Optimal attitude estimation using Set-Valued Observers

An optimal Set-Valued Observer (SVO) for attitude estimation that merges rate gyro readings with body frame vectorial observations is proposed. The observer provides singularity-free estimates and considers sensor readings corrupted by bounded (but unknown) measurement noise. The suggested solution is an alternative method to the ones available in the literature, with the guarantee that the state is inside the estimated set. Optimal estimates are obtained, provided that there is no uncertainty in the angular velocity measurements, whereas the case with noisy rate gyros measurements is addressed by resorting to a relaxation of the problem. The sensor readings are exploited directly in the observer, without intermediate attitude estimate computation. Moreover, the feasibility of the technique is demonstrated in simulation.