Authors:
Jakub Prüher
and
Miroslav Šimandl
Affiliation:
University of West Bohemia, Czech Republic
Keyword(s):
Nonlinear Filtering, Bayesian Quadrature, Gaussian Process.
Related
Ontology
Subjects/Areas/Topics:
Informatics in Control, Automation and Robotics
;
Nonlinear Signals and Systems
;
Signal Processing, Sensors, Systems Modeling and Control
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
signifi
cantly improved estimate credibility and a comparable root-mean-square error.
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