Sparse-grid quadrature nonlinear filtering

In this paper, a novel nonlinear filter named Sparse-grid Quadrature Filter (SGQF) is proposed. The filter utilizes weighted sparse-grid quadrature points to approximate the multi-dimensional integrals in the nonlinear Bayesian estimation algorithm. The locations and weights of the univariate quadra...

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Published inAutomatica (Oxford) Vol. 48; no. 2; pp. 327 - 341
Main Authors Jia, Bin, Xin, Ming, Cheng, Yang
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier Ltd 01.02.2012
Elsevier
Subjects
Online AccessGet full text
ISSN0005-1098
1873-2836
DOI10.1016/j.automatica.2011.08.057

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Abstract In this paper, a novel nonlinear filter named Sparse-grid Quadrature Filter (SGQF) is proposed. The filter utilizes weighted sparse-grid quadrature points to approximate the multi-dimensional integrals in the nonlinear Bayesian estimation algorithm. The locations and weights of the univariate quadrature points with a range of accuracy levels are determined by the moment matching method. Then the univariate quadrature point sets are extended to form a multi-dimensional grid using the sparse-grid theory. Compared with the conventional point-based methods, the estimation accuracy level of the SGQF can be flexibly controlled and the number of sparse-grid quadrature points for the SGQF is a polynomial of the dimension of the system, which alleviates the curse of dimensionality for high dimensional problems. The Unscented Kalman Filter (UKF) is proven to be a subset of the SGQF at the level-2 accuracy. The performance of this filter is demonstrated by an orbit estimation problem. The simulation results show that the SGQF achieves higher accuracy than the Extended Kalman Filter (EKF), the UKF, and the Cubature Kalman Filter (CKF). In addition, the SGQF is computationally much more efficient than the multi-dimensional Gauss–Hermite Quadrature Filter (GHQF) with the same performance.
AbstractList In this paper, a novel nonlinear filter named Sparse-grid Quadrature Filter (SGQF) is proposed. The filter utilizes weighted sparse-grid quadrature points to approximate the multi-dimensional integrals in the nonlinear Bayesian estimation algorithm. The locations and weights of the univariate quadrature points with a range of accuracy levels are determined by the moment matching method. Then the univariate quadrature point sets are extended to form a multi-dimensional grid using the sparse-grid theory. Compared with the conventional point-based methods, the estimation accuracy level of the SGQF can be flexibly controlled and the number of sparse-grid quadrature points for the SGQF is a polynomial of the dimension of the system, which alleviates the curse of dimensionality for high dimensional problems. The Unscented Kalman Filter (UKF) is proven to be a subset of the SGQF at the level-2 accuracy. The performance of this filter is demonstrated by an orbit estimation problem. The simulation results show that the SGQF achieves higher accuracy than the Extended Kalman Filter (EKF), the UKF, and the Cubature Kalman Filter (CKF). In addition, the SGQF is computationally much more efficient than the multi-dimensional Gauss-Hermite Quadrature Filter (GHQF) with the same performance.
Author Xin, Ming
Jia, Bin
Cheng, Yang
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Issue 2
Keywords Nonlinear filter
Bayesian estimation
Kalman filter
Gauss–Hermite Quadrature
Unscented Kalman filter
Sparse-grid
Orbit estimation
Performance evaluation
Non linear filter
Modeling
Quadrature
System with n degrees of freedom
Multigrid
Sparse matrix
System identification
Localization
Bayes estimation
Set point
Hermite polynomial
Gauss approximation
Dimensionality
Optimal filter
Orbit
Gauss-Hermite Quadrature
Moment method
Extended Kalman filter
Weight
Point estimation
Discrete time
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Snippet In this paper, a novel nonlinear filter named Sparse-grid Quadrature Filter (SGQF) is proposed. The filter utilizes weighted sparse-grid quadrature points to...
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StartPage 327
SubjectTerms Accuracy
Algorithms
Applied sciences
Automation
Bayesian estimation
Computer science; control theory; systems
Computer simulation
Control theory. Systems
Exact sciences and technology
Filtering
Fundamental areas of phenomenology (including applications)
Gauss–Hermite Quadrature
Kalman filter
Kalman filters
Mathematics
Modelling and identification
Nonlinear filter
Nonlinearity
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Orbit estimation
Physics
Quadratures
Sciences and techniques of general use
Solid dynamics (ballistics, collision, multibody system, stabilization...)
Solid mechanics
Sparse-grid
Unscented Kalman filter
Title Sparse-grid quadrature nonlinear filtering
URI https://dx.doi.org/10.1016/j.automatica.2011.08.057
https://www.proquest.com/docview/1019626976
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