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In this correspondence paper, a novel robust extended Kalman filter (REKF) for discrete-time nonlinear systems with stochastic uncertainties is proposed. The filter is derived to guarantee an optimized upper bound on the state estimation error covariance despite the model uncertainties as well as the linearization errors. Further analysis shows that the proposed filter has robustness against process noises, measurement noises, and model uncertainties. In addition, the new method is applied in an X-ray pulsar positioning system. It is illustrated through numerical simulations that the REKF is more effective than the standard extended Kalman filter and the extended robust H?? filter.