Abstract : This paper proposes an attitude estimation methodology for the case where attitude sensors provide discrete-time samples of vector measurements at different sample rates and with time delays. The proposed methodology is based on a cascade combination of an output predictor and an attitude observer or filter. The predictor compensates for the effect of sampling and delays in vector measurements and provides continuous-time predictions of outputs. These predictions are then used in an observer or filter to estimate the current attitude. The primary contribution of the paper is to exploit the underlying symmetry of the attitude kinematics to design a recursive predictor that is computationally simple and generic, in the sense that it can be combined with any asymptotically stable observer or filter. We prove that the predictor is able to reproduce the continuous time delay-free vector measurements. In a simulation example, we demonstrate good performance of the combined predictor-observer even in presence of measurement noise and delay uncertainties.