Exteroceptive measurement filtering embedded within an SO(3)-based attitude estimator

Abstract

A nonlinear deterministic attitude estimator is developed. The estimator evolves directly on the special orthogonal group of rigid-body rotations. Similar estimators in the literature are characterized by constant estimator gains that amplify noise across all frequencies. The proposed method accounts for undesirable noise in exteroceptive measurements by incorporating a strictly positive real (SPR) filter in the estimator structure. By tuning the “embedded” SPR filter over a frequency bandwidth undesirable noise corrupting exteroceptive measurements may be rejected. Rate-gyro bias estimation is also considered. The proposed attitude estimator is shown to asymptotically converge to the desired equilibrium point (i.e., when the estimated attitude and bias are equal to their true counterparts), provided a restriction on the set of initial conditions is satisfied. Moreover, exponential convergence is shown in a certain region about the desired equilibrium point. The proposed method is demonstrated in simulation.