Low-complexity active impulse noise control method based on recursive minimum robust estimation

Abstract

The present invention discloses a low-complexity active impulse noise control method based on recursive minimum robust estimation, expands the FxlogRLS algorithm, and performs active control on impulse noise based on the filtered input recursive minimum M estimation algorithm (abbreviated as FxRLM‑NKP) of the nearest Kronecker product. The coefficient vector w(n) of the adaptive controller is decomposed into two groups of short sub-filter vectors w1(n) and w2(n) by using the Kronecker product, thereby establishing a signal model. A set of cost functions is defined by using a robust estimator with adaptive parameters, thereby deriving the corresponding adaptive control algorithm. The use of the Kronecker integral decomposition reduces the computational complexity of the adaptive control algorithm; the adaptive M estimator makes the present invention (FxRLM‑NKP algorithm) robust to impulse noise. Experimental results show that the present invention exhibits good performance in active control of impulse noise and has the advantage of low computational complexity.

Description

Technical Field

[0001] The present invention belongs to the technical field of active noise control (ANC), and more specifically, relates to a low-complexity active impulse noise control method based on recursive minimum robust estimation. Background Art

[0002] Active Noise Control (ANC), or active noise control, is a method of attenuating unwanted low-frequency interference by introducing a controllable secondary sound source. This technology has been widely used in various applications to reduce harmful noise, such as broadband noise in cabins and flight decks, narrowband transformer noise, noise in pipes, and discomfort noise in living and working environments. The controlled noise source is called primary noise or reference noise. The filtered input least mean square (FxLMS) algorithm is the most commonly used adaptive algorithm in active noise control because it is effective in most cases, has low computational complexity, and is easy to implement.

[0003] Impulse noise is widely present in various acoustic environments, such as the knocking of workpieces in workshops, the noise generated by pile drivers, the sound of gunfire on the battlefield, the sound of firecrackers, the slamming of doors, the sound of objects falling to the ground, etc. This type of noise is more likely to have sharp spikes or outliers than normally distributed noise. For the active control of impulse noise, researchers have developed a large number of adaptive algorithms, such as the improved filtered input least mean square (FxLMS) algorithm, the filtered minimum mean p-norm algorithm (FxLMP), the logarithmic transformation FxlogLMS algorithm, the M-estimator-based FxLMS algorithm, the recursive least squares (RLS)-based FxlogRLS algorithm, the Hampel function-based FxRLM algorithm, the state detection-based post-filtering algorithm, the IVSSPFFxAPSA algorithm with post-adaptive filter and variable step size, and the hybrid method based on the FxLMS and FxRLS classes. Among these methods, the FxlogRLS algorithm uses a logarithmic function to attenuate impulse noise and considers the substitution error to avoid the instability of the adaptive filter, so it has received great attention. However, this algorithm has high computational complexity. Summary of the invention

[0004] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a low-complexity active impulse noise control method based on recursive minimum robust estimation, which reduces the computational complexity while obtaining good noise reduction performance.

[0005] To achieve the above-mentioned object of the invention, the present invention provides a low-complexity active impulse noise control method based on recursive minimum robust estimation, which is characterized by comprising the following steps:

[0006] (1) Initialization

[0007] First, construct the first group of P with length L 1 The sub-filter w 1，p (n) and a second group of P lengths L 2 The sub-filter w 2，p (n), n represents the time, and then initialize:

[0008] w 1，p (0) = [η 0 … 0] T ,p=1,2,...,P,0<η≤1

[0009] w 2，p (0) = [η 0 … 0] T ,p=1,2,...,P,0<η≤1

[0010] Among them, the parameter η can be selected in the range of greater than 0 and less than or equal to 1, P<min{L 1 , L 2}, so the first and second groups of sub-filter vectors at time 0 are:

[0011]

[0012]

[0013] Initialize the two sets of correlation inverse matrices Q at time 0 1 (0), Q 2 (0):

[0014]

[0015]

[0016] in, and The size is PL 1 ×PL 1 and PL 2 ×PL 2 The identity matrix, parameter δ 1 ,δ 2 Select according to the specific implementation situation;

[0017] (2) Collect the reference pulse noise, obtain the sampling value x(n), and construct the reference pulse noise signal vector x(n) at time n:

[0018] x(n)=[x(n)x(n-1) … x(n-L+1)] T

[0019] Where L = L 1 L 2, the value of the vector is 0 when the small remainder is equal to 0;

[0020] The signal after the reference pulse noise passes through the primary path P(z) is the primary noise d(n);

[0021] (3) Starting from time n = 1, adaptively calculate the coefficient vector w(n) of the adaptive filter W(z) at time n

[0022] 3.1) Calculate the filtered reference signal x f (n)

[0023]

[0024] in, is the estimate of the secondary path S(z) The corresponding time domain impulse response, * indicates the convolution operation;

[0025] 3.2) Calculate the sub-filter vector w 1 (n)

[0026] 3.2.1) Calculate the sub-filter reference signal

[0027]

[0028] in, represents the Kronecker product;

[0029] In this way, the synthesized sub-filter reference signal vector is obtained

[0030] 3.2.2) Calculate the sub-filter signal x 2，p (n):

[0031]

[0032] In this way, the synthesized sub-filter signal vector x is obtained 2 (n):

[0033]

[0034] 3.2.3) Calculate the sub-filter error signal e 1 (n):

[0035]

[0036] 3.2.4) Calculate the weighting factor γ 1 (n):

[0037]

[0038] where ξ 1 Is to use e 1 (n) is calculated by the variance estimator and median operation;

[0039] 3.2.5) Calculate the Kalman filter gain subvector k 2 (n):

[0040]

[0041] where λ 1 is the forgetting factor, which takes a value between 0 and 1;

[0042] 3.2.6) Calculate the error of substitution

[0043]

[0044] 3.2.7) Calculate the sub-filter vector w 1 (n):

[0045]

[0046] 3.2.8) Update the correlation inverse matrix, that is, calculate the correlation inverse matrix Q 2 (n):

[0047]

[0048] 3.3) Calculate the sub-filter vector w 2 (n)

[0049] 3.3.1) Calculate the sub-filter reference signal

[0050]

[0051] In this way, the synthesized sub-filter reference signal vector is obtained

[0052]

[0053] 3.3.2) Calculate the sub-filter signal x 1，p (n):

[0054]

[0055] In this way, the synthesized sub-filter signal vector x is obtained 1 (n):

[0056]

[0057] 3.3.3) Calculate the sub-filter error signal e 2 (n):

[0058]

[0059] 3.3.4) Calculate the weighting factor γ 2 (n):

[0060]

[0061] where ξ 2 Is to use e 2 (n) is calculated by the variance estimator and median operation;

[0062] 3.3.5) Calculate the Kalman filter gain subvector k 1 (n):

[0063]

[0064] where λ 2 is the forgetting factor, which takes a value between 0 and 1;

[0065] 3.3.6) Calculate the error of substitution

[0066]

[0067] 3.3.7) Calculate the sub-filter vector w 2 (n):

[0068]

[0069] 3.3.8) Update the correlation inverse matrix, that is, calculate the correlation inverse matrix Q 1 (n):

[0070]

[0071] 3.4) Calculate the filter coefficient vector w(n) at time n

[0072]

[0073] (4) The coefficient vector w(n) obtained at each time instant n is sent to the control filter W(z), which filters the reference pulse noise to generate a filter signal y(n), which drives the speaker to generate a cancellation signal y′(n) to attenuate the primary noise d(n), thereby realizing active control of the pulse noise.

[0074] The object of the invention of the present invention is achieved in this way:

[0075] The present invention is based on a low-complexity active impulse noise control method based on recursive minimum robust estimation, expands the FxlogRLS algorithm, and uses a filter input recursive minimum M estimation algorithm based on the nearest Kronecker product (abbreviated as FxRLM-NKP) to actively control impulse noise. The coefficient vector w(n) of the adaptive controller is decomposed into two groups of short sub-filter vectors w using the Kronecker product. 1 (n), w 2 (n), thereby establishing a signal model. A set of cost functions are defined by a robust estimator with adaptive parameters, from which the corresponding adaptive control algorithm is derived. The use of Kronecker integral decomposition reduces the computational complexity of the adaptive control algorithm; the adaptive M estimator makes the present invention (FxRLM-NKP algorithm) robust to impulse noise. Experimental results show that the present invention exhibits good performance in impulse noise active control and has the advantage of low computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 It is a schematic diagram of the principle of a single-channel feed-forward active noise control (ANC) system;

[0077] Figure 2 It is a flowchart of a specific implementation method of a low-complexity active impulse noise control method based on recursive minimum robust estimation of the present invention;

[0078] Figure 3 It is a graph showing the computational complexity of the FxlogRLS, FxRLM and FxRLM-NKP algorithms (the present invention) as a function of the parameter P;

[0079] Figure 4 It is a graph showing the computational complexity of the FxlogRLS, FxRLM and FxRLM-NKP algorithms (the present invention) as a function of the adaptive filter length L;

[0080] Figure 5 The simulation results are as follows when P = 10 and the impulse noise model parameter α = 1.5: (a) original primary impulse noise, (b) residual noise of the FxLMS algorithm, (c) residual noise of the FxlogRLS algorithm, (d) residual noise of the FxRLM algorithm, and (e) residual noise of the FxRLM-NKP algorithm.

[0081] Figure 6 The simulation experimental results are as follows when P=5 and the pulse noise model parameter α=1.8: (a) original primary pulse noise, (b) residual noise of FxLMS algorithm, (c) residual noise of FxlogRLS algorithm, (d) residual noise of FxRLM algorithm, and (e) residual noise of FxRLM-NKP algorithm. DETAILED DESCRIPTION

[0082] The specific implementation of the present invention is described below in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when the detailed description of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

[0083] 1. Signal model and optimization criteria

[0084] Figure 1 Figure 1 is a schematic diagram of the principle of a single-channel feedforward active noise control (ANC) system. Figure 1 As shown in Figure 1, it consists of a reference microphone for picking up the reference noise, i.e., the impulse noise ≤(n) that needs to be controlled, an error microphone for measuring the residual noise e(n), and a secondary sound source for generating a cancellation signal y′(n) to attenuate the primary noise d(n). Among them, P(z) is the primary path, W(z) is the control filter, S(z) is the secondary path, and its estimation is Filter the reference noise x(n). In order to improve the stability of the algorithm, Figure 1 The substitution error e caused by the change in the order of signal operations between the algorithm derivation process and the active noise control application is also considered. r (n).

[0085] Depend on Figure 1 It can be seen that the error signal e(n) of the active noise control system at time n can be expressed as:

[0086] e(n)=d(n)+s(n)*[w T (n-1)x(n)], (1)

[0087] Where s(n) is the impulse response corresponding to the secondary path S(z), * denotes linear convolution, and the superscript T Represents the transpose operation;

[0088] w(n)=[w 0 (n) w 1 (n) … w L - 1 (n)] T (2)

[0089] is the coefficient vector of the adaptive filter W(z) of length L at time n, and:

[0090] x(n)=[x(n) x(n-1) … x(n-L+1)] T (3)

[0091] is the reference impulse noise signal vector at time n. In practical active noise control system applications, S(z) is unknown and must be estimated. Therefore, the reference signal is passed through the estimated secondary path to generate the filtered reference signal. Thus, the error signal can be rewritten as:

[0092]

[0093] Where:

[0094]

[0095] is the filtered reference signal;

[0096]

[0097] yes The corresponding time domain impulse response.

[0098] In the active control of impulse noise, a large number of experiments show that the error signal also has an impulse characteristic. This characteristic of the reference signal and the error signal causes the coefficient vector of the filter to also have an impulse characteristic, which means that the matrix represented by a set of vectors shortened by the filter coefficient vector is low-rank. The present invention uses a low-rank model associated with the Kronecker product between a set of short vectors to approximate the coefficient vector of the filter. Therefore, the Kronecker product can be used to decompose the adaptive filter coefficient vector into:

[0099]

[0100] Where w 1，p (n) and w 2，p (n) are respectively the length of L 1 and L 2 The sub-filter, Denote the Kronecker product, and assume that L = L 1 L 2 And P<min{L 1 , L 2 By using the following relationship:

[0101]

[0102] In the formula and The sizes are L 1 ×L 1 and L 2 ×L 2 The error signal in formula (4) can be expressed in the following two equivalent forms:

[0103]

[0104]

[0105] Where:

[0106]

[0107]

[0108]

[0109]

[0110]

[0111]

[0112] In order to smooth the instantaneous fluctuations caused by strong pulses in the impulse noise and reduce the adverse effects of the pulse characteristics on the adaptive filter, a robust M-estimator is used to define a set of cost functions as follows:

[0113]

[0114] Where 0<λ 1 ,λ 2 <1 is the two forgetting factors,

[0115]

[0116]

[0117] is the a posteriori error at time i, and ρ(·) is the Cauchy estimator, defined as:

[0118]

[0119] Using ε l The variance estimator and median operation of (n) have an effect on the parameter ξ l Perform adaptive estimation.

[0120] It is worth mentioning that the algorithm proposed in the present invention is very different from the logarithmic transformation method. The former algorithm uses the Cauchy estimator to establish the cost function and estimates its parameters in an adaptive manner, thereby better tracking the impulse noise. More importantly, the algorithm proposed in the present invention uses the Kronecker product to decompose the coefficient vector of the adaptive filter into two groups of shorter sub-filters, which can greatly reduce the computational complexity of the adaptive algorithm.

[0121] 2. Adaptive Algorithm

[0122] Based on formula (17), About w 1The derivative of (n) can be calculated as

[0123]

[0124] Where ρ′(·) is the first-order derivative of ρ(·). Let

[0125]

[0126] And let formula (21) equal to 0, we can get a regular equation as follows:

[0127] R 2 (n)w 1 (n) = p 2 (n), (23)

[0128] In the formula

[0129]

[0130]

[0131] In a similar way, another canonical equation can be derived from formula (17) as follows:

[0132] R 1 (n)w 2 (n) = p 1 (n), (26)

[0133] Where:

[0134]

[0135]

[0136]

[0137] Based on formula (20), γ 1 (i) and γ 2 (i) It can be calculated that:

[0138]

[0139] Based on formulas (23)-(25), (26), (27) and formula (29), the complete FxRLM-NKP algorithm can be derived, and its process is summarized as follows: Figure 2 As shown. Note that in the algorithm implementation, using 1 (n-1) and w 2 The prior error of (n-1) is not related to w 1 (n) and w 2 (n) The related a posteriori errors are calculated separately for γ 1 (n) and γ1 (n). Because the adaptive parameter ξ l The statistical properties of recent noise samples are captured, so the effect of this approximation is negligible.

[0140] The signal flow path of the ANC system is different from the typical derivation process, and this difference leads to the substitution error in the error signal. In the active control of impulse noise, this substitution error cannot be ignored due to its rapid mutation. Therefore, the substitution error must be incorporated into the update equation of the proposed algorithm to deal with its adverse effects. To this end, we express the primary noise d(n) and the estimated value of the secondary path into the following two equivalent forms according to the error formula in equations (1), (9) and (10):

[0141]

[0142] and

[0143]

[0144] Where:

[0145]

[0146]

[0147]

[0148]

[0149] Substitute the estimates of formulas (31) and (32) into formulas (9) and (10), respectively, and replace the original e 1 (n) and e 2 (n) are rewritten as e r1 (n) and e r2 (n), the error signal can be obtained:

[0150]

[0151]

[0152] Specifically, if Figure 2 As shown, the low-complexity active impulse noise control method based on recursive minimum robust estimation of the present invention comprises the following steps:

[0153] Step S1: Initialization

[0154] First, construct the first group of P with length L 1 The sub-filter w 1，p (n) and a second group of P lengths L 2 The sub-filter w2，p (n), n represents the time, and then initialize:

[0155] w 1，p (0) = [η 0 … 0] T ,p=1,2,...,P,0<η≤1

[0156] w 2，p (0) = [η 0 … 0] T ,p=1,2,...,P,0<η≤1

[0157] Among them, the parameter η can be selected in the range of greater than 0 and less than or equal to 1, P<min{L 1 , L 2}, so the first and second groups of sub-filter vectors at time 0 are:

[0158]

[0159]

[0160] Initialize the two sets of correlation inverse matrices Q at time 0 1 (0), Q 2 (0):

[0161]

[0162]

[0163] in, and The size is PL 1 ×PL 1 and PL 2 ×PL 2 The identity matrix, parameter δ 1 ,δ 2 Select according to the specific implementation situation;

[0164] Step S2: Construct reference impulse noise signal vector

[0165] The reference pulse noise is collected to obtain the sampling value x(n), and the reference pulse noise signal vector x(n) at time n is constructed:

[0166] x(n)=[x(n) x(n-1) … x(n-L+1)] T

[0167] Where L = L 1 L 2 , the value of the vector is 0 when the small remainder is equal to 0;

[0168] The signal after the reference pulse noise passes through the primary path P(z) is the primary noise d(n);

[0169] Step S3: Adaptively calculate the adaptive filter coefficient vector

[0170] Starting from time n=1, the coefficient vector w(n) of the adaptive filter W(z) at time n is adaptively calculated, specifically:

[0171] Step S3.1: Calculate the filtered reference signal x f (n)

[0172]

[0173] in, is the estimate of the secondary path S(z) The corresponding time domain impulse response, * indicates the convolution operation;

[0174] Step S3.2: Calculate the sub-filter vector w 1 (n)

[0175] Step S3.2.1: Calculate sub-filter reference signal

[0176]

[0177] in, represents the Kronecker product;

[0178] In this way, the synthesized sub-filter reference signal vector is obtained

[0179]

[0180] Step S3.2.2: Calculate the sub-filtered signal x 2,p (n):

[0181]

[0182] In this way, the synthesized sub-filter signal vector x is obtained 2 (n):

[0183]

[0184] Step S3.2.3: Calculate the sub-filter error signal e 1 (n):

[0185]

[0186] Step S3.2.4: Calculate the weighting factor γ 1 (n):

[0187]

[0188] where ξ 1 Is to use e 1 (n) is calculated by the variance estimator and median operation;

[0189] Step S3.2.5: Calculate the Kalman filter gain subvector k 2 (n):

[0190]

[0191] where λ 1 is the forgetting factor, which takes a value between 0 and 1;

[0192] Step S3.2.6: Calculate the substitution error

[0193]

[0194] Step S3.2.7: Calculate the sub-filter vector w 1 (n):

[0195]

[0196] Step S3.2.8: Update the correlation inverse matrix, that is, calculate the correlation inverse matrix Q 2 (n):

[0197]

[0198] Step S3.3: Calculate the sub-filter vector w 2 (n)

[0199] Step S3.3.1: Calculate sub-filter reference signal

[0200]

[0201] In this way, the synthesized sub-filter reference signal vector is obtained

[0202]

[0203] Step S3.3.2: Calculate the sub-filtered signal x 1，p (n):

[0204]

[0205] In this way, the synthesized sub-filter signal vector x is obtained 1 (n):

[0206]

[0207] Step S3.3.3: Calculate the sub-filter error signal e 2 (n):

[0208]

[0209] Step S3.3.4: Calculate the weighting factor γ 2 (n):

[0210]

[0211] where ξ 2 Is to use e 2 (n) is calculated by the variance estimator and median operation;

[0212] Step S3.3.5: Calculate the Kalman filter gain subvector k 1 (n):

[0213]

[0214] where λ 2 is the forgetting factor, which takes a value between 0 and 1;

[0215] Step S3.3.6: Calculate the substitution error

[0216]

[0217] Step S3.3.7: Calculate the sub-filter vector w 2 (n):

[0218]

[0219] Step S3.3.8: Update the correlation inverse matrix, that is, calculate the correlation inverse matrix Q 1 (n):

[0220]

[0221] Step S3.4: Calculate the filter coefficient vector w(n) at time n

[0222]

[0223] Step S4: Send the coefficient vector to the control filter

[0224] The coefficient vector w(n) obtained at each moment n is sent to the control filter W(z), which filters the reference pulse noise to generate a filtered signal y(n), which drives the speaker to generate a cancellation signal y′(n) to attenuate the primary noise d(n), thereby realizing active control of the pulse noise.

[0225] 3. Experimental verification

[0226] The effectiveness of the low-complexity active impulse noise control method (FxRLM-NKP algorithm) based on recursive minimum robust estimation proposed in this invention is verified by experiments, and compared with FxLMS, ​​FxlogRLS, and FxRLM algorithms. The primary path P(z) and the secondary path S(z) are modeled as FIR filters with lengths of 1536 and 512, respectively, and it is assumed that the secondary path S(z) is known a priori, that is, The length of the adaptive control filter w(n) is L=1024, and the sub-filter w 1 (n) and w 2 (n) length L 1 =L 2 = 32. Two reference noise signals are modeled using the symmetric α-stable (SαS) distribution, one corresponding to strong impulse noise α = 1.5 and the other corresponding to weak impulse noise α = 1.8.

[0227] The computational complexity is evaluated based on the number of multiplications / divisions required to implement the active noise control (ANC) algorithm. The computations corresponding to addition and subtraction operations are not considered because they are much faster to compute on most general-purpose hardware platforms. Figure 3 The computational complexity of the FxlogRLS, FxRLM and FxRLM-NKP algorithms is plotted as a function of the parameter P, where the length of the adaptive filter L = 1024. As can be seen from the figure, as the value of P increases, the computational complexity of the proposed FxRLM-NKP algorithm increases. If P ≤ 22, its computational complexity is lower than that of the other two algorithms.

[0228] Figure 4 The computational complexity of the FxlogRLS, FxRLM and FxRLM-NKP algorithms (the present invention) is plotted as a function of the adaptive filter length L, where the parameter P is 5 and 10, respectively. It can be seen that as the adaptive filter length L increases, the computational complexity of the algorithms increases. In contrast, the computational complexity of the FxRLM-NKP algorithm proposed in the present invention is much smaller than that of the other two algorithms, especially for a larger L, which indicates that in terms of computational efficiency, the algorithm proposed in the present invention is the most effective of the three compared algorithms.

[0229] Figure 5 and Figure 6The noise reduction performance of the four algorithms was compared. It can be seen that for the two types of impulse noise used in the experiment, the FxLMS algorithm performed the worst due to its lack of robustness. The FxlogRLS algorithm uses a logarithmic function to define the cost function, which avoids large fluctuations in the filter coefficients and achieves good control performance. Due to the insensitivity of the robust estimator to impulse noise, the FxRLM algorithm achieves good noise reduction performance. The FxRLM-NKP algorithm proposed in the present invention achieves control performance similar to that of the FxRLM algorithm, but the computational complexity of the former is much lower. Among the three compared robust control algorithms, the FxRLM-NKP algorithm has the lowest computational complexity.

[0230] Although the above describes the illustrative specific embodiments of the present invention to facilitate those skilled in the art to understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations using the concept of the present invention are protected.

Claims

1. A low-complexity active impulse noise control method based on recursive minimum robust estimation, characterized in that: The following steps are involved: (1) Initialization First, construct the first group of P sub-filters w of length L1 1，p (n) and a second group of P sub-filters w of length L2 2，p (n), n represents the time, and then initialize: w 1，p (0)=[η 0…0] T ,p=1,2,...,P,0<η≤1 w 2，p (0)=[η 0…0] T ,p=1,2,...,P,0<η≤1 Among them, the parameter η can be selected in the range of greater than 0 and less than or equal to 1, P<min{L1, L2}, so that the first and second groups of sub-filter vectors at time 0 are: Initialize two sets of related inverse matrices Q1(0) and Q2(0) at time 0: in, and They are unit matrices of size PL1×PL1 and PL2×PL2 respectively, and the parameters δ1 and δ2 are selected according to the specific implementation situation; (2) Collect the reference pulse noise, obtain the sampling value x(n), and construct the reference pulse noise signal vector x(n) at time n: x(n)=[x(n) x(n-1)…x(n-L+1)] T Among them, L = L1L2, the value of the vector is 0 when the small remainder is equal to 0; The signal after the reference pulse noise passes through the primary path P(z) is the primary noise d(n); (3) Starting from time n = 1, adaptively calculate the coefficient vector w(n) of the adaptive filter W(z) at time n 3.1) Calculate the filtered reference signal x f (n) in, is the estimate of the secondary path S(z) The corresponding time domain impulse response, * indicates the convolution operation; 3.2) Calculate the sub-filter vector w1(n) 3.2.1) Calculate the sub-filter reference signal in, represents the Kronecker product; In this way, the synthesized sub-filter reference signal vector is obtained 3.2.2) Calculate the sub-filter signal x 2，p (n): In this way, the synthesized sub-filter signal vector x2(n) is obtained: 3.2.3) Calculate the sub-filter error signal e1(n): 3.2.4) Calculate the weighting factor γ1(n): where ξ1 is calculated using the variance estimator and median operation of e1(n); 3.2.5) Calculate the Kalman filter gain sub-vector k2(n): Where λ1 is the forgetting factor, which takes a value between 0 and 1; 3.2.6) Calculate the error of substitution 3.2.7) Calculate the sub-filter vector w1(n): 3.2.8) Update the correlation inverse matrix, that is, calculate the correlation inverse matrix Q2(n): 3.3) Calculate the sub-filter vector w2(n) 3.3.1) Calculate the sub-filter reference signal In this way, the synthesized sub-filter reference signal vector is obtained 3.3.2) Calculate the sub-filter signal x1, p (n): In this way, the synthesized sub-filter signal vector x1(n) is obtained: 3.3.3) Calculate the sub-filter error signal e2(n): 3.3.4) Calculate the weighting factor γ2(n): where ξ2 is calculated using the variance estimator and median operation of e2(n); 3.3.5) Calculate the Kalman filter gain sub-vector k1(n): Where λ2 is the forgetting factor, which takes a value between 0 and 1; 3.3.6) Calculate the error of substitution 3.3.7) Calculate the sub-filter vector w2(n): 3.3.8) Update the correlation inverse matrix, that is, calculate the correlation inverse matrix Q1(n): 3.4) Calculate the filter coefficient vector w(n) at time n (4) The coefficient vector w(n) obtained at each time instant n is sent to the control filter W(z), which filters the reference pulse noise to generate a filter signal y(n), which drives the speaker to generate a cancellation signal y′(n) to attenuate the primary noise d(n), thereby realizing active control of the pulse noise.

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