  Gaussian mixtures are a common density representation in nonlinear,
non-Gaussian Bayesian state estimation. Selecting an appropriate number of
Gaussian components, however, is difficult as one has to trade of computational
complexity against estimation accuracy. In this paper, an adaptive Gaussian
mixture filter based on statistical linearization is proposed. Depending on the
nonlinearity of the considered estimation problem, this filter dynamically
increases the number of components via splitting. For this purpose, a measure
is introduced that allows for quantifying the locally induced linearization
error at each Gaussian mixture component. The deviation between the nonlinear
and the linearized state space model is evaluated for determining the splitting
direction. The proposed approach is not restricted to a specific statistical
linearization method. Simulations show the superior estimation performance
compared to related approaches and common filtering algorithms.
