Generalized Jacobi Spectral Method in Solving Nonlinear Filtering Problems

Xue Luo; Fang Wang

doi:10.1109/CDC.2018.8619484

Generalized Jacobi Spectral Method in Solving Nonlinear Filtering Problems

Xue Luo
, Fang Wang

School of Mathematical Sciences

Beihang University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

The on-and off-line algorithm for the nonlinear filtering (NLF) problems was developed by Yau and the first author, and the Hermite spectral method (HSM) has been implemented to serve as the off-line computations. Notice that the true states in real applications can always be assumed to be bounded. In this paper, we shall investigate the Jacobi spectral method (JSM) instead to numerically solve the forward Kolmogorov equation (FKE) arising in NLF problems. The convergence rate of JSM to FKE is analyzed in the suitable function space, which is twice as fast as that in HSM. The formulation has been detailed for an essentially infinite-dimensional NLF problem, the 1-d cubic sensor problem. Compared with HSM, the JSM yields more accurate result.

Original language	English
Title of host publication	2018 IEEE Conference on Decision and Control, CDC 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	7206-7212
Number of pages	7
ISBN (Electronic)	9781538613955
DOIs	https://doi.org/10.1109/CDC.2018.8619484
State	Published - 2 Jul 2018
Event	57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: 17 Dec 2018 → 19 Dec 2018

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2018-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	57th IEEE Conference on Decision and Control, CDC 2018
Country/Territory	United States
City	Miami
Period	17/12/18 → 19/12/18

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10.1109/CDC.2018.8619484

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Luo, X., & Wang, F. (2018). Generalized Jacobi Spectral Method in Solving Nonlinear Filtering Problems. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 7206-7212). Article 8619484 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619484

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title = "Generalized Jacobi Spectral Method in Solving Nonlinear Filtering Problems",

abstract = "The on-and off-line algorithm for the nonlinear filtering (NLF) problems was developed by Yau and the first author, and the Hermite spectral method (HSM) has been implemented to serve as the off-line computations. Notice that the true states in real applications can always be assumed to be bounded. In this paper, we shall investigate the Jacobi spectral method (JSM) instead to numerically solve the forward Kolmogorov equation (FKE) arising in NLF problems. The convergence rate of JSM to FKE is analyzed in the suitable function space, which is twice as fast as that in HSM. The formulation has been detailed for an essentially infinite-dimensional NLF problem, the 1-d cubic sensor problem. Compared with HSM, the JSM yields more accurate result.",

author = "Xue Luo and Fang Wang",

note = "Publisher Copyright: {\textcopyright} 2018 IEEE.; 57th IEEE Conference on Decision and Control, CDC 2018 ; Conference date: 17-12-2018 Through 19-12-2018",

year = "2018",

month = jul,

day = "2",

doi = "10.1109/CDC.2018.8619484",

language = "英语",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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Luo, X & Wang, F 2018, Generalized Jacobi Spectral Method in Solving Nonlinear Filtering Problems. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619484, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 7206-7212, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 17/12/18. https://doi.org/10.1109/CDC.2018.8619484

Generalized Jacobi Spectral Method in Solving Nonlinear Filtering Problems. / Luo, Xue; Wang, Fang.
2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 7206-7212 8619484 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - The on-and off-line algorithm for the nonlinear filtering (NLF) problems was developed by Yau and the first author, and the Hermite spectral method (HSM) has been implemented to serve as the off-line computations. Notice that the true states in real applications can always be assumed to be bounded. In this paper, we shall investigate the Jacobi spectral method (JSM) instead to numerically solve the forward Kolmogorov equation (FKE) arising in NLF problems. The convergence rate of JSM to FKE is analyzed in the suitable function space, which is twice as fast as that in HSM. The formulation has been detailed for an essentially infinite-dimensional NLF problem, the 1-d cubic sensor problem. Compared with HSM, the JSM yields more accurate result.

AB - The on-and off-line algorithm for the nonlinear filtering (NLF) problems was developed by Yau and the first author, and the Hermite spectral method (HSM) has been implemented to serve as the off-line computations. Notice that the true states in real applications can always be assumed to be bounded. In this paper, we shall investigate the Jacobi spectral method (JSM) instead to numerically solve the forward Kolmogorov equation (FKE) arising in NLF problems. The convergence rate of JSM to FKE is analyzed in the suitable function space, which is twice as fast as that in HSM. The formulation has been detailed for an essentially infinite-dimensional NLF problem, the 1-d cubic sensor problem. Compared with HSM, the JSM yields more accurate result.

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T2 - 57th IEEE Conference on Decision and Control, CDC 2018

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ER -

Generalized Jacobi Spectral Method in Solving Nonlinear Filtering Problems

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