Paper E. (Semi-)Analytic Gaussian Mixture Filter. Edited version of the paper: M. F. Huber, F. Beutler, and U. D. Hanebeck. (Semi-)Analytic Gaussian Mixture Filter. In Proceedings of the 18th IFACWorld Congress, pages 10014-10020,Milano, Italy, August 2011

In nonlinear filtering, special types of Gaussian mixture filters are a straightforward extension of Gaussian filters, where linearizing the system model is performed individually for each Gaussian component. In this paper, two novel types of linearization are combined with Gaussian mixture filters. The first linearization is called analytic stochastic linearization, where the linearization is performed analytically and exactly, i.e., without Taylor-series expansion or approximate sample-based density representation. In cases where a full analytical linearization is not possible, the second approach decomposes the nonlinear system into a set of nonlinear subsystems that are conditionally integrable in closed form. These approaches aremore accurate than fully applying classical linearization.