Elsevier

Signal Processing

Volume 81, Issue 2, February 2001, Pages 381-387
Signal Processing

Method to update the coefficients of the secondary path filter under active noise control

https://doi.org/10.1016/S0165-1684(00)00214-0Get rights and content

Abstract

In active noise control systems using a filtered-x algorithm, the secondary path must be identified before the coefficients of the noise control filter are updated. The secondary path, however, has an impulse response that is continually changing in practical systems. This change degrades noise reduction and the stability of the system. Therefore, the coefficients of the secondary path filter must be adjusted to actual impulse response samples at specific intervals. This paper proposes a method to update the coefficients under active noise control without feeding extra noise to the secondary source. Instead, this method uses estimation errors. The coefficients of the noise control filter generally have the different estimation errors whenever the coefficients are updated. To use the estimation error, this method implements the additional filter modeled on the overall path from a detection sensor to an error sensor, through the primary path, the control filter and the secondary path. Two different coefficient sets of the noise control filter derive two equations on this overall path. A solution of these concurrent equations naturally yields the impulse response samples of the secondary path. This paper uses a system identification technique to solve the concurrent equations. This technique is practical in that calculation errors are distributed equally over all coefficients of the secondary path filter. Finally, computer simulations explained in this paper confirm that the concurrent equation method can refresh the coefficients under active noise control.

Introduction

A feedforward active noise control system using a filtered-x algorithm [11] is generally composed of three filters: a noise control filter, a secondary path filter, and a feedback control filter [1]. Only one of these filters, the noise control filter driving the secondary source, has coefficients that are constantly updated. The other two filters, the secondary path filter and feedback control filter, have coefficients set to the value of impulse response samples estimated prior to the start of active noise control. The focus of this paper is on a method to update the coefficients of the secondary path filter modeled on the secondary path from the secondary source to an error sensor under active noise control. The feedback control filter, which diminishes the gain of a feedback path from the secondary source to a detection sensor, is examined in another paper [4].

In practical systems, the impulse response of the secondary path is expected to change after coefficients are set. This change naturally increases the difference between actual impulse response samples and the coefficients of the secondary path filter, thereby narrowing the range of stability in the filtered-x algorithm [8], [10]. At worst, such a system becomes uncontrollable. One method to solve this problem is to refresh the coefficients of the secondary path filter at specific intervals.

In the feedforward type of system, only two signals – namely, the outputs from error and detection sensors – can be used to estimate the coefficients of the secondary path filter and noise control filter. These two outputs, however, make up only one equation with two unknown elements corresponding to the impulse responses of the secondary path and primary path, from a detection sensor to an error sensor. To update the coefficients of the secondary path filter under active noise control, another independent equation is requisite. Feeding extra noise to the secondary source [2] is the simplest way of obtaining another independent equation. This extra noise, however, creates a new noise source in the active noise control system.

Saito [9] has proposed a method to derive the two independent equations by adding an extra tap to the noise control filter that has as many taps as the number of impulse response samples of the primary path. This additional tap, however, is equivalent to the superposition of white noise on the output of the noise control filter. This superposition is also similar to adding white noise to the coefficients of the noise control filter.

This paper presents a method that uses the estimation error included in the coefficients of the noise control filter to derive two independent equations. Although this estimation error is expected to be independent of the error sensor output, it is not recognized as another noise source. This independent relation makes possible two equations with two unknown elements.

A solution of these concurrent equations yields impulse response samples of the secondary path. This paper explains a new system identification technique to solve these concurrent equations because traditional methods, such as, the elimination technique, causes a calculation error to diverge. This technique is practical since calculation errors are uniformly distributed over the coefficients of the secondary path filter. The uniform distribution prevents a calculation error from diverging.

The coefficients of the secondary path filter can also be indirectly updated by determining and then adding estimated distances from actual impulse response samples of the secondary path. The final part of this paper explains simulation results to confirm the applicability of this indirect estimation method.

Section snippets

Principle

Fig. 1 shows our proposed method that is characterized by the additional filter. This additional filter is a model of the overall path, including the primary path, noise control filter, and secondary path. The transfer function of this overall path from a detection sensor to an error sensor, S(z), is expressed as

S(z)=P(z)−H(z)C(z),where H(z),P(z), and C(z) are the transfer functions of the noise control filter, primary path and secondary path, respectively.

If degradation of noise reduction is

Additional constant technique

The simplest way to solve Eq. (15) is to set h as

h(1)≠0,h(2)=h(3)=⋯=h(M)=0.This relation can be obtained by adding a constant, a, to only the first element of H1 asH2=[H1(1)+aH1(2)H1(M)]T.This additional constant simplifies W to a diagonal matrix,W=aI,where I is an identity matrix. Hence, substituting Eq. (18) into Eq. (15) yieldsC=W−1s=a−1[s1(1)s2(2)s2(I)]TA problem in this technique is that adding a is equivalent to increasing the estimation error of the noise control filter coefficients,

System identification technique

Another way of deriving concurrent equations without a noticeable increase of noise is to use the estimation error in the coefficients of the noise control filter. In practical systems, different estimation errors are supposed to remain in H1 and H2, set at specific intervals. On this supposition, the coefficients vectors, H1,H2,S1, and S2, are obtained by the following procedure:

(1)Stop updating the coefficients of the noise control filter. Then, the coefficient vector is H1.
(2)Estimate the

Conclusion

This paper has presented the concurrent equation method to refresh the coefficients of the secondary path filter under active noise control without feeding extra noise to the secondary source and explained practical techniques to solve the concurrent equations. One of them, the additional constant technique, can be used for the estimation in the initial stage prior to the start of active noise control. The others, the direct and indirect estimation techniques, are also practical because they

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