On the Design of Globally Exponentially Stable Hybrid Attitude and   Gyro-bias Observers
  This paper presents hybrid attitude and gyro-bias observers designed directly on the Special Orthogonal group SO(3). The proposed hybrid observers, enjoying global exponential stability, rely on a hysteresis-based switching between different configurations derived from a set of potential functions on SO(3). Different sets of potential functions have been designed via an appropriate angular warping transformation applied to some smooth and non-smooth potential functions on SO(3). We show that the proposed hybrid observers can be expressed solely in terms of inertial vector measurements and biased angular velocity readings. Simulation results are given to illustrate the effectiveness of the proposed attitude estimation approach. 
Soulaimane Berkane, Abdelkader Abdessameud and Abdelhamid Tayebi
math.OC