Multi-modal densities appear frequently in time series and
practical applications. However, they cannot be represented
by common state estimators, such as the Extended Kalman
Filter (EKF) and the Unscented Kalman Filter (UKF), which
additionally suffer from the fact that uncertainty is often not
captured sufficiently well, which can result in incoherent and
divergent tracking performance. In this paper, we address these issues by devising a non-linear filtering algorithm where
densities are represented by Gaussian mixture models, whose
parameters are estimated in closed form. The resulting method exhibits a superior performance on typical benchmarks.