Nonlinear Stochastic Attitude Filters on the Special Orthogonal Group 3: Ito and Stratonovich

This paper formulates the attitude filtering problem as a nonlinear stochastic filter problem evolved directly on the Special Orthogonal Group 3 ( ${\mathbb {SO}}(3)$ ). One of the traditional potential functions for nonlinear deterministic complimentary filters is studied and examined against angular velocity measurements corrupted with noise. This paper demonstrates that the careful selection of the attitude potential function allows to attenuate the noise associated with the angular velocity measurements and results into superior convergence properties of estimator and correction factor. The problem is formulated as a stochastic problem through mapping $ {\mathbb {SO}}(3)$ to Rodriguez vector parameterization. Two nonlinear stochastic complimentary filters are developed on $ {\mathbb {SO}}(3)$ . The first stochastic filter is driven in the sense of Ito and the second one considers Stratonovich. The two proposed filters guarantee that errors in the Rodriguez vector and estimates are semi-globally uniformly ultimately bounded in mean square. Simulation results are presented to illustrate the effectiveness of the proposed filters considering high level of uncertainties in angular velocity as well as body-frame vector measurements.