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

2015/04/22 by Simo Särkkä, Särkkä, Simo, Jouni Hartikainen +5
Mathematics · #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Methodology (stat.ME) #math.DS #stat.ME #stat.ML

paper · pdf · doi:10.48550/arxiv.1504.05994

arxiv created 2015/04/22 · arxiv updated 2015/04/24

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.

Related

• Student-t Process Quadratures for Filtering of Non-Linear Systems with Heavy-Tailed Noise
• Improved Calibration of Numerical Integration Error in Sigma-Point Filters
• Discrete-Time Nonlinear Filtering Algorithms Using Gauss–Hermite Quadrature
• On the Correspondence between Gaussian Processes and Geometric Harmonics
• Variable sigma Gaussian processes: An expectation propagation perspective