  This paper introduces two novel nonlinear stochastic attitude estimators
developed on the Special Orthogonal Group \mathbb{SO}\left(3\right) with the
tracking error of the normalized Euclidean distance meeting predefined
transient and steady-state characteristics. The tracking error is confined to
initially start within a predetermined large set such that the transient
performance is guaranteed to obey dynamically reducing boundaries and decrease
smoothly and asymptotically to the origin in probability from almost any
initial condition. The proposed estimators produce accurate attitude estimates
with remarkable convergence properties using measurements obtained from
low-cost inertial measurement units. Unit-quaternion representation of the
proposed filters are presented. The estimators proposed in continuous form are
complemented by their discrete versions for the implementation purposes. The
simulation results illustrate the effectiveness and robustness of the proposed
estimators against uncertain measurements and large initialization error,
whether in continuous or discrete form. Keywods: Attitude estimates, transient,
steady-state error, nonlinear filter, special orthogonal group, SO(3),
stochastic system, stochastic differential equations, Ito, Stratonovich,
asymptotic stability, Wong-Zakai, inertial measurment unit, IMU, prescribed
performance function, Euler Angles, roll, bitch, yaw, color noise, white noise,
Nonlinear attitude filter, Nonlinear attitude observer, Orientation, nonlinear
stochastic attitude filter on SO(3), unit-quaternion based nonlinear stochastic
attitude filter, discrete stochastic attitude filter.
