Gyro-free attitude observer of rigid body via only time-varying reference vectors

An observer is proposed to estimate attitude and angular velocity subject to time-varying inertia reference vectors and unavailability of angular velocity, simultaneously. To deal with the absence of the angular velocity information, the Lyapunov transformation is proposed and the quadratic term on the angular velocity in the dynamic equation is canceled to facilitate the observer design. Therefore both the attitude and angular momentum should be estimated, and the angular velocity information is synthesized from these two signals. Besides, in face of time-varying reference vectors, a set of virtual constant inertia vectors and the counterparts in the body-attached frame are introduced in the angular momentum observer. The measured reference vectors are then used to provide the upper and lower bounds of the norm of the attitude estimation error, and thus the observer gains can be dynamically adjusted based on these bounds. Simulation results are provided to verify the effectiveness of the proposed scheme.