Simultaneous input and state estimation for linear time-invariant continuous-time stochastic systems with unknown inputs

Sze Zheng Yong; Minghui Zhu; Emilio Frazzoli

doi:10.1109/ACC.2015.7171109

Simultaneous input and state estimation for linear time-invariant continuous-time stochastic systems with unknown inputs

Sze Zheng Yong, Minghui Zhu, Emilio Frazzoli

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

2 Scopus citations

Abstract

In this paper, we present an optimal filter for linear time-invariant continuous-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense. The optimality of the proposed filter is proven by reduction to an equivalent system without unknown inputs. Then, a second proof is given for a special case by limiting case approximations of the optimal discrete-time filter [1], thus establishing the connection between the continuous- and discrete-time filters. Conditions for the existence of a steady-state solution for the proposed filter are also given. Moreover, we show that a principle of separation of estimation and control holds for linear systems with unknown inputs. An example is given to demonstrate these claims.

Original language	English (US)
Title of host publication	ACC 2015 - 2015 American Control Conference
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2511-2518
Number of pages	8
ISBN (Electronic)	9781479986842
DOIs	https://doi.org/10.1109/ACC.2015.7171109
State	Published - Jul 28 2015
Externally published	Yes
Event	2015 American Control Conference, ACC 2015 - Chicago, United States Duration: Jul 1 2015 → Jul 3 2015

Publication series

Name	Proceedings of the American Control Conference
Volume	2015-July
ISSN (Print)	0743-1619

Other

Other	2015 American Control Conference, ACC 2015
Country/Territory	United States
City	Chicago
Period	7/1/15 → 7/3/15

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.1109/ACC.2015.7171109

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Yong, S. Z., Zhu, M., & Frazzoli, E. (2015). Simultaneous input and state estimation for linear time-invariant continuous-time stochastic systems with unknown inputs. In ACC 2015 - 2015 American Control Conference (pp. 2511-2518). Article 7171109 (Proceedings of the American Control Conference; Vol. 2015-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2015.7171109

Simultaneous input and state estimation for linear time-invariant continuous-time stochastic systems with unknown inputs. / Yong, Sze Zheng; Zhu, Minghui; Frazzoli, Emilio.
ACC 2015 - 2015 American Control Conference. Institute of Electrical and Electronics Engineers Inc., 2015. p. 2511-2518 7171109 (Proceedings of the American Control Conference; Vol. 2015-July).

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

Yong, SZ, Zhu, M & Frazzoli, E 2015, Simultaneous input and state estimation for linear time-invariant continuous-time stochastic systems with unknown inputs. in ACC 2015 - 2015 American Control Conference., 7171109, Proceedings of the American Control Conference, vol. 2015-July, Institute of Electrical and Electronics Engineers Inc., pp. 2511-2518, 2015 American Control Conference, ACC 2015, Chicago, United States, 7/1/15. https://doi.org/10.1109/ACC.2015.7171109

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title = "Simultaneous input and state estimation for linear time-invariant continuous-time stochastic systems with unknown inputs",

abstract = "In this paper, we present an optimal filter for linear time-invariant continuous-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense. The optimality of the proposed filter is proven by reduction to an equivalent system without unknown inputs. Then, a second proof is given for a special case by limiting case approximations of the optimal discrete-time filter [1], thus establishing the connection between the continuous- and discrete-time filters. Conditions for the existence of a steady-state solution for the proposed filter are also given. Moreover, we show that a principle of separation of estimation and control holds for linear systems with unknown inputs. An example is given to demonstrate these claims.",

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N2 - In this paper, we present an optimal filter for linear time-invariant continuous-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense. The optimality of the proposed filter is proven by reduction to an equivalent system without unknown inputs. Then, a second proof is given for a special case by limiting case approximations of the optimal discrete-time filter [1], thus establishing the connection between the continuous- and discrete-time filters. Conditions for the existence of a steady-state solution for the proposed filter are also given. Moreover, we show that a principle of separation of estimation and control holds for linear systems with unknown inputs. An example is given to demonstrate these claims.

AB - In this paper, we present an optimal filter for linear time-invariant continuous-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense. The optimality of the proposed filter is proven by reduction to an equivalent system without unknown inputs. Then, a second proof is given for a special case by limiting case approximations of the optimal discrete-time filter [1], thus establishing the connection between the continuous- and discrete-time filters. Conditions for the existence of a steady-state solution for the proposed filter are also given. Moreover, we show that a principle of separation of estimation and control holds for linear systems with unknown inputs. An example is given to demonstrate these claims.

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Simultaneous input and state estimation for linear time-invariant continuous-time stochastic systems with unknown inputs

Abstract

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