Near-optimal deterministic filtering on the unit circle

Paul Coote; Jochen Trumpf; Robert Mahony; Jan C. Willems

doi:10.1109/CDC.2009.5399999

Near-optimal deterministic filtering on the unit circle

Paul Coote^*, Jochen Trumpf, Robert Mahony, Jan C. Willems

^*Corresponding author for this work

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

14 Citations (Scopus)

Abstract

We present a near-optimal deterministic filter for systems that evolve on the unit circle. Unlike suboptimal filtering algorithms that rely on approximations of the system, the proposed approach preserves the non-linear system model. This leads to an explicit bound on the optimality gap in terms of the tracking error. Specifically, the optimality gap is bounded by a term that is fourth-order in the tracking error. A simulation demonstrates that the filter can track a signal on the unit circle in the presence of large disturbances. An optimal algorithm for recursive estimation of static (non-dynamic) data on the unit circle appears as a special case of the proposed filter.

Original language	English
Title of host publication	Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5490-5495
Number of pages	6
ISBN (Print)	9781424438716
DOIs	https://doi.org/10.1109/CDC.2009.5399999
Publication status	Published - 2009
Event	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China Duration: 15 Dec 2009 → 18 Dec 2009

Publication series

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

Conference

Conference	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Country/Territory	China
City	Shanghai
Period	15/12/09 → 18/12/09

Access to Document

10.1109/CDC.2009.5399999

Cite this

Coote, P., Trumpf, J., Mahony, R., & Willems, J. C. (2009). Near-optimal deterministic filtering on the unit circle. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 5490-5495). Article 5399999 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2009.5399999

Coote, Paul ; Trumpf, Jochen ; Mahony, Robert et al. / Near-optimal deterministic filtering on the unit circle. Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. pp. 5490-5495 (Proceedings of the IEEE Conference on Decision and Control).

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title = "Near-optimal deterministic filtering on the unit circle",

abstract = "We present a near-optimal deterministic filter for systems that evolve on the unit circle. Unlike suboptimal filtering algorithms that rely on approximations of the system, the proposed approach preserves the non-linear system model. This leads to an explicit bound on the optimality gap in terms of the tracking error. Specifically, the optimality gap is bounded by a term that is fourth-order in the tracking error. A simulation demonstrates that the filter can track a signal on the unit circle in the presence of large disturbances. An optimal algorithm for recursive estimation of static (non-dynamic) data on the unit circle appears as a special case of the proposed filter.",

author = "Paul Coote and Jochen Trumpf and Robert Mahony and Willems, {Jan C.}",

year = "2009",

doi = "10.1109/CDC.2009.5399999",

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isbn = "9781424438716",

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

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booktitle = "Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009",

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note = "48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 ; Conference date: 15-12-2009 Through 18-12-2009",

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Coote, P, Trumpf, J , Mahony, R & Willems, JC 2009, Near-optimal deterministic filtering on the unit circle. in Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009., 5399999, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 5490-5495, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, 15/12/09. https://doi.org/10.1109/CDC.2009.5399999

Near-optimal deterministic filtering on the unit circle. / Coote, Paul; Trumpf, Jochen ; Mahony, Robert et al.
Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. p. 5490-5495 5399999 (Proceedings of the IEEE Conference on Decision and Control).

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

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AU - Coote, Paul

AU - Trumpf, Jochen

AU - Mahony, Robert

AU - Willems, Jan C.

PY - 2009

Y1 - 2009

N2 - We present a near-optimal deterministic filter for systems that evolve on the unit circle. Unlike suboptimal filtering algorithms that rely on approximations of the system, the proposed approach preserves the non-linear system model. This leads to an explicit bound on the optimality gap in terms of the tracking error. Specifically, the optimality gap is bounded by a term that is fourth-order in the tracking error. A simulation demonstrates that the filter can track a signal on the unit circle in the presence of large disturbances. An optimal algorithm for recursive estimation of static (non-dynamic) data on the unit circle appears as a special case of the proposed filter.

AB - We present a near-optimal deterministic filter for systems that evolve on the unit circle. Unlike suboptimal filtering algorithms that rely on approximations of the system, the proposed approach preserves the non-linear system model. This leads to an explicit bound on the optimality gap in terms of the tracking error. Specifically, the optimality gap is bounded by a term that is fourth-order in the tracking error. A simulation demonstrates that the filter can track a signal on the unit circle in the presence of large disturbances. An optimal algorithm for recursive estimation of static (non-dynamic) data on the unit circle appears as a special case of the proposed filter.

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U2 - 10.1109/CDC.2009.5399999

DO - 10.1109/CDC.2009.5399999

M3 - Conference contribution

SN - 9781424438716

T3 - Proceedings of the IEEE Conference on Decision and Control

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EP - 5495

BT - Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009

PB - Institute of Electrical and Electronics Engineers Inc.

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Y2 - 15 December 2009 through 18 December 2009

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Coote P, Trumpf J , Mahony R, Willems JC. Near-optimal deterministic filtering on the unit circle. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc. 2009. p. 5490-5495. 5399999. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2009.5399999

Near-optimal deterministic filtering on the unit circle

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