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.