This work presents a filter for estimating the state of nonlinear dynamic systems. It is based on optimal recursive approximation the state densities by means of Dirac mixture functions in order to allow for a closed form solution of the prediction and filter step. The approximation approach is based on a systematic minimization of a distance measure and is hence optimal and deterministic. In contrast to non-deterministic methods we are able to determine the optimal number of components in the Dirac mixture. A further benefit of the proposed approach is the consideration of measurements during the approximation process in order to avoid parameter degradation.