Neural-adaptive Stochastic Attitude Filter on SO(3)

Abstract

Successful control of a rigid-body rotating in three dimensional space requires accurate estimation of its attitude. The attitude dynamics are highly nonlinear and are posed on the Special Orthogonal Group $SO(3)$. In addition, measurements supplied by low-cost sensing units pose a challenge for the estimation process. This paper proposes a novel stochastic nonlinear neural-adaptive-based filter on $SO(3)$ for the attitude estimation problem. The proposed filter produces good results given measurements extracted from low-cost sensing units (e.g., IMU or MARG sensor modules). The filter is guaranteed to be almost semi-globally uniformly ultimately bounded in the mean square. In addition to Lie Group formulation, quaternion representation of the proposed filter is provided. The effectiveness of the proposed neural-adaptive filter is tested and evaluated in its discrete form under the conditions of large initialization error and high measurement uncertainties. keywords / index-terms: Neuro-adaptive, stochastic differential equations (SDEs), Brownian motion process, attitude estimator, Special Orthogonal Group, Unit-quaternion, SO(3), IMU, MARG.