CN101558997A - Electroencephalograph signal identification method based on second-order blind identification - Google Patents

Abstract

The invention pertains to the technical field of biomedical engineering and information, and realizes individual identity authentication and identification through acquiring and analyzing the electroencephalograph (EEG) signals in human brain. Experimenters are trained through different stimulation patterns, thus leading the experimenters to adapt to the different stimulation patterns and generate different EEG signals; the EEG signals generated due to the stimulation are analyzed through second-order blind identification; individual characteristic signals are extracted for classification and identification so as to determine the target characteristics; and finally the train is finished. When in identification, only the target characteristics of the acquired EEG signals are extracted for classification and compared with the formwork of each experimenter, the identification result can be determined. Research results show that the highest identification rate is 88 percent, the average identification rate is about 83 percent, and the method can realize individual identification and identity authentication.

Description

EEG signal identification method based on second-order blind identification

Technical field

The present technique invention belongs to biomedical engineering and areas of information technology.

Technical background:

Identification and checking are the important prerequisites that guarantees national public safety and information security.In applications such as national security, public security, the administration of justice, ecommerce, E-Government, safety inspection, guard monitors, all need identification accurately and evaluation.The verification method of traditional identify label article (as key, certificate, bank card) etc.; Another kind of is the verification method that indicates knowledge (as user name, password etc.) based on identity.But marking object is lost easily or is palmed off, and sign knowledge is forgotten easily or decoded.Biometrics identification technology has brought the possibility that realizes for this hope.People may forget or lose their card or password, but can never forget or lose the biological characteristic of oneself, as people's face, fingerprint, iris, palmmprint, brain wave etc.Therefore, have better safety, reliability and effectiveness, just more and more be subject to people's attention, and begin to enter the every field of our social life, meet the challenge of New Times based on the individual identity identification system of biometrics identification technology.From beginning of the nineties late 1980s, along with becoming increasingly conspicuous of information security importance, biometrics identification technology research begins to become a research focus.Biometrics identification technology (Biometrics) is meant that high-tech means is close combines by computer and optics, acoustics, biosensor and biostatistics's principle etc., utilizes inherent physiological property of human body (as fingerprint, people's face, iris, brain wave, pulse etc.) or behavior characteristics (as person's handwriting, voice, gait etc.) to carry out the authentication of personal identification.Biometrics identification technology do not have can forget, be difficult for forge or stolen, carry and advantage such as available whenever and wherever possible, safer, secret than traditional identity identifying method, make things convenient for.Can be used for identifying that the biological characteristic with authenticating identity should have characteristics such as universality, uniqueness, stability and collection property.At present, comparative maturity and several biometrics identification technologies of having application prospect most comprise fingerprint, people's face, people's face thermogram, iris, retina, hand-type, vocal print and signature etc.Wherein, iris identification and fingerprint recognition are acknowledged as the most reliable two kinds of biological identification technologies.

People's any physiology or behavior characteristics just can be used as biological characteristic in principle and are used for the identity discriminating as long as it satisfies following condition: (1) universality, and everyone has; (2) uniqueness, everyone is different; (3) stability is constant a certain period; (4) collection property, quantitative measurement easily.Certainly, only satisfying above condition may not be feasible, and actual system also should consider: (1) performance, i.e. Shi Bie accuracy, speed, robustness and for reaching the requirement resource needed; (2) acceptability, people are to the acceptance level of this bio-identification; (3) but fraudulence, can be by the out-trick complexity of system of the method for subjectivity swindle.

There is such or such problem in biological identification technology commonly used at present, and for example recognition of face is powerless for twins; Application on Voiceprint Recognition is imitated easily; Fingerprint recognition can be subjected to the influence of finger injuries, also usurps easily simultaneously.Brain electricity (EEG) signal is not only a very useful clinical diagnosis instrument, and is a kind of living things feature recognition instrument that well is used for authentication.At first, it possesses universality, and everyone has brain wave; Secondly because causing, differences such as everyone brain characteristic, mode of thinking, memory have different EEG signals between men; The 3rd, EEG also possesses certain stability, and within a certain period of time, the EEG signal can keep relative stability, and is last, and the EEG signal is convenient to gather.Biological recognition system based on the EEG signal can reach certain accuracy and fast speeds, and can not produce any injury to human body, and people also can accept.Because the EEG signal derives from the thinking activities of brain, be difficult to forge, the robustness of system is very high.The EEG signals of human brain researched and analysed show, Different Individual can produce different Nerve impulse reactions in different brain districts, according to this EEG signals difference, can extract individual EEG signals feature, utilize the sorting algorithm of setting, can make that EEG signals possesses the individual specificity.Based on above analysis, be a kind of new identity identification system that application prospect is arranged based on the biological identification system of brain electricity.

Summary of the invention

The present invention utilizes the classification to motion imagination EEG signals, realization is to experimenter's identification, only adopt the electrode signal relevant to carry out data analysis with the motion imagination, adopting after deliberation to the motion imagination highly effective signal processing of EEG signals and feature extraction method---second-order blind identification and Fisher distance are extracted feature, carry out tagsort by neutral net, thereby realize the identification of identity.This method is fit to comprise physical disabilities, and all kinds of crowds such as dysopia have the better suitability.

The present invention comprises following steps:

Step 1, experimenter are with the polar cap that powers on, original brain electricity (EEG) signal is to lead the EEG amplifier collection that meets 10/20 method that international electroencephalography can demarcate by 64, sample rate is 250Hz, is reference electrode with the left mastoid process, and the band filter passband is 1-50Hz, choose 6 electrodes and gather the EEG signals (C3 in 10/20 international standard that can demarcate of just international electroencephalography, C4, P3, P4, O1 and O2 be totally 6 electrode positions), gather experimenter's EEG signals that different motion is imagined process.

Step 2, the stimulation programs (the prompting experimenter begins imagery motion) that basis configures on computer screen, the experimenter makes the different motion of four classes and imagines (motion of imagination left hand, the right hand move, lower limb is moving and tongue moves) according to requirement of experiment.The experimenter is familiar with experimentation through training.

Because everyone is different to the adaptability of the different motion imagination, we allow the experimenter attempt four kinds of different motion imagination types in learning process, and by study and test, we just can determine that any motion imagination type is the most suitable.For example, after the experimenter is by study and test, we find to imagine the discrimination height of the moving discrimination of tongue than other three kinds motion imagination types, we just think and may this experimenter be more suitable for moving with imagining tongue, in use from now on, only need imagination tongue to move and get final product, need not to imagine that other have moved.

Step 3, the EEG signals that collects is carried out pretreatment.At first the EEG signals of obtaining is screened, get rid of obviously unusual EEG signals of a part, then remaining EEG signals is removed the eye electricity, gone pretreatment such as artefact, baseline correction, linearity correction, the pretreated EEG signals of process is with further signal processing.

Step 4, EEG Processing.Through still comprising a lot of irrelevant current potential and background noises of bringing out in the pretreated EEG signals, therefore spatial resolution and signal to noise ratio are very low, for the useful signal of identification from background noise, must further handle, the present invention adopts a kind of blind source separation algorithm---and second-order blind identification comes EEG signals is further handled, and its specific algorithm is as follows:

Make EEG signals continuous time of corresponding n the electrode of n column vector of x (t), then x _i(t) EEG signals of corresponding i electrode.Each x _i(t) can regard n source s as _i(t) linear instantaneous mixes, and hybrid matrix is A, then

x(t)＝A _s(t) (1)

The EEG signals x (t) that SOBI only utilizes sensor measurement to obtain obtains being similar to A ^-1Split-matrix W makes

$\hat{s}\left(t\right)=\mathrm{Wx}\left(t\right)---\left(2\right)$

Be source signal continuous time that recovers.

The SOBI algorithm has two steps: at first EEG signals carry out zero-meanization, be shown below:

y(t)＝B(x(t)-<x(t)>) (3)

Angle brackets＜〉express time is average, so the average of y is zero.The value of matrix B makes correlation matrix＜y (t) y (t) of y ^TBe unit matrix, its value is provided by following formula

$B=\mathrm{diag}\left({\mathrm{\&lambda;}}_i^{-1/2}\right)U^T---\left(4\right)$

λ wherein _iBe correlation matrix＜(x (t)-＜x (t) 〉) (x (t)-＜x (t) 〉) ^TEigenvalue, U each row then be its characteristic of correspondence vector.

In second step, construct one group of diagonal matrix: choose one group of time delay τ, the symmetrization correlation matrix of signal calculated y (t) and its time-delay signal y (t+ τ):

R _τ＝sym(<y(t)y(t+τ) ^T>) (5)

Wherein

sym(M)＝(M+M ^T)/2 (6)

This is a function that asy matrix is changed into relevant symmetrical matrix.The process of symmetrization has been lost some information, but effective solution is provided.

Calculated R τ, again R τ has been carried out diagonalization: by spin matrix V, the utilization iterative method makes

∑ _τ∑ _i≠j(V ^TR _τV) _ij ² (7)

Obtain minimum, then the estimation of separation matrix

W＝V ^TB (8)

Step 5, feature extraction

In order to classify, at first to carry out feature extraction.Feature extraction will go out the data point that can distinguish sample type in all extracting data exactly, i.e. characteristic point, and the present invention adopts the Fisher distance to determine feature.In sort research, Fisher distance usually is used to represent the difference between type, and the size of Fisher distance is directly proportional with discrimination between type, if discrimination is bigger between type, i.e. and obvious difference, then the fisher distance is bigger, otherwise the Fisher distance is less.

Fisher between two classes is as follows apart from computing formula:

$F=\frac{{({\mathrm{\&mu;}}_1-{\mathrm{\&mu;}}_2)}^2}{{\mathrm{\&sigma;}}_1^2+{\mathrm{\&sigma;}}_2^2}---\left(9\right)$

Wherein F represents the Fisher distance, and μ and σ are respectively average and variance, and 1,2 of subscripts are represented two different classes respectively.

For three classes or above situation, the Fisher range formula can be promoted, as follows:

$F=\frac{{({\mathrm{\&mu;}}_1-{\mathrm{\&mu;}}_2)}^2+{({\mathrm{\&mu;}}_1-{\mathrm{\&mu;}}_3)}^2+...+{({\mathrm{\&mu;}}_{n-1}-{\mathrm{\&mu;}}_n)}^2}{{\mathrm{\&sigma;}}_1^2+{\mathrm{\&sigma;}}_2^2+...+{\mathrm{\&sigma;}}_n^2}---\left(10\right)$

For each data point, the size of Fisher distance has been represented this data point as the contribution degree of feature to classification, and the point that the Fisher distance is big more is big more in the contribution of minute apoplexy due to endogenous wind.

What of characteristic point number are closely related with final discrimination, algorithm complexity and recognition rate, and characteristic point is too much or very few, all can influence discrimination, and discrimination is reduced, and characteristic point is many more in addition, and algorithm is complicated more, discerns slow more; Otherwise characteristic point is few more, and algorithm is simple more, discerns fast more.Therefore, the quantity of characteristic point is very big to the final properties influence.Through test discovery repeatedly, feature extraction adopts the Fisher distance to determine feature, to a data fetch 8-12 characteristic point of every electrode, 48--72 characteristic point altogether; Can reach high recognition, and recognition speed is not slow yet, algorithm complex is general.

Step 6, use BP neutral net are carried out classification learning and test.BP neutral net input layer is totally 60 unit, 10 unit of hidden layer, 1 unit of output layer.With the input layer of above-mentioned 60 features as the BP neutral net, each experimenter move at every turn the imagination EEG signals be input to input layer by the feature that step 5 extracts, each experimenter's learning process has 20 data (each 5 of types are imagined in four kinds of motions), and we have determined the parameters of neutral net by learning process.Test process also has 20 data, and by test process, we can determine to be fit to this experimenter's motion imagination type (discrimination is the highest).

Step 7, the eeg data input neural network of the unknown is discerned and authenticated.The experimenter has determined BP neural network structure and suitable he (she's) motion imagination type by behind the above-mentioned steps 1-6, and just can discern and authenticate this moment.The experimenter puts on electrode cap, according to the step 2 setting in motion imagination (type is imagined in the optimal a kind of motion that only needs to determine in the step 6), gather EEG signals, after the pretreatment, the algorithm of introducing according to step 5 extracts 60 characteristic quantities, and the characteristic quantity that extracts is input in the definite neutral net of step 6.If identification, then neutral net output experimenter's coding; If authentication, then whether neutral net output then change this experimenter (0 or 1) into.

Identification of the present invention refers to and select this section EEG signals from several experimenter is for which experimenter; Then for determining that whether this section EEG signals is certain experimenter, the former is a multiple-choice question to verification process, and the latter is a True-False.

What the present invention used is EEG signals, be EEG signals to be carried out information characteristics extract, the method of using is to imagine various motion mode by brain, and it is carried out feature extraction and classification, thus the process that realization is discerned or authenticated individual identity by EEG signals.As identification, provide a kind of novel cryptographic system, can solve the problem that some people with disability can not finish daily identification, also can be used for the occasion that identification is being had higher requirements EEG signals.

The innovative point of this method has:

1, adopts the input signal of EEG signals as identification, fingerprint different from the past, iris etc.

2, gathered the EEG signals of imagining based on motion, just the experimenter also is applicable to other EEG signals (bringing out current potential etc. such as visual evoked potential, incident) certainly in four kinds of EEG signals that produced when moving of the imagination.

3, adopted second-order blind identification and Fisher distance that EEG signals is carried out information retrieval.

4, identification and authentication function have been realized simultaneously.Identification refers to judges it is whose EEG signals from some individuals' EEG signals, judge whether a certain EEG signals is target person's EEG signals and authenticate to refer to.

5,, select to be fit to experimenter's motion imagination type automatically at different experimenters' characteristics.

Description of drawings

Fig. 1 electrode choose sketch map,

Fig. 2 is based on the identification system feature extraction flow chart of EEG signals,

Fig. 3 is based on the identification flow chart of EEG signals.

The specific embodiment

The inventive method in the EEG signals identification system, is used for realizing the identification to individual identity, presses accompanying drawing 1,2,3.Can realize through the following steps:

Step 1, experimenter are with the polar cap that powers on, original brain electricity (EEG) signal is to lead the EEG amplifier collection that meets 10/20 method that international electroencephalography can demarcate by 64, sample rate is 250Hz, with the left mastoid process is reference electrode, the band filter passband is 1-50Hz, choose 6 electrodes and gather EEG signals, concrete electrode position as shown in Figure 1.C3 in 10/20 international standard that just international electroencephalography can be demarcated, C4, P3, P4, O1 and O2 be totally 6 electrode positions, gathers experimenter's EEG signals of different motion imagination process.

Step 2, the stimulation programs (the prompting experimenter begins imagery motion) that basis configures on computer screen, the experimenter makes the different motion of four classes and imagines (motion of imagination left hand, the right hand move, lower limb is moving and tongue moves) according to requirement of experiment.The experimenter is familiar with experimentation through training.

Step 3, the EEG signals that collects is carried out pretreatment.At first the EEG signals of obtaining is screened, get rid of obviously unusual EEG signals of a part, then remaining EEG signals is removed the eye electricity, gone pretreatment such as artefact, baseline correction, linearity correction, the pretreated EEG signals of process is with further signal processing.

Step 4, EEG Processing.Through still comprising a lot of irrelevant current potential and background noises of bringing out in the pretreated EEG signals, therefore spatial resolution and signal to noise ratio are very low, for the useful signal of identification from background noise, must further handle, the present invention adopts a kind of blind source separation algorithm---and second-order blind identification comes EEG signals is further handled, and its specific algorithm is as follows:

Make EEG signals continuous time of corresponding n the electrode of n column vector of x (t), then x _i(t) EEG signals of corresponding i electrode.Each x _i(t) can regard n source s as _i(t) linear instantaneous mixes, and hybrid matrix is A, then

x(t)＝As(t) (1)

The EEG signals x (t) that SOBI only utilizes sensor measurement to obtain obtains being similar to A ^-1Split-matrix W makes

$\hat{s}\left(t\right)=\mathrm{Wx}\left(t\right)---\left(2\right)$

Be source signal continuous time that recovers.

The SOBI algorithm has two steps: at first EEG signals carry out zero-meanization, be shown below:

y(t)＝B(x(t)-<x(t)>) (3)

Angle brackets＜〉express time is average, so the average of y is zero.The value of matrix B makes correlation matrix＜y (t) y (t) of y ^TBe unit matrix, its value is provided by following formula

$B=\mathrm{diag}\left({\mathrm{\&lambda;}}_i^{-1/2}\right)U^T---\left(4\right)$

λ wherein _iBe correlation matrix＜(x (t)-＜x (t) 〉) (x (t)-＜x (t) 〉) ^TEigenvalue, U each row then be its characteristic of correspondence vector.

In second step, construct one group of diagonal matrix: choose one group of time delay τ, the symmetrization correlation matrix of signal calculated y (t) and its time-delay signal y (t+ τ):

R _τ＝sym(<y(t)y(t+τ) ^T>) (5)

Wherein

sym(M)＝(M+M ^T)/2 (6)

This is a function that asy matrix is changed into relevant symmetrical matrix.The process of symmetrization has been lost some information, but effective solution is provided.

Calculated R τ, again R τ has been carried out diagonalization: by spin matrix V, the utilization iterative method makes

∑ _τ∑ _i≠j(V ^TR _τV) _ij ² (7)

Obtain minimum, then the estimation of separation matrix

W＝V ^TB (8)

Step 5, feature extraction

In order to classify, at first to carry out feature extraction.Feature extraction will go out the data point that can distinguish sample type in all extracting data exactly, i.e. characteristic point, and the present invention adopts the Fisher distance to determine feature.In sort research, Fisher distance usually is used to represent the difference between type, and the size of Fisher distance is directly proportional with discrimination between type, if discrimination is bigger between type, i.e. and obvious difference, then the fisher distance is bigger, otherwise the Fisher distance is less.

Fisher between two classes is as follows apart from computing formula:

$F=\frac{{({\mathrm{\&mu;}}_1-{\mathrm{\&mu;}}_2)}^2}{{\mathrm{\&sigma;}}_1^2+{\mathrm{\&sigma;}}_2^2}---\left(9\right)$

Wherein F represents the Fisher distance, and μ and σ are respectively average and variance, and 1,2 of subscripts are represented two different classes respectively.

For three classes or above situation, the Fisher range formula can be promoted, as follows:

$F=\frac{{({\mathrm{\&mu;}}_1-{\mathrm{\&mu;}}_2)}^2+{({\mathrm{\&mu;}}_1-{\mathrm{\&mu;}}_3)}^2+...+{({\mathrm{\&mu;}}_{n-1}-{\mathrm{\&mu;}}_n)}^2}{{\mathrm{\&sigma;}}_1^2+{\mathrm{\&sigma;}}_2^2+...+{\mathrm{\&sigma;}}_n^2}---\left(10\right)$

For each data point, the size of Fisher distance has been represented this data point as the contribution degree of feature to classification, and the point that the Fisher distance is big more is big more in the contribution of minute apoplexy due to endogenous wind.

What of characteristic point number are closely related with final discrimination, algorithm complexity and recognition rate, and characteristic point is too much or very few, all can influence discrimination, and discrimination is reduced, and characteristic point is many more in addition, and algorithm is complicated more, discerns slow more; Otherwise characteristic point is few more, and algorithm is simple more, discerns fast more.Therefore, the quantity of characteristic point is very big to the final properties influence.Through test discovery repeatedly, feature extraction adopts the Fisher distance to determine feature, to 10 characteristic points of data fetch of every electrode, 60 characteristic points altogether; Can reach high recognition, and recognition speed is not slow yet, algorithm complex is general.

Step 6, extract each experimenter's EEG signals feature according to flow process shown in Figure 2, by BP neural network learning and identification, determine neural network structure and motion imagination type, training process finishes.BP neutral net input layer is totally 60 unit, 10 unit of hidden layer, 1 unit of output layer.With the input layer of above-mentioned 60 features as the BP neutral net, each experimenter move at every turn the imagination EEG signals be input to input layer by the feature that step 5 extracts, each experimenter's learning process has 20 data (each 5 of types are imagined in four kinds of motions), and we have determined the parameters of neutral net by learning process.Test process also has 20 data, and by test process, we can determine to be fit to this experimenter's motion imagination type (discrimination is the highest).

Step 7, each experimenter's identity is discerned and authenticated according to flow process shown in Figure 3.The eeg data input neural network of the unknown is discerned and authenticated.The experimenter has determined BP neural network structure and suitable he (she's) motion imagination type by behind the above-mentioned steps 1-6, and just can discern and authenticate this moment.The experimenter puts on electrode cap, according to the step 2 setting in motion imagination (type is imagined in the optimal a kind of motion that only needs to determine in the step 6), gather EEG signals, after the pretreatment, the algorithm of introducing according to step 5 extracts 60 characteristic quantities, and the characteristic quantity that extracts is input in the definite neutral net of step 6.If identification, then neutral net output experimenter's coding; If authentication, then whether neutral net output then change this experimenter (0 or 1) into.

Some at present external researchs mainly with visual stimulus or myoelectricity as features sources, this research imagines that with motion EEG signals as identification, can be fit to various crowds such as deformity, and adaptability is preferably arranged.On method, adopt second-order blind identification to carry out signal processing, and adopt the Fisher distance to extract feature.As can be seen from the results, the imagination tongue signal of telecommunication discrimination that beats one's brains is the highest, reaches 88.1%, four kind of imagery motion EEG signals average recognition rate 82.8%, and other more external method of discrimination exceeds about 5 percentage points.

Claims (2)

1, based on the EEG signal identification method of second-order blind identification, it is characterized in that: the present invention comprises following steps:

Step (1), experimenter are with the polar cap that powers on, original EEG signals is to lead the EEG amplifier collection that meets 10/20 method that international electroencephalography can demarcate by 64, and sample rate is 250Hz, is reference electrode with the left mastoid process, the band filter passband is 1-50Hz, choose 6 electrodes and gather EEG signals, 6 electrodes are the C3 in 10/20 international standard that can demarcate of international electroencephalography, C4, P3, P4,6 electrode positions of O1 and O2 are gathered experimenter's EEG signals that different motion is imagined process;

Step (2), the stimulation programs that basis configures on computer screen, the prompting experimenter begins imagery motion, and the experimenter is according to requirement of experiment, make the different motion imagination of four classes, the motion of imagination left hand, the right hand move, lower limb is moving and tongue is moving, and the experimenter is familiar with experimentation through training;

Step (3), the EEG signals that collects is carried out pretreatment, at first the EEG signals of obtaining is screened, get rid of obviously unusual EEG signals of a part, then remaining EEG signals is removed the eye electricity, gone artefact, baseline correction, linearity correction pretreatment;

Step (4), EEG Processing through still comprising a lot of irrelevant current potential and background noises of bringing out in the pretreated EEG signals, adopt the second-order blind identification in the blind source separation algorithm to come EEG signals is further handled;

Step (5), feature extraction adopt the Fisher distance to determine feature, to a data fetch 8-12 characteristic point of every electrode, 48--72 characteristic point altogether;

Step (6), use BP neutral net are carried out classification learning and test.We can determine to be fit to this experimenter's motion imagination type;

Step (7), the eeg data input neural network of the unknown is discerned and authenticated.The experimenter is by behind the above-mentioned steps 1-6, the motion imagination type of having determined the BP neural network structure and being fit to, just can discern and authenticate this moment, the experimenter puts on electrode cap, according to the step 2 setting in motion imagination, only needs optimal a kind of motion imagination type of determining in the step 6, gather EEG signals, after the pretreatment, the algorithm of introducing according to step 5 extracts characteristic quantity, and the characteristic quantity that extracts is input in the definite neutral net of step 6.If identification, then neutral net output experimenter's coding; If authentication, then whether neutral net output then change this experimenter into.

2, the EEG signal identification method based on second-order blind identification as claimed in claim 1 is characterized in that:

The specific algorithm of step (4), EEG Processing is as follows: make EEG signals continuous time of corresponding n the electrode of n column vector of x (t), then x _i(t) EEG signals of corresponding i electrode.Each x _i(t) can regard n source s as _i(t) linear instantaneous mixes, and hybrid matrix is A, then

x(t)＝As(t) (1)

The EEG signals x (t) that SOBI only utilizes sensor measurement to obtain obtains being similar to A ^-1Split-matrix W makes $\hat{s}\left(t\right)=\mathrm{Wx}\left(t\right)---\left(2\right)$

Be source signal continuous time that recovers,

The SOBI algorithm has two steps: at first EEG signals carry out zero-meanization, be shown below:

y(t)＝B(x(t)-<x(t)>) (3)

Angle brackets＜〉express time is average, so the average of y is zero.The value of matrix B makes correlation matrix＜y (t) y (t) of y ^TBe unit matrix, its value is provided by following formula,

$B=\mathrm{diag}\left({\mathrm{\&lambda;}}_i^{-1/2}\right)U^T---\left(4\right)$

λ wherein _iBe correlation matrix＜(x (t)-＜x (t) 〉) (x (t)-＜x (t) 〉) ^TEigenvalue, U each row then be its characteristic of correspondence vector,

In second step, construct one group of diagonal matrix: choose one group of time delay τ, the symmetrization correlation matrix of signal calculated y (t) and its time-delay signal y (t+ τ):

R _τ＝sym(<y(t)y(t+τ) ^T>) (5)

Sym (M)=(M+M wherein ^T)/2 (6)

This is a function that asy matrix is changed into relevant symmetrical matrix.The process of symmetrization has been lost some information, but effective solution is provided,

Calculated R τ, again R τ has been carried out diagonalization: by spin matrix V, the utilization iterative method makes

∑ _τ∑ _i≠j(V ^TR _τV) _ij ² (7)

Obtain minimum, then the estimation of separation matrix

W＝V ^TB (8)。

Images