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 in | Automatica (Oxford) Vol. 48; no. 2; pp. 327 - 341 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Kidlington
Elsevier Ltd
01.02.2012
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0005-1098 1873-2836 |
| DOI | 10.1016/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. |
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| 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 |
| Author_xml | – sequence: 1 givenname: Bin surname: Jia fullname: Jia, Bin email: bj179@msstate.edu – sequence: 2 givenname: Ming surname: Xin fullname: Xin, Ming email: xin@ae.msstate.edu – sequence: 3 givenname: Yang surname: Cheng fullname: Cheng, Yang email: cheng@ae.msstate.edu |
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| 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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| 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 |
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