A quasi-Gaussian Kalman filter

Suman Chakravorty; Mrinal Kumar; Puneet Singla

doi:10.1109/acc.2006.1655484

A quasi-Gaussian Kalman filter

Suman Chakravorty, Mrinal Kumar, Puneet Singla

Aerospace Engineering

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

9 Scopus citations

Abstract

In this paper, we present a Gaussian approximation to the nonlinear filtering problem, namely the quasi-Gaussian Kalman filter. Starting with the recursive Bayes filter, we invoke the Gaussian approximation to reduce the filtering problem into an optimal Kalman recursion. We use the moment evolution equations for stochastic dynamic equations to evaluate the prediction terms in the Kalman recursions. We propose two methods, one based on stochastic linearization and the other based on a direct evaluation of the innovations terms, to perform the measurement update in the Kalman recursion. We test our filter on a simple two dimensional example, where the nonlinearity of the system dynamics and the measurement equations can be varied, and compare its performance to that of an extended Kalman filter.

Original language	English (US)
Title of host publication	Proceedings of the 2006 American Control Conference
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	970-975
Number of pages	6
ISBN (Print)	1424402107, 9781424402106
DOIs	https://doi.org/10.1109/acc.2006.1655484
State	Published - 2006
Event	2006 American Control Conference - Minneapolis, MN, United States Duration: Jun 14 2006 → Jun 16 2006

Publication series

Name	Proceedings of the American Control Conference
Volume	2006
ISSN (Print)	0743-1619

Other

Other	2006 American Control Conference
Country/Territory	United States
City	Minneapolis, MN
Period	6/14/06 → 6/16/06

All Science Journal Classification (ASJC) codes

Electrical and Electronic Engineering

Access to Document

10.1109/acc.2006.1655484

Cite this

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title = "A quasi-Gaussian Kalman filter",

abstract = "In this paper, we present a Gaussian approximation to the nonlinear filtering problem, namely the quasi-Gaussian Kalman filter. Starting with the recursive Bayes filter, we invoke the Gaussian approximation to reduce the filtering problem into an optimal Kalman recursion. We use the moment evolution equations for stochastic dynamic equations to evaluate the prediction terms in the Kalman recursions. We propose two methods, one based on stochastic linearization and the other based on a direct evaluation of the innovations terms, to perform the measurement update in the Kalman recursion. We test our filter on a simple two dimensional example, where the nonlinearity of the system dynamics and the measurement equations can be varied, and compare its performance to that of an extended Kalman filter.",

author = "Suman Chakravorty and Mrinal Kumar and Puneet Singla",

year = "2006",

doi = "10.1109/acc.2006.1655484",

language = "English (US)",

isbn = "1424402107",

series = "Proceedings of the American Control Conference",

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

pages = "970--975",

booktitle = "Proceedings of the 2006 American Control Conference",

address = "United States",

note = "2006 American Control Conference ; Conference date: 14-06-2006 Through 16-06-2006",

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Chakravorty, S, Kumar, M & Singla, P 2006, A quasi-Gaussian Kalman filter. in Proceedings of the 2006 American Control Conference., 1655484, Proceedings of the American Control Conference, vol. 2006, Institute of Electrical and Electronics Engineers Inc., pp. 970-975, 2006 American Control Conference, Minneapolis, MN, United States, 6/14/06. https://doi.org/10.1109/acc.2006.1655484

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AU - Kumar, Mrinal

AU - Singla, Puneet

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N2 - In this paper, we present a Gaussian approximation to the nonlinear filtering problem, namely the quasi-Gaussian Kalman filter. Starting with the recursive Bayes filter, we invoke the Gaussian approximation to reduce the filtering problem into an optimal Kalman recursion. We use the moment evolution equations for stochastic dynamic equations to evaluate the prediction terms in the Kalman recursions. We propose two methods, one based on stochastic linearization and the other based on a direct evaluation of the innovations terms, to perform the measurement update in the Kalman recursion. We test our filter on a simple two dimensional example, where the nonlinearity of the system dynamics and the measurement equations can be varied, and compare its performance to that of an extended Kalman filter.

AB - In this paper, we present a Gaussian approximation to the nonlinear filtering problem, namely the quasi-Gaussian Kalman filter. Starting with the recursive Bayes filter, we invoke the Gaussian approximation to reduce the filtering problem into an optimal Kalman recursion. We use the moment evolution equations for stochastic dynamic equations to evaluate the prediction terms in the Kalman recursions. We propose two methods, one based on stochastic linearization and the other based on a direct evaluation of the innovations terms, to perform the measurement update in the Kalman recursion. We test our filter on a simple two dimensional example, where the nonlinearity of the system dynamics and the measurement equations can be varied, and compare its performance to that of an extended Kalman filter.

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T3 - Proceedings of the American Control Conference

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BT - Proceedings of the 2006 American Control Conference

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Y2 - 14 June 2006 through 16 June 2006

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A quasi-Gaussian Kalman filter

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