NDLI: Extensions to the Theory of Widely Linear Complex Kalman Filtering

Content Provider	IEEE Xplore Digital Library
Author	Wenbing Dang Scharf, L.L.
Copyright Year	1991
Abstract	For an improper complex signal x, its complementary covariance Exx^T is not zero and thus it carries useful statistical information about x. Widely linear processing exploits Hermitian and complementary covariance to improve performance. In this paper, we extend the existing theory of widely linear complex Kalman filters (WLCKF) and unscented WLCKFs [D. P. Mandic and S. L. Goh,Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models (New York: Wiley, 2009)]. We propose a WLCKF which can deal with more general dynamical models of complex-valued states and measurements than the WLCKFs in Mandic and Goh. The proposed WLCKF has an equivalency with the corresponding dual channel real KF. Our analytical and numerical results show the performance improvement of a WLCKF over a complex Kalman filter (CKF) that does not exploit complementary covariance. We also develop an unscented WLCKF which uses modified complex sigma points. The modified complex sigma points preserve complete first and second moments of complex signals, while the sigma points in Mandic and Goh only carry the mean and Hermitian covariance, but not complementary covariance of complex signals.
Sponsorship	IEEE Signal Processing Society
Starting Page	6669
Ending Page	6674
Page Count	6
File Size	1202583
File Format	PDF
ISSN	1053587X
Volume Number	60
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-12-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Vectors Covariance matrix Kalman filters Government Mathematical model Equations Noise measurement widely linear transformation Complementary covariance Kalman filter sigma points unscented Kalman filtering
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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