### Abstract

Original language | English |
---|---|

Pages (from-to) | 31-45 |

Number of pages | 15 |

Journal | International journal of adaptive control and signal processing |

Volume | 30 |

Issue number | 1 |

DOIs | |

Publication status | Published - 20 May 2016 |

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### Keywords

- METIS-312796
- IR-97867

### Cite this

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**A numerically stable, finite memory, fast array recursive least squares algorithm for broadband active noise control.** / van Ophem, S.; Berkhoff, Arthur P.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - A numerically stable, finite memory, fast array recursive least squares algorithm for broadband active noise control

AU - van Ophem, S.

AU - Berkhoff, Arthur P.

PY - 2016/5/20

Y1 - 2016/5/20

N2 - For broadband active noise control applications with a rapidly changing primary path, it is desirable to find algorithms with a rapid convergence, a fast tracking performance, and a low computational cost. Recently, a promising algorithm has been presented, called the fast-array Kalman filter, which uses rotation matrices to calculate the filter parameters. However, when this algorithm is implemented, it can show unstable behavior because of finite precision error propagation. In this paper, a novel algorithm is presented, which exhibits the fast convergence and tracking properties and the linear calculation complexity of the fast-array Kalman filter but does not suffer from the mentioned numerical problems. This is accomplished by running two finite length growing memory recursive least squares filters in parallel and using a convex combination of the two filters when the control signal is calculated. A reset of the filter parameters with proper re-initialization is enforced periodically. The mixing parameters will be chosen in such a way that the total available information used for the calculation of the control signal will be approximately equal at every time instance. The performance of the filter is shown in numerical simulations and real-time lab experiments. The numerical experiments show that the algorithm performs better numerically than the fast-array sliding window recursive least squares filter, while achieving a comparable convergence rate and tracking performance. The real-time lab experiments confirm the behavior shown in the simulations

AB - For broadband active noise control applications with a rapidly changing primary path, it is desirable to find algorithms with a rapid convergence, a fast tracking performance, and a low computational cost. Recently, a promising algorithm has been presented, called the fast-array Kalman filter, which uses rotation matrices to calculate the filter parameters. However, when this algorithm is implemented, it can show unstable behavior because of finite precision error propagation. In this paper, a novel algorithm is presented, which exhibits the fast convergence and tracking properties and the linear calculation complexity of the fast-array Kalman filter but does not suffer from the mentioned numerical problems. This is accomplished by running two finite length growing memory recursive least squares filters in parallel and using a convex combination of the two filters when the control signal is calculated. A reset of the filter parameters with proper re-initialization is enforced periodically. The mixing parameters will be chosen in such a way that the total available information used for the calculation of the control signal will be approximately equal at every time instance. The performance of the filter is shown in numerical simulations and real-time lab experiments. The numerical experiments show that the algorithm performs better numerically than the fast-array sliding window recursive least squares filter, while achieving a comparable convergence rate and tracking performance. The real-time lab experiments confirm the behavior shown in the simulations

KW - METIS-312796

KW - IR-97867

U2 - 10.1002/acs.2574

DO - 10.1002/acs.2574

M3 - Article

VL - 30

SP - 31

EP - 45

JO - International journal of adaptive control and signal processing

JF - International journal of adaptive control and signal processing

SN - 0890-6327

IS - 1

ER -