Gaussian Process Quadrature Moment Transform
@article{Prher2018GaussianPQ, title={Gaussian Process Quadrature Moment Transform}, author={Jakub Pr{\"u}her and Ondřej Straka}, journal={IEEE Transactions on Automatic Control}, year={2018}, volume={63}, pages={2844-2854} }
Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules, which cannot account for the approximation errors. Our aim is to design a method for moment transformation of Gaussian random variables, which accounts for the error in the numerically computed mean. We employ an instance of Bayesian quadrature, called Gaussian process quadrature (GPQ…
Figures and Tables from this paper
15 Citations
Student-t process quadratures for filtering of non-linear systems with heavy-tailed noise
- Mathematics, Computer Science2017 20th International Conference on Information Fusion (Fusion)
- 2017
The aim of this article is to design a moment transformation for Student-t distributed random variables, which is able to account for the error in the numerically computed mean, and is shown to outperform the state-of-the-art moment transforms.
A Probabilistic Taylor Expansion with Applications in Filtering and Differential Equations
- MathematicsArXiv
- 2021
New probabilistic versions of the classical extended Kalman filter for non-linear state estimation and the Euler method for solving ordinary differential equations are introduced.
Improved Calibration of Numerical Integration Error in Sigma-Point Filters
- MathematicsIEEE Transactions on Automatic Control
- 2021
The Bayes–Sard quadrature method is investigated in the context of sigma-point filters, which enables uncertainty due to quadratures to be formalized within a probabilistic model.
Stochastic Integration Filter: Theoretical and Implementation Aspects
- Computer Science2018 21st International Conference on Information Fusion (FUSION)
- 2018
The paper analyzes theoretical consequences of using stochastic integration rules and proposes several modifications that improve the performance of the stoChastic integration filter, which is an representative of the Gaussian filter and computes the state and measurement predictive moments by making use of a stochastically integration rule.
Adaptive Bayesian quadrature based statistical moments estimation for structural reliability analysis
- EngineeringReliab. Eng. Syst. Saf.
- 2020
Fully symmetric kernel quadrature
- Computer Science, MathematicsSIAM J. Sci. Comput.
- 2018
This article shows 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 symmetrical sets.
Combining Gaussian processes and polynomial chaos expansions for stochastic nonlinear model predictive control
- Engineering
- 2021
Model predictive control is an advanced control approach for multivariable systems with constraints, which is reliant on an accurate dynamic model. Most real dynamic models are however affected by…
Improved Cubature Kalman Filtering on Matrix Lie Groups Based on Intrinsic Numerical Integration Error Calibration with Application to Attitude Estimation
- MathematicsMachines
- 2022
This paper investigates the numerical integration error calibration problem in Lie group sigma point filters to obtain more accurate estimation results. On the basis of the theoretical framework of…
On Stability of a Class of Filters for Nonlinear Stochastic Systems
- MathematicsSIAM J. Control. Optim.
- 2020
Stability properties of a broad class of commonly used filters, including the extended and unscented Kalman filters, for discrete and continuous-time stochastic dynamic systems with non-linear state dynamics and linear measurements are considered.
Masterarbeit Machine Learning Uncertainty Propagation in Probabilistic Ordinary Differential Equation Solvers
- Computer Science
- 2021
A novel fully probabilistic approach to e-ciently compute the expected value and variance of the ODE solutions is proposed, which provides estimated numerical uncertainties, which can be further utilized in a computation pipeline.
References
SHOWING 1-10 OF 53 REFERENCES
Bayesian Quadrature Variance in Sigma-Point Filtering
- Computer Science, MathematicsICINCO
- 2015
This work proposes a method for incorporating information about the integral approximation error into the filtering algorithm by exploiting features of a Bayesian quadrature—an alternative to classical numerical integration.
Gaussian process quadratures in nonlinear sigma-point filtering and smoothing
- Mathematics, Computer Science17th International Conference on Information Fusion (FUSION)
- 2014
It is shown that with suitable selections of Hermite polynomial covariance functions the Gaussian process quadratures can be reduced to unscented transforms, spherical cubature rules, and to Gauss-Hermite rules previously proposed for approximate nonlinear Kalman filter and smoothing.
On the relation between Gaussian process quadratures and sigma-point methods
- Mathematics, Computer Science
- 2015
It is shown that many sigma-point methods can be interpreted as Gaussian quadrature based methods with suitably selected covariance functions, and this interpretation also extends to more general multivariate Gauss--Hermite integration methods and related spherical cubature rules.
Moment Estimation Using a Marginalized Transform
- MathematicsIEEE Transactions on Signal Processing
- 2012
A method for estimating mean and covariance of a transformed Gaussian random variable, based on evaluations of the transforming function, which resembles the unscented transform and Gauss-Hermite integration in that respect and performs better than these methods.
Analytic moment-based Gaussian process filtering
- Computer ScienceICML '09
- 2009
An analytic moment-based filter for nonlinear stochastic dynamic systems modeled by Gaussian processes that avoids finite-sample approximations and is compared to a variety of Gaussian filters.
Robust Filtering and Smoothing with Gaussian Processes
- Computer ScienceIEEE Transactions on Automatic Control
- 2012
We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by…
Active Learning of Model Evidence Using Bayesian Quadrature
- Computer ScienceNIPS
- 2012
This work proposes a novel Bayesian Quadrature approach for numerical integration when the integrand is non-negative, such as the case of computing the marginal likelihood, predictive distribution, or normalising constant of a probabilistic model.
A Numerical-Integration Perspective on Gaussian Filters
- Computer ScienceIEEE Transactions on Signal Processing
- 2006
A common base is provided for the first time to analyze and compare Gaussian filters with respect to accuracy, efficiency and stability factor and to help design more efficient filters by employing better numerical integration methods.
Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models
- Computer Science
- 1996
A new algorithm based on a Monte Carlo method that can be applied to a broad class of nonlinear non-Gaussian higher dimensional state space models on the provision that the dimensions of the system noise and the observation noise are relatively low.