This paper addresses the problem of attitude and rate gyro bias estimation using Set-Valued Observers (SVOs). We propose a singularity-free solution that exploits rate gyro measurements and vector observations corrupted by bounded noise providing bounds on the attitude of the rigid body and on the bias of the rate gyros. The sensor readings are fused directly by the SVO, without intermediate attitude computation. By taking advantage of the powerful new multi-core processors it is possible to increase the estimator convergence rate without compromising the execution time. The feasibility of the technique is demonstrated in simulation.