Abstract : This paper provides a nonlinear attitude estimation method for vehicles performing high acceleration maneuvers when measurements of linear velocity and the ambient magnetic field are delayed. Linear velocity is measured using the Global Positioning System (GPS) and the delays of GPS and magnetometer measurements are assumed to be known constants. Our proposed method consists of a delayed observer coupled with a dynamic predictor. The delayed observer uses delayed measurements and provides estimates of delayed attitude and velocity states that are in turn used in the predictor to generate estimates of the current attitude and velocity. A key contribution of the paper is effective use of the underlying symmetries of the system in order to design a generic predictor that can be coupled to different observers. We prove exponential convergence of the predicted attitude and velocity for a specific observer choice drawn from the literature.