Approximate non-Gaussian filtering with linear state and observation relations

Two approaches to the non-Gaussian filtering problem are presented. The proposed filters retain the computationally attractive recursive structure of the Kalman filter and they approximate well the exact minimum variance filter in cases where either 1) the state noise is Gaussian or its variance small in comparison to the observation noise variance, or 2) the observation noise is Gaussian and the system is one step observable. In both cases, the state estimate is formed as a linear prediction corrected by a nonlinear function of past and present observations. Some simulation results are presented.