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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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 58; no. 10; pp. 4977 - 4993
Main Authors: Arasaratnam, Ienkaran, Haykin, Simon, Hurd, Thomas R
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.10.2010
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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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Summary: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.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2010.2056923