  This paper proposes a real-time neural network (NN) stochastic filter-based
controller on the Lie Group of the Special Orthogonal Group $SO(3)$ as a novel
approach to the attitude tracking problem. The introduced solution consists of
two parts: a filter and a controller. Firstly, an adaptive NN-based stochastic
filter is proposed that estimates attitude components and dynamics using
measurements supplied by onboard sensors directly. The filter design accounts
for measurement uncertainties inherent to the attitude dynamics, namely unknown
bias and noise corrupting angular velocity measurements. The closed loop
signals of the proposed NN-based stochastic filter have been shown to be
semi-globally uniformly ultimately bounded (SGUUB). Secondly, a novel control
law on $SO(3)$ coupled with the proposed estimator is presented. The control
law addresses unknown disturbances. In addition, the closed loop signals of the
proposed filter-based controller have been shown to be SGUUB. The proposed
approach offers robust tracking performance by supplying the required control
signal given data extracted from low-cost inertial measurement units. While the
filter-based controller is presented in continuous form, the discrete
implementation is also presented. Additionally, the unit-quaternion form of the
proposed approach is given. The effectiveness and robustness of the proposed
filter-based controller is demonstrated using its discrete form and considering
low sampling rate, high initialization error, high-level of measurement
uncertainties, and unknown disturbances. Keywords: Neuro-adaptive, estimator,
filter, observer, control system, trajectory tracking, Lyapunov stability,
stochastic differential equations, nonlinear filter, attitude tracking control,
observer-based controller.
