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 linearizationmethod. Simulations show the superior estimation performance compared to related approaches and common filtering algorithms.