A numerically stable, finite memory, fast array recursive least squares filter for broadband active noise control
A numerically stable, finite memory, fast array recursive least squares filter for broadband active noise control
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.
active noise control, recursive least squares, primary path tracking, round-off errors, Science & Technology, Technology, Automation & Control Systems, Engineering, Electrical & Electronic, Engineering, ADAPTIVE FILTERS, CONVEX COMBINATION, ALGORITHM, 0102 Applied Mathematics, 0906 Electrical and Electronic Engineering, Industrial Engineering & Automation, 4007 Control engineering, mechatronics and robotics, 4009 Electronics, sensors and digital hardware
31-45
van Ophem, S.
bb3fb37e-577b-4152-86bc-2248943f882d
Berkhoff, A.P.
42d2587c-a84a-42fb-a7d4-cb78bc2f62a4
6 January 2016
van Ophem, S.
bb3fb37e-577b-4152-86bc-2248943f882d
Berkhoff, A.P.
42d2587c-a84a-42fb-a7d4-cb78bc2f62a4
van Ophem, S. and Berkhoff, A.P.
(2016)
A numerically stable, finite memory, fast array recursive least squares filter for broadband active noise control.
International Journal of Adaptive Control and Signal Processing, 30 (1), .
(doi:10.1002/acs.2574).
Abstract
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.
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More information
Accepted/In Press date: 25 April 2015
e-pub ahead of print date: 20 May 2015
Published date: 6 January 2016
Keywords:
active noise control, recursive least squares, primary path tracking, round-off errors, Science & Technology, Technology, Automation & Control Systems, Engineering, Electrical & Electronic, Engineering, ADAPTIVE FILTERS, CONVEX COMBINATION, ALGORITHM, 0102 Applied Mathematics, 0906 Electrical and Electronic Engineering, Industrial Engineering & Automation, 4007 Control engineering, mechatronics and robotics, 4009 Electronics, sensors and digital hardware
Identifiers
Local EPrints ID: 494864
URI: http://eprints.soton.ac.uk/id/eprint/494864
ISSN: 1099-1115
PURE UUID: 8488bcac-6584-460b-9e4f-dc0d679369c4
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Date deposited: 18 Oct 2024 16:32
Last modified: 19 Oct 2024 02:13
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Author:
S. van Ophem
Author:
A.P. Berkhoff
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