This technical note outlines the formulation of a novel discrete-time robust extended Kalman filter for uncertain systems with uncertainties described in terms of Sum Quadratic Constraints. The robust filter is an approximate set-valued state estimator which is robust in the sense that it can handle modeling uncertainties in addition to exogenous noise. Riccati and filter difference equations are obtained as an approximate solution to a reverse-time optimal control problem defining the set-valued state estimator. In order to obtain a solution to the set-valued state estimation problem, the discrete-time system dynamics are modeled backwards in time.