On the relation between Gaussian process quadratures and sigma-point methods
Abstract
This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing algorithms. We show that many sigma-point methods can be interpreted as Gaussian quadrature based methods with suitably selected covariance functions. We show that this interpretation also extends to more general multivariate Gauss--Hermite integration methods and related spherical cubature rules. Additionally, we discuss different criteria for selecting the sigma-point locations: exactness for multivariate polynomials up to a given order, minimum average error, and quasi-random point sets. The performance of the different methods is tested in numerical experiments.
Cite
@article{arxiv.1504.05994,
title = {On the relation between Gaussian process quadratures and sigma-point methods},
author = {Simo Särkkä and Jouni Hartikainen and Lennart Svensson and Fredrik Sandblom},
journal= {arXiv preprint arXiv:1504.05994},
year = {2015}
}