Bayesian Quadrature in Nonlinear Filtering

Jakub Prüher, Miroslav Šimandl

2015

Abstract

The paper deals with the state estimation of nonlinear stochastic discrete-time systems by means of quadrature-based filtering algorithms. The algorithms use quadrature to approximate the moments given by integrals. The aim is at evaluation of the integral by Bayesian quadrature. The Bayesian quadrature perceives the integral itself as a random variable, on which inference is to be performed by conditioning on the function evaluations. Advantage of this approach is that in addition to the value of the integral, the variance of the integral is also obtained. In this paper, we improve estimation of covariances in quadrature-based filtering algorithms by taking into account the integral variance. The proposed modifications are applied to the Gauss-Hermite Kalman filter and the unscented Kalman filter algorithms. Finally, the performance of the modified filters is compared with the unmodified versions in numerical simulations. The modified versions of the filters exhibit significantly improved estimate credibility and a comparable root-mean-square error.

Paper Citation

in Harvard Style

Prüher J. and Šimandl M. (2015). Bayesian Quadrature in Nonlinear Filtering . In Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-758-122-9, pages 380-387. DOI: 10.5220/0005534003800387

in Bibtex Style

@conference{icinco15,
author={Jakub Prüher and Miroslav Šimandl},
title={Bayesian Quadrature in Nonlinear Filtering},
booktitle={Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2015},
pages={380-387},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005534003800387},
isbn={978-989-758-122-9},
}

in EndNote Style

TY - CONF
JO - Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - Bayesian Quadrature in Nonlinear Filtering
SN - 978-989-758-122-9
AU - Prüher J.
AU - Šimandl M.
PY - 2015
SP - 380
EP - 387
DO - 10.5220/0005534003800387