A Computationally Efficient and Robust Implementation of the Continuous-Discrete Extended Kalman Filter

John Bagterp Jørgensen; Per Grove Thomsen; Henrik Madsen; Morten Rode Kristensen

doi:10.1109/ACC.2007.4282549

A Computationally Efficient and Robust Implementation of the Continuous-Discrete Extended Kalman Filter

John Bagterp Jørgensen, Per Grove Thomsen, Henrik Madsen, Morten Rode Kristensen

Department of Chemical and Biochemical Engineering

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

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Abstract

We present a novel numerically robust and computationally efficient extended Kalman filter for state estimation in nonlinear continuous-discrete stochastic systems. The resulting differential equations for the mean-covariance evolution of the nonlinear stochastic continuous-discrete time systems are solved efficiently using an ESDIRK integrator with sensitivity analysis capabilities. This ESDIRK integrator for the mean- covariance evolution is implemented as part of an extended Kalman filter and tested on a PDE system. For moderate to large sized systems, the ESDIRK based extended Kalman filter for nonlinear stochastic continuous-discrete time systems is more than two orders of magnitude faster than a conventional implementation. This is of significance in nonlinear model predictive control applications, statistical process monitoring as well as grey-box modelling of systems described by stochastic differential equations.

Original language	English
Title of host publication	American Control Conference, 2007. ACC '07
Publisher	IEEE
Publication date	2007
ISBN (Print)	1-4244-0988-8
DOIs	https://doi.org/10.1109/ACC.2007.4282549
Publication status	Published - 2007
Event	American Control Conference 2007 - New York City, United States Duration: 11 Jul 2007 → 13 Jul 2007 http://a2c2.org/conferences/acc2007/

Conference

Conference	American Control Conference 2007
Country/Territory	United States
City	New York City
Period	11/07/2007 → 13/07/2007
Internet address	http://a2c2.org/conferences/acc2007/

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Copyright: 2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

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title = "A Computationally Efficient and Robust Implementation of the Continuous-Discrete Extended Kalman Filter",

abstract = "We present a novel numerically robust and computationally efficient extended Kalman filter for state estimation in nonlinear continuous-discrete stochastic systems. The resulting differential equations for the mean-covariance evolution of the nonlinear stochastic continuous-discrete time systems are solved efficiently using an ESDIRK integrator with sensitivity analysis capabilities. This ESDIRK integrator for the mean- covariance evolution is implemented as part of an extended Kalman filter and tested on a PDE system. For moderate to large sized systems, the ESDIRK based extended Kalman filter for nonlinear stochastic continuous-discrete time systems is more than two orders of magnitude faster than a conventional implementation. This is of significance in nonlinear model predictive control applications, statistical process monitoring as well as grey-box modelling of systems described by stochastic differential equations.",

author = "J{\o}rgensen, {John Bagterp} and Thomsen, {Per Grove} and Henrik Madsen and Kristensen, {Morten Rode}",

note = "Copyright: 2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE; American Control Conference 2007, ACC 2007 ; Conference date: 11-07-2007 Through 13-07-2007",

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AU - Jørgensen, John Bagterp

AU - Thomsen, Per Grove

AU - Madsen, Henrik

AU - Kristensen, Morten Rode

N1 - Copyright: 2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

PY - 2007

Y1 - 2007

N2 - We present a novel numerically robust and computationally efficient extended Kalman filter for state estimation in nonlinear continuous-discrete stochastic systems. The resulting differential equations for the mean-covariance evolution of the nonlinear stochastic continuous-discrete time systems are solved efficiently using an ESDIRK integrator with sensitivity analysis capabilities. This ESDIRK integrator for the mean- covariance evolution is implemented as part of an extended Kalman filter and tested on a PDE system. For moderate to large sized systems, the ESDIRK based extended Kalman filter for nonlinear stochastic continuous-discrete time systems is more than two orders of magnitude faster than a conventional implementation. This is of significance in nonlinear model predictive control applications, statistical process monitoring as well as grey-box modelling of systems described by stochastic differential equations.

AB - We present a novel numerically robust and computationally efficient extended Kalman filter for state estimation in nonlinear continuous-discrete stochastic systems. The resulting differential equations for the mean-covariance evolution of the nonlinear stochastic continuous-discrete time systems are solved efficiently using an ESDIRK integrator with sensitivity analysis capabilities. This ESDIRK integrator for the mean- covariance evolution is implemented as part of an extended Kalman filter and tested on a PDE system. For moderate to large sized systems, the ESDIRK based extended Kalman filter for nonlinear stochastic continuous-discrete time systems is more than two orders of magnitude faster than a conventional implementation. This is of significance in nonlinear model predictive control applications, statistical process monitoring as well as grey-box modelling of systems described by stochastic differential equations.

U2 - 10.1109/ACC.2007.4282549

DO - 10.1109/ACC.2007.4282549

M3 - Article in proceedings

SN - 1-4244-0988-8

BT - American Control Conference, 2007. ACC '07

PB - IEEE

T2 - American Control Conference 2007

Y2 - 11 July 2007 through 13 July 2007

ER -

A Computationally Efficient and Robust Implementation of the Continuous-Discrete Extended Kalman Filter

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