  This paper proposes two novel nonlinear attitude filters evolved directly on
the Special Orthogonal Group SO(3) able to ensure prescribed measures of
transient and steady-state performance. The tracking performance of the
normalized Euclidean distance of attitude error is trapped to initially start
within a large set and converge systematically and asymptotically to the origin
from almost any initial condition. The convergence rate is guaranteed to be
less than the prescribed value and the steady-state error does not exceed a
predefined small value. The first filter uses a set of vectorial measurements
with the need for attitude reconstruction. The second filter instead uses only
a rate gyroscope measurement and two or more vectorial measurements. These
filters provide good attitude estimates with superior convergence properties
and can be applied to measurements obtained from low cost inertial measurement
units (IMUs). Simulation results illustrate the robustness and effectiveness of
the proposed attitude filters with guaranteed performance considering high
level of uncertainty in angular velocity along with body-frame vector
measurements. Keywords: Attitude, estimate, estimator, observer, filter,
nonlinear deterministic attitude filter, special orthogonal group, Euler
angles, angle-axis, Rodrigues vector, mapping, parameterization, prescribed
performance, representation, robust, Multiplicative Extended Kalman Filter, KF,
EKF, MEKF, asymptotic stability, almost global asymptotic, noise, rotational
matrix, identity, origin, orientation, body frame, inertial frame, rigid body,
three dimensional, 3D, space, micro electromechanical systems, sensor, MEMS,
roll, pitch, yaw, UAVs, QUAV, SVD, fixed, moving, vehicles, robot, robotic
system, spacecraft, submarine, underwater vehicle, passive complementary
filter, explicit complementary filter, autonomous, comparative study, SO(3).
