Importance Gauss-Hermite Gaussian Filter for Models with Non-Additive Non-Gaussian Noises

The paper deals with the state estimation of nonlinear stochastic systems with non-additive non-Gaussian noises. A new algorithm is proposed based on the computationally efficient Gaussian filter. The non-additivity and non-Gaussianity of the noises prevents the usage of standard quadratures to evaluate the moment integrals present in the Gaussian filter as these are not Gauss-weighted. The proposed algorithm leverages the importance Gauss-Hermite method to evaluate the integrals by means of the Gaussian proposal PDF. In order to improve the evaluation quality, an iterative improvement of the proposal PDF is employed. The paper also discusses the algorithm for special cases of the model with either process or measurement noise being additive yet non-Gaussian. The performance of the proposed algorithm is illustrated using a numerical example.