This paper copes with the problem of nonlinear Bayesian state estimation. A nonlinear filter, the Sliced Gaussian Mixture Filter (SGMF), employs linear substructures in the nonlinear measurement and prediction model in order to simplify the estimation process. Here, a special density representation, the sliced Gaussian mixture density, is used to derive an exact solution of the Chapman-Kolmogorov equation. The sliced Gaussian mixture density is obtained by a systematic and deterministic approximation of a continuous density minimizing a certain distance measure. In contrast to previous work, improvements of the SGMF presented here include an extended system model and the processing of multi-dimensional nonlinear subspaces. As an application for the SGMF, cooperative passive target tracking, where sensors take angular measurements from a target, is considered in this paper. Finally, the performance of the proposed estimator is compared to the marginalized particle filter (MPF) in simulations.