll (0.008° vs. 5.15°). The covariance propagation of the filter remained stable even during aggressive maneuvers, reflecting its robustness in highly dynamic scenarios. The simulation results highlight the superiority of the LGEKF in drift mitigation and estimation efficiency, making it ideal for real-time applications in autonomous navigation vehicles in underwater environments and other Global Positioning System (GPS)-denied environments.