Gaussian Process Quadrature Moment Transform

Prüher, Jakub; Straka, Ondřej

doi:10.1109/tac.2017.2774444

Cited by 15 publications

(19 citation statements)

References 34 publications

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“…Among many other filters, (2.11) is satisfied by the aforementioned Kalman--Bucy filters based on the unscented transform and Gaussian tensor-product rules. Filters that do not satisfy this assumption include kernel-based Gaussian process cubature filters [45,35].…”

Section: Gaussian Integration Filtersmentioning

confidence: 99%

On Stability of a Class of Filters for Nonlinear Stochastic Systems

Karvonen¹,

Bonnabel²,

Moulines³

et al. 2020

SIAM J. Control Optim.

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Section: Gaussian Integration Filtersmentioning

confidence: 99%

On Stability of a Class of Filters for Nonlinear Stochastic Systems

Karvonen¹,

Bonnabel²,

Moulines³

et al. 2020

SIAM J. Control Optim.

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“…Then the prediction covariance matrix in (24) can be obtained by (25) when a = b or by adding (27) to (25) in case a = b.…”

Section: Uncertainty Calibration Of Sigma Points Transform a Gamentioning

confidence: 99%

“…In the application of GNSS/INS, GP has also been used to enhance central difference KF, which however needs the ground truth to identify the residue between approximated model and reference model [26]. Recently, a quadrature rule named Gaussian process quadrature (GPQ) is proposed to further account for the uncertainty consisted in numerically computed moments, base on which a new quadrature KF is derived without a model identification step [27]. However, the GPQ-based KF may still suffer from non-Gaussian measurement noise, and the fixed selection of kernel parameters for GP measurement model approximation is invalid due to the changing sensor environment, which is not the case for process model.…”

Section: Introductionmentioning

confidence: 99%

Performance Enhancement of Robust Cubature Kalman Filter for GNSS/INS Based on Gaussian Process Quadrature

et al. 2020

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The sigma-point Kalman filters are generally considered to outperform extended Kalman filter in the application of GNSS/INS, where cubature Kalman filter (CKF) is widely approved because of its rigorous mathematic derivation. In order to improve the robustness of GNSS/INS under GNSS-challenged environment, a robust CKF (RCKF) is developed based on novel sigma-point update framework (NSUF) in our previous work, whereas the efficiency of NSUF is still plagued by the unknown process model uncertainty. In this paper, an enhanced RCKF is proposed based on Gaussian process quadrature (GPQ), where the uncertainty consisted in sigma points transform is processed by GPQ conditioning on the approximated posterior PDF. Experiment result on loosely coupled GNSS/INS demonstrates the superiority of proposed method, where the heading error and roll error are reduced by 60.5% and 37.5% respectively compared with RCKF, and it achieves better position result than GP-CKF under GNSS outage. INDEX TERMS Land vehicle navigation, sigma-point Kalman filter, Gaussian process quadrature, sigma points transform.

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“…Finally, it is worth remarking that this article is not the first instance of fully symmetric sets being used in conjunction with kernel quadrature. Arguably the simplest non-trivial fully symmetric kernel quadrature rule (this rule appears briefly in Section 4.3) has seen use in approximate filtering of non-linear systems [58,50,51], but without an efficient weight computation algorithm.…”

Section: Introductionmentioning

confidence: 99%

Fully Symmetric Kernel Quadrature

Karvonen¹,

Särkkä²

2018

SIAM J. Sci. Comput.

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Kernel quadratures and other kernel-based approximation methods typically suffer from prohibitive cubic time and quadratic space complexity in the number of function evaluations. The problem arises because a system of linear equations needs to be solved. In this article we show that the weights of a kernel quadrature rule can be computed efficiently and exactly for up to tens of millions of nodes if the kernel, integration domain, and measure are fully symmetric and the node set is a union of fully symmetric sets. This is based on the observations that in such a setting there are only as many distinct weights as there are fully symmetric sets and that these weights can be solved from a linear system of equations constructed out of row sums of certain submatrices of the full kernel matrix. We present several numerical examples that show feasibility, both for a large number of nodes and in high dimensions, of the developed fully symmetric kernel quadrature rules. Most prominent of the fully symmetric kernel quadrature rules we propose are those that use sparse grids.

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Gaussian Process Quadrature Moment Transform

Cited by 15 publications

References 34 publications

On Stability of a Class of Filters for Nonlinear Stochastic Systems

On Stability of a Class of Filters for Nonlinear Stochastic Systems

Performance Enhancement of Robust Cubature Kalman Filter for GNSS/INS Based on Gaussian Process Quadrature

Fully Symmetric Kernel Quadrature

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