Optimal discretization and updating procedures for Gauss qudarature estimators

This paper presents an alternative method in dealing with non-linear estimation problems. The principle is to approximate the integration of the conditional density functions by using Gaussian Qudrature Formulae and set up the grid for the current filtering density simultaneously. The grid is centered at the filtering mean. The size of the region where the grid locates is changed according to the conditional distribution. A method for choosing the number of nodes and the integration interval to minimize the integration error is given. For the case that the system noises and measurement noises are white gaussian and the measurement function is linearizable, the accuracy of the representation of the filtering density can be theoretically controlled by a priori choice of the number of nodes and the truncation factor.