  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.
