阅读说明：本技术 基于小波去噪和music算法的波达方向定位方法 (Direction-of-arrival positioning method based on wavelet denoising and MUSIC algorithm ) 是由 王超懿 刘华巍 王艳 刘建坡 张士柱 于 2021-09-10 设计创作，主要内容包括：本发明涉及一种基于小波去噪和MUSIC算法的波达方向定位方法,包括：步骤(1)：确定麦克风的阵元数量及摆放位置,根据所述麦克风的阵元数量及摆放位置确定阵列的导向矩阵,通过所述阵列接收信源信号；步骤(2)：通过小波去噪法对接收到的信源信号进行降噪；步骤(3)：通过MUSIC算法对降噪后的信源信号进行方位角估计。本发明能够有效对信源信号的方位角进行准确估计,同时对噪声环境具有较好的抗干扰性。(The invention relates to a method for positioning the direction of arrival based on wavelet denoising and MUSIC algorithm, which comprises the following steps: step (1): determining the number and the placement positions of array elements of a microphone, determining a guide matrix of an array according to the number and the placement positions of the array elements of the microphone, and receiving an information source signal through the array; step (2): denoising the received information source signal by a wavelet denoising method; and (3): and carrying out azimuth estimation on the source signal subjected to noise reduction through a MUSIC algorithm. The method can effectively and accurately estimate the azimuth angle of the information source signal, and has better anti-interference performance to the noise environment.)

1. A method for positioning the direction of arrival based on wavelet denoising and MUSIC algorithm is characterized by comprising the following steps:

step (1): determining the number and the placement positions of array elements of a microphone, determining a guide matrix of an array according to the number and the placement positions of the array elements of the microphone, and receiving an information source signal through the array;

step (2): denoising the received information source signal by a wavelet denoising method;

and (3): and carrying out azimuth estimation on the source signal subjected to noise reduction through a MUSIC algorithm.

2. The wavelet denoising and MUSIC algorithm-based direction-of-arrival positioning method according to claim 1, wherein the frequency domain formula of the source signal received by the array in step (1) is: x (t) ═ a (θ) s (t) + n (t), where a (θ) is the steering matrix of the array, s (t) is the source signal, and n (t) is the noise signal.

3. The wavelet denoising and MUSIC algorithm-based direction-of-arrival positioning method according to claim 1, wherein the step (2) comprises:

step (21): performing wavelet decomposition on the received information source signal;

step (22): filtering noise of the information source signal after wavelet decomposition by a preset threshold function;

step (23): and performing signal recovery on the information source signal subjected to noise filtering through wavelet inverse transformation.

4. The method for wavelet de-noising and MUSIC algorithm-based direction-of-arrival localization according to claim 3, wherein the step (21) is performed by performing wavelet decomposition on the received source signal, and the formula is as follows:wherein the content of the first and second substances,in order to be a function of the wavelet,which is the basis function of the wavelet transform,to perform complex conjugate transformation on ψ (), a is a scale for controlling wavelet function expansion, b is the amount of translation, and x (t) is the received source signal.

5. The wavelet denoising and MUSIC algorithm-based direction-of-arrival positioning method according to claim 3, wherein the formula of the preset threshold function in the step (22) is: new (u, c) ═ alphaSoft (u, c) + β hard (u, c), where α is a soft threshold corresponding weight, β is a hard threshold corresponding weight, c is a corresponding noise threshold, u is a source signal after wavelet decomposition, soft (u, c) is a soft threshold and soft (u, c) ═ sign (u) max { | u | -c,0}, sign () is a sign function, hard (u, c) is a hard threshold and hard (u, c) is a wavelet decomposition

6. The wavelet denoising and MUSIC algorithm-based direction-of-arrival positioning method according to claim 3, wherein the inverse wavelet transform formula in step (23) is:wherein f (t) is the recovered source signal, #_a,b(t) is a function of the wavelet,a is the scale for controlling the expansion and contraction of the wavelet function, and b is the translation amount.

7. The wavelet denoising and MUSIC algorithm-based direction-of-arrival positioning method according to claim 1, wherein the step (3) comprises:

step (31): fourier transform is carried out on the information source signals subjected to noise reduction to obtain frequency domain signals;

step (32): calculating a covariance matrix of the frequency domain signal

Step (33): covariance matrix of frequency domain signals using singular value decompositionPerforming characteristic decomposition to obtain a characteristic value;

step (34): determining a signal subspace and a noise subspace according to the characteristic values;

step (35): and according to the signal parameter range, performing spectral peak search in the noise subspace, and finding out the angle corresponding to the maximum value, wherein the angle corresponding to the maximum value is the incident azimuth angle of the signal source.

8. The wavelet denoising and MUSIC algorithm-based direction-of-arrival positioning method according to claim 7, wherein the formula of step (33) is:wherein, U_sIs a signal subspace, U_NIs the noise subspace, H is the complex conjugate transform of the matrix,is a covariance matrix of the signal.

9. The wavelet denoising and MUSIC algorithm-based direction-of-arrival positioning method according to claim 7, wherein the formula of the spectral peak search in the step (35) is:wherein a (theta) is a steering matrix of the array,is the noise subspace, and H is the complex conjugate transform of the matrix.

10. The wavelet denoising and MUSIC algorithm-based direction-of-arrival positioning method according to claim 7, wherein the angle corresponding to the maximum point in step (35) is the incident azimuth of the source signal, and the formula is:wherein a (theta) is a steering matrix of the array,is the noise subspace, and H is the complex conjugate transform of the matrix.

Technical Field

The invention relates to the technical field of direction of arrival positioning, in particular to a method for positioning the direction of arrival based on wavelet denoising and MUSIC algorithm.

Background

The multiple signal classification (MUSIC) algorithm is an algorithm based on a feature structure, and the basic idea of the algorithm is to perform feature decomposition on a covariance matrix of arbitrary array output data to obtain a signal subspace corresponding to a signal component and a noise subspace orthogonal to the signal component, and then estimate parameters of a signal by using the orthogonality of the two subspaces.

The MUSIC algorithm has high resolution, estimation accuracy and stability under specific conditions. However, in the case of limited fast beat numbers and low signal-to-noise ratio, the noise covariance MUSIC algorithm performance can suffer. In a real environment, vehicle signals are susceptible to high frequency environmental noise interference, such as wind noise and the like. Therefore, it is desirable to reduce the interference caused by noise to the source signal.

In the wavelet denoising process, different threshold functions have different effects on signal filtering. The hard threshold method can well reserve local characteristics such as signal edges and the like, and soft threshold processing needs to be relatively smooth, but distortion phenomena such as edge blurring and the like can be caused.

Disclosure of Invention

The technical problem to be solved by the invention is to provide a method for positioning the direction of arrival based on wavelet denoising and MUSIC algorithm, which can effectively and accurately estimate the azimuth angle of an information source signal.

The technical scheme adopted by the invention for solving the technical problems is as follows: a method for positioning the direction of arrival based on wavelet denoising and MUSIC algorithm is provided, which comprises the following steps:

step (1): determining the number and the placement positions of array elements of a microphone, determining a guide matrix of an array according to the number and the placement positions of the array elements of the microphone, and receiving an information source signal through the array;

step (2): denoising the received information source signal by a wavelet denoising method;

and (3): and carrying out azimuth estimation on the source signal subjected to noise reduction through a MUSIC algorithm.

The frequency domain formula of the source signal received by the array in the step (1) is as follows: x (t) ═ a (θ) s (t) + n (t), where a (θ) is the steering matrix of the array, s (t) is the source signal, and n (t) is the noise signal.

The step (2) comprises the following steps:

step (21): performing wavelet decomposition on the received information source signal;

step (22): filtering noise of the information source signal after wavelet decomposition by a preset threshold function;

step (23): and performing signal recovery on the information source signal subjected to noise filtering through wavelet inverse transformation.

In the step (21), wavelet decomposition is performed on the received information source signal, and the formula is as follows:wherein the content of the first and second substances,in order to be a function of the wavelet,which is the basis function of the wavelet transform,to perform complex conjugate transformation on ψ (), a is a scale for controlling wavelet function expansion, b is the amount of translation, and x (t) is the received source signal.

The formula of the preset threshold function in the step (22) is as follows: new (u, c) ═ α · soft (u, c) + β · hard (u, c), where α is a soft threshold corresponding weight, β is a hard threshold corresponding weight, c is a corresponding noise threshold, u is a wavelet decomposed source signal, soft (u, c) is a soft threshold and soft (u, c) ═ sign (u) max { | u | -c,0}, sign () is a sign function, hard (u, c) is a hard threshold and the sign () is a sign function

The inverse wavelet transform formula in the step (23) is as follows:wherein f (t) is the recovered source signal, #_a,b(t) is a function of the wavelet,a is for controlling the wavelet function extensionThe scale of the contraction, b is the translation amount.

The step (3) comprises the following steps:

step (31): fourier transform is carried out on the information source signals subjected to noise reduction to obtain frequency domain signals;

step (32): calculating a covariance matrix of the frequency domain signal

Step (33): covariance matrix of frequency domain signals using singular value decompositionPerforming characteristic decomposition to obtain a characteristic value;

step (34): determining a signal subspace and a noise subspace according to the characteristic values;

step (35): and according to the signal parameter range, performing spectral peak search in the noise subspace, and finding out the angle corresponding to the maximum value, wherein the angle corresponding to the maximum value is the incident azimuth angle of the signal source.

The formula of the step (33) is as follows:wherein, U_sIs a signal subspace, U_NIs the noise subspace, H is the complex conjugate transform of the matrix,is a covariance matrix of the signal.

The formula of the spectral peak search in the step (35) is as follows:wherein a (theta) is a steering matrix of the array,is the noise subspace, and H is the complex conjugate transform of the matrix.

The angle corresponding to the maximum point in the step (35) is an information sourceThe incident azimuth angle of the signal is expressed as:wherein a (theta) is a steering matrix of the array,is the noise subspace, and H is the complex conjugate transform of the matrix.

Advantageous effects

Due to the adoption of the technical scheme, compared with the prior art, the invention has the following advantages and positive effects: the azimuth angle of the information source signal can be effectively and accurately estimated through the MUSIC algorithm, and meanwhile, the noise environment has better anti-interference performance through a wavelet denoising method; in the wavelet denoising process, the soft threshold and the hard threshold are combined to filter noise after wavelet decomposition, and experiments show that the method has a good effect; the invention can be applied to the actual living environment and is easy to popularize.

Drawings

FIG. 1 is a process flow diagram of an embodiment of the present invention;

FIG. 2 is a schematic of an original signal, a hard threshold, a soft threshold, and an improved threshold of an embodiment of the present invention;

FIG. 3 is an exemplary diagram of signals before and after wavelet de-noising according to an embodiment of the present invention;

fig. 4 is a schematic diagram of array element placement according to an embodiment of the present invention.

Detailed Description

The invention will be further illustrated with reference to the following specific examples. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and such equivalents may fall within the scope of the present invention as defined in the appended claims.

The embodiment of the present invention relates to a method for positioning direction of arrival based on wavelet denoising and MUSIC algorithm, which is suitable for sound signals emitted by vehicles in a field environment, and referring to fig. 1, the method includes:

step (1): determining the number and the placement position of array elements of a microphone (see figure 4 in detail), determining a steering matrix of an array according to the number and the placement position of the array elements, and receiving a signal source signal through the array;

the array of the embodiment adopts a uniform four-circle array of micro-aperture microphone array to collect acoustic signals in the environment.

The source signal in step (1) is a narrowband signal, and a frequency domain signal formula of the received narrowband signal may be represented as:

X(t)＝a(θ)s(t)+N(t)

where a (θ) is the steering matrix of the array, s (t) is the source signal, and n (t) is the noise signal.

Step (2): and denoising the received information source signal by a wavelet denoising method.

The step (2) specifically comprises:

step (21): the received source signal is subjected to wavelet decomposition, and the embodiment adopts Sym8 wavelet to perform 5-layer wavelet transform decomposition signal. Threshold quantization of wavelet decomposition high frequency coefficients. And selecting a threshold value for each layer of high-frequency coefficients from the 1 st layer to the 5 th layer to perform threshold value quantization processing.

In the step (21), wavelet decomposition is performed on the received information source signal, and the formula is as follows:

wherein the content of the first and second substances,in order to be a function of the wavelet,which is the basis function of the wavelet transform,for complex conjugate transformation of ψ (), a is for controlling wavelet function expansionScale, b is the amount of translation, and x (t) is the received source signal.

Step (22): filtering noise of the information source signal after wavelet decomposition by a preset threshold function;

the soft threshold is defined as: soft (u, c) ═ sign (u) max { | u | -c,0}, sign () is a sign function;

the hard threshold is defined as:

referring to fig. 2, the hard thresholding method can preserve local features such as signal edges well, and the soft thresholding is relatively smooth, but causes distortion such as edge blurring.

Based on this, the present embodiment improves the threshold function, that is, combines the soft threshold and the hard threshold to obtain the preset threshold function, and the formula is:

new(u,c)＝α·soft(u,c)+β·hard(u,c)

wherein α is a weight corresponding to the soft threshold and is taken as 0.5, β is a weight corresponding to the hard threshold and is taken as 0.5, and c is a corresponding noise threshold, and the noise threshold c is a global threshold, which is easy to adjust, i.e. c ═ σ; and u is the source signal after wavelet decomposition.

The improved threshold function (namely the preset threshold function) not only retains local characteristics such as signal edges and the like, but also avoids edge blurring, and the noise is filtered while the effective characteristics of the signal are retained.

Step (23): and performing signal recovery on the information source signal subjected to noise filtering through wavelet inverse transformation.

The inverse wavelet transform formula in the step (23) is as follows:

wherein f (t) is the recovered source signal, #_a,b(t) is the basis function of the wavelet,a is the scale for controlling the expansion and contraction of the wavelet function, and b is the translation amount.

And (3): and carrying out azimuth estimation on the source signal subjected to noise reduction through a MUSIC algorithm.

The step (3) specifically comprises:

step (31): fourier transform is carried out on the information source signals subjected to noise reduction to obtain frequency domain signals;

step (32): by means of a covariance matrix of the frequency domain signalThe formula is as follows:

where L is the signal length, X is the frequency domain signal, and H is the complex conjugate transform of the matrix.

Step (33): covariance matrix of frequency domain signals using singular value decompositionAnd carrying out characteristic decomposition to obtain a characteristic value.

Step (34): and determining a signal subspace and a noise subspace according to the characteristic value.

The formula of the step (34) is as follows:

wherein, U_sIs a signal subspace, U_NIs the noise subspace, H is the complex conjugate transform of the matrix,is a covariance matrix of the signal.

Step (35): and according to the signal parameter range, performing spectral peak search in the noise subspace.

The formula of the spectral peak search in the step (35) is as follows:

wherein a (theta) is a steering matrix of the array,is the noise subspace, and H is the complex conjugate transform of the matrix.

Step (36): and finding out an angle corresponding to the maximum value, wherein the angle corresponding to the maximum value is an incident azimuth angle of the information source signal.

The angle corresponding to the maximum point in the step (36) is an incident azimuth angle of the source signal, and the formula is as follows:

wherein a (theta) is a steering matrix of the array,is the noise subspace, and H is the complex conjugate transform of the matrix.

The experimental results are as follows:

the experiment was carried out 1000 times of monte carlo algorithm simulations of the above procedure by python, setting the noise signal energy and the original signal energy to 1:1, and the results are shown in table 1 by taking MSE (mean square error) as the criterion for evaluation.

TABLE 1 comparison of recognition results of DOA location estimation techniques

	Horizontal azimuth MSE	Vertical azimuth MSE
			Before denoising	4.3552	0.1132
After denoising	3.7168	0.1106

Data in the analysis table can be obtained, the mean square error of the estimated positioning angle can be effectively reduced under the condition of low signal to noise ratio, and the method is more suitable for vehicle identification in the field environment.

The above embodiments are merely preferred embodiments of the present invention, which are not intended to limit the scope of the present invention, and various changes may be made in the above embodiments of the present invention. All simple and equivalent changes and modifications made according to the claims and the content of the specification of the present application fall within the scope of the claims of the present patent application. The invention has not been described in detail in order to avoid obscuring the invention.