Motion Reconstruction of Fast-rotating Rigid Bodies

Abstract Motion reconstruction and navigation require accurate orientation estimation. Modern orientation estimation methods utilize filtering algorithms, such as the Kalman filter or Madgwick's algorithm. However, these methods do not address potential sensor saturation, which may occur within short time periods in highly dynamic applications, such as, e.g., particle tracking in snow avalanches, leading to inaccurate orientation estimates. In this paper, we present two algorithms for orientation estimation combining magnetometer and partially saturated gyrometer readings. One algorithm incorporates magnetic field vector observations and the full nonlinearity of the exponential map. The other, computationally more efficient algorithm builds on a linearization of the exponential map and is solved analytically. Both algorithms are then applied to measurement data from four different experiments, with two of them being snow avalanche experiments. Moreover, Madgwick's filtering algorithm was used to validate the proposed algorithms. The two algorithms improved the orientation estimation significantly in all experiments. Hence, the proposed algorithms can improve the performance of existing sensor fusion algorithms significantly.