  We propose an attitude and gyro-bias estimation scheme for accelerated rigid
body systems using an inertial measurement unit (IMU) and a global positioning
system (GPS). The proposed scheme allows to obtain attitude estimates directly
on the Special Orthogonal group $SO(3)$ while estimating the gyro bias and the
unknown apparent acceleration of the vehicle. We prove semi-global exponential
stability of the estimation errors. Furthermore, a new switching technique for
the attitude state is introduced which results in a velocity-aided hybrid
attitude observer with proven global exponential stability.
