NIRK-based accurate continuous–discrete extended Kalman filters for estimating continuous-time stochastic target tracking models

This paper presents three state estimators grounded in the variable-stepsize Gauss- and Lobatto-type Nested Implicit Runge–Kutta (NIRK) formulas of orders 4 and 6 and designed for treating continuous-time stochastic systems arisen in radar tracking. Our filters are built within the Extended Kalman F...

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Vydané v:	Journal of computational and applied mathematics Ročník 316; s. 260 - 270
Hlavní autori:	Kulikova, M.V., Kulikov, G.Yu
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier B.V 15.05.2017
Predmet:	Accuracy Adaptive MDE solver with local and global error controls Automatic control Construction methods Continuous-time stochastic target tracking model Continuous–discrete stochastic system Estimators Extended Kalman filter Gauss- and Lobatto-type nested implicit Runge–Kutta formulas Mathematical models Matlab Mazzoni’s hybrid method Permissible error Radar tracking 65L05 93E11 Continuous-time stochastic target tracking model Mazzoni’s hybrid method Gauss- and Lobatto-type nested implicit Runge–Kutta formulas Continuous–discrete stochastic system Adaptive MDE solver with local and global error controls Extended Kalman filter
ISSN:	0377-0427, 1879-1778
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Abstract	This paper presents three state estimators grounded in the variable-stepsize Gauss- and Lobatto-type Nested Implicit Runge–Kutta (NIRK) formulas of orders 4 and 6 and designed for treating continuous-time stochastic systems arisen in radar tracking. Our filters are built within the Extended Kalman Filtering (EKF) framework and based on accurate numerical integrations of the corresponding Moment Differential Equations (MDEs). Automatic local and global error regulation mechanisms implemented in these methods allow the committed discretization error to be under control and made negligible in automatic mode. The latter raises the state estimation accuracy of the constructed filters, significantly. This also leads to the advanced notion of Accurate Continuous–Discrete Extended Kalman Filtering (ACD-EKF) developed by Kulikov and Kulikova in 2013–2016. Our novel methods are constructed within the same approach, but possess the improved accuracy and efficiency in comparison to their predecessors due to both more effective error control mechanisms implemented for integrating MDEs and more accurate iterations used for treating arisen nonlinear equations in the revised filters. Numerical experiments with the updated state estimators and their comparison to the cited earlier-designed ACD-EKFs are fulfilled in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn, in Matlab. This examination suggests that the novel state estimation algorithms outperform their predecessors and possess a promising potential for solving target tracking tasks in real-world applications.
AbstractList	This paper presents three state estimators grounded in the variable-stepsize Gauss- and Lobatto-type Nested Implicit Runge-Kutta (NIRK) formulas of orders 4 and 6 and designed for treating continuous-time stochastic systems arisen in radar tracking. Our filters are built within the Extended Kalman Filtering (EKF) framework and based on accurate numerical integrations of the corresponding Moment Differential Equations (MDEs). Automatic local and global error regulation mechanisms implemented in these methods allow the committed discretization error to be under control and made negligible in automatic mode. The latter raises the state estimation accuracy of the constructed filters, significantly. This also leads to the advanced notion of Accurate Continuous-Discrete Extended Kalman Filtering (ACD-EKF) developed by Kulikov and Kulikova in 2013-2016. Our novel methods are constructed within the same approach, but possess the improved accuracy and efficiency in comparison to their predecessors due to both more effective error control mechanisms implemented for integrating MDEs and more accurate iterations used for treating arisen nonlinear equations in the revised filters. Numerical experiments with the updated state estimators and their comparison to the cited earlier-designed ACD-EKFs are fulfilled in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn, in Matlab. This examination suggests that the novel state estimation algorithms outperform their predecessors and possess a promising potential for solving target tracking tasks in real-world applications. This paper presents three state estimators grounded in the variable-stepsize Gauss- and Lobatto-type Nested Implicit Runge–Kutta (NIRK) formulas of orders 4 and 6 and designed for treating continuous-time stochastic systems arisen in radar tracking. Our filters are built within the Extended Kalman Filtering (EKF) framework and based on accurate numerical integrations of the corresponding Moment Differential Equations (MDEs). Automatic local and global error regulation mechanisms implemented in these methods allow the committed discretization error to be under control and made negligible in automatic mode. The latter raises the state estimation accuracy of the constructed filters, significantly. This also leads to the advanced notion of Accurate Continuous–Discrete Extended Kalman Filtering (ACD-EKF) developed by Kulikov and Kulikova in 2013–2016. Our novel methods are constructed within the same approach, but possess the improved accuracy and efficiency in comparison to their predecessors due to both more effective error control mechanisms implemented for integrating MDEs and more accurate iterations used for treating arisen nonlinear equations in the revised filters. Numerical experiments with the updated state estimators and their comparison to the cited earlier-designed ACD-EKFs are fulfilled in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn, in Matlab. This examination suggests that the novel state estimation algorithms outperform their predecessors and possess a promising potential for solving target tracking tasks in real-world applications.
Author	Kulikov, G.Yu Kulikova, M.V.
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Cites_doi	10.1109/CCA.2014.6981432 10.1007/s00180-007-0094-4 10.1109/TAC.2007.904453 10.1109/TSP.2010.2056923 10.1109/JPROC.2003.823141 10.1515/rnam-2015-0021 10.1109/9.847726 10.1109/MCS.2008.923231 10.1109/TAC.2009.2019800 10.1016/j.ejcon.2014.11.003 10.1109/ECC.2015.7330944 10.1109/TSP.2015.2493985 10.1109/CDC.2013.6761125 10.1109/TAC.2013.2272136 10.1016/j.cam.2016.06.013 10.1093/imanum/drr060 10.1137/140979952
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Keywords	65L05 93E11 Continuous-time stochastic target tracking model Mazzoni’s hybrid method Gauss- and Lobatto-type nested implicit Runge–Kutta formulas Continuous–discrete stochastic system Adaptive MDE solver with local and global error controls Extended Kalman filter
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SubjectTerms	Accuracy Adaptive MDE solver with local and global error controls Automatic control Construction methods Continuous-time stochastic target tracking model Continuous–discrete stochastic system Estimators Extended Kalman filter Gauss- and Lobatto-type nested implicit Runge–Kutta formulas Mathematical models Matlab Mazzoni’s hybrid method Permissible error Radar tracking
Title	NIRK-based accurate continuous–discrete extended Kalman filters for estimating continuous-time stochastic target tracking models
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