  In this work, asymptotically stable state estimation schemes are proposed for
rigid body motion, using the framework of geometric mechanics. Rigorous
stability analyses of the estimation schemes presented here guarantee the
nonlinear stability of these schemes. The stability of these schemes does not
depend on the characteristics of the sensor measurement noise or external
disturbances. In addition, they are robust to initial errors in the state
estimates and do not need to be re-tuned when sensor noise properties change.
In the first part of this dissertation, estimation of rigid body states is
considered, given the dynamics model of the rigid body. In the second part, an
estimation scheme that does not require knowledge of the dynamics of the rigid
body is derived, based on onboard sensor measurements obtained at an
appropriate frequency. The frequency of such measurements must be suitably high
to resolve the motion of the rigid body. These attitude and pose estimation
schemes are obtained by applying the Lagrange-d'Alembert principle from
variational mechanics, to a Lagrangian constructed from state estimation errors
and a dissipative term linear in the velocity estimation errors.
