CN101729157B - Method for separating vibration signal blind sources under a kind of strong noise environment - Google Patents

Abstract

The invention discloses a vibration signal blind source separation algorithm in a strong noise environment. The method of the present invention is as follows: the first step, for a group of given noise-containing mixed signals, the mixed signal is denoised by the time-delay autocorrelation method, and the mixed signal after denoising is obtained; the second step is for the first step The obtained mixed signal is subjected to de-averaging and robust whitening preprocessing to further reduce the influence of the noise signal on the separation result; the third step is to calculate the second-order and fourth-order cumulants of the initial separation signal, and use the second-order and fourth-order cumulants The sum of the diagonal elements of the cumulant matrix is used as the cost function, and by maximizing the cost function, the cumulant matrices are jointly approximated to be diagonalized, and the separation of independent source signals is realized, thereby obtaining an orthogonal separation matrix. The present invention combines the existing noise reduction method with a blind separation algorithm to realize the separation of mixed signals in a strong noise environment, and has the advantages of better separation effect and faster convergence speed than the existing algorithm, and the noise reduction effect is not limited by threshold setting.

Description

A Method of Blind Source Separation of Vibration Signals in Strong Noise Environment

technical field

The invention relates to a separation technology of aliasing vibration signals, in particular to a separation technology of aliasing vibration signals in a strong noise environment.

Background technique

Blind separation of aliased vibration signals in a strong noise environment, because it is closer to the actual situation, is an important signal processing method for identifying vibration source signals and weak signals, and has become the research focus of relevant scientific research institutions and scholars from various countries.

Most of the existing methods are based on the fact that when the noise is neglected, the separation of the instantaneous aliasing signal can be achieved by optimizing the independence criterion with the optimization method. As a signal with a time structure, the vibration signal can usually use the sum of squares of the diagonal elements of the second-order cumulant matrix as a cost function, and optimize the cost function to achieve the separation of mixed signals, which has low complexity and fast calculation speed, but Not robust to noisy signals. The JADE algorithm based on the fourth-order cumulant matrix takes advantage of the characteristic that the high-order cumulant of the noise signal is zero, and realizes the separation of mixed signals by jointly approximately diagonalizing each fourth-order cumulant matrix. It is complex, slow to calculate, sensitive to outliers, and only robust to Gaussian white noise.

For the noise-containing aliasing signal, it is considered to use the wavelet denoising method to denoise the noise-containing signal first, so as to reduce the influence of the noise signal on the separation effect, and then separate the denoising aliasing signal. However, in the wavelet noise reduction method, the selection of the threshold is very important, and improper selection will lead to the failure of the algorithm.

Contents of the invention

The object of the present invention is to provide an aliasing vibration signal separation algorithm that has good separation performance, fast separation speed and strong robustness to noise in a strong noise environment.

In order to achieve the above object, the present invention adopts the following technical solutions:

The blind source separation method of a kind of strong noise environment of the present invention is characterized in that, the method comprises the following steps:

(1) A set of given noise-containing mixed signals is subjected to noise reduction processing by the autocorrelation method, and then the mixed signal after the autocorrelation method noise reduction processing is subjected to the second noise reduction by the time delay method, and the noise reduction is obtained The mixed signal x(t), where t is the time series;

(2), de-meaning the mixed signal x(t) after noise reduction described in step (1) and robust whitening preprocessing to filter out the white Gaussian in the mixed signal x(t) after noise reduction noise;

The robust whitening preprocessing method is as follows:

(A) Calculate the covariance matrix C _x (τ _j ) of the mixed signal x(t) after noise reduction under time delay τ _j , and adjust the covariance matrix C _x (τ _j ) as:

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>$

In the above formula, τ _j represents the jth delay, j=1, 2,..., J, J is the number of delays and is a natural number, T represents the transpose of the matrix, and M _x (τ _j ) is constructed as A combination matrix M, and perform singular value decomposition, namely:

M=[M _x (τ ₁ ),..., M _x (τ _J )]

M=U∑V ^T

In the above formula, U is an orthogonal matrix with the same dimension as M matrix; ∑ is a diagonal matrix composed of singular values of M; V is an orthogonal matrix;

(B) Randomly select the parameter matrix α=[α ₁ ,…,α _j ,…,α _J ] ^T , where α _j represents the jth vector of the parameter matrix α, for the time delay τ _j , calculate:

f _j ＝U ^T M _x (τ _j )U

The linear combination is:

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; J</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}$

When matrix F satisfies positive definiteness, then go to step (D), otherwise go to step (C);

(C) Adjust the parameter matrix α according to the eigenvector u corresponding to the minimum eigenvalue of the matrix F, namely:

$\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; +</span>\frac{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; J</span>}}\mathrm{<span\; class="notranslate">\; u</span>}{<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; J</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}$

Go to step (B) then, until matrix F satisfies positive definiteness;

(D) When the randomly selected parameter matrix α meets the requirements of positive definiteness, use the selected parameter matrix to calculate the target matrix C, and perform eigenvalue decomposition on it, namely:

$\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; J</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>$

C = RDR ^T

When the randomly selected parameter matrix α does not meet the requirement of positive definiteness, the parameter matrix α obtained in step (C) is used to calculate the target matrix C, and its eigenvalue decomposition is performed, namely:

$\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; J</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>$

C = RDR ^T

In the formula, D is a diagonal matrix composed of eigenvalues of the target matrix C, and R is an eigenvector matrix composed of eigenvectors corresponding to each eigenvalue;

(E) Calculate the whitening matrix Q=D ^−1/2 R ^T , and the whitening signal is z(t)=Q·x(t).

(3), calculate the second-order and fourth-order cumulants of the initial separation signal, and use the sum of squares of the diagonal elements of the second-order and fourth-order cumulant matrices as a cost function;

The initial separation signal described is as follows:

The initial orthogonal separation matrix is W, then the initial separation signal y(t)=W z(t);

(4), by maximizing the cost function in step (3), realize the joint approximate diagonalization of each second-order and fourth-order cumulant matrices, obtain the separation of the mixed signal that filters out the white Gaussian noise described in step (2). Orthogonal separation matrix P to obtain separation matrix H and separation signal s(t); where H=PQ, s(t)=H·x(t).

The blind source separation method in a strong noise environment is characterized in that the orthogonal separation matrix P is obtained by the Givens rotation method.

The beneficial effects of the present invention are that the present invention is an algorithm for blind separation of aliased vibration signals in a strong noise environment, including four steps of noise reduction, robust preprocessing, construction of a cost function, and optimization of the cost function to solve the separation matrix. Before the separation, the noise signal is fully filtered to reduce the influence of the noise signal on the separation result, and finally achieve the separation of the aliased signal in a strong noise environment.

In step (1), the present invention adopts the time-delay autocorrelation noise reduction method. When using this method to reduce the noise of the aliasing noise signal, the secondary noise reduction can be realized without setting a threshold, and the automatic Correlation processing can retain the periodic useful information in the vibration signal and remove random non-periodic noise, and the feasibility of its noise reduction effect has been affirmed by the industry. Therefore, this method can effectively filter out the noise signal in the aliased noise-containing signal.

In the (2) step, the present invention proposes to use a robust preprocessing method to filter out the white Gaussian noise in the aliasing signal for the aliasing signal after denoising in the (1) step, further reducing the impact of noise on the separation result. Impact.

In step (3), the advantages of the algorithm based on the second-order cumulant and the fourth-order cumulant are comprehensively considered, and the sum of the squares of the diagonal elements of the second-order cumulant and the fourth-order cumulant matrix is used as the cost function to make the algorithm converge The speed is faster than the fourth-order cumulant algorithm and it is not sensitive to outliers, and it avoids the disadvantage that the second-order cumulant algorithm cannot separate signals with the same spectral structure.

In step (4), the present invention utilizes an optimization method to optimize the cost function to realize the joint approximate diagonalization of the second-order cumulant and the fourth-order cumulant, thereby realizing the separation of aliasing signals.

Therefore, compared with the existing algorithm, the present invention has the advantages of good and stable separation effect in a strong noise environment, and is not limited by threshold setting, and has the characteristics of fast convergence speed for the separation of multiple aliased signals.

Description of drawings

Fig. 1 is a flow chart of the method of the present invention.

detailed description

Below in conjunction with accompanying drawing, the technical scheme of invention is described in detail:

The implementation of the present invention is further described in conjunction with the accompanying drawings. Fig. 1 is a flow chart of the method of the present invention, as shown in Fig. 1, the algorithm includes the following four steps.

Step 1: For a given set of noise-containing mixed signals, first perform autocorrelation processing on the mixed signals, and then remove the part of the autocorrelation-processed signal at zero delay and near the maximum delay to achieve the quadratic Noise reduction to obtain the noise-reduced mixed signal. Specifically:

The noise-containing aliasing signal is denoised by the autocorrelation noise reduction method, and the autocorrelation function of the signal x(t) is defined as:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span><span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; lim</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; L</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, L is the period of the signal x(t), and τ is the delay parameter.

Autocorrelation processing is performed on the noisy aliasing signal to reduce the random Gaussian noise signal in the aliasing signal. In order to further reduce the influence of the noise signal, the time delay processing is performed on the data after autocorrelation processing, that is, the time delay is removed as The data near zero and the delay is near the maximum value. The length of data to remove depends on the situation.

The noise reduction methods that can also be used in this step 1 include: wavelet noise reduction method, median filter and other methods, but the autocorrelation noise reduction method does not need to set a threshold during the noise reduction process, and will not destroy the original structure of the signal.

Step 2: Perform de-meaning and robust whitening preprocessing on the noise-reduced mixed signal x(t) (where t is a time series).

The robust whitening preprocessing method used in this step is:

(A) Calculate the covariance matrix C _x (τ _j ) of the noise-reduced mixed signal at different time delays τ _j , in order to make the covariance matrix have a better symmetrical structure, adjust it to

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

In the formula, j=1, 2,..., J (J is the number of time delays and is a natural number), T represents the transposition of the matrix, constructs M _x (τ _j ) into a large combination matrix M, and performs singular value decomposition, that is

M=[M _x (τ ₁ ),..., M _x (τ _J )] (3)

M=U∑V ^T (4)

In the formula, U is an orthogonal matrix with the same dimension as M matrix; ∑ is a diagonal matrix composed of singular values of M; V is an orthogonal matrix.

(B) Randomly select the parameter matrix α=[α ₁ ,…,α _j ,…,α _J ] ^T , for each time delay τ _j , calculate

f _j ＝U ^T M _x (τ _j )U(5)

Doing a linear combination has

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; J</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

Judging whether the matrix F satisfies the positive definiteness, if the matrix F is positive definite, then go to (D), otherwise go to (C).

(C) Adjust the parameter α according to the eigenvector u corresponding to the minimum eigenvalue of the matrix F, namely

$\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; +</span>\frac{{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; J</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; J</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Then go to (B) until matrix F satisfies positive definiteness.

(D) When the randomly selected parameter matrix α meets the requirements of positive definiteness, use the selected parameter matrix to calculate the target matrix C, and perform eigenvalue decomposition on it, namely:

$\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; J</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

C = RDR ^T (9)

When the randomly selected parameter matrix α does not meet the requirement of positive definiteness, the parameter matrix α obtained in step (C) is used to calculate the target matrix C, and its eigenvalue decomposition is performed, namely:

$\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; J</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

C = RDR ^T (11)

In the formula, D is a diagonal matrix composed of eigenvalues of the target matrix C, and R is an eigenvector matrix composed of eigenvectors corresponding to each eigenvalue; (E) obtain the whitening matrix Q=D ^-1/2 R ^T , the whitening signal is z(t)=Qx(t).

Step 3: Calculate the second-order and fourth-order cumulants of the initial separation signal, and use the sum of squares of the diagonal elements of the second-order and fourth-order cumulant matrices as a cost function. The implementation process is as follows:

Let y(t) be the initial separation signal, and W be the initial orthogonal separation matrix with the same dimension as the aliasing signal, then y(t)=Wz(t). The second-order and fourth-order cumulants of the initial separation signal are defined as:

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ijlk</span>}}^{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

In order to realize the joint approximate diagonalization of each cumulant matrix, the sum of the squares of the diagonal elements of the cumulant matrix is used as the cost function, namely

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; !</span>}\underset{\mathrm{<span\; class="notranslate">\; ijlk</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ijlk</span>}}^{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

Among them, N is the number of source signals. According to the principle of superposition, two cost functions of formula (13) are superimposed to obtain the algorithm cost function of the present invention:

ψ ₂₄ =ψ ₂ +ψ ₄ (14)

Step 4: By maximizing the cost function, the joint approximate diagonalization of each cumulant matrix is realized to obtain the separation matrix and the separation signal.

In the process of realizing the separation of aliased signals, two steps are generally included: that is, signal whitening and performing orthogonal rotation transformation on the whitened signal. The details are as follows:

(1) Whitening of aliased signals to remove the correlation between signals and reduce the computational complexity of subsequent steps. The whitening process of this step is realized by step 2. I won't go into details here.

(2) Orthogonal transformation of the whitening signal. Usually, maximizing the cost function of formula (14) is to find an orthogonal separation matrix P.

Here the Givens rotation method is used to obtain an orthogonal separation matrix.

The resulting separation matrix is the product of the whitening matrix and the orthogonal separation matrix, ie H=PQ. The separated signal is s(t)=Hx(t).

Claims (2)

1. a blind source separation method for strong noise environment, is characterized in that, the method comprises the following steps:

(1), the mixed signal of one group of given Noise is carried out noise reduction process through autocorrelation method, then the mixed signal after autocorrelation method noise reduction process is realized secondary noise reduction through time delay method, obtain the mixed signal x (t) after noise reduction, wherein t is time series;

(2) additive white Gaussian in the mixed signal x (t) after, the mixed signal x (t) after the noise reduction described in step (1) being removed described in average and sane whitening pretreatment filtering noise reduction;

Described sane whitening pretreatment method is as follows:

(A) the mixed signal x (t) after noise reduction is calculated at time delay τ _junder covariance matrix C _x(τ _j), and by covariance matrix C _x(τ _j) be adjusted to:

$M_x\left({\mathrm{\&tau;}}_j\right)=\frac{1}{2}\&lsqb;C_x\left({\mathrm{\&tau;}}_j\right)+C_x^T\left({\mathrm{\&tau;}}_j\right)\&rsqb;$

In above formula, τ _jrepresent a jth time delay, j=1,2 ..., J, J are time delay number and are natural number, and T represents transpose of a matrix, by M _x(τ _j) be configured to a combinatorial matrix M, and carry out singular value decomposition, that is:

M＝[M _x(τ ₁),…,M _x(τ _J)]

M＝U∑V ^T

In above formula, U is the orthogonal matrix identical with Metzler matrix dimension; ∑ is the diagonal matrix be made up of the singular value of M; V is orthogonal matrix;

(B) random selecting parameter matrix α=[α ₁..., α _j..., α _j] ^t, wherein α _jrepresent a jth element of parameter matrix α, α _jit is scalar; For time delay τ _j, calculate:

f _j＝U ^TM _x(τ _j)U

Carry out linear combination to have:

$F=\underset{j=1}{\overset{J}{\&Sigma;}}{\mathrm{\&alpha;}}_j{f}_j$

When matrix F meets orthotropicity, then forward step (D) to, otherwise forward step (C) to;

(C) the characteristic vector u corresponding to the minimal eigenvalue of matrix F adjusts parameter matrix α, that is:

$\mathrm{\&alpha;}=\mathrm{\&alpha;}+\frac{{\&lsqb;u^T{f}_{1}u...u^T{f}_{J}u\&rsqb;}^T}{\left|\right|\&lsqb;u^T{f}_{1}u...u^T{f}_{J}u\&rsqb;\left|\right|}$

Then go to step (B), until matrix F meets orthotropicity;

(D) when the parameter matrix α of random selecting meet orthotropicity require time, utilize selected parameter matrix to calculate objective matrix C, and Eigenvalues Decomposition done to it, that is:

$C=\underset{j=1}{\overset{J}{\&Sigma;}}{\mathrm{\&alpha;}}_j{M}_x\left({\mathrm{\&tau;}}_j\right)$

C＝RDR ^T

When the parameter matrix α of random selecting do not meet orthotropicity require time, the parameter matrix α utilizing step (C) to obtain to calculate objective matrix C, and makes Eigenvalues Decomposition to it, that is:

$C=\underset{j=1}{\overset{J}{\&Sigma;}}{\mathrm{\&alpha;}}_j{M}_x\left({\mathrm{\&tau;}}_j\right)$

C＝RDR ^T

In formula, D is the diagonal matrix be made up of the characteristic value of objective matrix C, and R is the eigenvectors matrix be made up of each characteristic value characteristic of correspondence vector;

(E) whitening matrix Q=D is tried to achieve ^-1/2r ^t, whitened signal is z (t)=Qx (t);

(3), second order and the fourth order cumulant of initially-separate signal is calculated, using the diagonal element quadratic sum of second order and fourth order cumulant matrix as cost function;

Described initially-separate signal is as follows:

Initial orthogonal separation matrix is W, then initially-separate signal y (t)=Wz (t);

(4), by cost function in maximization steps (3), realize the joint approximate diagonalization of each second order and fourth order cumulant matrix, obtain making the orthogonal separation matrix P that the mixed signal of the described filtering additive white Gaussian of step (2) is separated, thus obtain separation matrix H and separation signal s (t); Wherein H=PQ, s (t)=Hx (t).

2. the blind source separation method of a kind of strong noise environment according to claim 1, is characterized in that described orthogonal separation matrix P adopts Givens rotary process to try to achieve.