Multi-channel Kalman filters for active noise control

Ophem, S. van; Berkhoff, Arthur P.

doi:10.1121/1.4792646

Cited by 10 publications

(9 citation statements)

References 9 publications

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“…In Fraanje et al a forgetting factor, which exponentially weights the data, was proposed to improve the tracking performance. Although the improved tracking was observed by Van Ophem and Berkhoff , a disastrous instability caused by the round‐off errors in digital systems was also observed by the authors . An alternative solution for improving the tracking performance has been proposed by Sayed in the form of a sliding window.…”

Section: Introductionmentioning

confidence: 99%

“…With such noise sources, the primary path can change rapidly, violating the assumption of a system with slowly variating dynamics. Some examples of ANC with moving noise sources are given by Omoto and Fujiwara , Berkhoff , and Van Ophem and Berkhoff .…”

Section: Introductionmentioning

confidence: 99%

“…It was shown by Fraanje et al that the modified filtered‐RLS algorithm is a special case of a Kalman filter, which allows an efficient implementation in the form of a fast‐array implementation, as earlier described by Sayed . A real‐time implementation of this fast‐array Kalman filter was presented by Van Ophem and Berkhoff . In this implementation, an output normal parameterization of the estimated secondary path was used to reduce the amount of floating point operations and to remove redundancy from the state space model.…”

Section: Introductionmentioning

confidence: 99%

“…Although the fast‐array Kalman filter shows the desired high rate of convergence, it was shown by Van Ophem and Berkhoff that the tracking performance is diminishing with progressing time. The reason for this behavior is that the Kalman filter uses all old data to calculate the estimate of the filter coefficients.…”

Section: Introductionmentioning

confidence: 99%

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

Ophem

Berkhoff

2015

Adaptive Control & Signal

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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. 32S. VAN OPHEM AND A. P. BERKHOFF fxLMS [2], fast affine projections, and preconditioned LMS [1]. Another way to improve the rate of convergence can be obtained by reformulating the ANC problem as a state estimation problem, as proposed by Sayyarrodsari et al. [3].The assumption of the linear time-invariant adaptive filter and secondary path also potentially influences the tracking performance of primary path changes. These changes will occur when the primary noise source is moving relative to the ANC system or the reference microphone is moving. Some examples of moving noise sources are airplanes and cars. With such noise sources, the primary path can change rapidly, violating the assumption of a system with slowly variating dynamics. Some examples of ANC with moving noise sources are given by Omoto and Fujiwara [4], Berkhoff [5], and Van Ophem and Berkhoff [6].The availability of affordable, high-performance digital signal processors makes it possible to implement more advanced signal processing algorithms with a potentially better performance than the fxLMS algorithms. Therefore, recent research has been focused on alternatives, such as the modified filtered-reference Recursive Least Squares (RLS) algorithm. This algorithm has a high rate of convergence, but is computationally demanding. It was shown by Fraanje et al.[7] that the modified filtered-RLS algorithm is a special case of a Kalman filter, which allows an efficient implementation in the form of a fast...

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Ophem

Berkhoff

2015

Adaptive Control & Signal

Self Cite

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“…Ophem and Berkhoff extended this approach to MIMO systems [5], [6], and pursued investigations on tracking and convergence, however they encountered numerical stability problems [7], [8]. They also included the secondary path estimation in their model.…”

Section: Introductionmentioning

confidence: 99%

Time-domain Kalman filter for active noise cancellation headphones

Liebich

Fabry

Jax

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-Noise pollution has a large negative influence on the health of humans, especially in case of long-term exposure. Various passive hearing protection approaches are available. However, they often lack good protection against low frequency noise. For these applications, the principle of Active Noise Cancellation (ANC) offers a promising supplement. It relies on anti-phase compensation of the noise signal. Within the area of ANC, only few publications deal with the Kalman filter approach. The state-of-the-art in literature is briefly reviewed. The algorithm presented in this contribution is inspired by the time-domain Kalman filter. The Kalman filter has the favorable property of fast convergence as well as good tracking properties. Especially the tracking of time-varying noise conditions is often a drawback of least-mean-square (LMS) and recursive-least-square (RLS) approaches. The proposed algorithm uses the Kalman equations which are extended by online model parameter estimation based on observable signals. This results in faster convergence and higher robustness against dynamically changing noise conditions. The performance of the algorithm is evaluated by means of convergence, tracking and stability with measured acoustic paths from a real-time system.

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Frequency domain stability and relaxed convergence conditions for filtered error adaptive feedforward

Spanjer,

Köroğlu,

Hakvoort

2024

Adaptive Control & Signal

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SummaryThe convergence of filtered error and filtered reference adaptive feedforward is limited by three effects: model mismatch, unintended input‐disturbance interaction and too fast parameter adaptation. In this article, the first two effects are considered for MIMO systems under the slow parameter adaptation assumption. The convergence with model mismatch is conventionally guaranteed using a strictly positive‐real condition. This condition can be easily verified in the frequency domain, but due the high‐frequency parasitic dynamics of real systems, it is hardly ever satisfied. Nevertheless, filtered error and filtered reference adaptive feedforward have successfully been implemented in numerous applications without satisfying the strictly positive‐real condition. It is shown in this article that the strictly positive‐real condition can be relaxed to a power‐weighted integral condition, that is less conservative and provides a practical check for the convergence of filtered error adaptive feedforward for real systems in the frequency domain. The effects of input‐disturbance interaction are analysed and conditions for the stability are given in the frequency domain. Both conditions give clear indicators for frequency domain filter tuning, and are verified on an experimental active vibration isolation system.

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Multi-channel Kalman filters for active noise control

Cited by 10 publications

References 9 publications

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

Time-domain Kalman filter for active noise cancellation headphones

Frequency domain stability and relaxed convergence conditions for filtered error adaptive feedforward

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