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Designing robust algorithms in the face of estimation uncertainty is a challenging task. Indeed, controllers seldom consider estimation uncertainty and only rely on the most likely estimated state. Consequently, sudden changes in the environment or the robot’s dynamics can lead to catastrophic behaviors. Leveraging recent results in risk-sensitive optimal control, this paper presents a risk-sensitive Extended Kalman Filter that can adapt its estimation to the control objective, hence allowing safe output-feedback Model Predictive Control (MPC). By taking a pessimistic estimate of the value function resulting from the MPC controller, the filter provides increased robustness to the controller in phases of uncertainty as compared to a standard Extended Kalman Filter (EKF). The filter has the same computational complexity as an EKF and can be used for real-time control. The paper evaluates the risk-sensitive behavior of the proposed filter when used in a nonlinear MPC loop on a planar drone and industrial manipulator in simulation, as well as on an external force estimation task on a real quadruped robot. These experiments demonstrate the ability of the approach to significantly improve performance in face of uncertainties.