Comparison of an attitude estimator based on the Lagrange-d´Alembert principle with some state-of-the-art filters

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 linearly on the angular velocity estimation error is introduced, and the discrete Lagrange-d´Alembert principle is applied to the Lagrangian with this dissipation. An implicit and an explicit first-order version of this discrete-time estimation scheme is presented. A comparison of this estimator is made with certain state-of-the-art attitude estimators in the absence of bias in sensor readings. Numerical simulations show that this estimator is robust and unlike extended Kalman filter-based schemes, its convergence does not depend on the gain values. In addition, the variational estimator is found to be more computationally efficient than these other estimators.