Cubature Kalman Filtering for Continuous-Discrete Systems: Theory and Simulations

In this paper, we extend the cubature Kalman filter (CKF) to deal with nonlinear state-space models of the continuous-discrete kind. To be consistent with the literature, the resulting nonlinear filter is referred to as the continuous-discrete cubature Kalman filter (CD-CKF). We use the Itô-Taylor...

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Veröffentlicht in:	IEEE transactions on signal processing Jg. 58; H. 10; S. 4977 - 4993
Hauptverfasser:	Arasaratnam, Ienkaran, Haykin, Simon, Hurd, Thomas R
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York, NY IEEE 01.10.2010 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Applied sciences Bayesian filters Cadmium Computer science; control theory; systems Control theory. Systems Cuba cubature Kalman filter (CKF) Detection, estimation, filtering, equalization, prediction Difference equations Differential equations Exact sciences and technology Filtering theory Gaussian processes Information, signal and communications theory Integral equations Integrals Itô-Taylor expansion Kalman filters Mathematical analysis Mathematical models Miscellaneous nonlinear filtering Nonlinear filters Nonlinearity Radar Signal and communications theory Signal processing Signal, noise square-root filtering Stochastic processes Stochasticity System theory Telecommunications and information theory Transforms Differential equation Kalman filter Non linear filter Gaussian distribution Word length Discrete system cubature Kalman filter (CKF) Difference equation Implementation Discrete filter Series expansion Bayesian filters Kalman filtering Itô-Taylor expansion Stochastic equation Finite word Taylor series Systems theory State space method Extended Kalman filter square-root filtering Simulation Weight function Non linear model Signal processing nonlinear filtering Continuous system
ISSN:	1053-587X, 1941-0476
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Zusammenfassung:	In this paper, we extend the cubature Kalman filter (CKF) to deal with nonlinear state-space models of the continuous-discrete kind. To be consistent with the literature, the resulting nonlinear filter is referred to as the continuous-discrete cubature Kalman filter (CD-CKF). We use the Itô-Taylor expansion of order 1.5 to transform the process equation, modeled in the form of stochastic ordinary differential equations, into a set of stochastic difference equations. Building on this transformation and assuming that all conditional densities are Gaussian-distributed, the solution to the Bayesian filter reduces to the problem of how to compute Gaussian-weighted integrals. To numerically compute the integrals, we use the third-degree cubature rule. For a reliable implementation of the CD-CKF in a finite word-length machine, it is structurally modified to propagate the square-roots of the covariance matrices. The reliability and accuracy of the square-root version of the CD-CKF are tested in a case study that involves the use of a radar problem of practical significance; the problem considered herein is challenging in the context of radar in two respects- high dimensionality of the state and increasing degree of nonlinearity. The results, presented herein, indicate that the CD-CKF markedly outperforms existing continuous-discrete filters.
Bibliographie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23
ISSN:	1053-587X 1941-0476
DOI:	10.1109/TSP.2010.2056923