  This article presents an extended state observer for vehicle modeled as a
rigid body in three-dimensional translational and rotational motions. The
extended state observer is applicable to a rotorcraft aerial vehicle with a
fixed plane of rotors, modeled as an under-actuated system on the tangent
bundle of the six-dimensional Lie group of rigid body motions, SE(3). The
extended state observer is designed to estimate the resultant external
disturbance force and disturbance torque acting on the vehicle. It guarantees
stable convergence of disturbance estimation errors in finite time when the
disturbances are constant and finite time convergence to a bounded neighborhood
of zero errors for time-varying disturbances. This extended state observer
design is based on a H\"{o}lder-continuous fast finite time stable
differentiator that is similar to the super-twisting algorithm, to obtain fast
convergence. Numerical simulations are conducted to validate the proposed
extended state observer. The proposed extended state observer is compared with
other existing research to show its advantages. A set of experimental results
implementing disturbance rejection control using feedback of disturbance
estimates from the extended state observer is also presented.
