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A coordinated flight model for estimating the orientation of an aircraft under track from velocity measurements into an extended Kalman filter (EKF) framework is placed here. In doing so, it makes two contributions. First, the EKF provides a rigorous framework for addressing this problem, blending modelling error and measurement error. Second, the EKF supplements the estimated orientation with a measure of the uncertainty in that estimate. Such estimates of uncertainty are crucial in a number of applications, including using the orientation estimates to approximate the radar cross section of the aircraft under track, in an attempt to identify targets. The EKF's performance is demonstrated using both a straight-and-level manoeuvre and a complicated manoeuvre recorded on-board a manoeuvring F-15. In both cases, the state estimates of the EKF are similar to the results obtained from a coordinated flight model. The true orientations almost always fall within one standard deviation of the estimates, as determined by the estimated covariance.