Guaranteed Performance of Nonlinear Attitude Filters on the Special Orthogonal Group SO(3)

Abstract

This paper proposes two novel nonlinear attitude filters evolved directly on the special orthogonal group SO(3), able to ensure prescribed measures of transient and steady-state performance. The tracking performance of the normalized Euclidean distance of attitude error is trapped to initially start within a large set and converge systematically and asymptotically to the origin from almost any initial condition. The convergence rate is guaranteed to be less than the prescribed value, and the steady-state error does not exceed a predefined small value. The first filter uses a set of vectorial measurements with the need for attitude reconstruction. The second filter does not require attitude reconstruction and instead uses only a rate gyroscope measurement and two or more vectorial measurements. These filters provide good attitude estimates with superior convergence properties and can be applied to measurements obtained from low-cost inertial measurement units. The simulation results illustrate the robustness and effectiveness of the proposed attitude filters with guaranteed performance considering high level of uncertainty in angular velocity along with body-frame vector measurements.