Equivariant Filter (EqF): A General Filter Design for Systems on Homogeneous Spaces

Pieter Van Goor; Tarek Hamel; Robert Mahony

doi:10.1109/CDC42340.2020.9303813

Equivariant Filter (EqF): A General Filter Design for Systems on Homogeneous Spaces

Pieter Van Goor, Tarek Hamel, Robert Mahony

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

21 Citations (Scopus)

Abstract

The kinematics of many mechanical systems encountered in robotics and other fields, such as single-bearing attitude estimation and SLAM, are naturally posed on homogeneous spaces: That is, their state lies in a smooth manifold equipped with a transitive Lie-group symmetry. This paper shows that any system posed in a homogeneous space can be extended to a larger system that is equivariant under a symmetry action. The equivariant structure of the system is exploited to propose a novel new filter, the Equivariant Filter (EqF), based on linearisation of global error dynamics derived from the symmetry action. The EqF is applied to an example of estimating the positions of stationary landmarks relative to a moving monocular camera that is intractable for previously proposed symmetry based filter design methodologies.

Original language	English
Title of host publication	2020 59th IEEE Conference on Decision and Control, CDC 2020
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5401-5408
Number of pages	8
ISBN (Electronic)	9781728174471
DOIs	https://doi.org/10.1109/CDC42340.2020.9303813
Publication status	Published - 14 Dec 2020
Event	59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of Duration: 14 Dec 2020 → 18 Dec 2020

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2020-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	59th IEEE Conference on Decision and Control, CDC 2020
Country/Territory	Korea, Republic of
City	Virtual, Jeju Island
Period	14/12/20 → 18/12/20

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10.1109/CDC42340.2020.9303813

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Van Goor, P., Hamel, T., & Mahony, R. (2020). Equivariant Filter (EqF): A General Filter Design for Systems on Homogeneous Spaces. In 2020 59th IEEE Conference on Decision and Control, CDC 2020 (pp. 5401-5408). Article 9303813 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2020-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC42340.2020.9303813

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abstract = "The kinematics of many mechanical systems encountered in robotics and other fields, such as single-bearing attitude estimation and SLAM, are naturally posed on homogeneous spaces: That is, their state lies in a smooth manifold equipped with a transitive Lie-group symmetry. This paper shows that any system posed in a homogeneous space can be extended to a larger system that is equivariant under a symmetry action. The equivariant structure of the system is exploited to propose a novel new filter, the Equivariant Filter (EqF), based on linearisation of global error dynamics derived from the symmetry action. The EqF is applied to an example of estimating the positions of stationary landmarks relative to a moving monocular camera that is intractable for previously proposed symmetry based filter design methodologies.",

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language = "English",

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Van Goor, P, Hamel, T & Mahony, R 2020, Equivariant Filter (EqF): A General Filter Design for Systems on Homogeneous Spaces. in 2020 59th IEEE Conference on Decision and Control, CDC 2020., 9303813, Proceedings of the IEEE Conference on Decision and Control, vol. 2020-December, Institute of Electrical and Electronics Engineers Inc., pp. 5401-5408, 59th IEEE Conference on Decision and Control, CDC 2020, Virtual, Jeju Island, Korea, Republic of, 14/12/20. https://doi.org/10.1109/CDC42340.2020.9303813

Equivariant Filter (EqF): A General Filter Design for Systems on Homogeneous Spaces. / Van Goor, Pieter; Hamel, Tarek; Mahony, Robert.
2020 59th IEEE Conference on Decision and Control, CDC 2020. Institute of Electrical and Electronics Engineers Inc., 2020. p. 5401-5408 9303813 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2020-December).

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

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AB - The kinematics of many mechanical systems encountered in robotics and other fields, such as single-bearing attitude estimation and SLAM, are naturally posed on homogeneous spaces: That is, their state lies in a smooth manifold equipped with a transitive Lie-group symmetry. This paper shows that any system posed in a homogeneous space can be extended to a larger system that is equivariant under a symmetry action. The equivariant structure of the system is exploited to propose a novel new filter, the Equivariant Filter (EqF), based on linearisation of global error dynamics derived from the symmetry action. The EqF is applied to an example of estimating the positions of stationary landmarks relative to a moving monocular camera that is intractable for previously proposed symmetry based filter design methodologies.

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PB - Institute of Electrical and Electronics Engineers Inc.

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Equivariant Filter (EqF): A General Filter Design for Systems on Homogeneous Spaces

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