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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Veröffentlicht in:Journal of computational and applied mathematics Jg. 316; S. 260 - 270
Hauptverfasser: Kulikova, M.V., Kulikov, G.Yu
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 15.05.2017
Schlagworte:
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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Beschreibung
Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2016.08.036