CN107622242A - The acceleration separation method of blind source mixed signal in a kind of engineering - Google Patents
The acceleration separation method of blind source mixed signal in a kind of engineering Download PDFInfo
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Abstract
The present invention relates to a kind of acceleration separation method of blind source mixed signal in engineering.Because different types of signal has different intrinsic kurtosis values；Mixed signal reach be kept completely separate when, each signal is up to its intrinsic kurtosis value, then it is each separation signal kurtosis cumulant also just reached stationary value；The shortcoming that convergence rate and steady-state error characteristic can not meet simultaneously be present for the fixed step size Natural Gradient Algorithm of blind source signal separation, the Step-varied back propagation algorithm controlled using the kurtosis cumulant composition differential related to separating signal, as long as in the initial step length range of choice of permission, an optional initial step length value, algorithm will adaptively adjust acceleration step-length, as a result can not only accelerate separating rate but also take into account separation accuracy.The inventive method pertains only to select step-length initial valueValue；The speed that algorithm completes separation will be quicker than the separation of fixed step size, and almost close consistent, and has preferably stable crosstalk error；Therefore, there is engineering use value.
Description
Technical Field
The invention belongs to a processing technology of blind source signal separation, and relates to an accelerated separation method of blind source mixed signals in engineering on the premise of establishing feasible engineering parameters through experiments, in particular to a digital signal processing method of a variable-step accelerated separation process based on the proportional differential control of kurtosis cumulant of a separation signal.
Background
There are many effective algorithms, which are different in form, and all of which can be classified as LMS (Least Mean Square) type algorithms. The algorithms all have a preferred problem of learning rate parameters, and how to improve the convergence rate of the algorithms and improve the steady-state performance of the algorithms is one of the hot spots of blind source separation research. The current consensus is that an effective learning rate of variable step size must be found and the variable step size must closely match the separation state to achieve effective acceleration. Some algorithms construct a variable step learning rate on the basis of the initial step, and although the aim of acceleration is also achieved, excessive parameters are added artificially, so that the method is not beneficial to the practical use of engineering.
In the automatic PID algorithm, the difference between a preset value and an output feedback value is utilized, and a proportional term P is obtained by multiplying the input deviation of a regulator by a coefficient and is used as the output of the regulator; increasing the ratio may reduce the time from non-steady state to steady state. The integral term I part is to accumulate the difference between the preset value and the feedback value in time; when a certain value is accumulated, the processing is carried out again, so that oscillation is avoided, but the regulation has obvious lag. The differential item D gives corresponding regulation action in advance according to the rate of the change of the difference value; it can predict the variation trend of error and give adjustment in advance.
In the blind source separation algorithm, the kurtosis accumulated value increases along with the improvement of the separation degree, the stable value when the complete separation is achieved is equivalent to a preset value, and the kurtosis accumulated value in the separation process is equivalent to output feedback. Because different types of signals have different intrinsic kurtosis values, when the mixed signal reaches complete separation, each signal will reach its intrinsic kurtosis value (actually, the kurtosis value when separation under a small stable error is reached), and the accumulated amount of kurtosis of each separated signal reaches a stable value; the stable values reached by different signal mixtures will be different, and the stable value of the natural implicit existence is the preset value of the method. And note that the kurtosis accumulation of the split signals is a one-way process of varying from small to large up to steady, with the purpose of varying the step size to steadily accelerate the process.
Therefore, the invention uses the separating signal kurtosis value to form the variable step learning rate controlled by PD (probability Differentiation), and can give an advance prediction adjustment on the basis of Proportion action, so that the separating speed can be accelerated and the stable crosstalk error can be achieved due to the close correlation of the separating degree, thereby achieving complete separation. And the variable step length algorithm based on the proportional-derivative control reveals a potential rule that the separation process can follow, and the value parameter alpha (alpha) involved in the calculation>, 0) and the obtained initial step length eta 0 In the case where the data are separated to the best by experiment, the obtained data of both are subjected to unary nonlinear fitting to obtain α = f (η) 0 ) (at a certain η) 0 Value range), has good goodness of fit. Thus explaining at η 0 Value a range of values, α and η 0 The relationship of values is also a possible underlying rule that constitutes a fully adaptive variable step size algorithm to some extent.
Disclosure of Invention
The invention aims to provide an accelerated separation method of blind source mixed signals in engineering, which can solve the defects of the blind source signal separation method of the fixed step length natural gradient algorithm, improve the convergence rate of the algorithm and improve the signal processing method of the steady-state performance of the algorithm.
In order to achieve the purpose, the technical scheme of the invention is as follows: a method for accelerating separation of blind source mixed signals in engineering comprises the following steps,
s1, calculating an initial separation matrix of blind source mixed signals:
selecting an initial step value eta 0 Selecting an initial transformation matrix W 0 Wherein, W 0 Is the unit matrix 0.1 x I, and the initial transformation matrix W is calculated by formula (1) 1 ：
Wherein eta is k In order to change the step-size learning rate,is a non-linear function vector, W k 、W k+1 Respectively are the transformation matrixes of the kth iteration and the 1 + th iteration;
s2, calculating a new separation matrix and outputting signals:
different types of signals have different intrinsic kurtosis values, and the cumulative value J of the kurtosis of the signals is separated according to the correlation between two iterations all (k) Analyzing the influence on the next iterative operation, wherein the process is a discrete process, the kurtosis accumulated value is continuously increased, the process reflects that the deviation of the separated output kurtosis accumulated value and the preset value is smaller and smaller, and the first-order backward difference of the deviation information can approximately replace the differentiation to calculate the variable step length value for predicting acceleration;
if the step size between two iterations is expressed as Δ K, and the value of Δ K is taken to be equal to the initial step size value η 0 Then, between two iterations, the error e (k) and the error change rate of the preset value and the output value can be approximated by equations (2) and (3), and the change of the proportion and the differentiation is reflected:
wherein, gamma is the proportionality coefficient of delta K, when m (K) is no proportionality coefficient gamma, the ratio of error variation value and step value changes from large to small and is stabilized at 0 or a value close to 0 along with the completion of separation; thus, a new variable step learning rate is constructed:
wherein the first term is an error ratio term and the initial step value eta 0 The degree of proportional adjustment is determined; the second term is a derivative term, coefficient beta (beta)> 0) influences the action degree of the differential terms together with the initial step value; taking into account the initial step value eta 0 When the sampling is larger, the error reflecting speed is larger, the differential action coefficient beta is correspondingly reduced, otherwise, overlarge overshoot is possibly caused, oscillation occurs, and the value of the beta is as follows:
wherein, α (α)>, 0) and the obtained initial step value eta 0 Correlation;
calculating the variable step length eta according to the formulas (2) to (5) i Then, a new separation matrix W is calculated according to equation (1) i And calculates a new output signal:
Y＝W i X (6)；
s3, calculating a new variable step length value: repeating step 2 according to the new output signal, and calculating new kurtosis value accumulation value J all (k) And a new variable step size value eta k ；
S4, circularly executing calculation: repeating the steps S2 and S3 according to the new separation matrix until the separation signal reaches a stable kurtosis accumulated value or a preset crosstalk error value;
s5, final separation signal output calculation: according to the matrix W which finally achieves complete separation out And calculating and outputting a separation signal.
In an embodiment of the present invention, in the step S2, the kurtosis value of the separation signal uses the negative entropy of the edge of the separation signal as a fourth-order edge accumulation amount which is approximately as follows:
wherein, K 2 4 (i) The square of the fourth order cumulant of the ith component of the neural network output vector y, and the fourth order edge cumulant k 4 (i) The normalization calculation of (2) is called the kurtosis of the signal and is used for measuring the degree of deviation of the signal from the Gaussian; the kurtosis of the Gaussian signal is equal to 0, the kurtosis of the under Gaussian signal is less than 0, and the kurtosis of the over Gaussian signal is greater than 0; thus, the cumulative amount of kurtosis of the separated signal can be replaced by calculating the negative entropy sum of the edges of the separated signal:
in the blind source separation process, J all (k) Non-negative and changes from small to large, eventually reaching a stable value, reflecting the state of completion of the separation.
In an embodiment of the present invention, in the step S1, a non-linear function vector is selected for separation of the under-gaussian mixture signals Separation selection nonlinear function vector of super-Gaussian source mixed signal
In an embodiment of the present invention, the value law of α may be obtained by performing unary nonlinear fitting according to experimental data to obtain α = f (η) 0 )。
Compared with the prior art, the invention has the following beneficial effects:
1. firstly, the invention has the main characteristics of engineering use value: (1) The invention uses the separation signal kurtosis value to form PD (probability Differentiation) controlled variable step learning rate, and can provide a prediction adjustment in advance on the basis of proportional action, so that the separation speed can be accelerated and the stability can be considered because the separation signal kurtosis value is closely related to the separation degree; (2) Because the separation signal kurtosis value is used for forming the variable-step learning rate controlled by PD (probability Differentiation), only one initial step parameter is determined, and a self-adaptive variable-step blind source separation algorithm is formed, which is beneficial to adding in the application of actual engineering; (3) The mixed signal achieves obviously high separation speed by utilizing the algorithm of the invention, is obviously superior to the iterative operation speed of fixed step length, has the same precision as the fixed step length natural gradient algorithm, and is beneficial to the requirement of actual engineering;
2. the invention can form a signal separation processing link of practical engineering application in various signal processing and signal communication fields. For example, in the case of "double talk" in video conference voice communication, in various fields requiring blind source signal separation such as where a microphone simultaneously picks up echo interference, separation processing can be performed in a short time as a basis for identifying and extracting a target signal.
Drawings
Fig. 1 is a block diagram of an implementation of the core principles of the present invention.
Fig. 2 is a block diagram of an implementation of the core principles of the present invention.
FIG. 3 is a one-dimensional non-linear fit of the data from Table 1 according to the present invention.
Fig. 4 is a source signal diagram of the (experimental) super gaussian signal of the present invention.
Fig. 5 is a mixed signal plot of the (experimental) super-gaussian source signal of the present invention.
Fig. 6 is a graph of the separation signal (η 0= 0.6) of the (experimental) superss mixed signal of the present invention.
Fig. 7 is a mixing matrix and a performance matrix for the (experimental) ultra-gaussian mixture signal (η 0= 0.6) of the present invention.
Fig. 8 is a source signal diagram of the inventive (test) super-gaussian signal.
Fig. 9 is a mixed signal diagram of the (test) super-gaussian source signal of the present invention.
Fig. 10 is a graph of the separated signal (η 0= 0.6) of the inventive (test) super gaussian mixture signal.
Fig. 11 is a mixing matrix and a performance matrix of the inventive (test) super gaussian mixture signal (η 0= 0.6).
Detailed Description
The technical scheme of the invention is specifically explained below with reference to the accompanying drawings.
The invention relates to an accelerated separation method of blind source mixed signals in engineering, which comprises the following steps,
s1, calculating an initial separation matrix of blind source mixed signals:
selecting an initial step value eta 0 Selecting an initial transformation matrix W 0 (identity matrix 0.1 × i), calculating an initial transformation matrix W by equation (1) 1 ：
Wherein eta is k In order to change the step-size learning rate,for the non-linear function vectors, the non-linear function vectors are selected for the separation of the under-Gaussian mixture signalsSeparation selection nonlinear function of super-Gaussian source mixed signal(Vector)W k 、W k+1 Respectively are the transformation matrixes of the kth iteration and the 1 + th iteration;
s2, calculating a new separation matrix and outputting signals:
different types of signals have different intrinsic kurtosis values, and the cumulative value J of the kurtosis of the signals is separated according to the correlation between two iterations all (k) Analyzing the influence on the next iterative operation, wherein the process is a discrete process, the kurtosis accumulated value is continuously increased, the process reflects that the difference between the separated output kurtosis accumulated value and a preset value (a stable value which is inherent in the recessiveness, namely when a mixed signal is completely separated, each signal reaches the inherent kurtosis value, the kurtosis accumulated value of each separated signal also reaches the stable value, different signals are mixed, the reached stable values are different) is smaller and smaller, and the first-order backward difference of the deviation information can approximately replace the differentiation to calculate the variable step size value for predicting acceleration;
if the step size between two iterations is expressed as Δ K, and the value of Δ K is taken to be equal to the initial step size value η 0 Then, between two iterations, the error e (k) and the error change rate of the preset value and the output value can be approximated by equations (2) and (3), and the change of the proportion and the differentiation is reflected:
wherein, gamma is the proportionality coefficient of delta K, when m (K) is no proportionality coefficient gamma, the ratio of error variation value and step value changes from large to small and is stabilized at 0 (or a value close to 0) along with the completion of separation; thus, a new variable step learning rate is constructed:
wherein the first term is an error ratio term and the initial step value eta 0 The proportion regulation degree is determined; the second term is a derivative term, coefficient beta (beta)> 0) influences the action degree of the differential terms together with the initial step value; taking into account the initial step value eta 0 When the sampling is larger, the error reflecting speed is larger, the differential action coefficient beta is correspondingly reduced, otherwise, overlarge overshoot is possibly caused, oscillation occurs, and the value of the beta is as follows:
wherein, alpha (alpha)>, 0) and the obtained initial step value eta 0 Correlation; the value law of alpha can be obtained by carrying out unary nonlinear fitting according to experimental data to obtain alpha = f (eta) 0 )；
Calculating the variable step length eta according to the formulas (2) to (5) i Then, a new separation matrix W is calculated according to equation (1) i And calculates a new output signal:
Y＝W i X (6)；
s3, calculating a new variable step length value: repeating the step 2 according to the new output signal, and calculating a new kurtosis value accumulation value J all (k) And a new variable step size value eta k ；
S4, circularly executing calculation: repeating the steps S2 and S3 according to the new separation matrix until the separation signal reaches a stable kurtosis accumulated value or a preset crosstalk error value;
s5, final separation signal output calculation: according to the matrix W which finally achieves complete separation out And calculating and outputting a separation signal.
In step S2, the kurtosis value of the separation signal is obtained by using the negative entropy of the edge of the separation signal as the fourth-order edge accumulation amount which is approximated as follows:
wherein, K 2 4 (i) The square of the fourth order cumulant of the ith component of the neural network output vector y, and the fourth order edge cumulant k 4 (i) The normalization calculation of (a) is called the kurtosis of the signal, and is used for measuring the degree of deviation of the signal from the Gaussian; the kurtosis of the Gaussian signal is equal to 0, the kurtosis of the under Gaussian signal is less than 0, and the kurtosis of the over Gaussian signal is greater than 0; thus, instead of the cumulative amount of kurtosis of the isolated signal, the sum of negative entropies of the edges of the isolated signal can be calculated:
in the blind source separation process, J all (k) Non-negative and changes from small to large, eventually reaching a stable value, reflecting the state of completion of the separation.
The following is a specific example of the present invention.
As shown in fig. 1, the adaptive method for accelerating separation of blind source mixed signals according to the present invention includes the following steps:
step 1: calculating an initial separation matrix of the separation signals: initial step value eta of super-Gaussian mixed signal separation 0 Selecting 0.1-1.0 initial value, selecting initial transformation matrix W 0 (identity matrix 0.1 × i), calculating an initial transformation matrix W by equation (1) 1 ：
Wherein eta is k For the variable step learning rate (substituting the initial value in this step), is non-linearFunction vector, under-Gaussian mixture signal separation selectionIn a super Gaussian source experiment, a nonlinear function is taken asW k 、W k+1 The transformation matrixes of the k-th iteration and the k + 1-th iteration are respectively;
step 2: calculate new separation matrix and output signal: different types of signals have different inherent kurtosis values, when a mixed signal reaches complete separation, each signal reaches the inherent kurtosis value, and the accumulated quantity of the kurtosis of each separated signal also reaches a stable value (different signals are mixed, the reached stable values of the different signals are different);
the influence on the next iteration operation is obtained according to the analysis of the kurtosis accumulated value of the related separation signals between two iterations, the process is a discrete process, the kurtosis accumulated value is continuously increased, the smaller and smaller deviation of the separation output kurtosis accumulated quantity and a preset value (a stable value which is implicitly inherent) is reflected, and the first-order backward difference of the deviation information can approximately replace differentiation to calculate the variable step length for predicting acceleration;
thus, the kurtosis accumulation is calculated from the initial isolated signal. If the step length between two iterations is expressed as delta K, and the delta K is equal to the initial value eta of the step length 0 Then, between two iterations, the proportional term e (k) (error of preset value and output value) and the derivative term (error change rate) can be approximately replaced by the following expressions (2) and (3), and the change of the proportion and the derivative is reflected:
wherein, gamma is the proportionality coefficient of delta K, when m (K) is no proportionality coefficient gamma, the ratio of error variation value and step value changes from large to small and is stabilized at 0 (or a value close to 0) along with the completion of separation; thus, a new variable step learning rate is constructed:
wherein the first term is an error ratio term and the initial step value eta 0 The proportion regulation degree is determined; the second term is a derivative term, coefficient beta (beta)> 0) influences the action degree of the differential terms together with the initial step value; taking into account the initial step value eta 0 When the sampling is larger, the error reflecting speed is larger, the differential action coefficient beta is correspondingly reduced, otherwise, overlarge overshoot is possibly caused, oscillation occurs, and the value of the beta is as follows:
wherein, α (α)>, 0) and the obtained initial step value eta 0 Correlation; corresponding to each η 0 Taking a value, namely taking an alpha value; calculating a new separation matrix W according to the formula (1) i And calculates a new output signal:
Y＝W i X (6)；
step 3, calculating a new step size change value: repeating the step 2 according to the new output signal, and calculating a new kurtosis value accumulation value J all (k) And a new variable step size value eta k ；
And 4, circularly executing calculation: repeating the step 2 and the step 3 according to the new separation matrix until the separation signal reaches a stable kurtosis accumulated value or a preset crosstalk error value;
and 5: corresponding to each eta 0 And (3) comprehensively observing the iteration times of stable crosstalk errors, re-taking the alpha value, executing the step (1) to the step (5), and re-calculating according to the formulas (1) and (6) to obtain a new separation matrix and an output signal until the optimal separation is obtainedAlpha values of speed and accuracy, recording the eta taken at that time 0 To a value, and to achieve the desired value of alpha.
Step 6: eta 0 When the values are respectively 0.1-1.0, obtaining a corresponding better alpha value, and fitting a curve function by using unary nonlinear regression:
if b (1) =0.6, b (2) =2, the function relationship is:
α＝0.6+2η 0 2 (1.2≥η 0 ＞0) (10)
and 7: and (3) forming an adaptive variable step length algorithm by using the formula (10) to obtain a separation result of the test.
Referring to fig. 1, fig. 1 is a block diagram of a core implementation of the present invention.
In the blind source separation algorithm, the kurtosis cumulative value increases along with the increase of the separation degree, the stable value when the complete separation is achieved is equivalent to a preset value (both the super Gaussian mixed signal and the sub-Gaussian mixed signal have the characteristic), and the kurtosis cumulative value in the separation process is equivalent to output feedback. Because different types of signals have different intrinsic kurtosis values, when the mixed signals reach complete separation, each signal reaches the intrinsic kurtosis value (actually, the kurtosis value when the mixed signals reach separation under a small stable error), and the accumulated amount of the kurtosis of each separated signal also reaches the stable value; the stable values reached by different signal mixtures will be different, and the stable value of the natural implicit existence is the preset value of the method. And note that the kurtosis accumulation of the split signals is a one-way process of varying from small to large up to steady, with the purpose of varying the step size to steadily accelerate the process.
Therefore, the invention uses the separating signal kurtosis value to form the variable step learning rate controlled by PD (probability Differentiation), and can give an advance prediction adjustment on the basis of Proportion action, so that the separation can be accelerated because the advance prediction adjustment is closely related to the separation degreeSpeed and stability. The variable step length algorithm based on the proportional-derivative control reveals a potential rule that the separation process can follow, and a value parameter alpha (alpha) involved in the calculation>, 0) and the obtained initial step length eta 0 In the case where the data are separated to the best by experiment, the obtained data of both are subjected to unary nonlinear fitting to obtain α = f (η) 0 ) (at a certain η) 0 Operation value range) and has good goodness of fit. Thus explaining at η 0 A value in a range of values, alpha and eta 0 The relationship of values is also a possible underlying rule to some extent that constitutes a fully adaptive variable step size algorithm.
Referring to Table 1 and FIG. 3, table 1 shows the relationship between eta and 0 when the value is 0.1-1.2, separating the experimental super-Gaussian mixed signal to obtain a corresponding better alpha value; FIG. 3 is a one-dimensional non-linear fit of the data from Table 1 according to the present invention.
TABLE 1 separation of (experimental) superss mixture signals according to the invention, corresponding better alpha values are obtained when the eta 0 value is 0.1-1.0
| η 0 Value of | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 |
| Alpha value | 0.55 | 0.60 | 0.85 | 0.90 | 1.10 | 1.40 | 1.50 | 1.80 | 2.10 | 2.50 |
The data in table 1 are the basis for fitting curves; according to a unary non-linearity, taking into account the characteristics of the exponential changeRegression fitting gave the results:
i.e. as long as the initial step length eta is selected 0 The value of the parameter alpha is automatically obtained. From fig. 3, it is shown that the fitted curve has a better fit with the original data, and therefore has practical use value in engineering.
See FIGS. 4-7, and Table 2; FIGS. 4, 5 and 6 are graphs of the (experimental) ultra Gaussian source signal, the mixed signal and the split signal, respectively, of the present invention; FIG. 7 is a mixing matrix and a performance matrix for the (experimental) superss mixed signal of the present invention; table 2 shows the kurtosis contrast of the (experimental) super Gaussian source signal and the isolated signal.
Table 2 shows the kurtosis contrast between the ultra Gaussian source signal and the isolated signal (. Eta.0 = 0.6) according to the invention
| Source signal sequence | s 1 (n) | s 2 (n) | s 3 (n) | s 4 (n) | s 5 (n) |
| Corresponding kurtosis | 1.8390 | 2.8505 | 1.8201 | 1.4489 | 3.0873 |
| Separating signal sequences | y 1 (n) | y 2 (n) | y 3 (n) | y 4 (n) | y 5 (n) |
| Corresponding to kurtosis | 1.0866 | 2.6628 | 1.4842 | 3.2611 | 1.3852 |
The experimental conditions are as follows:
the super Gaussian signal source is 5 voice signals (16 kHz sampling rate/16bit, 15000 data points, 3 male voice signals and 2 female voice signals), and digital signals are acquired by a computer sound card.
In the super Gaussian source experiment, a nonlinear function is taken asExperiment with random mixing matrix A 1 The source signals are mixed.
And (3) processing results: initial learning rate η 0 =0.1, initial matrix W (0) =0.1I. The experimental separation results of the algorithm, the superss separation signal, are shown in fig. 6.
The corresponding relation between the separation signal and the source signal of the super-Gaussian source experiment is as follows: y is 1 →s 4 ,y 2 →s 2 ,y 3 →s 1 ,y 4 →s 5 ，y 5 →s 3 . The kurtosis values of the super-Gaussian source signal and the separation signal are shown in Table 2, and the performance matrix after separation is G 1 ＝W 1 A 1 ，A 1 And G 1 As shown in fig. 7. From G 1 It is seen in the matrix that only one element per column per row has a much larger absolute value than the other elements, indicating a better recovery of the source signal, except for the variation in amplitude, order and phase of the split signals (negative sign is inverted). And from table 2, the kurtosis of the separation signal and the source signal is relatively close, thereby achieving the separation purpose.
Referring to table 3, table 3 shows the number of iterations, elapsed time and final settling error for completing the separation of the (experimental) superss mixture signal of the algorithm of the present invention and the fixed step size algorithm.
Table 3 shows the iteration number, the elapsed time and the final stable error of the separation of the superss mixed signal of the invention (experimental) algorithm and the fixed step length algorithm
Two blind source separation experimental conditions:
separating conditions of super-Gaussian mixed signals: (1) the adaptive variable step natural gradient algorithm is provided. Using the formulas (4), (5) and (10) as step length adjustment terms, and the initial value eta of the step length 0 Respectively taking the values of 0.1-1.2; (2) and (4) a fixed step length natural gradient algorithm, wherein the fixed step lengths are respectively 0.1-0.9.
The experimental results are as follows: the steady state error of the super Gaussian mixture signal when the separation is finished is 0.0282, wherein the iteration number of the separation finished is set as n 1 The time t elapsed for completing the separation can be calculated 2 ＝T×(n 2 /N), the relevant results when separation was completed are shown in table 3. The result shows that the separation speed with fixed step length has the best effect when the step length is 0.8, the separation precision of the method is the same as that of the fixed step length when the initial step length is 0.1-1.1, the separation speed is superior to that of a fixed step length algorithm, and the separation speed is close to the same.
Referring to fig. 8-11, and table 4, fig. 8, 9, and 10 are graphs of the (test) superss source signal, the mixed signal, and the split signal, respectively, of the present invention; FIG. 11 is a mixing matrix and a performance matrix for the (test) ultra-Gaussian mixture signal of the present invention; table 4 is the kurtosis contrast of the (test) super gaussian source signal and the isolated signal.
Table 4 shows the contrast in kurtosis between the inventive (test) super-Gaussian source signal and the isolated signal (. Eta.0 = 0.6)
| Source signal sequence | s 1 (n) | s 2 (n) | s 3 (n) | s 4 (n) | s 5 (n) |
| Corresponding kurtosis | 4.9219 | 3.9686 | 3.8687 | 1.8201 | 4.5867 |
| Separating signal sequences | y 1 (n) | y 2 (n) | y 3 (n) | y 4 (n) | y 5 (n) |
| Corresponding kurtosis | 4.4760 | 4.2291 | 1.4412 | 6.6366 | 5.4399 |
The experimental conditions are as follows:
the super Gaussian signal source is another 5 voice signals (16 kHz sampling rate/1696t, 15000 data points, 3 male voice signals and 2 female voice signals), and digital signals are acquired through a computer sound card.
In a super Gaussian source experiment, a nonlinear function is taken asExperiment with random mixing matrix A 2 The source signals are mixed.
And (3) processing results: initial learning rate η 0 =0.1, initial matrix W (0) =0.1I. The experimental separation results of the algorithm, the superss separation signal, are shown in fig. 10.
The corresponding relation between the separation signal and the source signal of the super-Gaussian source experiment is as follows: y is 1 →s 2 ,y 2 →s 3 ,y 3 →s 4 ,y 4 →s 1 ，y 5 →s 5 . The kurtosis values of the super-Gaussian source signal and the separation signal are shown in Table 4, and the performance matrix after separation is G 2 ＝W 2 A 2 ，A 2 And G 2 As shown in fig. 11. From G 2 It is seen in the matrix that only one element per column per row has a much larger absolute value than the other elements, indicating a better recovery of the source signal, except for the variation in amplitude, order and phase of the split signals (negative sign is inverted). And it is seen from table 4 that the kurtosis of the separation signal and the source signal are relatively close, thereby achieving the separation purpose.
Referring to table 5, table 5 shows the iteration number, the elapsed time and the final stable error of the separation of the super-gaussian mixture signal according to the algorithm (test) of the present invention.
Table 5 shows the number of iterations, elapsed time and final settling error for separating the superss mixture of the present invention (test) algorithm and the fixed step size algorithm
Two blind source separation experimental conditions:
separating conditions of super-Gaussian mixed signals: (1) the adaptive variable step size natural gradient algorithm is provided. Using the formulas (4), (5) and (10) as step length adjustment terms, and the initial value eta of the step length 0 Respectively taking the values of 0.1-1.2; (2) and (4) a fixed step length natural gradient algorithm, wherein the fixed step lengths are respectively 0.1-0.9.
The experimental results are as follows: the steady state error of the super Gaussian mixture signal when the separation is finished is 0.0031, wherein the iteration number of the finished separation is set as n 1 The time t elapsed for completing the separation can be calculated 2 ＝T×(n 2 /N), the relevant results when separation was completed are shown in table 3. The result shows that the separation speed with fixed step length has the best effect when the step length is 0.8, the separation precision of the method is the same as that of the fixed step length when the initial step length is 0.1-1.1, the separation speed is superior to that of a fixed step length algorithm, and the separation speed is close to the same. It can be seen that the adaptive algorithm formed by the formulas (4), (5) and (10) is feasible for the ultra-gaussian mixture signal class, and the expected target of both separation speed and separation precision is achieved.
The above are preferred embodiments of the present invention, and all changes made according to the technical solutions of the present invention that produce functional effects do not exceed the scope of the technical solutions of the present invention belong to the protection scope of the present invention.
Claims (4)
1. An accelerated separation method for blind source mixed signals in engineering is characterized in that: comprises the following steps of (a) carrying out,
s1, calculating an initial separation matrix of blind source mixed signals:
selecting an initial step value eta 0 Selecting an initial transformation matrix W 0 Wherein, W 0 Calculating an initial transformation matrix W by formula (1) as an identity matrix 0.1 x I 1 ：
Wherein eta k In order to change the step-size learning rate,is a non-linear function vector, W k 、W k+1 Respectively are the transformation matrixes of the kth iteration and the 1 + th iteration;
s2, calculating a new separation matrix and outputting signals:
different types of signals have different intrinsic kurtosis values, and the cumulative value J of the kurtosis of the signals is separated according to the correlation between two iterations all (k) Analyzing the influence on the next iterative operation, wherein the process is a discrete process, the kurtosis accumulated value is continuously increased, the process reflects that the deviation of the separated output kurtosis accumulated value and the preset value is smaller and smaller, and the first-order backward difference of the deviation information can approximately replace the differentiation to calculate the variable step length value for predicting acceleration;
if the step size between two iterations is expressed as Δ K, and the value of Δ K is taken to be equal to the initial step size value η 0 Then, between two iterations, the error e (k) and the error change rate of the preset value and the output value can be approximated by equations (2) and (3), and the change of the proportion and the differentiation is reflected:
wherein, gamma is the proportionality coefficient of delta K, when m (K) is no proportionality coefficient gamma, the ratio of error variation value and step value changes from large to small and is stabilized at 0 or a value close to 0 along with the completion of separation; thus, a new variable step learning rate is constructed:
wherein the first term is an error ratio term and the initial step value eta 0 The proportion regulation degree is determined; the second term is a derivative term, coefficient beta (beta)>, 0) the degree of action of the differential term is influenced together with the initial step value; taking into account the initial step value eta 0 When the value is larger, the error reflecting speed is larger, the differential action coefficient beta is correspondingly reduced, otherwise, overlarge overshoot is possibly caused, oscillation occurs, and the value of beta is as follows:
wherein, alpha (alpha)>, 0) and the obtained initial step value eta 0 Correlation;
calculating the variable step length eta according to the formulas (2) to (5) i Then, a new separation matrix W is calculated according to the formula (1) i And calculates a new output signal:
Y＝W i X (6)；
s3, calculating a new variable step length value: repeating step 2 according to the new output signal, and calculating new kurtosis value accumulation value J all (k) And a new variable step size value eta k ；
S4, circularly executing calculation: repeating the steps S2 and S3 according to the new separation matrix until the separation signal reaches a stable kurtosis accumulated value or a preset crosstalk error value;
s5, final separation signal output calculation: according to the matrix W which finally achieves complete separation out And calculating and outputting a separation signal.
2. The method according to claim 1, wherein the method for accelerating separation of blind source mixed signals in engineering comprises: in step S2, the kurtosis value of the separation signal is obtained by using the negative entropy of the edge of the separation signal as the fourth-order edge accumulation amount which is approximated as follows:
wherein, K 2 4 (i) The square of the fourth order cumulant of the ith component of the neural network output vector y, and the fourth order edge cumulant k 4 (i) The normalization calculation of (2) is called the kurtosis of the signal and is used for measuring the degree of deviation of the signal from the Gaussian; the kurtosis of the Gaussian signal is equal to 0, the kurtosis of the under Gaussian signal is less than 0, and the kurtosis of the over Gaussian signal is greater than 0; thus, instead of the cumulative amount of kurtosis of the isolated signal, the sum of negative entropies of the edges of the isolated signal can be calculated:
in the blind source separation process, J all (k) Non-negative and changes from small to large, eventually reaching a stable value, reflecting the state of completion of the separation.
3. The method according to claim 1, wherein the method for accelerating separation of blind source mixed signals in engineering comprises: in step S1, a non-linear function vector is selected for the separation of the under-Gaussian mixture signalsSeparation selection nonlinear function vector of super-Gaussian source mixed signal
4. The method according to claim 1, wherein the method comprises: the value law of alpha can be obtained by carrying out unary nonlinear fitting according to experimental data to obtain alpha = f (eta) 0 )。
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