Gaussian Filter based on Deterministic Sampling for High Quality Nonlinear Estimation

In this paper, a Gaussian filter for nonlinear Bayesian estimation is introduced that is based on a deterministic sample selection scheme. For an effective sample selection, a parametric density function representation of the sample points is employed, which allows approximating the cumulative distribution function of the prior Gaussian density. The computationally demanding parts of the optimization problem formulated for approximation are carried out off-line for obtaining an efficient filter, whose estimation quality can be altered by adjusting the number of used sample points. The improved performance of the proposed Gaussian filter compared to the well-known unscented Kalman fiter is demonstrated by means of two examples.