CN101819782B - Variable-step self-adaptive blind source separation method and blind source separation system - Google Patents

Abstract

The invention relates to a variable-step self-adaptive EASI blind source separation processing method, belonging to the technical field of signal processing. The method adopts a minimum mean square error criterion to estimate a global matrix reflecting separation precision to control step length; and compared with the traditional EASI algorithm, the method overcomes the inherent contradiction between the convergence velocity and the steady-state error of the traditional EASI algorithm. The invention can precisely separate composite signals, raise the convergence velocity, reduce the steady-state error and achieve better stability. The invention has wide application prospects in the fields of wireless communication signal processing, radar signal processing, image signal processing, speech signal processing and the like.

Description

A kind of variable-step self-adaptive blind source separation method and blind source separation system

Technical field

The present invention relates to the signal processing technology field, is a kind of blind source separation method.

Background technology

In many cases, source signal is to mix each other, and the purpose that observation signal is handled is exactly to recover each original source signal that can't directly observe.The detachment process of blind source can be described as: through seeking a nonsingular linear transformation matrix, so that make each component of output separate as much as possible, farthest approach each source signal.Promptly setting up objective function realizes approaching with optimizing.(list of references: [1] Cardoso J F, Laheld B.Equivariant adaptive source separation [J] .IEEETransaction on Signal Processing, 44 (12): 3017-3030,1996.)

EASI (Equivariant Adaptive Source Separation waits to change self-adaptation) algorithm is classical adaptive blind source separation algorithm, belongs to LMS (Least Mean Squares, least mean-square error) type algorithm.All there is the optimal selection problem of a step-length in LMS type learning algorithm, and step-length is the key point that influences algorithm the convergence speed and steady-state behaviour.If adopt big step-length, then algorithm convergence is fast, but the separation accuracy of signal (being steady-state behaviour) is poor; And adopt little step-length, then steady-state behaviour is good, but algorithm convergence is slow.Traditional EASI algorithm all adopts fixed step size, and this has just determined traditional EASI algorithm to have the inner contradictions of speed of convergence and steady-state error.Adopt big step-length, the Signal Separation precision can not get guaranteeing; If adopt little step-length, speed of convergence is slow, after can causing receiving all mixed signals, and the signal separation of failing to succeed.

Summary of the invention

Technical matters to be solved by this invention is, proposes a kind of variable-step self-adaptive blind source separation method, solves blind source signal is being carried out in the separating process speed of convergence and this contradiction of steady-state error that LMS type algorithm exists.In signal processing, can separate mixed signal effectively, improved speed of convergence, reduced steady-state error, the stability of algorithm convergence is better simultaneously.

The technical scheme that the present invention solves the problems of the technologies described above is on the basis of EASI algorithm, to use minimum mean square error criterion; The overall matrix of estimating system obtains the estimated value of algorithm performance index (PI) thus, comes the step-length of control system through this estimated value; Adopt bigger step-length at the Signal Separation initial stage; To accelerate convergence of algorithm speed, slowly reduce step-length then, improve the steady-state error of algorithm.Variable-step self-adaptive EASI blind source separation method specifically comprises, n independent identically distributed unknown source signal s (k)=[s ₁(k), s ₂(k) ..., s _n(k)] ^TTransmission through channel hybrid matrix H obtains m mixed signal x (k)=[x ₁(k), x ₂(k) ..., x _m(k)] ^TSeparation matrix W is upgraded in all mixed signal pointwises, can be according to formula: W (k+1)=W (k)+μ (k) [I-y (k) y ^T(k)-g (y (k)) y ^T(k)+y (k) g ^T(y (k))] W (k) all mixed signal pointwises renewal separation matrix W to receiving, the separation matrix of being set up changes with the variation of step-length.With whole mixed signals through separation matrix W, according to formula: y=Wx is with Signal Separation.In the process that makes up separation matrix; Control the size of step-length according to the estimated value of performance index; According to formula: when

confirms that some signals are sent into down; Upgrade the step-length of separation matrix W, step-length is constantly reduced along with the decline of

value.Confirm that

value specifically comprises, utilize minimum mean square error criterion to obtain the estimated matrix of hybrid matrix H; Obtain the estimated matrix of global transmission matrix according to formula

; Call the estimated value

that formula obtains performance index according to global transmission matrix

; Confirm the required step-length of each iteration thus, and make up separation matrix by the separation matrix update module.

The present invention proposes a kind of variable-step self-adaptive EASI blind source separation system, comprises separation matrix update module, global transmission matrix estimation module, performance index estimation module, variable step module.Obtain m mixed signal x (k)=[x after the transmission of source signal s (k) through the channel hybrid matrix ₁(k), x ₂(k) ..., x _m(k)] ^TThe global transmission matrix estimation module is utilized minimum mean square error criterion

Obtain the estimated matrix of hybrid matrix H

, call formula

Obtain overall estimated matrix

The performance index estimation module is according to overall estimated matrix Call formula

Obtain the estimated value of performance index

, variable step module basis

The size of control step-length, call formula:

Confirm the step-length of some signals down; The separation matrix update module utilizes step-length according to formula: W (k+1)=W (k)+μ (k) [I-y (k) y ^T(k)-g (y (k)) y ^T(k)+y (k) g ^T(y (k))] W (k) makes up the separation matrix of every bit signal, and all signals are received and are obtained final separation matrix W, and whole mixed signals through separation matrix W, are obtained separate estimated signal.

This blind source separation method pointwise receives signal, adjusts step-length in real time, and update system can be carried out blind source quickly and efficiently with the mixed signal that receives and separate, to be recovered original signal adaptively.This blind source separation algorithm has improved convergence of algorithm speed, has reduced the steady-state error of algorithm, has improved signal blind source separation accuracy and separating effect, and has improved the stability of algorithm convergence, and the realizability of operation is stronger.Comparing existing classic method is significantly improved from restraining stability, error, speed aspect.The advantage that the present invention embodied makes it all have wide practical use in fields such as radio communication, radar, image, voice signal processing.

Description of drawings

Fig. 1 variable-step self-adaptive algorithm process of the present invention block diagram

Fig. 2 variable-step self-adaptive algorithm flow chart of the present invention

The source signal waveform that Fig. 3 is to be separated

Fig. 4 variable-step self-adaptive algorithm of the present invention separating property index (PI) distribution histogram

Fig. 5 classic method separating property index (PI) distribution histogram

Fig. 6 classic method and variable-step self-adaptive algorithm separating property index of the present invention (PI) change curve relatively

Embodiment

Traditional EASI algorithm is in the most ICA methods that propose, and learning rules all are the gradient descent algorithms of cost function or contrast function.Typical cost function has J (W)=E{ ρ (y) } form, wherein ρ is certain scalar function, and has some extra constraints usually, E{} representes to ask expectation.Here y=Wx supposes that W is a square formation and reversible.The probability density of function ρ and x has determined the form of contrast function J (W).

$\frac{\∂J\left(W\right)}{\∂W}=E\left\{\left(\frac{\∂\mathrm{\ρ}\left(y\right)}{\∂y}\right)x^T\right\}=E\left\{g\left(y\right)x^T\right\}=E\left\{g\left(y\right)y^T\right\}{\left(W^T\right)}^{-1}---\left(1\right)$

In the formula, g (y) is the gradient of ρ (y).Ask inverse of a matrix (W through introducing natural gradient ^T) ^-1, natural gradient is through taking advantage of W to matrix gradient type (1) right side ^TW obtains, and is E{g (y) y ^TW.Thereupon, the stochastic gradient algorithm of minimization cost function J (W) is:

ΔW＝-μg(y)y ^TW (2)

Wherein, μ is an iteration step length.

Consider the albefaction process of mixed vector x, at first x is linear transformation z=Qx, make z _iBe unit variance and zero covariance: E{zz ^T}=I (I is the unit square formation).With following modification rule

ΔQ＝μ(I-zz ^T)Q (3)

Vector after the use albefaction replaces original vector, and promptly z=QHs is prone to see that matrix QH is an orthogonal matrix.So its is contrary, promptly separation matrix also is a quadrature, representes the separation matrix of this quadrature with B.Yet if will keep the orthogonality of B in each step iteration, per step of B upgrades and just must satisfy specific constraint.With reference to formula (2), obtain the renewal sequence of B: B ← B+DB, wherein D=-μ g (y) y ^TThe orthogonality condition of upgrading matrix is: (B+DB) (B+DB) ^T=I+D+D ^T+ DD ^T=I has been BB in the formula ^TThe replacement of=I.Suppose that D is very little, first approximation provides condition: D=-D ^TOr D should be antisymmetric.This condition is used for the relative gradient learning rules, has

ΔB＝-μ[g(y)y ^T-yg ^T(y)]B (4)

In the formula, y=Bz.

With the synthetic uniform rules of (3) and (4) this two formula to the global system separation matrix.Because y=Bz=BQx, this overall matrix is W=BQ.Suppose two the same iteration step lengths of rule use, first approximation provides:

ΔW＝ΔBQ+BΔQ

＝-μ[g(y)y ^T-yg ^T(y)]BQ+μ[BQ-Bzz ^TB ^TBQ] (5)

＝μ[I-yy ^T-g(y)y ^T+yg ^T(y)]W

Here it is EASI algorithm.It has with albefaction with separate the good character of joining together.

Can find out that by formula (5) effect of step size mu is an amplitude of controlling the element that upgrades because of iteration in the separation matrix, so the selection of step-length is very important to the performance that improves Signal Separation.Choosing of optimal step size is a more scabrous problem.For time varying signal, make algorithm get caught up in its pace of change, then must there be a big step-length to come the speed of convergence of accelerating algorithm.When adopting fixed step size, reach convergence in order to make algorithm, its choosing value requires very little again, thus the best that can't reach speed of convergence and steady-state error is unified.In order to solve this difficult problem, the present invention utilizes minimum mean square error criterion, has proposed a kind of EASI algorithm of new adaptive step.

According to the estimated signal y (k) of the separation matrix W (k) of this signaling point, step size mu (k), output, call above-mentioned formula by the nonlinear function g (y (k)) of y (k) definition and obtain the separation matrix W (k+1) of some signals down.Wherein, y (k)=W (k) x (k).

Set up following variable step algorithmic formula:

$\left\{\begin{array}{c}W(k+1)=W\left(k\right)+\mathrm{\μ}\left(k\right)[I-y\left(k\right)y^T\left(k\right)-g\left(y\left(k\right)\right)y^T\left(k\right)+y\left(k\right)g^T\left(y\left(k\right)\right)]W\left(k\right)\\ y\left(k\right)=W\left(k\right)x\left(k\right)\end{array}\right.---\left(6\right)$

Through traditional fixed step size self-adaptation EASI blind source separation algorithm is improved, obtain variable-step self-adaptive EASI blind source separation algorithm suc as formula (6).Wherein, the separation matrix that W (k) obtains after through k point mixed signal for algorithm, W (k+1) is on the basis of W (k), through the separation matrix that obtains after the k+1 point mixed signal; Y (k) is the estimated signal that the separation matrix after k point mixed signal is upgraded through the k time obtains; Like this, after receiving all mixed signals, we obtain final separation matrix W.μ (k) is a variable step, and its big I is controlled according to the estimated value of performance index.

Concrete definite method of following surface analysis μ (k).

In the analytical algorithm performance, use performance index PI (Performance Index) to estimate usually, PI is confirmed by following formula:

$\mathrm{PI}\left(k\right)=\underset{i}{\mathrm{\Σ}}\{(\underset{j}{\mathrm{\Σ}}\frac{\left|G_k(i,j)\right|}{{\max }_j\left(\right|G_k(i,j)\left|\right)}-1)+(\underset{j}{\mathrm{\Σ}}\frac{|G_k(j,i)}{{\max }_j\left(\right|G_k(j,i)\left|\right)}-1)\}---\left(7\right)$

Wherein, G _k(i, j)=W (k) H is the global transmission matrix.Under the ideal situation, G _kShould be the matrix that each row of each row have only a nonzero element, unit matrix be as the criterion.If G _kBe accurate unit matrix, piece-rate system can be fully separated source signal, the signal after the separation except clooating sequence different with signal amplitude on have stretch, its signal characteristic and source signal are duplicate.Therefore, performance index PI (k) has characterized G _kDegree of approximation with accurate unit matrix.PI (k)=0 when isolated signal and source signal waveform are identical.

Analysis can know that separation accuracy has determined the size of performance index PI (k), and PI (k) has reflected the similarity degree of separation signal and source signal.Along with the raising of separation accuracy, PI (k) reduces gradually.At the Signal Separation initial stage, should adopt big step-length to improve speed of convergence, step-length should reduce to reduce steady-state error gradually then.Therefore, we can set up certain relation between the two, control step size mu (k) through PI (k).Yet PI in the practical application (k) is unknown.PI (k) depends on global transmission matrix G _k, G _k(i, j)=W (k) H.So; Expect the estimated value of PI (k), we at first are exactly the estimated matrix

that obtains hybrid matrix H

Utilize minimum mean square error criterion:

$\min \left(E\right\{\left|\right|x-\hat{H}y\left|{|}^2\right\})---\left(8\right)$

The decline of gradient at random real-time learning algorithm with common makes formula (8) minimization, obtains the estimated matrix

of hybrid matrix

$\mathrm{\Δ}\hat{H}\left(k\right)=\hat{H}(k+1)-\hat{H}\left(k\right)=-\mathrm{\η}\left(k\right)\frac{\∂{\left|\right|x\left(k\right)-\hat{H}y\left(k\right)\left|\right|}^2}{\∂\hat{H}}$

$=-\mathrm{\η}\left(k\right)\frac{\∂\left[{(x\left(k\right)-\hat{H}y\left(k\right))}^T(x\left(k\right)-\hat{H}y\left(k\right))\right]}{\∂\hat{H}}---\left(9\right)$

$=2\mathrm{\η}\left(k\right)[x\left(k\right)-\hat{H}y\left(k\right)]y^T\left(k\right)$

Make λ (k)=2 η (k), λ (k) is an iteration step length.The iterative formula that can get estimated matrix

is following:

$\hat{H}(k+1)=\hat{H}\left(k\right)+\mathrm{\λ}\left(k\right)[x\left(k\right)-\hat{H}\left(k\right)y\left(k\right)]y^T\left(k\right)---\left(10\right)$

Therefore, further can obtain the estimated matrix of global transmission matrix:

${\hat{G}}_k=W\left(k\right)\hat{H}\left(k\right)---\left(11\right)$

Utilize

, confirm the estimated value

of performance indices P I according to following formula

$\hat{P}I\left(k\right)=\underset{i}{\mathrm{\Σ}}\{(\underset{j}{\mathrm{\Σ}}\frac{\left|{\hat{G}}_k(i,j)\right|}{{\max }_j\left(\right|{\hat{G}}_k(i,j)\left|\right)}-1)+(\underset{j}{\mathrm{\Σ}}\frac{\left|{\hat{G}}_k(j,i)\right|}{{\max }_j\left(\right|{\hat{G}}_k(j,i)\left|\right)}-1)\}---\left(12\right)$

According to above analysis; Control the size of step-length with

, even step-length constantly reduces along with the decline of

value.Thus, variable step is confirmed as follows:

$\mathrm{\μ}\left(k\right)=\mathrm{\α}(1-e^{-\mathrm{\β}\·\hat{P}I\left(k\right)})---\left(13\right)$

Wherein, α, β are empirical constant, 0＜α＜1,0＜β＜1.The solution procedure of

is also relevant with step-length; By the influencing characteristic of step-length to the Signal Separation convergence process, we can use μ (k) to replace λ (k).

Above emphasis has been described through the value of estimated performance indices P I, and is expressed as variable step the function of time variable.Also can confirm variable step through other modes, the released state as different according to signal is taken as different expression-forms with step-length; Different acquiring methods according to the step-length gradient are taken as different expression-forms with step-length; According to fuzzy control theory, with the regulatory factor of fuzzy controller as step-length.

Below in conjunction with accompanying drawing and instance, further explain is done in enforcement of the present invention, but embodiment of the present invention is not limited in this.

Be illustrated in figure 1 as variable-step self-adaptive algorithm process schematic block diagram of the present invention.

To the observation signal that pointwise receives, utilization variable-step self-adaptive algorithm is learnt.W regulates to the separation matrix weights, and the step size mu of pointwise update algorithm is for the weights of regulating W are prepared next time.The data of any repeat as above step under receiving then, up to receiving all observation signals.

Suppose to have n independent identically distributed signal s (k)=[s ₁(k), s ₂(k) ..., s _n(k)] ^T, (i=1～n, k=1～L).Obtain m observation signal (mixed signal) x (k)=[x after the transmission through channel hybrid matrix H ₁(k), x ₂(k) ..., x _m(k)] ^T, (i=1～n, k=1～L).Wherein s (k), H, x (k) represent source signal, hybrid matrix and mixed signal respectively, and hypothesis m >=n (among the present invention, establishing m=n), and mutual statistical is independent between each source signal.Can set up the signal mixture model of blind source separation problem so, mixed signal is expressed as in this model: x (k)=Hs (k).

In actual reception signal x (k), because isolated component s _j(k) can not directly be observed, had hidden attribute, therefore also become " hidden variable ".Because hybrid matrix H also is unknown matrix, the observation signal vector x (k) that separation problem unique available information in blind source has only sensor to arrive.

On above-mentioned variable step basis, upgrade separation matrix W according to formula (6), be output as the estimation y (k) of source signal x (k) when making x (k), y (k)=W (k) x (k) through W (k).Simultaneously, upgrade the required step-length of next iteration according to formula (10) and formula (13).And y=Wx=WHs=Λ Ps, when Λ is a reversible diagonal matrix, when P is arbitrary displacement battle array, y=[y ₁, y ₂..., y _n] ^TEach component separate, source signal is able to separate.

Be illustrated in figure 2 as the schematic flow sheet that blind source signal is separated; Specifically comprise the steps: step 1: according to signal length L initialization μ; Initialization W=0.5I; Each element is interval [1 during

initialization; 1] produces at random, and choose appropriate nonlinear function g (y).Wherein choosing of g (y) can be confirmed according to the positive and negative of signal kurtosis.When the kurtosis of signal during less than zero (inferior gaussian signal), the nonlinear function of choosing is generally

When the kurtosis of signal during greater than zero (this signal of superelevation), the nonlinear function of choosing is generally g (y _i)=tanh (y _i).

Step 2: pointwise receives observation signal in real time, and iteration is carried out in the mixed signal pointwise that receives, and upgrades separation matrix W.Concrete steps are: observation signal obtains estimated value through separation matrix W, promptly according to y (k)=W (k) x (k), obtains the estimated signal y (k) of source signal x (k); Call formula W (k+1)=W (k)+μ (k) [I-y (k) y ^T(k)-g (y (k)) y ^T(k)+y (k) g ^T(y (k))] the mixed signal pointwise renewal separation matrix W of W (k) to receiving.

Step 3: in the process of upgrading separation matrix; The observation signal that utilizes this to receive constantly; The size of control step size mu (k) makes step-length constantly reduce along with the decline of

value according to

.Concrete steps are: on the basis of step 2; Call formula (10) and formula (11), calculate the estimated matrix

of hybrid matrix and the estimated matrix

of global transmission matrix respectively; According to

, call formula (12) calculated performance exponential estimation value

; According to

; Call formula (13) computes mu (k), for the renewal of separation matrix W is next time prepared.

Receive next signal constantly, to the signal cycle execution in step 2 and step 3 of every bit reception.

Step 4: receive all mixed signals, obtain final separation matrix W by step 2.Whole observation signal x through the final separation matrix W that obtains, are obtained separate estimated signal y=Wx.

Next 5 source signals (m=5) shown in Figure 3 are carried out emulation experiment by above-mentioned analysis, they are is-symbol signal, sinusoidal signal, FM signal, AM signal and [1,1] equally distributed random noise signal respectively.In the emulation; Each element of mixed signal H is interval [1; 1] produces at random; Nonlinear function is elected α=0.1 in

improved variable-step self-adaptive algorithm, β=0.001 as.Initialization μ=0.0005; W=0.5I; Each element produces in interval [1,1] at random during

initialization.In order to compare, also come separation signal, the fixed step size 0.0005 of the separating effect that selection can obtain simultaneously with traditional algorithm.

For more objective appraisal separation signal and the approximate degree of source signal; We do 500 Monte Carlo emulation to above-mentioned 5 signals, and Fig. 4 is variable-step self-adaptive algorithm separating property index of the present invention (PI) distribution histogram, can find out; The PI value basically all is distributed in [0; 0.6] between, and along with the increase of PI value, the distribution number of times is few more gradually.Fig. 5 is classic method separating property index (PI) distribution histogram, and it is unstable to find out that the PI value distributes, and distribution range is [0.4,1.8], and the PI value is generally bigger.

Therefore, the present invention has reduced the steady-state error of algorithm, has improved the precision that separate in the blind source of signal, has improved the separation signal effect.The stability of algorithm convergence is better, and the realizability of operation is stronger.

The present invention verifies the advantage of improved variable-step self-adaptive algorithm on speed of convergence through another group.We are reaching under the situation of the steady-state error similar with improved variable-step self-adaptive algorithm traditional algorithm, relatively both speed of convergence.Suppose that source signal counts m=8, their are is-symbol signal, sinusoidal signal, FM signal, AM signal, 2ASK signal, 4PSK signal, 8FSK signal and [1,1] equally distributed random noise signal respectively.Do Monte-Carlo Simulation 500 times, the starting point of each emulation source signal is different.In the emulation; Each element of mixed signal H is interval [1; 1] produces at random; Nonlinear function is elected initialization μ=0.0005 as; W=0.5I; Each element produces in interval [1,1] at random during

initialization.In order to compare, also come separation signal simultaneously with traditional algorithm, fixed step size elects 0.0003 as.

Simulation result such as Fig. 6 can find out, when the performance index PI value after two kinds of algorithm convergences was basic identical, the only needs of improved variable-step self-adaptive algorithm just can be restrained for about 7000 times, and the fixed step size algorithm needs iteration more than 15000 times.It is many that speed of convergence has improved twice.

Therefore, variable-step self-adaptive algorithm of the present invention has greatly improved convergence of algorithm speed when satisfying real-time processing requirements.

Claims (9)

1. a variable-step self-adaptive blind source separation method that is used for radar is characterized in that, n source radar signal s (k)=[s ₁(k), s ₂(k) ..., s _n(k)] ^TObtain m after the transmission through channel hybrid matrix H and mix radar signal x (k)=[x ₁(k), x ₂(k) ..., x _m(k)] ^TUtilize minimum mean square error criterion to obtain the estimated matrix of hybrid matrix H

Call formula

Obtain the estimated matrix of global transmission matrix, according to overall estimated matrix Call formula

Obtain the estimated value of performance index Estimated value according to performance index

The size of control variable step, call formula:

Confirm step-length, make step-length in iterative process along with

The decline of value and constantly reducing; According to the estimated signal y (k) of the separation matrix W (k) of this radar signal point, step size mu (k), output, by the nonlinear function g (y (k)) of y (k) definition, call formula W (k+1)=W (k)+μ (k) [I-y (k) y ^T(k)-g (y (k)) y ^T(k)+y (k) g ^T(y (k))] W (k) obtains down the separation matrix W (k+1) of some radar signals; All are mixed the radar signal pointwise upgrade separation matrix; With all mixing radar signal through final separation matrix, obtain the estimated signal of radar signal x (k) according to formula y (k)=W (k) x (k), wherein I is that unit square formation, α, β are empirical constant; 0＜α＜1,0＜β＜1.

2. variable-step self-adaptive blind source separation method according to claim 1; It is characterized in that; Wherein choosing according to the positive and negative of radar signal kurtosis of g (y (k)) come to be confirmed, when the kurtosis of radar signal less than zero the time, the nonlinear function of choosing is g (y (k))=(y (k)) ³When the kurtosis of radar signal greater than zero the time, the nonlinear function of choosing is g (y (k))=tanh (y (k)).

3. a variable-step self-adaptive blind source piece-rate system that is used for radar is characterized in that, comprises separation matrix update module, global transmission matrix estimation module, performance index estimation module, variable step module, n source radar signal s (k)=[s ₁(k), s ₂(k) ..., s _n(k)] ^TObtain m after the transmission through channel hybrid matrix H and mix radar signal x (k)=[x ₁(k), x ₂(k) ..., x _m(k)] ^T

Global transfer matrix estimation module using minimum mean square error criterion?

get mixed matrix H estimation matrix?

invoke formula?

to get global estimation matrix?

Performance estimation module based on the global estimation matrix?

invoke formula?

get performance index estimate?

The variable step module is according to the size of estimated value

the control variable step of performance index; Call formula:

confirms step-length, and step-length is constantly reduced along with the decline of

value in iterative process;

The separation matrix update module is called formula W (k+1)=W (k)+μ (k) [I-y (k) y according to the estimated signal y (k) of the separation matrix W (k) of this radar signal point, step size mu (k), output, by the nonlinear function g (y (k)) of y (k) definition ^T(k)-g (y (k)) y ^T(k)+y (k) g ^T(y (k))] W (k) obtains down the separation matrix W (k+1) of some radar signals; All are mixed the radar signal pointwise upgrade separation matrix; With all mixing radar signal through final separation matrix W, obtain the estimated signal of radar signal x (k) according to formula y (k)=W (k) x (k), wherein I is that unit square formation, α, β are empirical constant; 0＜α＜1,0＜β＜1.

4. a variable-step self-adaptive blind source separation method that is used for Flame Image Process is characterized in that, n source images signal s (k)=[s ₁(k), s ₂(k) ..., s _n(k)] ^TObtain m vision-mix signal x (k)=[x after the transmission through channel hybrid matrix H ₁(k), x ₂(k) ..., x _m(k)] ^TUtilize minimum mean square error criterion to obtain the estimated matrix of hybrid matrix H

Call formula

Obtain the estimated matrix of global transmission matrix, according to overall estimated matrix

Call formula

Obtain the estimated value of performance index

Estimated value according to performance index

The size of control variable step, call formula:

Confirm step-length, make step-length in iterative process along with The decline of value and constantly reducing; According to the estimated signal y (k) of the separation matrix W (k) of this picture signal point, step size mu (k), output, by the nonlinear function g (y (k)) of y (k) definition, call formula W (k+1)=W (k)+μ (k) [I-y (k) y ^T(k)-g (y (k)) y ^T(k)+y (k) g ^T(y (k))] W (k) obtains the separation matrix W (k+1) of next dot image signal; Separation matrix is upgraded in all vision-mix signal pointwises; Whole vision-mix signals through final separation matrix, are obtained the estimated signal of picture signal x (k) according to formula y (k)=W (k) x (k), and wherein I is that unit square formation, α, β are empirical constant; 0＜α＜1,0＜β＜1.

5. variable-step self-adaptive blind source separation method according to claim 4; It is characterized in that; Wherein choosing according to the positive and negative of picture signal kurtosis of g (y (k)) come to be confirmed, when the kurtosis of picture signal less than zero the time, the nonlinear function of choosing is g (y (k))=(y (k)) ³When the kurtosis of picture signal greater than zero the time, the nonlinear function of choosing is g (y (k))=tanh (y (k)).

6. a variable-step self-adaptive blind source piece-rate system that is used for Flame Image Process is characterized in that, comprises separation matrix update module, global transmission matrix estimation module, performance index estimation module, variable step module, n source images signal s (k)=[s ₁(k), s ₂(k) ..., s _n(k)] ^TObtain m vision-mix signal x (k)=[x after the transmission through channel hybrid matrix H ₁(k), x ₂(k) ..., x _m(k)] ^T

Global transfer matrix estimation module using minimum mean square error criterion?

get mixed matrix H estimation matrix?

invoke formula? to get global estimation matrix?

Performance estimation module based on the global estimation matrix?

invoke formula?

get performance index estimate?

The variable step module is according to the size of estimated value

the control variable step of performance index; Call formula:

confirms step-length, and step-length is constantly reduced along with the decline of

value in iterative process;

The separation matrix update module is called formula W (k+1)=W (k)+μ (k) [I-y (k) y according to the estimated signal y (k) of the separation matrix W (k) of this picture signal point, step size mu (k), output, by the nonlinear function g (y (k)) of y (k) definition ^T(k)-g (y (k)) y ^T(k)+y (k) g ^T(y (k))] W (k) obtains the separation matrix W (k+1) of next dot image signal; Separation matrix is upgraded in all vision-mix signal pointwises; Whole vision-mix signals through final separation matrix W, are obtained the estimated signal of picture signal x (k) according to formula y (k)=W (k) x (k), and wherein I is that unit square formation, α, β are empirical constant; 0＜α＜1,0＜β＜1.

7. one kind is used for the variable-step self-adaptive blind source separation method that voice signal is handled, and it is characterized in that n source voice signal s (k)=[s ₁(k), s ₂(k) ..., s _n(k)] ^TObtain m mixing voice signal x (k)=[x after the transmission through channel hybrid matrix H ₁(k), x ₂(k) ..., x _m(k)] ^TUtilize minimum mean square error criterion to obtain the estimated matrix of hybrid matrix H

Call formula

Obtain the estimated matrix of global transmission matrix, according to overall estimated matrix Call formula Obtain the estimated value of performance index

Estimated value according to performance index

The size of control variable step, call formula:

Confirm step-length, make step-length in iterative process along with

The decline of value and constantly reducing; According to the estimated signal y (k) of the separation matrix W (k) of this voice signal point, step size mu (k), output, by the nonlinear function g (y (k)) of y (k) definition, call formula W (k+1)=W (k)+μ (k) [I-y (k) y ^T(k)-g (y (k)) y ^T(k)+y (k) g ^T(y (k))] W (k) obtains down the separation matrix W (k+1) of some voice signals; Separation matrix is upgraded in all mixing voice signal pointwises; Whole mixing voice signals through final separation matrix, are obtained the estimated signal of voice signal x (k) according to formula y (k)=W (k) x (k), and wherein I is that unit square formation, α, β are empirical constant; 0＜α＜1,0＜β＜1.

8. variable-step self-adaptive blind source separation method according to claim 7; It is characterized in that; Wherein choosing according to the positive and negative of voice signal kurtosis of g (y (k)) come to be confirmed, when the kurtosis of voice signal less than zero the time, the nonlinear function of choosing is g (y (k))=(y (k)) ³When the kurtosis of voice signal greater than zero the time, the nonlinear function of choosing is g (y (k))=tanh (y (k)).

9. one kind is used for the variable-step self-adaptive blind source piece-rate system that voice signal is handled, and it is characterized in that, comprises separation matrix update module, global transmission matrix estimation module, performance index estimation module, variable step module, n source voice signal s (k)=[s ₁(k), s ₂(k) ..., s _n(k)] ^TObtain m mixing voice signal x (k)=[x after the transmission through channel hybrid matrix H ₁(k), x ₂(k) ..., x _m(k)] ^T

Global transfer matrix estimation module using minimum mean square error criterion?

get mixed matrix H estimation matrix?

invoke formula?

to get global estimation matrix?

Performance estimation module based on the global estimation matrix?

invoke formula?

get performance index estimate?

The variable step module is according to the size of estimated value

the control variable step of performance index; Call formula: confirms step-length, and step-length is constantly reduced along with the decline of

value in iterative process;

The separation matrix update module is called formula W (k+1)=W (k)+μ (k) [I-y (k) y according to the estimated signal y (k) of the separation matrix W (k) of this voice signal point, step size mu (k), output, by the nonlinear function g (y (k)) of y (k) definition ^T(k)-g (y (k)) y ^T(k)+y (k) g ^T(y (k))] W (k) obtains down the separation matrix W (k+1) of some voice signals; Separation matrix is upgraded in all mixing voice signal pointwises; Whole mixing voice signals through final separation matrix W, are obtained the estimated signal of voice signal x (k) according to formula y (k)=W (k) x (k), and wherein I is that unit square formation, α, β are empirical constant; 0＜α＜1,0＜β＜1.

Images