A Gaussian mixture filter with adaptive refinement for nonlinear state estimation

The state estimation of highly nonlinear dynamic systems is difficult because the probability distribution of their states can be highly non-Gaussian. An adaptive Gaussian mixture filter is developed in this work to address this challenge, in which the Gaussian mixture models are refined based on the system's local severity of nonlinearity to attain a high-fidelity estimation of the state distribution. A set of nonlinearity assessment criteria are designed to trigger the splitting of Gaussian components at both the prediction and update stages of Bayesian filtering and the error bound of estimated distribution is established. The new filter has been benchmarked against the existing methods on two challenging problems and it consistently provides among-the-best accuracy with a reasonable computational cost, which proves that it can be used as a reliable state estimator for engineering systems with highly nonlinear dynamics and subject to high magnitudes of uncertainties.