Nonlinear state estimation with nonlinear equality constraints

Jinya Su; Wen Hua Chen; Baibing Li

doi:10.1109/CDC.2014.7039401

Nonlinear state estimation with nonlinear equality constraints

Jinya Su, Wen Hua Chen, Baibing Li

Computing Science

Research output: Chapter in Book/Report/Conference proceeding › Published conference contribution

1 Citation (Scopus)

Abstract

This paper investigates the problem of state estimation of nonlinear systems with nonlinear equality constraints. By treating the nonlinear equality constraints as part of the new coordinate, a diffeomorphism is found such that an unconstrained reduced-order system is obtained. The existing unconstrained estimators can be applied to obtain the reduced-order state estimate. Then, based on the inverse transformation, the original states can be obtained by combing the reduced-order state estimate and the nonlinear equality constraints. Compared with the traditional model reduction approach, there exists one more freedom to choose the independent variables in the proposed approach. Compared with the null space approach, the proposed approach can handle nonlinear estimation with general nonlinear equality constraints. Finally, the estimation problem for a moving vehicle on a given circular path is used to illustrate the principle of the proposed approach.

Original language	English
Title of host publication	53rd IEEE Conference on Decision and Control,CDC 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	322-327
Number of pages	6
Edition	February
ISBN (Electronic)	9781467360906
ISBN (Print)	9781479977468
DOIs	https://doi.org/10.1109/CDC.2014.7039401
Publication status	Published - Dec 2014
Event	2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States Duration: 15 Dec 2014 → 17 Dec 2014

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Number	February
Volume	2015-February
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014
Country/Territory	United States
City	Los Angeles
Period	15/12/14 → 17/12/14

Keywords

Reduced order systems
Null space
Vehicles
Roads
Noise measurement
State estimation

Access to Document

10.1109/CDC.2014.7039401

Cite this

Su, J., Chen, W. H., & Li, B. (2014). Nonlinear state estimation with nonlinear equality constraints. In 53rd IEEE Conference on Decision and Control,CDC 2014 (February ed., pp. 322-327). [7039401] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2014.7039401

Nonlinear state estimation with nonlinear equality constraints. / Su, Jinya; Chen, Wen Hua; Li, Baibing.

53rd IEEE Conference on Decision and Control,CDC 2014. February. ed. Institute of Electrical and Electronics Engineers Inc., 2014. p. 322-327 7039401 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February).

Research output: Chapter in Book/Report/Conference proceeding › Published conference contribution

Su, J, Chen, WH & Li, B 2014, Nonlinear state estimation with nonlinear equality constraints. in 53rd IEEE Conference on Decision and Control,CDC 2014. February edn, 7039401, Proceedings of the IEEE Conference on Decision and Control, no. February, vol. 2015-February, Institute of Electrical and Electronics Engineers Inc., pp. 322-327, 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014, Los Angeles, United States, 15/12/14. https://doi.org/10.1109/CDC.2014.7039401

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title = "Nonlinear state estimation with nonlinear equality constraints",

abstract = "This paper investigates the problem of state estimation of nonlinear systems with nonlinear equality constraints. By treating the nonlinear equality constraints as part of the new coordinate, a diffeomorphism is found such that an unconstrained reduced-order system is obtained. The existing unconstrained estimators can be applied to obtain the reduced-order state estimate. Then, based on the inverse transformation, the original states can be obtained by combing the reduced-order state estimate and the nonlinear equality constraints. Compared with the traditional model reduction approach, there exists one more freedom to choose the independent variables in the proposed approach. Compared with the null space approach, the proposed approach can handle nonlinear estimation with general nonlinear equality constraints. Finally, the estimation problem for a moving vehicle on a given circular path is used to illustrate the principle of the proposed approach.",

keywords = "Reduced order systems, Null space, Vehicles, Roads, Noise measurement, State estimation",

author = "Jinya Su and Chen, {Wen Hua} and Baibing Li",

note = "Publisher Copyright: {\textcopyright} 2014 IEEE.; 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 ; Conference date: 15-12-2014 Through 17-12-2014",

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N2 - This paper investigates the problem of state estimation of nonlinear systems with nonlinear equality constraints. By treating the nonlinear equality constraints as part of the new coordinate, a diffeomorphism is found such that an unconstrained reduced-order system is obtained. The existing unconstrained estimators can be applied to obtain the reduced-order state estimate. Then, based on the inverse transformation, the original states can be obtained by combing the reduced-order state estimate and the nonlinear equality constraints. Compared with the traditional model reduction approach, there exists one more freedom to choose the independent variables in the proposed approach. Compared with the null space approach, the proposed approach can handle nonlinear estimation with general nonlinear equality constraints. Finally, the estimation problem for a moving vehicle on a given circular path is used to illustrate the principle of the proposed approach.

AB - This paper investigates the problem of state estimation of nonlinear systems with nonlinear equality constraints. By treating the nonlinear equality constraints as part of the new coordinate, a diffeomorphism is found such that an unconstrained reduced-order system is obtained. The existing unconstrained estimators can be applied to obtain the reduced-order state estimate. Then, based on the inverse transformation, the original states can be obtained by combing the reduced-order state estimate and the nonlinear equality constraints. Compared with the traditional model reduction approach, there exists one more freedom to choose the independent variables in the proposed approach. Compared with the null space approach, the proposed approach can handle nonlinear estimation with general nonlinear equality constraints. Finally, the estimation problem for a moving vehicle on a given circular path is used to illustrate the principle of the proposed approach.

KW - Reduced order systems

KW - Null space

KW - Vehicles

KW - Roads

KW - Noise measurement

KW - State estimation

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DO - 10.1109/CDC.2014.7039401

M3 - Published conference contribution

AN - SCOPUS:84988215568

SN - 9781479977468

T3 - Proceedings of the IEEE Conference on Decision and Control

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BT - 53rd IEEE Conference on Decision and Control,CDC 2014

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014

Y2 - 15 December 2014 through 17 December 2014

ER -

Nonlinear state estimation with nonlinear equality constraints

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