CN103763230B - A kind of improved self-adaptive blind source separation method - Google Patents

Abstract

For also there is no a kind of this defect of blind source separating scheme that can efficiently solve contradiction between convergence rate and crosstalk error in prior art, the invention provides a kind of improved self-adaptive blind source separation method NVS NGA, first the structure of traditional piece-rate system is improved, again the performance indications of blind source separating are improved, with improved separating property index as independent variable, with Rayleigh Distribution Function as dependent variable, with Rayleigh Distribution Function for variable step function.Compared with traditional blind source separation method, this method can quickly be efficiently separated out primary signal from the mixed signal receiving, and efficiently solve the contradiction between convergence rate and crosstalk error, not only fast convergence rate, crosstalk error are little, and stability is strong, all has wide practical use at aspects such as radio communication, image procossing, Speech processing.

Description

A kind of improved self-adaptive blind source separation method

Technical field

The invention belongs to signal processing technology field, especially relate to a kind of improved self-adaptive blind source separation method.

Background technology

Blind source separating refers in the case that the theoretical model of signal and source signal cannot accurately be known, how from aliasing letter The process of each source signal is isolated in number (observation signal).The base of blind source separating (Blind Source Separation, BSS) This task be unknown in source signal and the hybrid mode of source signal also unknown in the case of, from one group of observation signal receiving In recover source signal, at aspects such as recognition of face, Speech processing, processing of biomedical signals, satellite and microwave communications There is huge application potential.Blind source separation method can be divided into batch processing method and adaptive approach two big class.With batch processing Method is compared, and adaptive approach being capable of real-time tracking signal intensity.

Traditional adaptive blind source separation system, referred to as traditional piece-rate system, as shown in Figure 1.Traditional piece-rate system be by Unknown nonsingular hybrid matrix A is in series with separation matrix W (k)；By M source signal S (k)=[s independent mutually₁(k),s₂ (k),…,s_M(k)]^TCarry out being mixed to get observation signal X (k)=[x through a unknown nonsingular hybrid matrix A₁(k),x₂ (k),…,x_M(k)]^T, x_MK () is m-th observation signal.When ignoring transmission delay effect and noise, obtain

X(k)=AS(k) (1)

In formula, A is M × M dimension matrix.The target of blind source separating is when just knowing that observation signal X (k), is obtained by iteration To after separation matrix W (k) of a full rank, obtain separating signal Y (k) from observation signal X (k)

Y(k)=W(k)X(k) (2)

In formula, Y (k) is to source signal S (k) estimation, is M × 1 dimension matrix；W (k) is M × M dimension matrix.

Using the relation of mutual information and comentropy, the cost function of piece-rate system is defined as

In formula, H (y_m(k)) separate signal y m-th for separating in signal vector Y (k)_mThe entropy of (k), p_y(y_m(k)) for dividing Separate signal y m-th in signal vector Y (k)_mK the marginal probability density of (), E represents mathematic expectaion computing, and ln represents with e For the natural logrithm at bottom, det represents the determinant taking W (k).When cost function J (k) of piece-rate system is minimum, optimal Separation matrix W (k) can make each component in separation signal vector Y (k) independent of one another.Edgeworth using probability density launches And get fourth order cumulant, then

In formula, H_N(y_m(k)) Normal Distribution, with y_mK () has identical average and variance, if y_mK the average of () is 0th, variance is 1, H_N(y_m(k)) in subscript N represent normal distribution, thenCum represents y_m(k) tired Accumulated amount computing；

H (y_i(k)) substitute into J (k), J (k) is to ith row and jth column element w in W (k)_ijK the stochastic gradient of () is

In formula, w_ijK () is the ith row and jth column element of W (k)；Represent W^-1K () transposition obtains the i-th row of matrix With jth column element；Cum represents cumulant computing, and E represents mathematic expectaion computing；InRepresent stochastic gradient, For J (k) to W (k) ith row and jth column element w_ijThe stochastic gradient of (k),Transient expression formula can be obtained by formula (5)

In formula (6), the item in braces is only y_iK the function of (), makes it be

At this moment, formula (6) can be written as

Need exist for illustrating, the f (y that formula (7) is given_i(k)) it is very specific functional form, it is probability density Edgeworth launches and gets what fourth order cumulant obtained, referred to as excitation function.In practice, excitation function form is permissible Determine as needed, be also just to say, f (y_i(k)) it is y_iK which kind of concrete form of (), can choose according to actual needs.

J (k) seeks temporary gradients to all elements in W (k), obtains J (k) and to the temporary gradients of W (k) is

Using stochastic gradient and natural gradient relation, obtaining J (k) to the natural gradient of W (k) is

In formula,Represent the natural gradient to W (k) for the J (k)；I represents unit matrix；F (Y (k)) is really by probability distribution The nonlinear activation function that characteristic determines.At natural gradient criterion (Natural Gradient Algorithm, NGA) Under, the more new formula of separation matrix W (k) is

In formula, μ represents step-length, is constant；I represents a unit matrix.The blind source separating side of this tradition piece-rate system Method performance is commonly used crosstalk error index to weigh, and its expression is

In formula, PI represents crosstalk error；Max represents and takes maxima operation；C (k)=W (k) A=P (k) Λ is traditional segregative line The composite matrix of system, c_ilRepresent is the element of Matrix C (k) the i-th row l row, and P (k) and Λ represent a permutation matrix respectively And diagonal matrix, P (k), Λ, C (k) they are M × Metzler matrix.If hybrid system matrix A is known, A is taken advantage of by formula (11) right side The more new formula of overall Matrix C (k) is

C(k+1)=C(k)+μ[I-f(Y(k))Y^T(k)]C(k) (13)

However, in a practical situation, because hybrid system matrix A is unknown, therefore can not by formula (13) more New formula directly obtains C (k), also just cannot get PI (C (k)).

Additionally, traditional adaptive blind source separation algorithm adopts fixed step size, therefore exist convergence rate and crosstalk error it Between contradiction.Chinese scholars priority proposes some variable step size methods, but there is presently no one kind and highly desirable solve to receive Hold back the blind source separating scheme of contradiction between speed and crosstalk error.

Content of the invention

For solving the above problems, the invention discloses a kind of improved self-adaptive blind source separation method NVS-NGA, effectively Solve the contradiction between convergence rate and crosstalk error, obtain good separating effect.

In order to achieve the above object, the present invention provides following technical scheme：

A kind of improved self-adaptive blind source separation method, is realized based on improved adaptive blind source separation system, described changes The adaptive blind source separation system entering includes hybrid matrix A, separation matrix W (k) and the inverse system in parallel with separation matrix W (k) System W_a(k), described W_aThe inverse A of (k) and nonsingular hybrid matrix A^-1Approximately, described blind source separation method comprises the steps：

Step A, M source signal S (k)=[s unknown and independent of each other₁(k),s₂(k),…,s_M(k)]^TDivide through improving In system, unknown nonsingular hybrid matrix A carries out being mixed to get observation signal X (k)=[x₁(k),x₂(k),…,x_M(k)]^T；? When ignoring transmission delay effect and noise, obtain X (k)=AS (k), k is time serieses, subscript T represents conjugate transpose；M is just whole Number, represents the number of component in S (k)；A is M × M dimension matrix；

Step B, observation signal X (k) that step A is obtained=[x₁(k),x₂(k),…,x_M(k)]^TIt is simultaneously fed into improvement point Separation matrix W (k) and W in system_aK (), respectively obtains and separates signal Y (k)=W (k) X (k) and Y_a(k)=W_a(k) X (k), its Middle Y (k) is M × 1 dimensional vector, is an estimation of source signal S (k), and its component is separate；W (k) is to improve in piece-rate system One M × M ties up the final separation matrix of full rank；W_a(k) inverseIt is to unknown nonsingular mixed moment in improvement piece-rate system The final estimation of battle array A；W (k) and W_aK the dimension of () is identical, subscript " -1 " expression takes inverse operation；

Wherein separation matrix W (k) and W_aK the more new formula of () is：

Wherein I represents unit matrix；F (y (k)) is nonlinear activation primitive, and μ (k) is improved step factor, and it is public Formula is：

μ(k)=β{|PI(C_G(k))|/α²}exp{-[PI(C_G(k))]²/(2α²),

Wherein, β and α is the control parameter of μ (k)；Exp represents the exponential function with e as bottom, wherein PI (C_G(k)) for changing The separating property index entered, its formula is：

Wherein C_GK () is the overall matrix improving piece-rate system,c_ilThe i-th row for Matrix C (k) The element of l row, c_GilIt is Matrix C_GK the i-th row l column element of (), max represents and takes maxima operation.

The initial matrix improving piece-rate system is W (0) and W_a(0), whereinImprove the first of piece-rate system Begin overall matrix

A kind of preferred, described f (Y (k))=Y as the present invention³(k).

Specifically, described separation matrix W (k) and W_aK the more new formula of () obtains as follows：

Step a, using the relation of mutual information and comentropy, the cost function of piece-rate system is defined as

In formula, H (y_m(k)) separate signal y m-th for separating in signal vector Y (k)_mThe entropy of (k), p_y(y_m(k)) for dividing Separate signal y m-th in signal vector Y (k)_mK the marginal probability density of (), E represents mathematic expectaion computing, and ln represents with e For the natural logrithm at bottom, det represents the determinant taking W (k)；

Step b, calculates the natural gradient to W (k) for the J (k)

Step c, obtains separation matrix W (k) and W by J (k) to the natural gradient of W (k)_aThe more new formula of (k)

Beneficial effect：The present invention improves to the structure of traditional piece-rate system first, then the performance of blind source separating is referred to Mark improves, with improved separating property index as independent variable, with Rayleigh Distribution Function as dependent variable, with Rayleigh Distribution Function For variable step function.Compared with traditional blind source separation method, this method can from the mixed signal receiving fast and effeciently Isolate primary signal, efficiently solve the contradiction between convergence rate and crosstalk error；Not only fast convergence rate, cross-talk are missed Difference is little, and stability is strong；All have wide practical use at aspects such as radio communication, image procossing, Speech processing.

Brief description

Fig. 1 is traditional adaptive blind source separation system structural representation；

The improved self-adaptive blind source separation method schematic diagram that Fig. 2 provides for the present invention；

Fig. 3 is the convergence graph of three kinds of separating property indexs under the conditions of Stationary Random Environments；

Fig. 4 is simulation result figure of the present invention, and wherein (a) is source signal figure, and (b) is mixed signal figure；

Fig. 5 is separating resulting figure under the conditions of Stationary Random Environments, and wherein (a) is the separation signal graph after being tested using NGA, B () is the separation signal graph after being tested using VS-NGA, (c) is the separation signal graph after being tested using NVS-NGA；

Fig. 6 is PI meansigma methodss curve under the conditions of Stationary Random Environments；

Fig. 7 is the PI meansigma methodss curve under the conditions of non-stationary environment.

Specific embodiment

The technical scheme present invention being provided below with reference to specific embodiment is described in detail it should be understood that following concrete Embodiment is only illustrative of the invention and is not intended to limit the scope of the invention.

As shown in Fig. 2 the present invention improves to the structure of former piece-rate system first, traditional piece-rate system separates square Battle array W (k) one inverse A with nonsingular hybrid matrix A of upper parallel connection^-1Approximate inverse system W_a(k), matrix W_a(k), W_aK () is referred to as simultaneously Connection separation matrix, this improved structure part is concatenated into nonsingular hybrid matrix A again；And the performance indications of blind source separating are entered Row improve, using improved separating property index as Rayleigh Distribution Function independent variable, using Rayleigh Distribution Function as variable step Function, thus having invented a kind of improved self-adaptive blind source separation method NVS-NGA, this method comprises the steps：

Step A, M source signal S (k)=[s unknown and independent of each other₁(k),s₂(k),…,s_M(k)]^TDivide through improving In system, unknown nonsingular hybrid matrix A carries out being mixed to get observation signal X (k)=[x₁(k),x₂(k),…,x_M(k)]^T； When ignoring transmission delay effect and noise, obtain X (k)=AS (k), k is time serieses, subscript T represents conjugate transpose；M is just Integer, represents the number of component in S (k)；A is M × M dimension matrix.

Step B, observation signal X (k) that step A is obtained=[x₁(k),x₂(k),…,x_M(k)]^TIt is simultaneously fed into improvement point Separation matrix W (k) and W in system_aK (), respectively obtains and separates signal Y (k)=W (k) X (k) and Y_a(k)=W_a(k) X (k), its Middle Y (k) is M × 1 dimensional vector, is an estimation of source signal S (k), and its component is separate；W (k) is to improve in piece-rate system One M × M ties up the final separation matrix of full rank；W_a(k) inverseIt is to unknown nonsingular mixed moment in improvement piece-rate system The final estimation of battle array A；W (k) and W_aK the dimension of () is identical, subscript " -1 " expression takes inverse operation.

Based on improved adaptive blind source separation system, we first have to the blind source separating performance indications of computed improved：

Due to improving separate section W (k) and W in piece-rate system (as shown in Figure 2)_aK () is parallel-connection structure, separate when improving After system operation, optimal separation matrix W in parallel will be obtained_a(k)；To now W_a(k) inverseAs improvement segregative line In system, hybrid matrix A's is approximate, and the overall matrix thus obtaining improving piece-rate system is designated as C_G(k), and

With improving the overall Matrix C of piece-rate system_GK the C (k) in () substituted (12), obtains separating property index parameter For

This separating property index is one kind improvement to formula (12), referred to as improves separating property index.

Because, in traditional self-adaptive blind source separation method, step size mu is fixed value, tracking performance is poor, is unfavorable for solving blind Contradiction between source separation convergence rate and crosstalk error.For this technical problem of effectively solving, the present invention by PI value and walks The long factor combines, and builds a variable step function, specifically, is with crosstalk error PI (C_G(k)) it is independent variable, with auspicious Sharp distribution function is dependent variable, and obtaining variable step formula is

μ(k)=β{|PI(C_G(k))|/α²}exp{-[PI(C_G(k))]²/(2α²)} (16)

In formula, β and α is the control parameter of μ (k), can choose α=10, β=0.1 by experiment；Exp represents the finger with e as bottom Number function.

Based on the variable step function shown in formula (16), using natural gradient criterion, obtain improving in piece-rate system, separating square Battle array W (k) and W_aK the more new formula of (), comprises the following steps that：

Using the relation of mutual information and comentropy, the cost function of piece-rate system is defined as

In formula, H (y_m(k)) separate signal y m-th for separating in signal vector Y (k)_m(k) entropy, p_y(y_m(k)) be Separate in signal vector Y (k) and separate signal y m-th_mThe marginal probability density of (k), E represents mathematic expectaion computing, ln represent with E is the natural logrithm at bottom, and det represents the determinant taking W (k)；

Calculate the natural gradient to W (k) for the J (k)

Separation matrix W (k) and W are obtained to the natural gradient of W (k) by J (k)_aThe more new formula of (k)

Wherein, μ (k) is formula（16）Shown improved step factor；I represents unit matrix；F (Y (k)) is nonlinear Activation primitive, if the formula of pressing（7）Determine nonlinear activation primitive f (Y (k)), then this function is

By formula（18）Determine f (Y (k)), the Third-order cumulants cum (y of y (k) need to be calculated³(k)) and fourth order cumulant cum (y⁴ (k)), calculate sufficiently complex, be unfavorable for engineer applied.In order to reduce amount of calculation, nonlinear activation primitive is preferably formula (18) reduced form, i.e. f (Y (k))=Y³(k)；By separation matrix W in parallel_aK overall Matrix C that () and hybrid matrix A obtain_a (k)=W_a(k)A=P_a(k)Λ_aIt is referred to as the overall matrix of parallel connection part, P_a(k) and Λ_aRepresent permutation matrix and diagonal respectively Matrix, to W_aK () is inverted and can be obtainedDue to P_a(k) and Λ_aRepresent a permutation matrix respectively and to angular moment Battle array, can be obtained by matrix propertiesesWithAlso illustrate that a permutation matrix and diagonal matrix.

In the initial matrix W (0) and W that improve piece-rate system_a(0) in choosing, initial matrix W_a(0) selection need to meet bar Part：Choose suitable W_a(0) after, then improve the initially overall matrix of piece-rate systemBy PI (C_G(0)) substitute into the stepsize formula of Rayleigh Distribution Function form, obtain initial step length μ (0).

Up to the present, separating property index PI (C (k)) of traditional piece-rate system, the separating property of parallel connection part is had to refer to Mark PI (C_a(k)) and improve piece-rate system separating property index PI (C_G(k)).Their constringency performance is as shown in figure 3, Fig. 3 table Bright, in the whole separation process under the conditions of Stationary Random Environments, separate the initial stage, the value of PI is very big, illustrates that crosstalk error is very big；Separate Latter stage, the value of PI can become very little, illustrate that crosstalk error is less, separating effect is preferable.On the whole, PI value is in iteration During present one kind drop quickly to convergence stable trend, wherein improved separating property index PI (C_G(k)) performance Preferably, therefore using improvement separating property index PI (C_G(k)) contradiction that can preferably solve between convergence rate and crosstalk error.

In order to verify the effectiveness of the inventive method (referred to as NVS-NGA), with traditional blind source separating side of fixed step size Method NGA, traditional blind source separation method VS-NGA of variable step are comparison other, carry out emulation experiment with Matlab program and compare. In experiment, source signal is：S1=sign(cos(2*pi*155*t/fs));S2=sin(2*pi*800*t/fs);S3=sin(2* pi*90*t/fs);S4=sin (2*pi*9*t/fs) * sin (2*pi*300*t/fs), sampling number is 5000, and sample frequency is 10000Hz, hybrid matrix A₀=[0.3702 0.7143 -0.6188 -0.3002;0.0965 0.7408 0.9365 0.0443;0.3732 -0.3762 -0.2500-0.6735;-0.6674 0.6747 0.9162 -0.7381]；The fixation of NGA Step-length is μ=0.003；Make variable step using sigmoid function in VS-NGAIts Middle η (k)=| | I-f (Y (k)) Y^T(k) | | for I-f (Y (k)) Y^TThe norm of (k), α=10, β=0.1；In NVS-NGA, variable step For formula (16), parameter alpha=10, β=0.15.Shown in wherein source signal waveform such as Fig. 4 (a), shown in mixed waveform signal such as Fig. 4 (b).

Embodiment 1：Under the conditions of Stationary Random Environments, i.e. hybrid matrix A=A₀Shi Jinhang contrast experiment.All ginsengs in an experiment Number takes value given herein above, and 100 Monte-Carlo Simulation results are respectively as shown in Fig. 5 (a), Fig. 5 (b), Fig. 5 (c).Fig. 5 (a), Fig. 5 B () corresponds respectively to NGA method, VS-NGA method and NVS-NGA method gained of the present invention with Fig. 5 (c) and separates signal graph, Fig. 6 For PI meansigma methodss curve chart.Fig. 6 shows, NGA method restrains about in 2700 step, VS-NGA about restrains in 2300 steps, and this Bright method NVS-NGA about restrains in 1500 steps, has the crosstalk error of minimum after also showing the convergence of the inventive method NVS-NGA. Therefore, the separating property of the inventive method NVS-NGA preferably, has minimum crosstalk error and rapid convergence speed.

Embodiment 2：Tested under non-stationary environment, that is, hybrid matrix is A (k)=A₀+ B (k), B (k)=ρ B (k-1)+ τ * randn (4), B (0) are the null matrix of 4 × 4, ρ=0.9, τ=0.0001, and randn (4) is the random matrix of 4 ranks, Other conditions are constant, the experiment of 100 Monte-Carlo Simulation PI meansigma methodss curve, as shown in Figure 7.Fig. 7 shows, with NGA, VS-NGA method is compared, and the inventive method NVS-NGA still has convergence rate the fastest and minimum crosstalk error, therefore, The separating property of the inventive method NVS-NGA is preferably also.

Understand from above-described embodiment, the improved self-adaptive blind source separation method that the present invention provides, with existing fixed step Length compares with variable-step self-adaptive blind source separation method, improves convergence rate, and reduces crosstalk error, and separating property has It is obviously improved.

Technological means disclosed in the present invention program are not limited only to the technological means disclosed in above-mentioned embodiment, also include The technical scheme being made up of above technical characteristic combination in any.It should be pointed out that for those skilled in the art For, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications are also considered as Protection scope of the present invention.

Claims (3)

1. a kind of improved self-adaptive blind source separation method it is characterised in that：Real based on improved adaptive blind source separation system Existing, described improved adaptive blind source separation system include unknown nonsingular hybrid matrix A, separation matrix W (k) and with point From matrix W (k) inverse system W in parallel_a(k), described W_aThe inverse A of (k) and nonsingular hybrid matrix A^-1Approximately, described blind source separating Method comprises the steps：

Step A, M source signal S (k)=[s unknown and independent of each other₁(k),s₂(k),…,s_M(k)]^TThrough improving segregative line In system, unknown nonsingular hybrid matrix A carries out being mixed to get observation signal X (k)=[x₁(k),x₂(k),…,x_M(k)]^T；Neglecting When omiting transmission delay effect and noise, obtain X (k)=AS (k), k is time serieses, subscript T represents conjugate transpose；M is just whole Number, represents the number of component in S (k)；A is M × M dimension matrix；

Step B, observation signal X (k) that step A is obtained=[x₁(k),x₂(k),…,x_M(k)]^TIt is simultaneously fed into improvement segregative line Separation matrix W (k) and W in system_aK (), respectively obtains and separates signal Y (k)=W (k) X (k) and Y_a(k)=W_a(k) X (k), wherein Y K () is M × 1 dimensional vector, be an estimation of source signal S (k), and its component is separate；W (k) is to improve one in piece-rate system Individual M × M ties up the final separation matrix of full rank；W_a(k) inverseIt is to unknown nonsingular hybrid matrix in improvement piece-rate system The final estimation of A；W (k) and W_aK the dimension of () is identical, subscript " -1 " expression takes inverse operation；

Wherein separation matrix W (k) and W_aK the more new formula of () is：

$\left\{\begin{array}{c}W(k+1)=W\left(k\right)+\mathrm{\μ}\left(k\right)\[I-f\left(Y\left(k\right)\right)Y^T\left(k\right)\]W\left(k\right)\\ W_a(k+1)=W_a\left(k\right)+\mathrm{\μ}\left(k\right)\[I-f\left(Y\left(k\right)\right)Y^T\left(k\right)\]W_a\left(k\right)\end{array}\right.,$

Wherein I represents unit matrix；F (Y (k)) is nonlinear activation primitive, and μ (k) is improved step factor, its formula For：

μ (k)=β | PI (C_G(k))|/α²}exp{-[PI(C_G(k))]²/(2α²),

Wherein, β and α is the control parameter of μ (k), and exp represents the exponential function with e as bottom, wherein PI (C_G(k)) it is improved point From performance indications, its formula is：

$PI\left(C_G\right(k\left)\right)=\underset{i=1}{\overset{M}{\Σ}}\[(\underset{l=1}{\overset{M}{\Σ}}\frac{\left|c_{Gil}\right|}{\underset{j=1}{\overset{M}{max}}\left(c_{Gij}\right)}-1)\]+\underset{i=1}{\overset{M}{\Σ}}\[(\underset{l=1}{\overset{M}{\Σ}}\frac{\left|c_{Gli}\right|}{\underset{j=1}{\overset{M}{max}}\left(c_{Gji}\right)}-1)\],$

Wherein C_GK () is the overall matrix improving piece-rate system,c_GilIt is Matrix C_GThe i-th row l row of (k) Element, max represents and takes maxima operation；

Described separation matrix W (k) and W_aK the more new formula of () obtains as follows：

Step a, using the relation of mutual information and comentropy, the cost function of piece-rate system is defined as

$J\left(k\right)=H\left(y_m\right(k\left)\right)-ln\left|\det \left(W\right(k\left)\right)\right|=-\underset{m=1}{\overset{M}{\Σ}}E\left(\ln p_y\right(y_m\left(k\right)\left)\right)-ln\left|\det \left(W\right(k\left)\right)\right|,$

In formula, H (y_m(k)) separate signal y m-th for separating in signal vector Y (k)_mThe entropy of (k), p_y(y_m(k)) for separating signal Signal y is separated m-th in vectorial Y (k)_mK the marginal probability density of (), E represents mathematic expectaion computing, and ln represents with e as bottom Natural logrithm, det represents the determinant taking W (k)；

Step b, calculates the natural gradient to W (k) for the J (k)

$\▿J=\frac{\∂J\left(k\right)}{\∂W\left(k\right)}\·W^T\left(k\right)W\left(k\right)=-\[I-f\left(Y\right(k\left)\right)Y^T\left(k\right)\]W\left(k\right);$

Step c, obtains separation matrix W (k) and W by J (k) to the natural gradient of W (k)_aThe more new formula of (k)

$\left\{\begin{array}{c}W(k+1)=W\left(k\right)+\mathrm{\μ}\left(k\right)\[I-f\left(Y\left(k\right)\right)Y^T\left(k\right)\]W\left(k\right)\\ W_a(k+1)=W_a\left(k\right)+\mathrm{\μ}\left(k\right)\[I-f\left(Y\left(k\right)\right)Y^T\left(k\right)\]W_a\left(k\right)\end{array}\right..$

2. improved self-adaptive blind source separation method according to claim 1 it is characterised in that：Improve the first of piece-rate system Beginning matrix is W (0) and W_a(0), whereinImprove the initially overall matrix of piece-rate system

3. improved self-adaptive blind source separation method according to claim 1 and 2 it is characterised in that：Described f (Y (k))= Y³(k).