Optimal Filtering of Nonlinear Systems Based on Pseudo Gaussian Densities

We consider the problem of estimating the state of a discrete–time dynamic system comprising a linear system equation and a nonlinear measurement equation based on measurements corrupted by non–Gaussian noise. The problem is solved by recursively calculating the complete posterior density of the state given the measurements. For representing the resulting non–Gaussian posterior, a new exponential type density, the so called pseudo Gaussian density, is introduced. By converting the original nonlinear system to an equivalent linear representation in a higher–dimensional space, the parameters of the pseudo Gaussian posterior are obtained by means of a linear estimator operating in the higher–dimensional space. The resulting filtering algorithms are easy to implement and always guarantee valid posterior densities.