Bayesian Estimation and Tracking: A Practical Guide

11.1 One-Dimensional Gauss–Hermite Quadrature

The objective now is to expand in terms of orthogonal polynomials in some way. First, consider the one-dimensional case integral of the form

(11.6)

Expanding in a general set of orthogonal polynomials, can be approximated by

(11.7)

where { represent a set of orthogonal polynomials, with the polynomials and orthogonal with respect to a weight (or kernel) function over the interval such that

(11.8)

Here, c_l is a normalization constant and

(11.9) ...