Attitude Estimation on SO(3) Under Biased, Scaled, and Misaligned Rate Gyro Measurements

Abstract

This technical note presents a nonlinear attitude observer formulated directly on the special orthogonal group ($\mathsf {SO}(3)$). The observer uses body-fixed measurements from at least two noncollinear inertial reference directions, along with readings from a triaxial rate gyro. The rate gyro outputs are subject to nonidealities modeled as an affine transformation of the input. Under standard and mild assumptions, such as the requirement for persistent excitation of the true angular velocity and its derivative, the proposed estimator ensures almost global asymptotic stability, while simultaneously estimating attitude and intrinsic parameters of the rate gyro, including scaling factors, installation misalignment, and offset. The observer’s performance and effectiveness are demonstrated through extensive and realistic numerical simulations.