In this paper, the Prior Density Splitting Mixture Estimator (PDSME), a new Gaussian mixture filtering algorithm for nonlinear dynamical systems and nonlinear measurement equations, is introduced. This filter reduces the linearization error which typically arises if nonlinear state and measurement equations are linearized to apply linear filtering techniques. For that purpose, the PDSME splits the prior probability density into several components of a Gaussian mixture with smaller covariances. The PDSME is applicable to both prediction and filter steps. A measure for the linearization error similar to the Kullback-Leibler distance is introduced allowing the user to specify the desired estimation quality. An upper bound for the computational effort can be given by limiting the maximum number of Gaussian mixture components.