CN103763230A - Improved self-adaption blind source separation method - Google Patents
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Abstract
The invention provides an improved self-adaption blind source separation method NVS-NGA, and the improved self-adaption blind source separation method overcomes the defect that no blind source separation scheme capable of effectively handling the contradiction between the rate of convergence and babbling errors exists in the prior art. Firstly, a traditional separation system structure is improved, the performance index of blind source separation is improved, the improved separation performance index serves as an independent variable, and a Rayleigh distribution function serves as a dependent variable and a variable step size function. Compared with a traditional blind source separation method, the improved self-adaption blind source separation method can rapidly and effectively separate an original signal from a received mixed signal, can effectively handle the contradiction between the rate of convergence and the babbling errors, is high in rate of convergence, small in babbling error and high in stability, and has wide application prospects in the aspects of wireless communication, image processing, voice signal processing and the like.
Description
Technical field
The invention belongs to signal processing technology field, especially relate to a kind of improved self-adaptive blind source separation method.
Background technology
Blind source separates and refers in the case of the theoretical model of signal and source signal cannot accurately be known, how from mixed repeatedly signal (observation signal), to isolate the process of each source signal.Blind source separates (Blind Source Separation, BSS) basic task is in the case of the hybrid mode of source signal the unknown and source signal is also unknown, from one group of observation signal receiving, recover source signal, at aspects such as recognition of face, voice signal processing, processing of biomedical signals, satellite and microwave communications, there is huge application potential.Blind source separation method can be divided into batch processing method and the large class of adaptive approach two.Compared with batch processing method, adaptive approach can real-time tracking signal intensity.
Tradition adaptive blind source separation system, referred to as traditional piece-rate system, as shown in Figure 1.Tradition piece-rate system is in series by the nonsingular hybrid matrix A of the unknown and separation matrix W (k); By mutually source signal S (k)=[s independently of M
1(k), s
2(k) ..., s
m(k)]
tthrough a nonsingular hybrid matrix A of the unknown, be mixed to get observation signal X (k)=[x
1(k), x
2(k) ..., x
m(k)]
t, x
m(k) be M observation signal.When ignoring transmission delay effect and noise,
X(k)=AS(k) (1)
In formula, A is that M × M ties up matrix.The target that blind source separates is when only knowing observation signal X (k), obtains, after the separation matrix W (k) of a full rank, obtaining separation signal Y (k) from observation signal X (k) by iteration
Y(k)=W(k)X(k) (2)
In formula, Y (k) is an estimation to source signal S (k), is M × 1 dimension matrix; W (k) is that M × M ties up matrix.
Utilize the relation of mutual information and comentropy, the cost function of piece-rate system is defined as
In formula, H (y
m(k)) be m separation signal y in separation signal vector Y (k)
m(k) entropy, p
y(y
m(k)) be m separation signal y in separation signal vector Y (k)
m(k) marginal probability density, E represents mathematic expectaion computing, and ln represents the natural logrithm take e the end of as, and det represents to get the determinant of W (k).When the cost function J of piece-rate system (k) is while being minimum, best separation matrix W (k) can make in separation signal vector Y (k) each component independent of one another.Utilize the Edgeworth of probability density to launch and get fourth order cumulant,
In formula, H
n(y
m(k)) Normal Distribution, with y
m(k) there is identical average and variance, establish y
m(k) average is zero, variance is 1, H
n(y
m(k) the subscript N) represents normal distribution,
cum represents y
m(k) cumulant computing;
H (y
i(k)) substitution J (k), J (k) is capable and j column element w to i in W (k)
ij(k) random gradient is
In formula, w
ij(k) be the capable and j column element of the i of W (k);
represent W
-1(k) transposition obtains the capable and j column element of the i of matrix; Cum represents cumulant computing, and E represents mathematic expectaion computing;
in
represent random gradient,
for J (k) to W (k) i capable and j column element w
ij(k) random gradient,
transient expression formula by formula (5), can be obtained
In formula (6), the item in braces is only y
i(k) function, makes it be
At this moment, formula (6) can be written as
Here it should be noted that the f (y that formula (7) provides
i(k) being) very concrete functional form, is that the Edgeworth of probability density launches and get fourth order cumulant to obtain, and is referred to as excitation function.In practice, excitation function form can be determined as required, is also just to say, f (y
i(k)) be y
i(k) which kind of concrete form, can choose according to actual needs.
J (k) asks instantaneous gradient to all elements in W (k), obtains J (k) and to the instantaneous gradient of W (k) is
Utilize random gradient and natural gradient relation, obtain J (k) and to the natural gradient of W (k) be
In formula,
represent the natural gradient of J (k) to W (k); I representation unit matrix; F (Y (k)) is actual is the non-linear activation primitive being determined by probability density characteristics.Under natural gradient criterion (Natural Gradient Algorithm, NGA), the more new formula of separation matrix W (k) is
In formula, μ represents step-length, is constant; I represents a unit matrix.The conventional cross-talk error criterion of blind source separation method performance of this traditional piece-rate system is weighed, and its expression is
In formula, PI represents cross-talk error; Max represents to get maxima operation; C (k)=W (k) A=P (k) Λ is the composite matrix of traditional piece-rate system, c
ilwhat represent is the element of the capable l row of Matrix C (k) i, and P (k) and Λ represent respectively a permutation matrix and diagonal matrix, and P (k), Λ, C (k) are M × Metzler matrix.If hybrid system matrix A is known, the more new formula of taking advantage of A to obtain overall Matrix C (k) by formula (11) right side is
C(k+1)=C(k)+μ[I-f(Y(k))Y
T(k)]C(k) (13)
But in actual conditions, because hybrid system matrix A is unknown, more new formula that therefore can not through type (13) directly obtains C (k), also just can not get PI (C (k)).
In addition, traditional adaptive blind source separation algorithm adopts fixed step size, therefore has the contradiction between convergence rate and cross-talk error.Chinese scholars has successively proposed some variable step size methods, but also there is no a kind of blind source separation scheme that very effectively solves contradiction between convergence rate and cross-talk error at present.
Summary of the invention
For addressing the above problem, the invention discloses a kind of improved self-adaptive blind source separation method NVS-NGA, effectively solved the contradiction between convergence rate and cross-talk error, obtained good separating effect.
In order to achieve the above object, the invention provides following technical scheme:
A kind of improved self-adaptive blind source separation method, based on improved adaptive blind source separation system, realize, described improved adaptive blind source separation system comprises hybrid matrix A, separation matrix W (k) and the inverse system W in parallel with separation matrix W (k)
a(k), described W
a(k) with the contrary A of nonsingular hybrid matrix A
-1approximate, described blind source separation method comprises the steps:
Steps A, M the unknown and source signal S independent of each other (k)=[s
1(k), s
2(k) ..., s
m(k)]
tthrough improving unknown nonsingular hybrid matrix A in piece-rate system, be mixed to get observation signal X (k)=[x
1(k), x
2(k) ..., x
m(k)]
t; When ignoring transmission delay effect and noise, obtain X (k)=AS (k), k is time series, subscript T represents conjugate transpose; M is positive integer, represents the number of component in S (k); A is that M × M ties up matrix;
Step B, observation signal X (k)=[x that steps A is obtained
1(k), x
2(k) ..., x
m(k)]
tsend into simultaneously and improve separation matrix W (k) and W in piece-rate system
a(k), obtain respectively separation signal Y (k)=W (k) X (k) and Y
a(k)=W
a(k) X (k), wherein Y (k) is M × 1 dimensional vector, is an estimation of source signal S (k), its component is separate; W (k) is the final separation matrix that improves M × M dimension full rank in piece-rate system; W
a(k) contrary
it is the final estimation to improving unknown nonsingular hybrid matrix A in piece-rate system; W (k) and W
a(k) dimension is identical, and subscript " 1 " represents to get inverse operation;
Wherein separation matrix W (k) and W
a(k) more new formula is:
Wherein I representation unit matrix; F (y (k)) is nonlinear activation primitive, and μ (k) is improved step factor, and its formula is:
μ(k)=β{|PI(C
G(k))|/α
2}exp{-[PI(C
G(k))]
2/(2α
2)},
Wherein, β and α are the control parameters of μ (k); Exp represents the exponential function take e the end of as, wherein PI (C
g(k) be) improved separating property index, its formula is:
Wherein C
g(k) for improving the overall matrix of piece-rate system,
c
ilfor the element that the capable l of i of Matrix C (k) is listed as, c
gilit is Matrix C
g(k) the capable l column element of i, max represents to get maxima operation.
The initial matrix that improves piece-rate system is W (0) and W
a(0), wherein
improve the initial overall matrix of piece-rate system
Preferred as one of the present invention, described f (Y (k))=Y
3(k).
Concrete, described separation matrix W (k) and W
a(k) more new formula obtains as follows:
Step a, utilizes the relation of mutual information and comentropy, and the cost function of piece-rate system is defined as
In formula, H (y
m(k)) be m separation signal y in separation signal vector Y (k)
m(k) entropy, p
y(y
m(k)) be m separation signal y in separation signal vector Y (k)
m(k) marginal probability density, E represents mathematic expectaion computing, and ln represents the natural logrithm take e the end of as, and det represents to get the determinant of W (k);
Step b, calculates the natural gradient of J (k) to W (k)
Step c, obtains separation matrix W (k) and W by J (k) to the natural gradient of W (k)
a(k) more new formula
Beneficial effect: first the present invention improves the structure of traditional piece-rate system, the performance index that blinder source separated are improved, take improved separating property index as independent variable, take Rayleigh Distribution Function as dependent variable, take Rayleigh Distribution Function as variable step function.Compared with traditional blind source separation method, this method can fast and effeciently be isolated primary signal from the mixed signal receiving, and has effectively solved the contradiction between convergence rate and cross-talk error; Not only fast convergence rate, cross-talk error are little, and stability is strong; At aspects such as radio communication, image processing, voice signal processing, all have wide practical use.
Accompanying drawing explanation
Fig. 1 is traditional adaptive blind source separation system structural representation;
Fig. 2 is improved self-adaptive blind source separation method schematic diagram provided by the invention;
Fig. 3 is the convergence graph of the lower three kinds of separating property indexs of Stationary Random Environments condition;
Fig. 4 is simulation result figure of the present invention, and wherein (a) is source signal figure, is (b) mixed signal figure;
Fig. 5 is separating resulting figure under Stationary Random Environments condition, wherein (a) is for being used the separation signal figure after NGA tests, (b) for using the separation signal figure after VS-NGA tests, (c) for using the separation signal figure after NVS-NGA tests;
Fig. 6 is PI mean value curve under Stationary Random Environments condition;
Fig. 7 is the PI mean value curve under non-stationary environment condition.
Embodiment
Below with reference to specific embodiment, technical scheme provided by the invention is elaborated, should understands following embodiment and only for the present invention is described, is not used in and limits the scope of the invention.
As shown in Figure 2, first the present invention improves the structure of former piece-rate system, in traditional piece-rate system separation matrix W (k) upper in parallel one with the contrary A of nonsingular hybrid matrix A
-1approximate inverse system W
a(k), matrix W
a(k), W
a(k) be called separation matrix in parallel, this improves structure division and is concatenated into nonsingular hybrid matrix A again; And the performance index that blind source is separated are improved, independent variable using improved separating property index as Rayleigh Distribution Function, using Rayleigh Distribution Function as variable step function, thereby invented a kind of improved self-adaptive blind source separation method NVS-NGA, this method comprises the steps:
Steps A, M the unknown and source signal S independent of each other (k)=[s
1(k), s
2(k) ..., s
m(k)]
tthrough improving unknown nonsingular hybrid matrix A in piece-rate system, be mixed to get observation signal X (k)=[x
1(k), x
2(k) ..., x
m(k)]
t; When ignoring transmission delay effect and noise, obtain X (k)=AS (k), k is time series, subscript T represents conjugate transpose; M is positive integer, represents the number of component in S (k); A is that M × M ties up matrix.
Step B, observation signal X (k)=[x that steps A is obtained
1(k), x
2(k) ..., x
m(k)]
tsend into simultaneously and improve separation matrix W (k) and W in piece-rate system
a(k), obtain respectively separation signal Y (k)=W (k) X (k) and Y
a(k)=W
a(k) X (k), wherein Y (k) is M × 1 dimensional vector, is an estimation of source signal S (k), its component is separate; W (k) is the final separation matrix that improves M × M dimension full rank in piece-rate system; W
a(k) contrary
it is the final estimation to improving unknown nonsingular hybrid matrix A in piece-rate system; W (k) and W
a(k) dimension is identical, and subscript " 1 " represents to get inverse operation.
Based on improved adaptive blind source separation system, first we want the blind source separating property index of computed improved:
Owing to improving separating part W (k) and W in piece-rate system (as shown in Figure 2)
a(k) be parallel-connection structure, when improving after piece-rate system operation, will obtain best separation matrix W in parallel
a(k); Now W
a(k) contrary
as being similar to of hybrid matrix A in improvement piece-rate system, the overall matrix of the piece-rate system that is improved is thus designated as C
g(k), and
By the overall Matrix C of improving piece-rate system
g(k) C (k) in substituted (12), obtains separating property index parameter and is
This separating property index is that the one of formula (12) is improved, and is referred to as to improve separating property index.
In traditional self-adaptive blind source separation method, step size mu is fixed value, and tracking performance is poor, is unfavorable for solving blind source and separates the contradiction between convergence rate and cross-talk error.In order effectively to solve this technical problem, the present invention combines PI value and step factor, builds a variable step function, specifically, is with cross-talk error PI (C
g(k)) be independent variable, take Rayleigh Distribution Function as dependent variable, obtain variable step formula and be
μ(k)=β{|PI(C
G(k))|/α
2}exp{-[PI(C
G(k))]
2/(2α
2)} (16)
In formula, β and α are the control parameters of μ (k), can choose by experiment α=10, β=0.1; Exp represents the exponential function take e the end of as.
Based on the variable step function shown in formula (16), adopt natural gradient criterion, separation matrix W (k) and W in the piece-rate system that is improved
a(k) more new formula, concrete steps are as follows:
Utilize the relation of mutual information and comentropy, the cost function of piece-rate system is defined as
In formula, H (y
m(k)) be m separation signal y in separation signal vector Y (k)
m(k) entropy, p
y(y
m(k)) be m separation signal y in separation signal vector Y (k)
m(k) marginal probability density, E represents mathematic expectaion computing, and ln represents the natural logrithm take e the end of as, and det represents to get the determinant of W (k);
Calculate the natural gradient of J (k) to W (k)
By J (k), the natural gradient of W (k) is obtained to separation matrix W (k) and W
a(k) more new formula
Wherein, μ (k) is the improved step factor shown in formula (16); I representation unit matrix; F (Y (k)) is nonlinear activation primitive, if determine nonlinear activation primitive f (Y (k)) by formula (7), this function is
By formula (18), determine f (Y (k)), need to calculate the three rank cumulant cum (y of y (k)
3) and fourth order cumulant cum (y (k)
4(k)), calculate very complicatedly, be unfavorable for engineering application.In order to reduce amount of calculation, nonlinear activation primitive is preferably to the reduced form of formula (18), i.e. f (Y (k))=Y
3(k); By separation matrix W in parallel
aand the overall Matrix C that obtains of hybrid matrix A (k)
a(k)=W
a(k) A=P
a(k) Λ
abe called the overall matrix of part in parallel, P
aand Λ (k)
arepresent respectively a permutation matrix and diagonal matrix, to W
a(k) invert and can obtain
due to P
aand Λ (k)
arepresent respectively a permutation matrix and diagonal matrix, by matrix properties, can be obtained
with
also represent a permutation matrix and diagonal matrix.
At the initial matrix W (0) and the W that improve piece-rate system
a(0) in choosing, initial matrix W
a(0) choose need satisfy condition:
choose suitable W
a(0), after, improve the initial overall matrix of piece-rate system
by PI (C
g(0)) the stepsize formula of substitution Rayleigh Distribution Function form, obtains initial step length μ (0).
Up to the present, there are the separating property index PI (C (k)) of traditional piece-rate system, the separating property index PI (C of part in parallel
a) and improve the separating property index PI (C of piece-rate system (k)
g(k)).As shown in Figure 3, Fig. 3 shows their constringency performance, and in the whole separation process under Stationary Random Environments condition, at the separation initial stage, the value of PI is very large, illustrates that cross-talk error is very large; In the latter stage separating, it is very little that the value of PI can become, and illustrates that cross-talk error is less, and separating effect is better.On the whole, PI value presents a kind of fast-descending to restraining trend stably in iterative process, wherein improved separating property index PI (C
g(k) performance) is best, therefore adopts and improves separating property index PI (C
g(k)) can better solve the contradiction between convergence rate and cross-talk error.
In order to verify the validity of the inventive method (referred to as NVS-NGA), take traditional blind source separation method VS-NGA of traditional blind source separation method NGA of fixed step size, variable step as comparison other, carry out emulation experiment comparison by Matlab program.In experiment, source signal is: S1=sign (cos (2*pi*155*t/fs)); S2=sin (2*pi*800*t/fs); S3=sin (2*pi*90*t/fs); S4=sin (2*pi*9*t/fs) * sin (2*pi*300*t/fs), sampling number is 5000, sample frequency is 10000Hz, hybrid matrix A
0=[0.3702 0.7143-0.6188-0.3002; 0.0965 0.7408 0.9365 0.0443; 0.3732-0.3762-0.2500-0.6735;-0.6674 0.6747 0.9162-0.7381]; The fixed step size of NGA is μ=0.003; In VS-NGA, utilize sigmoid function to make variable step
wherein η (k)=|| I-f (Y (k)) Y
t(k) || be I-f (Y (k)) Y
t(k) norm, α=10, β=0.1; In NVS-NGA, variable step is formula (16), parameter alpha=10, β=0.15.Wherein source signal waveform is as shown in Fig. 4 (a), and mixed waveform signal is as shown in Fig. 4 (b).
Embodiment 1: under Stationary Random Environments condition, i.e. hybrid matrix A=A
0shi Jinhang contrast experiment.In experiment, all parameters are got above-mentioned set-point, and 100 Monte-Carlo Simulation results are respectively as shown in Fig. 5 (a), Fig. 5 (b), Fig. 5 (c) and Fig. 5 (d).Fig. 5 (a), Fig. 5 (b) and Fig. 5 (c) correspond respectively to NGA method, VS-NGA method and NVS-NGA method gained separation signal figure of the present invention, and Fig. 6 is PI mean value curve chart.Fig. 6 shows, NGA method restrains when 2700 step, VS-NGA restrains about 2300 steps, and the inventive method NVS-NGA restrains about 1500 steps, also shows to have minimum cross-talk error after the inventive method NVS-NGA convergence.Therefore, the separating property of the inventive method NVS-NGA is best, has minimum cross-talk error and rapid convergence speed.
Embodiment 2: test under non-stationary environment, hybrid matrix is A (k)=A
0+ B (k), B (k)=ρ B (k-1)+τ * randn (4), B (0) is the null matrix of 4 × 4, ρ=0.9, τ=0.0001, randn (4) is the random matrix on 4 rank, other condition is constant, the experiment of 100 Monte-Carlo Simulation PI mean value curve, as shown in Figure 7.Fig. 7 shows, compared with NGA, VS-NGA method, the inventive method NVS-NGA still has the fastest convergence rate and minimum cross-talk error, and therefore, the separating property of the inventive method NVS-NGA is also best.
Known from above-described embodiment, improved self-adaptive blind source separation method provided by the invention, compares with existing fixed step size and variable-step self-adaptive blind source separation method, has improved convergence rate, and has reduced cross-talk error, and separating property has obvious lifting.
The disclosed technological means of the present invention program is not limited only to the disclosed technological means of above-mentioned execution mode, also comprises the technical scheme being comprised of above technical characterictic combination in any.It should be pointed out that for those skilled in the art, under the premise without departing from the principles of the invention, can also make some improvements and modifications, these improvements and modifications are also considered as protection scope of the present invention.
Claims (4)
1. an improved self-adaptive blind source separation method, it is characterized in that: based on improved adaptive blind source separation system, realize, described improved adaptive blind source separation system comprises hybrid matrix A, separation matrix W (k) and the inverse system W in parallel with separation matrix W (k)
a(k), described W
a(k) with the contrary A of nonsingular hybrid matrix A
-1approximate, described blind source separation method comprises the steps:
Steps A, M the unknown and source signal S independent of each other (k)=[s
1(k), s
2(k) ..., s
m(k)]
tthrough improving unknown nonsingular hybrid matrix A in piece-rate system, be mixed to get observation signal X (k)=[x
1(k), x
2(k) ..., x
m(k)]
t; When ignoring transmission delay effect and noise, obtain X (k)=AS (k), k is time series, subscript T represents conjugate transpose; M is positive integer, represents the number of component in S (k); A is that M × M ties up matrix;
Step B, observation signal X (k)=[x that steps A is obtained
1(k), x
2(k) ..., x
m(k)]
tsend into simultaneously and improve separation matrix W (k) and W in piece-rate system
a(k), obtain respectively separation signal Y (k)=W (k) X (k) and Y
a(k)=W
a(k) X (k), wherein Y (k) is M × 1 dimensional vector, is an estimation of source signal S (k), its component is separate; W (k) is the final separation matrix that improves M × M dimension full rank in piece-rate system; W
a(k) contrary
it is the final estimation to improving unknown nonsingular hybrid matrix A in piece-rate system; W (k) and W
a(k) dimension is identical, and subscript " 1 " represents to get inverse operation;
Wherein separation matrix W (k) and W
a(k) more new formula is:
Wherein I representation unit matrix; F (Y (k)) is nonlinear activation primitive, and μ (k) is improved step factor, and its formula is:
μ(k)=β{|PI(C
G(k))|/α
2}exp{-[PI(C
G(k))]
2/(2α
2)},
Wherein, β and α are the control parameters of μ (k), and exp represents the exponential function take e the end of as, wherein PI (C
g(k) be) improved separating property index, its formula is:
3. improved self-adaptive blind source separation method according to claim 1 and 2, is characterized in that: described f (Y (k))=Y
3(k).
4. improved self-adaptive blind source separation method according to claim 1 and 2, is characterized in that: described separation matrix W (k) and W
a(k) more new formula obtains as follows:
Step a, utilizes the relation of mutual information and comentropy, and the cost function of piece-rate system is defined as
In formula, H (y
m(k)) be m separation signal y in separation signal vector Y (k)
m(k) entropy, p
y(y
m(k)) be m separation signal y in separation signal vector Y (k)
m(k) marginal probability density, E represents mathematic expectaion computing, and ln represents the natural logrithm take e the end of as, and det represents to get the determinant of W (k);
Step b, calculates the natural gradient of J (k) to W (k)
Step c, obtains separation matrix W (k) and W by J (k) to the natural gradient of W (k)
a(k) more new formula
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CN109086686B (en) * | 2018-07-12 | 2022-09-30 | 西安电子科技大学 | Blind source separation method under time-varying channel based on self-adaptive momentum factor |
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