### Abstract

The feed-forward broadband active noise control problem can be formulated as a state estimation problem 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 used 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 implementation was tested in simulations and in real-time experiments. It was found that for a constant primary path the Kalman filter has a fast rate of convergence and is able to track changes in the 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. It is shown that a forgetting factor lower than unity gives a significantly improved tracking performance. Numerical issues of the fast array form of the algorithm for such forgetting factors are discussed and possible solutions are presented.

Original language | English |
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Title of host publication | Proceedings Internoise 2013 |

Place of Publication | Innsbruck |

Publisher | INCE |

Pages | 1-10 |

Publication status | Published - 15 Sep 2013 |

Event | 42nd International Congress and Exposition on Noise Control Engineering, INTERNOISE 2013: Noise Control for Quality of Life - Innsbruck, Austria Duration: 15 Sep 2013 → 18 Sep 2013 Conference number: 42 http://www.internoise2013.com/ |

### Publication series

Name | paper no 0274 |
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Publisher | INCE |

### Conference

Conference | 42nd International Congress and Exposition on Noise Control Engineering, INTERNOISE 2013 |
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Abbreviated title | INTERNOISE 2013 |

Country | Austria |

City | Innsbruck |

Period | 15/09/13 → 18/09/13 |

Internet address |

### Keywords

- METIS-308939
- IR-94029

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## Cite this

Berkhoff, A. P., & van Ophem, S. (2013). Tracking and convergence of multi-channel Kalman filters for active noise control. In

*Proceedings Internoise 2013*(pp. 1-10). (paper no 0274). Innsbruck: INCE.