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A fast‐array Kalman filter solution to active noise control
Author(s) -
Fraanje Rufus,
Sayed Ali H.,
Verhaegen Michel,
Doelman Niek J.
Publication year - 2004
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.841
Subject(s) - control theory (sociology) , kalman filter , extended kalman filter , adaptive filter , convergence (economics) , computer science , state space , noise (video) , exponential function , signal (programming language) , controller (irrigation) , mathematics , algorithm , control (management) , statistics , artificial intelligence , mathematical analysis , agronomy , economics , image (mathematics) , biology , programming language , economic growth
A Kalman filter solution to active control and its fast‐array implementation are provided. The adaptive control problem is formulated as a state‐estimation problem and no interchanging of the adaptive filter and the secondary‐path is imposed. Moreover, no estimate of the disturbance signal is needed, and we exploit the structure in the state–space matrices to derive a fast‐array implementation. A minimum variance estimate of the controller coefficients and the secondary path state is obtained. When there is no uncertainty in the secondary path, state equivalence with the modified filtered‐RLS algorithm is proven. Using exponential forgetting, the analysis shows that in the generation of the filtered reference signal in the modified filtered‐RLS, exponential forgetting should be incorporated too. Simulations show the superiority in convergence of the fast‐array Kalman algorithm over the fast‐array modified filtered‐RLS algorithm. Copyright © 2004 John Wiley & Sons, Ltd.