# On the relation between Gaussian process quadratures and sigma-point methods

arXiv: https://arxiv.org/abs/1504.05994 · HTML: https://mlsanity.com/paper/1504.05994/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Apr 2015.

## Built on by (most cited first, 2 of 2)

- [Combining Gaussian processes and polynomial chaos expansions for stochastic nonlinear model predictive control](https://mlsanity.com/paper/2103.05441/) (2021)
- [Bayesian Quadrature](https://mlsanity.com/paper/2602.16218/) (2026)

## Abstract (arXiv)

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.