Two-Stage Extended Kalman Filters with Derivative-Free Local Linearizations
Publication: Journal of Engineering Mechanics
Volume 137, Issue 8
Abstract
This paper proposes a derivative-free two-stage extended Kalman filter (2-EKF) especially suited for state and parameter identification of mechanical oscillators under Gaussian white noise. Two sources of modeling uncertainties are considered: (1) errors in linearization, and (2) an inadequate system model. The state vector is presently composed of the original dynamical/parameter states plus the so-called bias states accounting for the unmodeled dynamics. An extended Kalman estimation concept is applied within a framework predicated on explicit and derivative-free local linearizations (DLL) of nonlinear drift terms in the governing stochastic differential equations (SDEs). The original and bias states are estimated by two separate filters; the bias filter improves the estimates of the original states. Measurements are artificially generated by corrupting the numerical solutions of the SDEs with noise through an implicit form of a higher-order linearization. Numerical illustrations are provided for a few single- and multidegree-of-freedom nonlinear oscillators, demonstrating the remarkable promise that 2-EKF holds over its more conventional EKF-based counterparts.
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Acknowledgments
D. Roy wishes to thank the Naval Science and Research Laboratory of the Government of India (Grant No. UNSPECIFIEDCP-5652) for funding the present work.
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Published In
Journal of Engineering Mechanics
Volume 137 • Issue 8 • August 2011
Pages: 537 - 546
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Dec 24, 2009
Accepted: Feb 10, 2011
Published online: Feb 12, 2011
Published in print: Aug 1, 2011
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