Method for improving convergence speed of multi-reference active noise reduction adaptive algorithm

Abstract

The invention discloses a method for improving the convergence speed of a multi-reference active noise reduction adaptive algorithm. The method comprises the following steps: filtering a reference signal picked up by a reference sensor by using a secondary path estimation function to obtain a filtered reference signal; calculating an auto-power spectral density function of the filtering reference signal in a frequency domain; performing eigenvalue decomposition on the auto-power spectral density function and designing a frequency domain preprocessing filter F (omega); performing inverse Fourier transform on the F (omega) to obtain a time domain preprocessing filter bank f (n) meeting causality; iteration of an intermediate control filter coefficient C (n) is carried out by using the filtering reference signal processed by the preprocessing filter bank f (n), and meanwhile, a cost function is made to be minimum; and recovering by using a preprocessing filter f (n) and an intermediate control filter C (n) to obtain a real control filter W (n), and carrying out noise reduction. According to the method, the convergence speed of a multi-reference filtering reference minimum mean square error adaptive active noise reduction algorithm can be improved on the premise of ensuring the causality of an active noise reduction system.

Description

Technical Field

[0001] The invention belongs to the technical field of active noise control, and in particular relates to a method for improving the convergence speed of a multi-reference filtering reference minimum mean square error active noise reduction adaptive algorithm. Background Art

[0002] Active Noise Control (ANC) technology is widely used in scenarios such as active noise-cancelling headphones, car cabin noise reduction and active sound barriers, and can effectively achieve noise control.

[0003] Due to its high robustness and simple implementation, the Filtered-x Least Mean Square (FxLMS) algorithm is widely used in active noise control systems. However, for systems with multiple reference signals, the convergence speed of the FxLMS algorithm is affected by the colorization and coupling of the reference signals. In addition, the non-flat response of the secondary path in the active noise control system will also lead to differences in the convergence speed of different frequency bands.

[0004] To address this problem, Elliott proposed a preprocessing algorithm (SJ Elliott, "Optimal controllers and adaptive controllers for multichannel feedforward control of stochastic disturbances," IEEE Transactions on signal Processing, 48 (4), 1053-1060 (2000)). This algorithm performs spectral decomposition on the reference signal autocorrelation matrix to obtain a reference signal preprocessing filter, and performs minimum phase / all-pass decomposition on the secondary path transfer function. The reference signal preprocessing filter and the minimum phase / all-pass decomposition results are used to iterate the control filter. The simulation results based on the ideal system show that this method can effectively improve the convergence speed. For multi-channel complex physical systems, the spectral decomposition of the reference signal autocorrelation matrix and the minimum phase / all-pass decomposition of the secondary path are difficult to solve quickly, so the algorithm is difficult to promote.

[0005] Bai et al. used singular value decomposition (SVD) and eigenvalue decomposition (EVD) to design reference signal preprocessing filters and secondary path decomposition (M. Bai, S. Elliott, "Preconditioning multichannel adaptive filtering algorithms using evd-and svd-based signal prewhitening and system decoupling," Journal of sound and vibration, 270 (4-5), 639-655 (2004)). The simulation results based on the crosstalk elimination system verified that this method can effectively improve the system convergence speed. However, the use of SVD and EVD methods for preprocessing filter design and secondary path decomposition will introduce additional delays, so this method cannot be applied to active noise control systems with strict causality requirements.

[0006] Based on this, it is necessary to provide an adaptive algorithm for multi-reference active noise control systems to improve the system convergence speed while ensuring the causality of the system. Summary of the invention

[0007] In order to overcome the deficiencies in the prior art, the present invention provides a method for improving the convergence speed of a multi-reference active noise reduction adaptive algorithm. The method can preprocess the filtered reference signal under the premise of ensuring the causality of the active noise reduction system, and improve the convergence speed of the multi-reference filtered reference minimum mean square error active noise reduction adaptive algorithm.

[0008] To achieve the above object, the technical solution adopted by the present invention is:

[0009] A method for improving the convergence speed of a multi-reference active noise reduction adaptive algorithm comprises the following steps:

[0010] Step 1: Measure the unit impulse response of the secondary path transfer function of the active noise control system and obtain the secondary path estimation function n is the time index, M is the unit impulse response order of the secondary path, and the superscript T is the transposition operator symbol;

[0011] Step 2: Filter the reference signal using the secondary path estimation function to obtain a filtered reference signal r(n) = [r0(n), r1(n), ..., r i (n)…,r R-1 (n)] T , where R is the number of reference signals, the i-th filtered reference signal where x i (n) = [x i (n),x i(n-1),…,x i (n-M+1)] T is the i-th reference signal vector;

[0012] Step 3: Calculate the autopower spectral density function of the filtered reference signal r(n) Where ω is the angular frequency, R rr (m) = E[r(n+m)r H (n)], -∞<m<+∞, E[] is the symbol of the expectation operation, and the superscript H is the symbol of the conjugate transposition operation;

[0013] Step 4: Auto-power spectral density function S rr (ω) perform eigenvalue decomposition and design a frequency domain preprocessing filter bank F(ω);

[0014] Step 5, performing inverse Fourier transform on the frequency domain preprocessing filter group F(ω) to obtain the time domain preprocessing filter group f(n);

[0015] Step 6: Use the time domain preprocessing filter group f(n) to filter the filtered reference signal r(n) to obtain the preprocessed filtered reference signal v(n) = [v0(n), v1(n), ..., v i (n),…,v R-1 (n)] T , where the i-th preprocessed filtered reference signal f ij (n) is used to generate v i (n) the jth set of preprocessing filter coefficients, i,j = 0, 1, ..., R-1;

[0016] Step 7, use the pre-processed filtered reference signal v(n) and the error signal e(n) to perform an intermediate control filter C(n) = [C0(n), C1(n), ..., C i (n),…,C R-1 (n)] iteration, while making the cost function J = E[e(n) T e(n)] is the smallest, the i-th filtered reference signal v i (n) The corresponding intermediate control filter C i Iteration formula for (n):

[0017] C i (n+1)=C i (n)-2μe(nD)v i (n)

[0018] Among them, μ is the iteration step size, v i (n)=[v i (n),v i (n-1),…,vi (n-L+1)] T is the i-th preprocessed filtered reference signal vector, L is the length of the intermediate control filter;

[0019] Step 8: Use the preprocessing filter group f(n) and the intermediate control filter C(n) to restore the real control filter W(n) and implement control.

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] (1) Compared with the reference preprocessing algorithm, the method proposed in the present invention preprocesses the filtered reference signal, and during the preprocessing process, the influence of the reference signal colorization characteristics and the non-flat response of the secondary path are compensated, and the reference signal is decoupled.

[0022] (2) Compared with the non-real-time algorithm, the present invention proposes a delayed update strategy to control the filter iteration, which can improve the convergence speed while ensuring the causality of the active noise control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a flowchart of the method of the present invention.

[0024] Figure 2 is the amplitude-frequency response of the preprocessing filter in the embodiment of the present invention, (a) is the preprocessing filter f 11 (n) is the amplitude-frequency response curve, (b) is the preprocessing filter f 12 (n) is the amplitude-frequency response curve, (c) is the preprocessing filter f 21 (n) is the amplitude-frequency response curve, (d) is the preprocessing filter f 22 (n) Amplitude-frequency response curve.

[0025] Figure 3 is a comparison diagram of the filtered reference signal spectra before and after preprocessing in an embodiment of the present invention, (a) is the autopower spectral density function of the first reference signal before and after preprocessing, (b) is the cross-power spectral density function of the first reference signal and the second reference signal before and after preprocessing, (c) is the cross-power spectral density function of the second reference signal and the first reference signal before and after preprocessing, and (d) is the autopower spectral density function of the second reference signal before and after preprocessing.

[0026] Figure 4 1 is a comparison diagram of the coherence coefficients of the filtered reference signals before and after preprocessing in an embodiment of the present invention, (a) is the coherence coefficient between the first reference signal and the first reference signal, (b) is the coherence coefficient between the first reference signal and the second reference signal, (c) is the coherence coefficient between the second reference signal and the first reference signal, and (d) is the coherence coefficient between the second reference signal and the second reference signal.

[0027] Figure 5 It is a comparison diagram of the mean square error convergence curves of the embodiment of the present invention and the traditional FxLMS algorithm.

[0028] Figure 6 It is a comparison diagram of the error signal spectrum before and after noise reduction by the embodiment of the present invention and the traditional FxLMS algorithm. DETAILED DESCRIPTION

[0029] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0030] A method to improve the convergence speed of multi-reference filtering reference minimum mean square error active noise reduction adaptive algorithm, such as Figure 1 As shown, the following steps are included:

[0031] Step 1: Measure the unit impulse response of the secondary path transfer function of the active noise control system and obtain the secondary path estimation function n is the time index, M is the unit impulse response order of the secondary path, and the superscript T is the transposition operator symbol;

[0032] Step 2: Filter the reference signal using the secondary path estimation function to obtain a filtered reference signal r(n) = [r0(n), r1(n), ..., r i (n)…,r R-1 (n)] T , where R is the number of reference signals, the i-th filtered reference signal where x i (n) = [x i (n),x i (n-1),…,x i (n-M+1)] T is the i-th reference signal vector;

[0033] Step 3: Calculate the autopower spectral density function of the filtered reference signal r(n) Where ω is the angular frequency, R rr (m) = E[r(n+m)r H (n)], -∞<m<+∞, E[] is the symbol of the expectation operation, and the superscript H is the symbol of the conjugate transposition operation;

[0034] Step 4: Calculate the power spectral density function S of the filtered reference signal rr (ω) performs eigenvalue decomposition and designs a frequency domain preprocessing filter bank F(ω). The frequency domain preprocessing filter bank F(ω) is:

[0035] F(ω)=D -1 / 2 (ω)Q H (ω)

[0036] D(ω) and Q(ω) are the autocorrelation functions of the filtered reference signal S rr The eigenvalue decomposition result of (ω), namely S rr (ω)=Q(ω)D(ω)Q H (ω), the inverse matrix D -1 / 2 The premise for the existence of (ω) is that the filtered reference signal does not have a frequency component with zero response within the target control frequency band.

[0038] Step 5, perform inverse Fourier transform on the preprocessing filter group F(ω), introduce a time delay of half the number of inverse Fourier transform points into the transformed time domain filter group f(n), the number of delay points is recorded as D, to ensure that the time domain preprocessing filter group f(n) is a causal filter;

[0039] Step 6: Use the preprocessing filter group f(n) to filter the filtered reference signal r(n) to obtain the preprocessed filtered reference signal v(n) = [v0(n), v1(n), ..., v i (n),…,v R-1 (n)] T , where the i-th preprocessed filtered reference signal f ij (n) is used to generate v i The j-th set of preprocessing filter coefficients (i, j = 0, 1, ..., R-1) of (n);

[0040] Step 7, use the preprocessed filtered reference signal v(n) and the error signal e(nD) delayed by D sampling points to perform an intermediate control filter C(n) = [C0(n), C1(n), ..., C i (n),…,C R-1 (n)] iteration, while making the cost function J = E[e(nD) T e(nD)] is the smallest, where the error signal is delayed by D sampling points to ensure that the preprocessed filtered reference signal v(n) is aligned with the error signal timing. The i-th filtered reference signal v i (n) The corresponding intermediate control filter C i Iteration formula for (n):

[0041] C i (n+1)=C i (n)-2μe(nD)v i (n)

[0042] Among them, μ is the iteration step size, v i(n)=[v i (n),v i (n-1),…,v i (n-L+1)] T is the i-th preprocessed filtered reference signal vector, L is the length of the intermediate control filter;

[0043] Step 8: Use the preprocessing filter group f(n) and the intermediate filter C(n) to restore the real control filter W(n). The restoration process can be expressed as W(z) = {z D C(z)F(z)} + , where z D represents a non-causal delay operation, whose non-causal delay is D sampling points, {} + To obtain the causal operator symbol, W(z), C(z) and F(z) are the discrete frequency domain forms of the real control filter W(n), the intermediate control filter C(n) and the preprocessing filter bank f(n), respectively, and z is a complex variable;

[0044] Step 9: Implement control using the real control filter W(n).

[0045] Figure 1 The flowchart of the method of the present invention is shown in FIG. The reference signal x(n) is filtered by the control filter W(z) and then propagated to the error point through the secondary path G(z) to be superimposed with the primary noise d(n) to generate the error signal e(n), wherein the primary noise d(n) is obtained by the reference signal x(n) through the primary path P(z). In the update filter stage, the reference

[0046] The signal x(n) first passes through the secondary path estimation function The filtered reference signal is obtained by filtering, and then the filtered reference signal is preprocessed using the preprocessing filter group F(z) to obtain the preprocessed filtered reference signal v(n), that is,

[0047] v(z)=F(z)x(z)

[0048] The preprocessing filter bank is calculated by steps 1-5, that is,

[0049] F(z)=D -1 / 2 (z)Q H (z)

[0050] D(z) and Q(z) are the autocorrelation functions of the filtered reference signal S rr The eigenvalue decomposition result of (z), namely S rr (z) = Q (z) D (z) Q H (z). The autocorrelation function of the preprocessed filtered reference signal is:

[0051] Svv (z) = F(z)S rr (z)F H (z)=I

[0052] This shows that the preprocessing filter bank F(z) has the effect of whitening, equalizing and removing spatial coupling on the filtered reference signal r(n), thereby improving the convergence speed of the system.

[0053] In order to ensure the causality of the preprocessing filter bank F(z), a time delay of half the number of inverse Fourier transform points needs to be introduced after the preprocessing filter bank is obtained by inverse Fourier transform, which is recorded as D sampling points.

[0054] The minimum mean square error algorithm is used to iterate the intermediate control filter C(z). According to the stochastic gradient descent method, the iterative formula is:

[0055] C i (n+1)=C i (n)-2μe(nD)v i (n)

[0056] Among them, μ is the iteration step size, v i (n)=[v i (n),v i (n-1),…,v i (n-L+1)] T is the i-th preprocessed filtered reference signal vector, and L is the length of the intermediate control filter. In order to ensure that the preprocessed filtered reference signal v(n) is aligned with the error signal in time sequence, the error signal of the delayed D sampling point is used in the iteration formula for iteration.

[0057] After the intermediate control filter iteration is completed, the formula W(z) = {z D C(z)F(z)} + The real control filter is recovered to realize real-time filtering control, where z D represents a non-causal delay operation, whose non-causal delay is D sampling points, {} + To obtain the causal operation symbol.

[0058] The present invention preprocesses the filtered reference signal to improve the convergence speed of the FxLMS algorithm, and introduces a certain delay in the updating process to ensure the causality of the system, so it is hereinafter referred to as the delayed update preconditioned LMS (Preconditioned Least Mean Square, Preconditioned LMS) algorithm.

[0059] The effect of the present invention is illustrated below by taking a dual-reference active noise reduction headrest system as an example. The active noise reduction headrest system is generally arranged near the human ear, and uses a loudspeaker as a secondary sound source. By reducing the noise of the error microphone near the human ear, a quiet zone is generated near the human ear. Each ear uses one control channel, including one secondary source and one error microphone. The error microphone is about 10 cm away from the center of the secondary sound source diaphragm. There are two channels for two ears. Generally speaking, the two channels of the active noise reduction headrest system are weakly coupled, and each channel can be regarded as a single-channel system. The active noise reduction headrest system usually uses multiple reference sensors to obtain reference signals related to human ear noise, and uses a multi-reference adaptive algorithm for noise reduction, but the traditional FxLMS algorithm is affected by the characteristics of the reference signal and the secondary path response, and the convergence speed is often slow. The above steps 1-9 can be used to implement the present invention and improve the convergence speed of the multi-reference FxLMS algorithm.

[0060] In order to illustrate the performance of this method, the following simulation is used to compare and verify the convergence speed of the traditional FxLMS algorithm and the PreconditionedLMS algorithm proposed in this invention. The system sampling rate is set to 1kHz, and the reference signal is obtained by mixing the two pink noise signals through the matrix M. The primary path is a 19th-order 100-400Hz bandpass FIR filter connected in series with 10 sampling points of pure time delay, and the secondary path is the actual measurement result of the headrest system in the laboratory. The form of M is:

[0061]

[0062] The number of frequency domain discrete points is set to 512. The preprocessing filter bank response obtained according to steps 1-5 is as follows: Figure 2 As shown, Figure 1 The filter bank F(z) used to preprocess the filtered reference signal. Figure 2 It is shown that the filter group has a large response at 35Hz. This is because the measured secondary path has a valley at this frequency, so the preprocessing filter F(z) needs a large gain at this location to achieve whitening of the filtered reference signal.

[0063] Figure 3 and Figure 4 The figure shows the effect of preprocessing the reference signal. Figure 3 The cross power spectrum function shown shows that the spectrum of the filtered reference signal after preprocessing basically presents the characteristics of white noise, which indicates that the preprocessing has achieved a good whitening effect. Figure 4 The figure shows the coherence coefficient between the reference signals. It can be seen that the coherence coefficient between the reference signals is basically reduced from about 0.45 to 0, which shows that the preprocessing achieves a good decoupling effect.

[0064] Figure 5The figure shows the mean square error convergence curves of the delayed update Preconditioned LMS algorithm and the traditional FxLMS algorithm. Wiener is the mean square error curve corresponding to the Wiener filter algorithm. The control filter length is set to 512, and the step size used by each algorithm is the maximum step size that guarantees convergence to the Wiener result. The step size of the delayed update Preconditioned LMS algorithm is 2×10 -5 , the step size of the FxLMS algorithm is 2×10 -1 .Depend on Figure 5 It can be seen that the delayed update Preconditioned LMS algorithm starts to converge later than the FxLMS algorithm. This is because a certain delay is introduced in its update structure. 4 The sampling point is basically converged to the Wiener result, while the FxLMS algorithm converges to 8×10 4 The sampling points converge to the Wiener result. Figure 6 The figure shows the error signal spectrum comparison after denoising by the delayed update Preconditioned LMS algorithm, the traditional FxLMS algorithm and the Wiener algorithm. ANC OFF is the error signal spectrum before denoising. It can be seen that both adaptive algorithms basically converge to the Wiener result.

[0065] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for improving the convergence speed of a multi-reference active noise reduction adaptive algorithm, characterized in that: The steps include: Step 1: Measure the unit impulse response of the secondary path transfer function of the active noise control system and obtain the secondary path estimation function n is the time index, M is the unit impulse response order of the secondary path, and the superscript T is the transposition operator symbol; Step 2: Filter the reference signal using the secondary path estimation function to obtain a filtered reference signal r(n) = [r0(n), r1(n), ..., r i (n)…,r R-1 (n)] T , where R is the number of reference signals, the i-th filtered reference signal where x i (n) = [x i (n),x i (n-1),…,x i (n-M+1)] T is the i-th reference signal vector; Step 3: Calculate the autopower spectral density function of the filtered reference signal r(n) Where ω is the angular frequency, R rr (m) = E[r(n+m)r H (n)], -∞<m<+∞, E[] is the symbol of the expectation operation, and the superscript H is the symbol of the conjugate transposition operation; Step 4: Auto-power spectral density function S rr (ω) perform eigenvalue decomposition and design a frequency domain preprocessing filter bank F(ω); Step 5, performing inverse Fourier transform on the frequency domain preprocessing filter group F(ω) to obtain the time domain preprocessing filter group f(n); Step 6: Use the time domain preprocessing filter group f(n) to filter the filtered reference signal r(n) to obtain the preprocessed filtered reference signal v(n) = [v0(n), v1(n), ..., v i (n),…,v R-1 (n)] T , where the i-th preprocessed filtered reference signal f ij (n) is used to generate v i (n) the jth set of preprocessing filter coefficients, i,j = 0, 1, ..., R-1; Step 7, use the pre-processed filtered reference signal v(n) and the error signal e(n) to perform an intermediate control filter C(n) = [C0(n), C1(n), ..., C i (n),…,C R-1 (n)] iteration, while making the cost function J = E[e(n) T e(n)] is the smallest, the i-th filtered reference signal v i (n) The corresponding intermediate control filter C i Iteration formula for (n): C i (n+1)=C i (n)-2μe(n-D)v i (n) Where μ is the iteration step size, v i (n)=[v i (n),v i (n-1),…,v i (n-L+1)] T is the i-th preprocessed filtered reference signal vector, L is the length of the intermediate control filter; Step 8: Use the preprocessing filter group f(n) and the intermediate control filter C(n) to restore the real control filter W(n) and implement control.

2. A method for improving the convergence speed of a multi-reference active noise reduction adaptive algorithm according to claim 1, characterized in that: In step 4, the frequency domain preprocessing filter bank F(ω) is: F(ω)=D -1 / 2 (oh)Q H (oh) D(ω) and Q(ω) are the autocorrelation functions of the filtered reference signal S rr The eigenvalue decomposition result of (ω), namely S rr (ω)=Q(ω)D(ω)Q H (ω).

3. A method for improving the convergence speed of a multi-reference active noise reduction adaptive algorithm according to claim 2, characterized in that: In step 5, a time delay of half the number of inverse Fourier transform points is introduced into the transformed time domain preprocessing filter group f(n), and the number of delay points is recorded as D, to ensure that the time domain preprocessing filter group f(n) is a causal filter.

4. A method for improving the convergence speed of a multi-reference active noise reduction adaptive algorithm according to claim 3, characterized in that: In step 7, when performing the iteration of the intermediate control filter, the error signal e(nD) delayed by D sampling points is used for iteration so that the cost function J=E[e(nD) T e(nD)] is minimized to ensure that the preprocessed filtered reference signal v(n) is time-aligned with the error signal during the iteration process.

5. A method for improving the convergence speed of a multi-reference active noise reduction adaptive algorithm according to claim 4, characterized in that: In step 8, the real control filter W(n) is recovered by the preprocessing filter group f(n) and the intermediate control filter C(n), that is, In(from)={from D C(z)F(z)} + in{} + To obtain the causal operator symbol, W(z), C(z) and F(z) are the discrete frequency domain forms of the real control filter W(n), the intermediate control filter C(n) and the preprocessing filter group f(n), respectively, and z is a complex variable.

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