Vehicle road noise control method and system using active noise reduction, electronic device, and storage medium

The vehicle road noise control method employs an improved multi-channel normalized FxLMS algorithm to address the slow convergence and single-channel limitations of existing systems, achieving faster and more accurate noise reduction for low-frequency road noise.

JP7689250B2Active Publication Date: 2025-06-05SUZHOU RUSHENG ELECTRONICS CO LTD
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Patent Information

Application Number
JP2024540549
Authority / Receiving Office
JP · JP
Patent Type
Patents
Current Assignee / Owner
Priority Date
2021-12-31
Filing Date
2022-11-18
Publication Date
2025-06-05
Estimated Expiration
2042-11-18

AI Technical Summary

Technical Problem

Existing active noise reduction systems for vehicle road noise, such as those using the FxLMS algorithm, suffer from slow convergence and are typically single-channel, which is inadequate for effectively addressing low-frequency road noise.

Method used

A vehicle road noise control method and system utilizing an improved multi-channel normalized FxLMS algorithm, which collects multi-channel reference signals, generates control signals, and updates filter coefficients to achieve faster convergence and more accurate noise reduction.

Benefits of technology

The improved algorithm achieves faster convergence and more accurate noise reduction compared to conventional multi-channel FxLMS algorithms, effectively addressing the challenges of low-frequency road noise pollution inside vehicles.

✦ Generated by Eureka AI based on patent content.

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Abstract

A method and system for controlling vehicle road noise using active noise reduction, an electronic device, and a storage medium are provided. The vehicle road noise control method includes the steps of: collecting a multi-channel reference signal of the vehicle road noise, generating a control signal based on a filter coefficient at a current time and the multi-channel reference signal, and feeding the control signal to an audio playback device of the vehicle, collecting audio signals at multiple sampling positions in the vehicle compartment and obtaining a vector of an error signal, filtering the reference signal to obtain a filtered reference signal, describing the filtered reference signal in a matrix form, and updating the filter coefficient according to the matrix form of the filtered reference signal and the vector of the error signal. The method can perform active noise reduction on the road noise caused by friction between the vehicle tires and the road surface, reduce noise pollution inside the vehicle, and has a fast convergence speed and excellent accuracy.
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Description

[Technical field]

[0001] This application claims priority to a Chinese patent application filed on December 31, 2021, application number CN2021116833265.

[0002] The present invention relates to the field of vehicle noise control, and relates to a vehicle road noise control method and system using active noise reduction, an electronic device, and a storage medium. [Background technology]

[0003] With the development of modern industry, the problem of noise pollution has attracted more and more people's attention, and high-intensity noise signals also affect the comfort of listeners. Due to the sound masking effect, the volume needs to be increased to achieve a higher signal-to-noise ratio and a clearer listening effect. The long-term high sound pressure caused by this will cause irreparable damage to hearing. As the vehicle becomes more intelligent, drivers and passengers have increasingly strict requirements for the acoustic environment inside the car. Noise inside the car reduces the comfort of the driver and passengers, causes irritation and fatigue of passengers inside the car, affects the clarity of AC conversations, and even affects the driver's perception of signal sounds outside the car, increasing the traffic list. NVH (Noise, Vibration, Harshness) of automobiles is an important issue that automobile manufacturers are concerned about. Methods of reducing noise by changing the structural design, adding vibration-damping materials, using devices such as shock absorber springs, etc. are collectively called passive noise control, which can achieve relatively good noise reduction effects for medium and high frequency noise. However, this method is not very effective against low frequencies, especially road noise caused by collisions and friction between the road surface and tires, which tend to be concentrated in low frequencies. In addition, passive noise control requires a long adjustment time and is difficult to control costs. The active noise reduction solution uses the car audio system to build an inverse signal of the noise signal, forming a secondary sound wave to offset the noise in the target area, reducing noise pollution and improving subjective listening comfort, while adding almost no additional weight to the car, contributing to the reduction of exhaust gases, and is an environmentally friendly and energy-saving solution.

[0004] The FxLMS (Filtered-x Least Mean Square) algorithm is often used in active noise control, and is widely used because it consumes little computing resources and has good algorithm robustness. However, the FxLMS algorithm has the problem of slow convergence, and is often a single-channel (SISO, Single Input Single Output) algorithm. A multi-channel algorithm (MIMO, Multiple Inputs Multiple Outputs) is required for road noise control, but in the multi-channel NFxLMS algorithm introduced in articles such as "A Diffusion Strategy for the Multichannel Active Noise Control System in Distributed Network", Ju-man Song, 2016, and "Multichannel Feedforward Active Noise Control System with Optimal Reference Microphone Selector Based on Time Difference of Arrival", Kenta Iwai, 2018, the channels are considered to be orthogonal to each other, and the effect of the coupling term is ignored, which causes a certain degree of error. Summary of the Invention [Problem to be solved by the invention]

[0005] The present invention aims to provide a method and system for controlling vehicle road noise using active noise reduction, which can reduce noise pollution inside the vehicle by performing active noise reduction on road noise caused by friction between vehicle tires and the road surface, and has a fast convergence speed and high accuracy.

[0006] Another object of the present invention is to provide an electronic device capable of executing the above-mentioned vehicle road noise control method.

[0007] Another object of the present invention is to provide a computer-readable storage medium storing a program capable of implementing the above-mentioned vehicle road noise control method. [Means for solving the problem]

[0008] The first aspect of the present invention is A step S1 of collecting a multi-channel reference signal of vehicle road noise, x k Step S1, where k=1, 2, ..., K, K is the number of channels of the reference signal, and n is a sampling time; Step S2: generating a control signal based on the current filter coefficient and the multi-channel reference signal, and feeding the control signal to an audio playback device of the vehicle; A step S3 of collecting speech signals at multiple sampling locations in the vehicle compartment to obtain a vector of error signals e(n); Filtering the reference signal to obtain a filtered reference signal

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[0009] In this specification, the reference signal refers to the vibration signal or noise signal of the suspension and body end caused by friction between the wheel and the road surface in actual physics, the control signal is amplified by a power amplifier device and then sent to an audio reproduction device (e.g., a voice coil of a speaker), where electro-acoustic conversion is performed and a secondary sound wave is formed to cancel the noise, and e(n) represents an error signal in the sense of signal processing, and is a signal collected by a sound collection device (e.g., a microphone) in a noise reduction area within the compartment in actual physics.

[0010] "Filter length" refers to the order of the filter, here referring to the number of zeros in the filter; the higher the order, the higher the frequency resolution, precision and effectiveness of the filter.

[0011] In one embodiment, the matrix form of the filter coefficients w(n) is: w(n)=[[w 1,1 (0),…,w J,K (0)]…[w 1,1 (N-1),…,w J,K (N-1)] T ∈R K·L·N×1 and ∈R K·L·N×1 represents a matrix with K L N rows and 1 column, In step S2, the control signal is expressed as follows:

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[0012] In one embodiment, in step S1, a vibration signal generated by friction between a wheel and a road surface is collected by a vibration sensor as the reference signal.

[0013] In one embodiment, the vibration sensor is mounted on the bottom plate of the vehicle.

[0014] In one embodiment, in step S1, a noise signal generated by friction between a wheel and a road surface is collected by a first microphone as the reference signal.

[0015] In one embodiment, the first microphone is located near the wheel of the vehicle.

[0016] In one embodiment, in step S2, the sound reproduction device includes a car speaker disposed within the vehicle compartment, the car speaker being disposed within the vehicle compartment or at least radiating sound into the vehicle compartment, including but not limited to a headrest speaker, a ceiling speaker, a door panel speaker, etc.

[0017] In one embodiment, in step S3, a plurality of second microphones are used to collect audio signals within the vehicle compartment, the plurality of second microphones being disposed at a plurality of sampling positions within the vehicle compartment.

[0018] A second aspect of the present invention is A road noise collecting device for collecting noise or vibration signals caused by friction between a wheel and a road surface; a control device for generating a multi-channel reference signal based on the noise or vibration signal collected by the road noise collecting device, and for generating a control signal based on a filter coefficient at a current time and the multi-channel reference signal; a sound reproduction device for generating a secondary sound wave for canceling noise within the compartment based on a control signal transmitted from the control device; an error signal collecting device for collecting audio signals at a plurality of positions in the compartment to obtain a vector of error signals e(n); The control device is also for filtering the reference signal, writing it in a matrix form, and updating filter coefficients based on the matrix form of the filtered reference signal and the vector of the error signal according to the following equation:

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[0019] In one embodiment, the reference signal is filtered to obtain a filtered reference signal.

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[0020] In one embodiment, the matrix form of the filter coefficients w(n) is: w(n)=[[w 1,1 (0),…,w J,K (0)]…[w 1,1 (N-1),…,w J,K (N-1)] T ∈R K·L·N×1 and ∈R K·K·N×1 represents a matrix with K L N rows and 1 column, In step S2, the control signal is expressed as follows:

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[0021] In one embodiment, the road noise collecting device includes a vibration sensor mounted on the bottom plate of the vehicle, or a first microphone mounted near the wheel of the vehicle.

[0022] In one embodiment, the error signal collection device includes a second microphone located at a plurality of sampling locations within the vehicle compartment.

[0023] In one embodiment, the sound reproduction device includes a car speaker that is located within or at least radiates sound into the vehicle compartment, including, but not limited to, a headrest speaker, a ceiling speaker, a door panel speaker, etc.

[0024] A third aspect of the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable by the processor, the electronic device realizing the vehicle road noise control method described above when the processor executes the program.

[0025] In one embodiment, the electronic device is a car audio system.

[0026] In a fourth aspect of the present invention, there is provided a computer-readable storage medium having a computer program stored therein, the computer program implementing the above-mentioned vehicle road noise control method when the program is executed by a processor. Effect of the Invention

[0027] With the above solution, the present invention has the following advantages over the prior art:

[0028] The vehicle road noise control method and system of the present invention uses an improved multi-channel normalized FxLMS algorithm for road noise caused by friction between tires and the road surface, normalizing the convergence factor and achieving faster convergence than the conventional FxLMS algorithm. The normalization calculation takes into account the coupling between channels, resulting in more accurate calculation and faster convergence speed than the conventional multi-channel NFxLMS algorithm.

[0029] In order to more clearly describe the technical solutions of the present invention, the following briefly introduces the necessary drawings used in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without the need for creative work. [Brief description of the drawings]

[0030] [Figure 1] 1 is a flowchart of a MIMO MNFxLMS algorithm according to an embodiment of the present invention. [Diagram 2] FIG. 2 is a block diagram of a MIMO MNFxLMS algorithm according to an embodiment of the present invention. [Diagram 3] 1 is a block diagram of a vehicle road noise control system according to an embodiment of the present invention. [Figure 4] FIG. 11 is a comparison diagram of the convergence performance at position 1 of three algorithms: MIMO FxLMS, ​​MIMO NFxLMS, ​​and MIMO MNFxLMS. [Diagram 5] FIG. 11 is a comparison diagram of the convergence performance at position 2 of three algorithms, namely, MIMO FxLMS, ​​MIMO NFxLMS, ​​and MIMO MNFxLMS. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0031] In order to facilitate understanding of the advantages and features of the present invention by those skilled in the art, preferred embodiments of the present invention will be described in detail below with reference to the drawings. Note that the description of these embodiments contributes to understanding the present invention, but does not constitute a limitation on the present invention.

[0032] In this embodiment, a vehicle road noise control method using active noise reduction is provided, which uses an improved multi-channel normalized FxLMS (MIMOMNFxLMS, ​​Multiple Inputs Multiple Outputs Modified Normalized Filtered-x Least Mean Square) algorithm for road noise caused by friction between vehicle tires and the road surface to perform active noise reduction. As shown in Figures 1 and 2, this method will be described in detail as follows.

[0033] (1) Collection of reference signals At each sampling time n, a reference signal is collected from a sensor, such as a vibration signal from a vibration sensor (typically mounted on the underside of the vehicle) or an audio signal from a microphone (typically mounted near the wheel of the vehicle). There are a total of K channel reference signals, x k Let (n), k = 1, 2, ..., K.

[0034] (2) Generation of control signals Current time parameter w k,l (n) and the reference signal obtained in the previous step, the control signal y l (n) is generated and fed to an audio reproduction device, specifically, in this embodiment, the audio reproduction device includes a car speaker.

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[0035] (3) Generation of a filtered reference signal The most important step in the FxLMS algorithm is to filter the reference signal. In general, the transfer function of the secondary channel includes the digital control signal y(n) passing through the transmission path of the DAC module, analog filter, power amplifier module, speaker, sound wave propagation in space, microphone, analog filter, and ADC module. The transfer function S of the secondary channel is obtained by online and offline system identification methods and is written as S'. Let s be a digital filter with length N, and l,m , l=1,2,…,L;m=1,2…M, which represents the transfer function from the lth speaker to the mth microphone, where M is the number of microphones. The calculated sampled reference signal is

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[0036] (4) The sampled reference signal is written in matrix form.

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[0037] (5) The error signal e obtained by collecting data from each microphone m (n) There are M microphone signals in total, and we obtain a vector of error signals, e(n) = [e 1 (n),…,e M (n)] T ∈R M×1 It is expressed as:

[0038] (6) Update the filter control parameter w(n),

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[0039] As shown in FIG. 3, the vehicle road noise control system of the present embodiment includes: A road noise collecting device 101 for collecting noise or vibration signals caused by friction between a wheel and a road surface; A control device 102 for generating a multi-channel reference signal based on the noise or vibration signal collected by the road noise collecting device 101, and for generating a control signal based on a filter coefficient at a current time and the multi-channel reference signal; a sound reproduction device 103 for generating a secondary sound wave for canceling noise within the compartment 200 based on a control signal sent from the control device 102; an error signal collector 104 for collecting audio signals at multiple positions in the compartment 200 to obtain a vector of error signals e(n); The control device 102 is also for filtering the reference signal, storing it in a matrix form, and updating a filter coefficient according to the matrix form of the filtered reference signal and the vector of the error signal, according to the following equation:

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[0040] The road noise collecting device 101 is electrically connected to the input end of the control device 102, and specifically includes a vibration sensor installed on the bottom plate of the vehicle, or a first microphone installed at a wheel location near the vehicle. The error signal collecting device 104 is electrically connected to the input end of the control device 102, and specifically includes a second microphone installed at a plurality of sampling positions in the vehicle compartment 200. The voice replay device 103 is electrically connected to the output end of the control device 102, and includes a car speaker, which is located in the vehicle compartment 200 or at least radiates sound to the vehicle compartment, and includes, but is not limited to, a headrest speaker, a ceiling speaker, a door panel speaker, etc.

[0041] Simulation Example The convergence performance of the algorithm is simulated. In the simulation experiment, the target noise is a wideband signal with a frequency band covering 80Hz to 320Hz, which is a typical frequency band distribution of road noise. The noise signal is a white noise signal generated through a bandpass filter. The number of channels of the reference signal is K=2, the number of speakers is L=5, and the number of microphones collecting the error signal is M=5. The transfer function between the speaker and the microphone is the transfer function of the secondary channel described above, which is obtained by collecting from an actual vehicle. In the simulation experiment, the change relationship of the noise energy according to the number of iterations (also corresponding to time) before and after the active noise control is compared, and more importantly, the conventional multi-channel FxLMS algorithm (MIMO FxLMS), the conventional multi-channel normalized FxLMS algorithm (MIMO NFxLMS), and the improved normalized FxLMS algorithm (MIMO MNFxLMS) proposed in the present invention are compared. Fig. 4 shows the change relationship of the residual noise signal amplitude at the first position with iteration, as can be seen from Fig. 4, the conventional FxLMS algorithm has a certain noise reduction effect, and after normalization is adopted, the algorithm converges faster, while the improved normalization algorithm of the present invention achieves a faster convergence effect. Fig. 5 shows the change relationship of the residual noise signal amplitude at the fifth position with iteration, as can be seen from Fig. 5, the conventional FxLMS algorithm has almost no noise reduction effect, and after normalization is adopted and processed, it achieves obvious noise reduction effect, while the improved normalization algorithm of the present invention is adopted and takes into account the coupling effect between channels, it can achieve a faster convergence speed and a larger noise reduction amount.

[0042] Those skilled in the art will understand that the singular forms "a," "one," "said," and "this," as used herein, may also include the plural, unless otherwise indicated. Furthermore, it should be understood that the term "comprising," as used in the specification of this application, refers to the presence of features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0043] Furthermore, it is understood that "plurality" in this disclosure refers to two or more, and other quantifiers are similar thereto. "And / or" describes a relational relationship between related objects, and indicates that three kinds of relations can exist, for example, "A and / or B" can represent three kinds of situations: A exists alone, A and B exist simultaneously, and B exists alone. The character " / " generally indicates that the related objects before and after are in an "or" relationship. The singular forms "a," "the," and "this" include the plural, unless the context clearly indicates otherwise.

[0044] Further, it is understood that the terms "first", "second", and the like are used to describe various pieces of information, but the information should not be limited to these terms. These terms are merely used to distinguish between the same types of information, and do not imply any particular order or importance. Indeed, expressions such as "first", "second", and the like may be used interchangeably. For example, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information, without departing from the scope of the present disclosure.

[0045] The above examples are merely for illustrating the technical ideas and features of the present invention, and are preferred embodiments, with the aim that those skilled in the art can understand the contents of the present invention and practice it, but they do not limit the scope of protection of the present invention. Any equivalent changes or modifications made substantially according to the idea of ​​the present invention shall be included in the scope of protection of the present invention.

Claims

1. A step S1 of collecting a multi-channel reference signal of vehicle road noise, comprising: k Step S1, where k=1, 2, . . . , K, K is the number of channels of the reference signal, and n is a sampling time; A method for controlling vehicle road noise by active noise reduction, comprising: a step S2 of generating a control signal based on a filter coefficient at a current time and the multi-channel reference signal, and feeding the control signal to an audio reproduction device of the vehicle; The vehicle road noise control method further comprises: A step S3 of collecting speech signals at multiple sampling locations in the vehicle compartment and obtaining a vector e(n) of error signals; Filtering the reference signal to obtain a filtered reference signal [0010] Step S4 to obtain: [0025] N is the filter length, L is the number of channels in the audio playback unit, M is the number of sampling positions, s l,m represents the transfer function from the l-th speaker to the m-th sampling position, and s l,m (i) is the i-th coefficient of this filter, x k Step S4, where (n-i) represents the k-th reference signal for the first i sampling times; Step S5 of writing the filtered reference signal in matrix form as shown in the following equation: [0030] [0045] [0050] represents a matrix of size K × L rows and M columns, and the elements of the matrix are the filtered reference signal at the current sampling time. [006] It is composed of [0070] represents a matrix of size K x L x N rows and M columns, whose elements consist of the filtered reference signals at the current and historical sampling times, [0080] represents a matrix of size K × L rows and M columns, and the elements of the matrix are the filtered reference signal at the previous N-1th time. [0097] ∈R K・L×M represents a matrix with K·L rows and M columns, and ∈R K・L・N×M Step S5, where K x L x N rows and M columns are represented as a matrix; Step S6 of updating the filter coefficients in step S2 according to the following formula: [0010] and step S6, where w(n+1) represents the updated filter coefficients and is for generating a control signal to be filtered and output at the next sampling time n+1, where w(n) represents the filter coefficients at the current time, μ is a convergence factor, δ is a regularization factor, and I is an identity matrix. A vehicle road noise control method comprising:

2. The matrix form of the filter coefficients w(n) is w(n) = [w 1,1 (0), ..., w J,K (0) ] ... [w 1,1 (N-1), ..., w J,K (N-1) T ∈R K・L・N×1 and ∈R K・L・N×1 represents a matrix with K x L x N rows and 1 column, In step S2, the control signal is expressed as follows: ##EQU00011## W k,l (i) is an element in the w(n) matrix, specifically, it represents the ith coefficient of a filter whose input is the kth reference signal and whose output is the lth audio reproducer. There are K·L such filters in total, and the order is N. Each order i of the K·L filters is expressed in the form of an array [w 1,1 (i), ..., w J,K (i)], and all the order coefficients together make up w(n).

2. The method of claim 1, wherein the vehicle road noise control method is a method for controlling a vehicle road noise.

3. In step S1, a vibration signal generated by friction between the wheel and the road surface is collected by a vibration sensor as the reference signal.

2. The method of claim 1, wherein the vehicle road noise control method is a method for controlling a vehicle road noise.

4. The vibration sensor is provided on the bottom plate of the vehicle.

4. The method of claim 3, wherein the vehicle road noise control method is a method for controlling a vehicle road noise.

5. In step S1, a noise signal generated by friction between the wheel and the road surface is collected by a first microphone as the reference signal.

2. The method of claim 1, wherein the vehicle road noise control method is a method for controlling a vehicle road noise.

6. The first microphone is mounted near the wheel of the vehicle.

6. The method of claim 5, wherein the vehicle road noise control method is a method for controlling a vehicle road noise.

7. In step S2, the audio reproduction device includes a car speaker installed in a compartment of a vehicle.

2. The method of claim 1, wherein the vehicle road noise control method is a method for controlling a vehicle road noise.

8. In step S3, a plurality of second microphones are used to collect audio signals in the vehicle compartment, the plurality of second microphones being disposed at a plurality of sampling positions in the vehicle compartment.

2. The method of claim 1, wherein the vehicle road noise control method is a method for controlling a vehicle road noise.

9. A vehicle road noise control system using active noise reduction, comprising: A road noise collecting device for collecting noise or vibration signals caused by friction between a wheel and a road surface; a control device for generating a multi-channel reference signal based on the noise or vibration signal collected by the road noise collecting device, and for generating a control signal based on a filter coefficient at a current time and the multi-channel reference signal; a sound reproduction device for generating a secondary sound wave for canceling noise within the compartment based on a control signal transmitted from the control device; an error signal collector for collecting audio signals at a plurality of positions in the compartment to obtain a vector of error signals e(n); The control device further filters the reference signal to obtain a filtered reference signal. ##EQU14## To obtain the following formula: ##EQU00015## where N is the filter length, L is the number of channels of the audio reproduction unit, M is the number of sampling positions, s l,m is the transfer function from the l th speaker to the m th sampling position, s l,m (i) is the i th coefficient of this filter, and x k (n−i) is the k th reference signal at the first i sampling times.

2. Writing the filtered reference signal in matrix form as shown in the following equation: ##EQU00016## ##EQU00017## however, [0018] represents a matrix of size K × L rows and M columns, and the elements of the matrix are the filtered reference signal at the current sampling time. [0019] It is composed of [0020] represents a matrix of size K x L x N rows and M columns, whose elements consist of the filtered reference signals at the current and historical sampling times, ##EQU00021## represents a matrix of size K × L rows and M columns, and the elements of the matrix are the filtered reference signal at the previous N-1th time. [0022] where ∈R K·L×M represents a matrix with K·L rows and M columns, and ∈R K·L·N×M represents a matrix with K·L·N rows and M columns, and updating filter coefficients based on a matrix form of the filtered reference signal and a vector of the error signal according to: ##EQU00012## however, where w(n+1) represents the updated filter coefficients, w(n) represents the filter coefficients at the current time, μ is the convergence factor, δ is the regularization factor, and I is the identity matrix.

1. A vehicle road noise control system using active noise reduction, comprising:

10. The road noise collecting device includes a vibration sensor mounted on the underside of the vehicle or a first microphone mounted at a location near the wheel of the vehicle, and the error signal collecting device includes a second microphone mounted at a plurality of sampling positions within the vehicle compartment.

10. The vehicle road noise control system of claim 9.

11. The audio reproduction device includes a car speaker installed within a vehicle compartment.

10. The vehicle road noise control system of claim 9.

12. The control signal is expressed as follows: [0023] W k,l (i) is an element in the w(n) matrix, specifically, it represents the ith coefficient of a filter whose input is the kth reference signal and whose output is the lth audio reproducer. There are K·L such filters in total, and the order is N. Each order i of the K·L filters is expressed in the form of an array [w 1,1 (i), ..., w J,K (i)], and all the order coefficients together make up w(n).

10. The vehicle road noise control system of claim 9.

13. An electronic device including a memory, a processor, and a computer program stored in the memory and executable by the processor, The processor, when executing the program, realizes the vehicle road noise control method according to any one of claims 1 to 8.

1. An electronic device comprising:

14. 1. A computer-readable storage medium, comprising: A computer program is stored, which, when executed by a processor, realizes the vehicle road noise control method according to any one of claims 1 to 8. A computer-readable storage medium comprising:

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