Discrete-time rigid body attitude state estimation based on the discrete Lagrange-d´Alembert principle

Discrete-time estimation of rigid body attitude and angular velocity without any knowledge of the attitude dynamics model, is treated using the discrete Lagrange-d´Alembert principle. Using body-fixed sensor measurements of direction vectors and angular velocity, a Lagrangian is obtained as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential obtained from Wahba´s function. An additional dissipation term that depends on the angular velocity estimation error is introduced, and the discrete Lagrange-d´Alembert principle is applied to the Lagrangian with this dissipation. An explicit first order and a symmetric second-order version of this discrete-time filtering scheme are also presented, with a discussion of their advantages. A numerical simulation comparing the performances of the second-order estimator and the first-order estimator is carried out.