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Multi-channel Kalman filters for active noise control

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Author: Ophem, S. van · Berkhoff, A.P.
Source:Journal of the Acoustical Society of America, 4, 133, 2105-2115
Identifier: 471473
doi: doi:10.1121/1.4792646
Keywords: Acoustics and Audiology · Urban Development · Built Environment · Physics & Electronics · AS - Acoustics & Sonar · TS - Technical Sciences


By formulating the feed-forward broadband active noise control problem as a state estimation problem it is possible to achieve a faster rate of convergence than the filtered reference least mean squares algorithm and possibly also a better tracking performance. A multiple input/multiple output Kalman algorithm is derived to perform this state estimation. To make the algorithm more suitable for real-time applications, the Kalman filter is written in a fast array form and the secondary path state matrices are implemented in output normal form. The resulting filter implementation is tested in simulations and in real-time experiments. It was found that for a constant primary path the filter has a fast rate of convergence and is able to track changes in the frequency spectrum. For a forgetting factor equal to unity the system is robust but the filter is unable to track rapid changes in the primary path. A forgetting factor lower than 1 gives a significantly improved tracking performance but leads to a numerical instability for the fast array form of the algorithm. © 2013 Acoustical Society of America.