Active control of time-varying broadband noise and vibrations using a sliding-window Kalman filter

S. van Ophem, Arthur P. Berkhoff

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

3 Citations (Scopus)
31 Downloads (Pure)


Recently, a multiple-input/multiple-output Kalman filter technique was presented to control time-varying broadband noise and vibrations. By describing the feed-forward broadband active noise control problem in terms of a state estimation problem it was possible to achieve a faster rate of convergence than instantaneousgradient least-mean-squares algorithms and possibly also a better tracking performance. A multiple input/ multiple output Kalman algorithm was derived to perform this state estimation. To make the algorithm more suitable for real-time applications, the Kalman filter was written in a fast array form and the secondary path state matrices were implemented in output normal form. The resulting filter implementation was verified in simulations and in real-time experiments. It was found that for a constant primary path the filter had a fast rate of convergence and was able to track time-varying spectra. For a forgetting factor equal to unity the system was robust but the filter was unable to track rapid changes in the primary path. A forgetting factor lower than unity gave a significantly improved tracking performance but led to a numerical instability for the fast array form of the algorithm. To improve the numerical behavior, while enabling fast tracking and convergence, several variants are described in this paper. Results will be shown for a sliding window Recursive Least Squares filter in fast array form, which will later be extended to a full Kalman filter implementation by taking into account the uncertainty of the secondary path between the control sources and the error sensors. Multiple variants will be discussed in this paper. The first variant is the standard sliding window technique, which applies both updates and downdates to the filter coefficients. The second variant is an algorithm which only applies an update step to the filter coefficients and interprets the downdate step as an addition of a covariance matrix to the Riccati equation. The third variant uses an implicit forgetting factor. These implementations use a factorized form of the hyperbolic orthogonal transformation matrix. The different techniques will be applied to measured data of noise in houses near the runway of an airport. Results are given of the performance regarding tracking, convergence and numerical stability of the algorithms.
Original languageEnglish
Title of host publication26th International Conference on Noise and Vibration Engineering (ISMA 2014)
Subtitle of host publicationProceedings of a meeting held 15-17 September 2014, Leuven, Belgium. Held in Conjunction with the 5th International Conference on Uncertainty in Structural Dynamics (USD 2014)
EditorsP. Sas, D. Moens, H. Denayer
PublisherCurran Associates Inc.
ISBN (Print)9781634395069
Publication statusPublished - 15 Sep 2014
Event26th International Conference on Noise and Vibration Engineering, ISMA 2014 - Leuven, Belgium
Duration: 15 Sep 201417 Sep 2014
Conference number: 26


Conference26th International Conference on Noise and Vibration Engineering, ISMA 2014
Abbreviated titleISMA
Internet address


  • IR-94005
  • METIS-308904

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