In this paper, we propose a set-valued filtering algorithm for non-linear discrete-time systems. At each step, the algorithm computes an ellipsoid of minimal size that guarantees to contain the true state of the system, despite the noise affecting the system and taking into explicit consideration the linearization error. The filter is based on a two-step prediction-correction structure, each step requiring the solution of a Semi-Definite optimization problem (SDP). The use of the algorithm is illustrated by an example of robust localization of a non-holonomic rover.