  Two nonlinear stochastic complimentary filters are developed on SO(3). They
guarantee that errors in the Rodriguez vector and estimates are semi-globally
uniformly ultimately bounded in mean square, and they converge to a small
neighborhood of the origin. Simulation results are presented to illustrate the
effectiveness of the proposed filters considering high level of uncertainties
in angular velocity as well as body-frame vector measurements. Keywords:
Attitude estimate, Attitude estimator, Attitude observer, Attitude filter,
Nonlinear stochastic filter, stochastic differential equations, Brownian motion
process, Ito, Stratonovich, Wong Zakai, Rodriguez vector, unit-quaternion,
special orthogonal group 3, Euclidean, Euler angles, Angle-axis, Mapping,
Parameterization, Representation, Robust, Invariant, Kalman Filter, Extended
Kalman Filter, Multiplicative Extended Kalman Filter, Unscented Kalman Filter,
Particle Filter, KF, EKF, MEKF, IEKF, first, second, Partial derivative,
operator, probability, small, error, dynamics, kinematics, equilibrium,
asymptotic, covariance, mean square, expected value, zero, unknown,
time-varying, global, semi-global, stable, stability, uncertain, white noise,
Gaussian noise, colored noise, bias, vectorial, vector measurement, angular
velocity, singular value decomposition, bounded, rotational matrix, identity,
deterministic, orientation, body frame, comparison, inertial frame, rigid body,
three dimensional, 3D, space, Attitude Control, Lie algebra, Lie group,
projection, Gyroscope, Inertial measurement units, micro electromechanical
systems, sensor, IMUs, MEMS, Roll, Pitch, Yaw, UAVs, QUAV, SVD, Fixed, Moving,
Vehicles, Robot, Robotic System, Spacecraft, submarine, Underwater vehicle,
Problem, advantage, integral, integration, passive complementary filter,
Disadvantage, autonomous, Review, Overview, Survey, comparative study, pose,
SDEs, SE(3), SO(3).
