CN103812808B - A kind of it is applicable to plural blind source separation method and the system that source number dynamically changes - Google Patents

Abstract

The present invention discloses and a kind of is applicable to plural blind source separation method and the system that source number dynamically changes.Described method includes: obtain observation signal；According to described observation signal, estimate the number of source signal；According to described number, from described observation signal, isolate source signal.Use method or the system of the present invention, in the case of the number at source signal is dynamically change, and the concrete signal form of expression of source signal is also the unknown, it is also possible to separated by source signal from the signal observed.Concrete, when the form of expression of source signal is plural form, it is also possible to from observation signal, isolate the source signal of plural form.

Description

A kind of it is applicable to plural blind source separation method and the system that source number dynamically changes

Technical field

The present invention relates to signal processing field, particularly relate to a kind of be applicable to the plural blind source separating that source number dynamically changes Method and system.

Background technology

Blind source separating is also known as Blind Signal Separation (blind source separation or blind signal Separation, BSS), its problem to be solved is not know source signal and (unknown aliasing system is not i.e. being received system System) parameter do in the case of any prior information assumes, how according only to the statistical iteration characteristic of signal by source signal from sight The aliasing signal measured recovers.

Source number refers to the number of source signal.As a example by mobile phone, when mobile phone runs voice procedure and upload program simultaneously, should Mobile phone can launch two different source signals simultaneously, and when mobile phone simply runs upload program, this mobile phone can only be launched One source signal.

In prior art, when the number of source signal is dynamically change, and the concrete signal form of expression of source signal is also It is unknown, does not also have a kind of method can be separated by source signal from the signal observed.

Summary of the invention

It is an object of the invention to provide and a kind of be applicable to plural blind source separation method and the system that source number dynamically changes, permissible In the case of number at source signal is dynamically change, and the concrete signal form of expression of source signal is also the unknown, from sight Source signal is separated by the signal measured.

For achieving the above object, the invention provides following scheme:

A kind of it is applicable to the plural blind source separation method that source number dynamically changes, including:

Obtain observation signal x (t)；

According to formula $\stackrel{\‾}{x}\left(t\right)=\frac{t-1}{t}\stackrel{\‾}{x}(t-1)+\frac{1}{t}x\left(t\right),$

$\mathrm{\Δx}\left(t\right)=\stackrel{\‾}{x}\left(t\right)-\stackrel{\‾}{x}(t-1),$

$C\left(t\right)=\frac{t-1}{t}[C(t-1)+\mathrm{\Δx}\left(t\right)\mathrm{\Δx}{\left(t\right)}^H]+\frac{1}{t}{[\mathrm{\Δx}\left(t\right)-\stackrel{\‾}{x}\left(t\right)][\mathrm{\Δx}\left(t\right)-\stackrel{\‾}{x}\left(t\right)]}^H,$ Calculate the association side of x (t) Difference matrix；

Wherein, t is the serial number of the observation signal got according to time order and function order, and the initial value of t is 1；For x The average of (t)；C (t) represents the covariance matrix of x (t)；Δ x (t) is the increment of x (t)；

According to formula ${\mathrm{\ψ}}^{\left(i\right)}=\mathrm{diag}\left(C\left(t\right){-\widehat{C{\left(t\right)}_i}\widehat{C{\left(t\right)}_i}}^H\right),$ $\widehat{C{\left(t\right)}_i}=U_i{\mathrm{\Λ}}_i$

$\hat{n}\left(t\right)=\underset{i}{\arg \min }\left\{\underset{i}{\arg \max }\right[{\left|\mathrm{trace}({\mathrm{\ψ}}^{\left(i\right)}-{\widehat{\mathrm{\ψ}}}^{\left(m\right)})\right|}^2\left]\right\},i=\mathrm{1,2},...,m,$

$C{\widetilde{\hat{\left(t\right)}}}_m={\tilde{U}}_m{\widetilde{\mathrm{\Λ}}}_m,$

${\widetilde{\mathrm{\ψ}}}^{\left(m\right)}=\mathrm{diag}(C\left(t\right)-\widetilde{\hat{C}{\left(t\right)}_m}{\widetilde{\hat{C}{\left(t\right)}_m}}^H)$

Calculate the number of source signal；

Wherein, m is the number of observation signal x (t) corresponding to t, Λ_iFor diagonal matrix, Λ_iDiagonal element be association side According to tactic front i eigenvalue from big to small, U in the eigenvalue of difference Matrix C (t)_iFor the matrix of m row m row, U_i's With Λ in diagonal_iIn the corresponding position of eigenvalue on, have and Λ_iIn the corresponding characteristic vector of eigenvalue, U_iIn Other element be zero,Number for source signal；For diagonal and Λ_mThe matrix intersected, and two matrixes exist Element sequence on diagonal is contrary；The matrix arranged for m row m,Diagonal inIn eigenvalue phase On corresponding position, have withIn the corresponding characteristic vector of eigenvalue,In other element be zero；

JudgeWhether it is equal toObtain the first judged result；

When described first judged result is for being, it is calculated albefaction observation signal z (t) according to z (t)=B (t) x (t)；

When described first judged result is no, randomly generate m of t-1 momentDimensional vector w_i(t-1), i=1, 2 ..., m, wherein w_i(t-1) for making W (t-1)^HThe optimal solution of A (t-1)=I mixes the vector of the i-th row of matrix W (t-1), and I is single Bit matrix；It is calculated albefaction observation signal z (t) according to z (t)=B (t) x (t)；Wherein, B (t) is whitening matrix；A (t-1) is The t-1 moment makes source signal become the unknown time-varying complex linear hybrid system of observation signal；

According to formula $w(t+1)=\underset{w}{\arg \max }\left|K\left(y\right)\right|$

||w(t+1)||²=1

$\begin{array}{c}K\left(y\right)\stackrel{\mathrm{\Δ}}{=}E\left[{\left|y\left(t\right)\right|}^4\right]-2{\left\{E\right[{\left|y\left(t\right)\right|}^2\left]\right\}}^2-{\left|E\right[y{\left(t\right)}^2\left]\right|}^2\\ =E\left\{{\left[y\left(t\right)y{\left(t\right)}^{*}\right]}^2\right\}-2E{\left[y\left(t\right){y\left(t\right)}^{*}\right]}^2\\ -E\left[y\left(t\right)y\left(t\right)\right]E\left[y^{*}\left(t\right)y^{*}\left(t\right)\right]\end{array}$

${{\▿}^{*}}_{w}J=2\left\{E\right[{\left|y\left(t\right)\right|}^{2}y{\left(t\right)}^{*}z\left(t\right)]-2E[y{\left(t\right)}^{*}z\left(t\right)]-E[y{\left(t\right)}^{*2}\left]E\right[y\left(t\right)z\left(t\right)\left]\right\}$

H₁J=4{E[|y(t)|²z(t)z(t)^H]-E[y(t)^*z(t)]E[y(t)z(t)^*]^T-E[y(t)z(t)]E[y(t)^*z (t)^*]^T-I}

H₂J=2{E[y(t)^*2z(t)z(t)^T]-2E[y(t)^*z(t)]E[y(t)^*z(t)]^T-2E[y(t)^*2]E[z(t)z(t )^T]}

y(t)=w(t)z(t)；

Wherein, w (t) is that t makes W (t)^HThe optimal solution of A (t)=I mixes the column vector of a m dimension of matrix W (t)；

$w(t+1)=\mathrm{sign}\left\{K\right[y\left(t\right)\left]\right\}[-{{\▿}^{*}}_{w}J+H_1\mathrm{Jw}\left(t\right)+H_2\mathrm{Jw}{\left(t\right)}^{*}]$

$E[\·\left(t\right)]=\frac{t-1}{t}E[\·(t-1)]+\frac{1}{t}\·\left(t\right)$

Calculate m new explanation w (t+1)；

Wherein, w (t+1) represents the new explanation after iteration, i.e. the t+1 moment makes W (t+1)^HThe optimal solution of A (t+1)=I mixes square I-th column vector in Zhen；K [y (t)] represents the kurtosis of y (t)；E is for asking expectation computing to accord with, and E [(t)] expression finds a function The expected value of (t), this expectation computing symbol represents the function expression following computing of execution in expectation computing symbol: $E[\·\left(t\right)]=\frac{t-1}{t}E[\·(t-1)]+\frac{1}{t}\·\left(t\right),$

According to formula $w_i\left(t\right)=w_i\left(t\right)-\underset{k=1}{\overset{i-1}{\mathrm{\Σ}}}{w}_k\left(t\right)w_k{\left(t\right)}^H{w}_i\left(t\right),$

$w_i\left(t\right)=\frac{w_i\left(t\right)}{\left|\right|w_i\left(t\right)\left|\right|},i=\mathrm{1,2},...,m$

Remove m new explanation w_iDependency between (t)；

According to formulaIt is calculated the value of source signal

Wherein, W (t)=[w₁(t)^Hw₂(t)^H…w_m(t)^H]。

A kind of it is applicable to the plural blind source separation system that source number dynamically changes, including:

Acquiring unit, is used for obtaining observation signal x (t)；

Source signal number calculating unit, for according to formula

$\mathrm{\Δx}\left(t\right)=\stackrel{\‾}{x}\left(t\right)-\stackrel{\‾}{x}(t-1),$

$C\left(t\right)=\frac{t-1}{t}[C(t-1)+\mathrm{\Δx}\left(t\right)\mathrm{\Δx}{\left(t\right)}^H]+\frac{1}{t}[\mathrm{\Δx}\left(t\right)-\stackrel{\‾}{x}\left(t\right)]{[\mathrm{\Δx}\left(t\right)-\stackrel{\‾}{x}\left(t\right)]}^H,$ Calculate the association side of x (t) Difference matrix；

Wherein, t is the serial number of the observation signal got according to time order and function order, and the initial value of t is 1；For x The average of (t)；C (t) represents the covariance matrix of x (t)；Δ x (t) is the increment of x (t)；

According to formula ${\mathrm{\ψ}}^{\left(i\right)}=\mathrm{diag}\left(C\left(t\right){-\widehat{C{\left(t\right)}_i}\widehat{C{\left(t\right)}_i}}^H\right),$ $\widehat{C{\left(t\right)}_i}=U_i{\mathrm{\Λ}}_i$

$\hat{n}\left(t\right)=\underset{i}{\arg \min }\left\{\underset{i}{\arg \max }\right[{\left|\mathrm{trace}({\mathrm{\ψ}}^{\left(i\right)}-{\widehat{\mathrm{\ψ}}}^{\left(m\right)})\right|}^2\left]\right\},i=\mathrm{1,2},...,m,$

$C{\widetilde{\hat{\left(t\right)}}}_m={\tilde{U}}_m{\widetilde{\mathrm{\Λ}}}_m,$

${\widetilde{\mathrm{\ψ}}}^{\left(m\right)}=\mathrm{diag}(C\left(t\right)-\widetilde{\hat{C}{\left(t\right)}_m}{\widetilde{\hat{C}{\left(t\right)}_m}}^H)$

Calculate the number of source signal；

Wherein, m is the number of observation signal x (t) corresponding to t, Λ_iFor diagonal matrix, Λ_iDiagonal element be association side According to tactic front i eigenvalue from big to small, U in the eigenvalue of difference Matrix C (t)_iFor the matrix of m row m row, U_i's With Λ in diagonal_iIn the corresponding position of eigenvalue on, have and Λ_iIn the corresponding characteristic vector of eigenvalue, U_iIn Other element be zero,Number for source signal；For diagonal and Λ_mThe matrix intersected, and two matrixes are right Element sequence on linea angulata is contrary；The matrix arranged for m row m,Diagonal inIn eigenvalue corresponding Position on, have withIn the corresponding characteristic vector of eigenvalue,In other element be zero；

Source signal separative element, is used for judgingWhether it is equal toObtain the first judged result；

When described first judged result is for being, it is calculated albefaction observation signal z (t) according to z (t)=B (t) x (t)；

When described first judged result is no, randomly generate m of t-1 momentDimensional vector w_i(t-1), i=1, 2 ..., m, wherein w_i(t-1) for making W (t-1)^HThe optimal solution of A (t-1)=I mixes the vector of the i-th row of matrix W (t-1), and I is single Bit matrix；It is calculated albefaction observation signal z (t) according to z (t)=B (t) x (t)；Wherein, B (t) is whitening matrix；A (t-1) is The t-1 moment makes source signal become the unknown time-varying complex linear hybrid system of observation signal；

According to formula $w(t+1)=\underset{w}{\arg \max }\left|K\left(y\right)\right|$

||w(t+1)||²=1

$\begin{array}{c}K\left(y\right)\stackrel{\mathrm{\Δ}}{=}E\left[{\left|y\left(t\right)\right|}^4\right]-2{\left\{E\right[{\left|y\left(t\right)\right|}^2\left]\right\}}^2-{\left|E\right[y{\left(t\right)}^2\left]\right|}^2\\ =E\left\{{\left[y\left(t\right)y{\left(t\right)}^{*}\right]}^2\right\}-2E{\left[y\left(t\right){y\left(t\right)}^{*}\right]}^2\\ -E\left[y\left(t\right)y\left(t\right)\right]E\left[y^{*}\left(t\right)y^{*}\left(t\right)\right]\end{array}$

${{\▿}^{*}}_{w}J=2\left\{E\right[{\left|y\left(t\right)\right|}^{2}y{\left(t\right)}^{*}z\left(t\right)]-2E[y{\left(t\right)}^{*}z\left(t\right)]-E[y{\left(t\right)}^{*2}\left]E\right[y\left(t\right)z\left(t\right)\left]\right\}$

H₁J=4{E[|y(t)|²z(t)z(t)^H]-E[y(t)^*z(t)]E[y(t)z(t)^*]^T-E[y(t)z(t)]E[y(t)^*z (t)^*]^T-I}

H₂J=2{E[y(t)^*2z(t)z(t)^T]-2E[y(t)^*z(t)]E[y(t)^*z(t)]^T-2E[y(t)^*2]E[z(t)z(t )^T]}

y(t)=w(t)z(t)；Wherein, w (t) is that t makes W (t)^HThe optimal solution of A (t)=I mixes of matrix W (t) The column vector of m dimension；

$w(t+1)=\mathrm{sign}\left\{K\right[y\left(t\right)\left]\right\}[-{{\▿}^{*}}_{w}J+H_1\mathrm{Jw}\left(t\right)+H_2\mathrm{Jw}{\left(t\right)}^{*}]$

$E[\·\left(t\right)]=\frac{t-1}{t}E[\·(t-1)]+\frac{1}{t}\·\left(t\right)$

CalculateIndividual new explanation w₊；

Wherein, w (t+1) represents the new explanation after iteration, i.e. the t+1 moment makes W (t+1)^HThe optimal solution of A (t+1)=I mixes square I-th column vector in Zhen；K [y (t)] represents the kurtosis of y (t)；E is for asking expectation computing to accord with, and E [(t)] expression finds a function The expected value of (t), this expectation computing symbol represents the function expression following computing of execution in expectation computing symbol: $E[\·\left(t\right)]=\frac{t-1}{t}E[\·(t-1)]+\frac{1}{t}\·\left(t\right)$

According to formula $w_i\left(t\right)=w_i\left(t\right)-\underset{k=1}{\overset{i-1}{\mathrm{\Σ}}}{w}_k\left(t\right)w_k{\left(t\right)}^H{w}_i\left(t\right),$

$w_i\left(t\right)=\frac{w_i\left(t\right)}{\left|\right|w_i\left(t\right)\left|\right|},$

Remove m new explanation w_iDependency between (t)；

According to formulaIt is calculated the value of source signal

Wherein, W (t)=[w₁(t)^Hw₂(t)^H…w_m(t)^H]。

The specific embodiment provided according to the present invention, the invention discloses techniques below effect:

The embodiment of the present invention is applicable to plural blind source separation method and the system that source number dynamically changes, by above public Formula, according to described observation signal, can estimate the number of source signal；According to described number, isolate from described observation signal Source signal；Thus be dynamically change at the number of source signal, and the concrete signal form of expression of source signal is also unknown In the case of, it is also possible to from the signal observed, source signal is separated.

Accompanying drawing explanation

In order to be illustrated more clearly that the embodiment of the present invention or technical scheme of the prior art, below will be to institute in embodiment The accompanying drawing used is needed to be briefly described, it should be apparent that, the accompanying drawing in describing below is only some enforcements of the present invention Example, for those of ordinary skill in the art, on the premise of not paying creative work, it is also possible to according to these accompanying drawings Obtain other accompanying drawing.

Fig. 1 is the general flow chart being applicable to the plural blind source separation method embodiment that source number dynamically changes of the present invention；

Fig. 2 is the structure chart being applicable to the plural blind source separation system embodiment that source number dynamically changes of the present invention.

Detailed description of the invention

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete Describe, it is clear that described embodiment is only a part of embodiment of the present invention rather than whole embodiments wholely.Based on Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under not making creative work premise Embodiment, broadly falls into the scope of protection of the invention.

Understandable for enabling the above-mentioned purpose of the present invention, feature and advantage to become apparent from, real with concrete below in conjunction with the accompanying drawings The present invention is further detailed explanation to execute mode.

Fig. 1 is the general flow chart being applicable to the plural blind source separation method embodiment that source number dynamically changes of the present invention.As Shown in Fig. 1, this method mainly comprises the steps that

Step 101: obtain observation signal；

Step 102: according to described observation signal, estimate the number of source signal；

Step 103: according to described number, isolate source signal from described observation signal.

Concrete, step 102 can use following manner to realize:

The observation signal got might as well be referred to as x (t)；

According to formula $\stackrel{\‾}{x}\left(t\right)=\frac{t-1}{t}\stackrel{\‾}{x}(t-1)+\frac{1}{t}x\left(t\right),$

$\mathrm{\Δx}\left(t\right)=\stackrel{\‾}{x}\left(t\right)-\stackrel{\‾}{x}(t-1),$

$C\left(t\right)=\frac{t-1}{t}[C(t-1)+\mathrm{\Δx}\left(t\right)\mathrm{\Δx}{\left(t\right)}^H]+\frac{1}{t}{[\mathrm{\Δx}\left(t\right)-\stackrel{\‾}{x}\left(t\right)][\mathrm{\Δx}\left(t\right)-\stackrel{\‾}{x}\left(t\right)]}^H,$ Calculate the association side of x (t) Difference matrix；

Wherein, t is the serial number of the observation signal got according to time order and function order, and the initial value of t is 1；For x The average of (t)；C (t) represents the covariance matrix of x (t)；Δ x (t) is the increment of x (t)；

According to formula ${\mathrm{\ψ}}^{\left(i\right)}=\mathrm{diag}\left(C\left(t\right){-\widehat{C{\left(t\right)}_i}\widehat{C{\left(t\right)}_i}}^H\right),$ $\widehat{C{\left(t\right)}_i}=U_i{\mathrm{\Λ}}_i$

$\hat{n}\left(t\right)=\underset{i}{\arg \min }\left\{\underset{i}{\arg \max }\right[{\left|\mathrm{trace}({\mathrm{\ψ}}^{\left(i\right)}-{\widehat{\mathrm{\ψ}}}^{\left(m\right)})\right|}^2\left]\right\},i=\mathrm{1,2},...,m,$

$C{\widetilde{\hat{\left(t\right)}}}_m={\tilde{U}}_m{\widetilde{\mathrm{\Λ}}}_m,$

${\widetilde{\mathrm{\ψ}}}^{\left(m\right)}=\mathrm{diag}(C\left(t\right)-\widetilde{\hat{C}{\left(t\right)}_m}{\widetilde{\hat{C}{\left(t\right)}_m}}^H)$

Calculate the number of source signal；

Wherein, m is the number of observation signal x (t) corresponding to t, Λ_iFor diagonal matrix, Λ_iDiagonal element be association side According to tactic front i eigenvalue from big to small, U in the eigenvalue of difference Matrix C (t)_iFor the matrix of m row m row, U_i's With Λ in diagonal_iIn the corresponding position of eigenvalue on, have and Λ_iIn the corresponding characteristic vector of eigenvalue, U_iIn Other element be zero,Number for source signal；For diagonal and Λ_mThe matrix intersected, and two matrixes exist Element sequence on diagonal is contrary；The matrix arranged for m row m,Diagonal inIn eigenvalue relative On the position answered, have withIn the corresponding characteristic vector of eigenvalue,In other element be zero；

In above-mentioned equation, Λ_iIn the element removed outside diagonal element be 0.Following formula is Λ_mWithExpression formula

${\mathrm{\Λ}}_m=\left[\begin{array}{ccccc}{\mathrm{\λ}}_1& 0& 0& ...& 0\\ 0& {\mathrm{\λ}}_2& 0& ...& 0\\ .& .& .& & \\ .& .& .& ...& 0\\ .& .& .& & \\ 0& ...& ...& & {\mathrm{\λ}}_m\end{array}\right]$ ${\widetilde{\mathrm{\Λ}}}_m=\left[\begin{array}{ccccc}0& 0& ...& 0& {\mathrm{\λ}}_1\\ 0& 0& ...& {\mathrm{\λ}}_2& 0\\ & & .& .& .\\ 0& ...& .& .& .\\ & & .& .& .\\ {\mathrm{\λ}}_m& ...& ...& & 0\end{array}\right]$

It can be seen thatFor diagonal and Λ_mThe matrix intersected, and the element sequence that two matrixes are on the diagonal It is contrary.

Step 103 can use following manner to realize:

JudgeWhether it is equal toObtain the first judged result；

When described first judged result is for being, it is calculated albefaction observation signal z (t) according to z (t)=B (t) x (t)；

When described first judged result is no, randomly generate m w_i(t-1)Dimensional vector w_-i, i=1,2 ..., M, wherein w_i(t-1) be the t-1 observation signal corresponding make W (t-1)^HThe optimal solution of A (t-1)=I mixes matrix, and I is unit Matrix；It is calculated albefaction observation signal z (t) according to z (t)=B (t) x (t)；Wherein, B (t) is whitening matrix；A (t-1) is The unknown time-varying complex linear hybrid system making source signal become observation signal that t-1 observation signal is corresponding；

According to formula $w_{+i}=-{{\▿}^{*}}_{w}J+H_{1}J{w}_{-i}+H_{2}J{w_{-i}}^{*}$

$w\_=\underset{w}{\arg \max }\left|K\left(y\right)\right|,$ ||w_-||²=1

$\begin{array}{c}K\left(y\right)\stackrel{\mathrm{\Δ}}{=}E\left[{\left|y\left(t\right)\right|}^4\right]-2{\left\{E\right[{\left|y\left(t\right)\right|}^2\left]\right\}}^2-{\left|E\right[y{\left(t\right)}^2\left]\right|}^2\\ =E\left\{{\left[y\left(t\right)y{\left(t\right)}^{*}\right]}^2\right\}-2E{\left[y\left(t\right){y\left(t\right)}^{*}\right]}^2\\ -E\left[y\left(t\right)y\left(t\right)\right]E\left[y^{*}\left(t\right)y^{*}\left(t\right)\right]\end{array}$

${{\▿}^{*}}_{w}J=2\left\{E\right[{\left|y\left(t\right)\right|}^{2}y{\left(t\right)}^{*}z\left(t\right)]-2E[y{\left(t\right)}^{*}z\left(t\right)]-E[y{\left(t\right)}^{*2}\left]E\right[y\left(t\right)z\left(t\right)\left]\right\}$

H₁J=4{E[|y(t)|²z(t)z(t)^H]-E[y(t)^*z(t)]E[y(t)z(t)^*]^T-E[y(t)z(t)]E[y(t)^*z (t)^*]^T-I}

H₂J=2{E[y(t)^*2z(t)z(t)^T]-2E[y(t)^*z(t)]E[y(t)^*z(t)]^T-2E[y(t)^*2]E[z(t)z(t )^T]}

y(t)=w(t)z(t)；

Wherein, w (t) is that t makes W (t)^HThe optimal solution of A (t)=I mixes the column vector of a m dimension of matrix W (t)；

$w(t+1)=\mathrm{sign}\left\{K\right[y\left(t\right)\left]\right\}[-{{\▿}^{*}}_{w}J+H_1\mathrm{Jw}\left(t\right)+H_2\mathrm{Jw}{\left(t\right)}^{*}]$

$E[\·\left(t\right)]=\frac{t-1}{t}E[\·(t-1)]+\frac{1}{t}\·\left(t\right)$

CalculateIndividual new explanation w₊；

Wherein, w (t+1) represents the new explanation after iteration, i.e. the t+1 moment makes W (t+1)^HThe optimal solution of A (t+1)=I mixes square I-th column vector in Zhen；K [y (t)] represents the kurtosis of y (t)；E is for asking expectation computing to accord with, and E [(t)] expression finds a function The expected value of (t), this expectation computing symbol represents the function expression following computing of execution in expectation computing symbol: $E[\·\left(t\right)]=\frac{t-1}{t}E[\·(t-1)]+\frac{1}{t}\·\left(t\right),$

According to formula $w_i\left(t\right)=w_i\left(t\right)-\underset{k=1}{\overset{i-1}{\mathrm{\Σ}}}{w}_k\left(t\right)w_k{\left(t\right)}^H{w}_i\left(t\right),$

$w_i\left(t\right)=\frac{w_i\left(t\right)}{\left|\right|w_i\left(t\right)\left|\right|},$

By this formula above, n (t) individual new explanation w can be removed₊Between dependency；

According to formulaIt is calculated the value of source signal

Wherein, W (t)=[w₁(t)^Hw₂(t)^H…w_m(t)^H]。

According to formulaM new explanation w may finally be utilized_iT () isolates from x (t)Individual source is believed Number.

It should be noted that the method for the embodiment of the present invention, source signal can be the signal of plural form.The present invention implements The method of example, from observation signal, can isolate the source signal of plural form.Certainly, if source signal can use real number table Show, then the method that can also use the present invention, be equivalent to calculate during try to achieve source signal plural number imaginary part value be Zero.

In sum, in the present embodiment, by above formula, the number of source signal according to described observation signal, can be estimated Mesh；According to described number, from described observation signal, isolate source signal；Thus be dynamically change at the number of source signal, And in the case of the concrete signal form of expression of source signal is also the unknown, it is also possible to from the signal observed, source signal is divided Separate out.

The invention also discloses and a kind of be applicable to the plural blind source separation system that source number dynamically changes.Fig. 2 is the present invention's It is applicable to the structure chart of the plural blind source separation system embodiment that source number dynamically changes.As in figure 2 it is shown, this system includes:

Acquiring unit 201, is used for obtaining observation signal x (t)；

Source signal number calculating unit 202, for according to formula

$\mathrm{\Δx}\left(t\right)=\stackrel{\‾}{x}\left(t\right)-\stackrel{\‾}{x}(t-1),$

$C\left(t\right)=\frac{t-1}{t}[C(t-1)+\mathrm{\Δx}\left(t\right)\mathrm{\Δx}{\left(t\right)}^H]+\frac{1}{t}{[\mathrm{\Δx}\left(t\right)-\stackrel{\‾}{x}\left(t\right)][\mathrm{\Δx}\left(t\right)-\stackrel{\‾}{x}\left(t\right)]}^H,$ Calculate the association side of x (t) Difference matrix；

Wherein, t is the serial number of the observation signal got according to time order and function order, and the initial value of t is 1；For x The average of (t)；C (t) represents the covariance matrix of x (t)；Δ x (t) is the increment of x (t)；

According to formula ${\mathrm{\ψ}}^{\left(i\right)}=\mathrm{diag}\left(C\left(t\right){-\widehat{C{\left(t\right)}_i}\widehat{C{\left(t\right)}_i}}^H\right),$ $\widehat{C{\left(t\right)}_i}=U_i{\mathrm{\Λ}}_i$

$\hat{n}\left(t\right)=\underset{i}{\arg \min }\left\{\underset{i}{\arg \max }\right[{\left|\mathrm{trace}({\mathrm{\ψ}}^{\left(i\right)}-{\widehat{\mathrm{\ψ}}}^{\left(m\right)})\right|}^2\left]\right\},i=\mathrm{1,2},...,m,$

$C{\widetilde{\hat{\left(t\right)}}}_m={\tilde{U}}_m{\widetilde{\mathrm{\Λ}}}_m,$

${\widetilde{\mathrm{\ψ}}}^{\left(m\right)}=\mathrm{diag}(C\left(t\right)-\widetilde{\hat{C}{\left(t\right)}_m}{\widetilde{\hat{C}{\left(t\right)}_m}}^H)$

Calculate the number of source signal；

Wherein, m is the number of observation signal x (t) corresponding to t, Λ_iFor diagonal matrix, Λ_iDiagonal element be association side According to tactic front i eigenvalue from big to small, U in the eigenvalue of difference Matrix C (t)_iFor the matrix of m row m row, U_i's With Λ in diagonal_iIn the corresponding position of eigenvalue on, have and Λ_iIn the corresponding characteristic vector of eigenvalue, U_iIn Other element be zero,Number for source signal；For diagonal and Λ_mThe matrix intersected, and two matrixes exist Element sequence on diagonal is contrary；The matrix arranged for m row m,Diagonal inIn eigenvalue relative On the position answered, have withIn the corresponding characteristic vector of eigenvalue,In other element be zero；

Source signal separative element 203, is used for judgingWhether it is equal toObtain the first judged result；

When described first judged result is for being, it is calculated albefaction observation signal z (t) according to z (t)=B (t) x (t)；

When described first judged result is no, randomly generate m of t-1 momentDimensional vector w_i(t-1), i=1, 2 ..., m, wherein w_i(t-1) for making W (t-1)^HThe optimal solution of A (t-1)=I mixes the vector of the i-th row of matrix W (t-1), and I is single Bit matrix；It is calculated albefaction observation signal z (t) according to z (t)=B (t) x (t)；Wherein, B (t) is whitening matrix；A (t-1) is The t-1 moment makes source signal become the unknown time-varying complex linear hybrid system of observation signal；

According to formula $w(t+1)=\underset{w}{\arg \max }\left|K\left(y\right)\right|$

||w(t+1)||²=1

$\begin{array}{c}K\left(y\right)\stackrel{\mathrm{\Δ}}{=}E\left[{\left|y\left(t\right)\right|}^4\right]-2{\left\{E\right[{\left|y\left(t\right)\right|}^2\left]\right\}}^2-{\left|E\right[y{\left(t\right)}^2\left]\right|}^2\\ =E\left\{{\left[y\left(t\right)y{\left(t\right)}^{*}\right]}^2\right\}-2E{\left[y\left(t\right){y\left(t\right)}^{*}\right]}^2\\ -E\left[y\left(t\right)y\left(t\right)\right]E\left[y^{*}\left(t\right)y^{*}\left(t\right)\right]\end{array}$

${{\▿}^{*}}_{w}J=2\left\{E\right[{\left|y\left(t\right)\right|}^{2}y{\left(t\right)}^{*}z\left(t\right)]-2E[y{\left(t\right)}^{*}z\left(t\right)]-E[y{\left(t\right)}^{*2}\left]E\right[y\left(t\right)z\left(t\right)\left]\right\}$

H₁J=4{E[|y(t)|²z(t)z(t)^H]-E[y(t)^*z(t)]E[y(t)z(t)^*]^T-E[y(t)z(t)]E[y(t)^*z (t)^*]^T-I}

H₂J=2{E[y(t)^*2z(t)z(t)^T]-2E[y(t)^*z(t)]E[y(t)^*z(t)]^T-2E[y(t)^*2]E[z(t)z(t )^T]}

y(t)=w(t)z(t)；

Wherein, w (t) is that t makes W (t)^HThe optimal solution of A (t)=I mixes the column vector of a m dimension of matrix W (t)；

$w(t+1)=\mathrm{sign}\left\{K\right[y\left(t\right)\left]\right\}[-{{\▿}^{*}}_{w}J+H_1\mathrm{Jw}\left(t\right)+H_2\mathrm{Jw}{\left(t\right)}^{*}]$

$E[\·\left(t\right)]=\frac{t-1}{t}E[\·(t-1)]+\frac{1}{t}\·\left(t\right)$

CalculateIndividual new explanation w₊；

Wherein, w (t+1) represents the new explanation after iteration, i.e. the t+1 moment makes W (t+1)^HThe optimal solution of A (t+1)=I mixes square I-th column vector in Zhen；K [y (t)] represents the kurtosis of y (t)；E is for asking expectation computing to accord with, and E [(t)] expression finds a function The expected value of (t), this expectation computing symbol represents the function expression following computing of execution in expectation computing symbol: $E[\·\left(t\right)]=\frac{t-1}{t}E[\·(t-1)]+\frac{1}{t}\·\left(t\right)$

According to formula $w_i\left(t\right)=w_i\left(t\right)-\underset{k=1}{\overset{i-1}{\mathrm{\Σ}}}{w}_k\left(t\right)w_k{\left(t\right)}^H{w}_i\left(t\right),$

$w_i\left(t\right)=\frac{w_i\left(t\right)}{\left|\right|w_i\left(t\right)\left|\right|},$

Remove m new explanation w_iDependency between (t)；

According to formulaIt is calculated the value of source signal

Wherein, W (t)=[w₁(t)^Hw₂(t)^H…w_m(t)^H]。

In sum, in the present embodiment, by above formula, the number of source signal according to described observation signal, can be estimated Mesh；According to described number, from described observation signal, isolate source signal；Thus be dynamically change at the number of source signal, And in the case of the concrete signal form of expression of source signal is also the unknown, it is also possible to from the signal observed, source signal is divided Separate out.

In this specification, each embodiment uses the mode gone forward one by one to describe, and what each embodiment stressed is and other The difference of embodiment, between each embodiment, identical similar portion sees mutually.For system disclosed in embodiment For, owing to it corresponds to the method disclosed in Example, so describe is fairly simple, relevant part sees method part and says Bright.

Principle and the embodiment of the present invention are set forth by specific case used herein, saying of above example Bright method and the core concept thereof being only intended to help to understand the present invention；Simultaneously for one of ordinary skill in the art, foundation The thought of the present invention, the most all will change.In sum, this specification content is not It is interpreted as limitation of the present invention.

Claims (2)

1. one kind is applicable to the plural blind source separation method that source number dynamically changes, it is characterised in that including:

Obtain observation signal x (t)；

According to formula

$\mathrm{\Δ}x\left(t\right)=\stackrel{\‾}{x}\left(t\right)-\stackrel{\‾}{x}(t-1),$

Calculate the covariance square of x (t) Battle array；

Wherein, t is the serial number of the observation signal got according to time order and function order, and the initial value of t is 1；For x's (t) Average；C (t) represents the covariance matrix of x (t)；Δ x (t) is the increment of x (t)；

According to formula

$\hat{n}\left(t\right)=\underset{i}{\arg \min }\{\underset{i}{\arg \max }\[|trace({\mathrm{\Ψ}}^{\left(i\right)}-{\widehat{\mathrm{\Ψ}}}^{\left(m\right)}){|}^2\]\},i=1,2,\mathrm{\Λ},m,$

$C{\left(\tilde{\hat{t}}\right)}_m={\tilde{U}}_m{\widetilde{\mathrm{\Λ}}}_m,$

${\widetilde{\mathrm{\Ψ}}}^{\left(m\right)}=diag\left(C\right(t)-{\widetilde{\hat{C}\left(t\right)}}_m{{\widetilde{\hat{C}\left(t\right)}}_m}^H)$

Calculate the number of source signal；

Wherein, m is the number of observation signal x (t) corresponding to t, Λ_iFor diagonal matrix, Λ_iDiagonal element be covariance square According to tactic front i eigenvalue from big to small, U in the eigenvalue of battle array C (t)_iFor the matrix of m row m row, U_iDiagonal angle With Λ in line_iIn the corresponding position of eigenvalue on, have and Λ_iIn the corresponding characteristic vector of eigenvalue, U_iIn its Its element is zero,Number for source signal；For diagonal and Λ_mThe matrix intersected, and two matrixes are at diagonal angle Element sequence on line is contrary；The matrix arranged for m row m,Diagonal inIn eigenvalue corresponding On position, have withIn the corresponding characteristic vector of eigenvalue,In other element be zero；

JudgeWhether it is equal toObtain the first judged result；

When described first judged result is for being, it is calculated albefaction observation signal z (t) according to z (t)=B (t) x (t)；

When described first judged result is no, randomly generate m of t-1 momentDimensional vector w_i(t-1), i=1,2, Λ, m, wherein w_i(t-1) for making W (t-1)^HThe optimal solution of A (t-1)=I mixes the vector of the i-th row of matrix W (t-1), and I is single Bit matrix；It is calculated albefaction observation signal z (t) according to z (t)=B (t) x (t)；Wherein, B (t) is whitening matrix；A(t-1) Source signal is made to become the unknown time-varying complex linear hybrid system of observation signal for the t-1 moment；

According to formula

||w(t+1)||²=1

$\begin{array}{c}K\[y\left(t\right)\]\stackrel{\mathrm{\Δ}}{=}E\[|y\left(t\right){|}^4\]-2{\{E\[|y\left(t\right){|}^2\]\}}^2-|E\[y{\left(t\right)}^2\]{|}^2\\ =E\left\{{\[y\left(t\right)y{\left(t\right)}^{*}\]}^2\right\}-2E{\[y\left(t\right)y{\left(t\right)}^{*}\]}^2\\ -E\[y\left(t\right)y\left(t\right)\]E\[y^{*}\left(t\right)y^{*}\left(t\right)\]\end{array}$

${{\▿}^{*}}_{w}J=2\{E\[|y\left(t\right){|}^{2}y{\left(t\right)}^{*}z\left(t\right)\]-2E\[y{\left(t\right)}^{*}z\left(t\right)\]-E\[y{\left(t\right)}^{*2}\]E\[y\left(t\right)z\left(t\right)\]\}$

H₁J=4{E [| y (t) |²z(t)z(t)^H]-E[y(t)^*z(t)]E[y(t)z(t)^*]^T-E[y(t)z(t)]E[y(t)^*z (t)^*]^T-I}

H₂J=2{E [y (t)^*2z(t)z(t)^T]-2E[y(t)^*z(t)]E[y(t)^*z(t)]^T-2E[y(t)^*2]E[z(t)z(t)^T]}

Y (t)=w (t) z (t)；

Wherein, w (t) is that t makes W (t)^HThe optimal solution of A (t)=I mixes the column vector of a m dimension of matrix W (t)；

$w(t+1)=sign\{K\[y\left(t\right)\]\}\[-{{\▿}^{*}}_{w}J+H_{1}Jw\left(t\right)+H_{2}Jw{\left(t\right)}^{*}\]$

$E\[\·\left(t\right)\]=\frac{t-1}{t}E\[\·(t-1)\]+\frac{1}{t}\·\left(t\right)$

Calculate m new explanation w (t+1)；

Wherein, w (t+1) represents the new explanation after iteration, i.e. the t+1 moment makes W (t+1)^HThe optimal solution of A (t+1)=I is mixed in matrix I-th column vector；K [y (t)] represents the kurtosis of y (t)；E is for asking expectation computing to accord with, and E [(t)] expression finds a function (t) Expected value, this expectation computing symbol represents the function expression following computing of execution in expectation computing symbol:

According to formula

$w_i\left(t\right)=\frac{w_i\left(t\right)}{\left|\right|w_i\left(t\right)\left|\right|},i=1,2,\mathrm{\Λ},m$

Remove m new explanation w_iDependency between (t)；

According to formulaIt is calculated the value of source signal

Wherein, W (t)=[w₁(t)^H w₂(t)^H L w_m(t)^H]。

2. one kind is applicable to the plural blind source separation system that source number dynamically changes, it is characterised in that including:

Acquiring unit, is used for obtaining observation signal x (t)；

Source signal number calculating unit, for according to formula

$\mathrm{\Δ}x\left(t\right)=\stackrel{\‾}{x}\left(t\right)-\stackrel{\‾}{x}(t-1),$

Calculate the covariance square of x (t) Battle array；

Wherein, t is the serial number of the observation signal got according to time order and function order, and the initial value of t is 1；For x's (t) Average；C (t) represents the covariance matrix of x (t)；Δ x (t) is the increment of x (t)；

According to formula

$\hat{n}\left(t\right)=\underset{i}{\arg \min }\{\underset{i}{\arg \max }\[|trace({\mathrm{\Ψ}}^{\left(i\right)}-{\widehat{\mathrm{\Ψ}}}^{\left(m\right)}){|}^2\]\},i=1,2,\mathrm{\Λ},m,$

$C{\left(\tilde{\hat{t}}\right)}_m={\tilde{U}}_m{\widetilde{\mathrm{\Λ}}}_m,$

${\widetilde{\mathrm{\Ψ}}}^{\left(m\right)}=diag\left(C\right(t)-{\widetilde{\hat{C}\left(t\right)}}_m{{\widetilde{\hat{C}\left(t\right)}}_m}^H)$

Calculate the number of source signal；

Wherein, m is the number of observation signal x (t) corresponding to t, Λ_iFor diagonal matrix, Λ_iDiagonal element be covariance square According to tactic front i eigenvalue from big to small, U in the eigenvalue of battle array C (t)_iFor the matrix of m row m row, U_iDiagonal angle With Λ in line_iIn the corresponding position of eigenvalue on, have and Λ_iIn the corresponding characteristic vector of eigenvalue, U_iIn its Its element is zero,Number for source signal；For diagonal and Λ_mThe matrix intersected, and two matrixes are at diagonal angle Element sequence on line is contrary；The matrix arranged for m row m,Diagonal inIn eigenvalue corresponding On position, have withIn the corresponding characteristic vector of eigenvalue,In other element be zero；

Source signal separative element, is used for judgingWhether it is equal toObtain the first judged result；

When described first judged result is for being, it is calculated albefaction observation signal z (t) according to z (t)=B (t) x (t)；

When described first judged result is no, randomly generate m of t-1 momentDimensional vector w_i(t-1), i=1,2, Λ, m, wherein w_i(t-1) for making W (t-1)^HThe optimal solution of A (t-1)=I mixes the vector of the i-th row of matrix W (t-1), and I is single Bit matrix；It is calculated albefaction observation signal z (t) according to z (t)=B (t) x (t)；Wherein, B (t) is whitening matrix；A(t-1) Source signal is made to become the unknown time-varying complex linear hybrid system of observation signal for the t-1 moment；

According to formula $w(t+1)=\underset{w}{\mathrm{argmax}}|K\[y\left(t\right)\]|$

||w(t+1)||²=1

$\begin{array}{c}K\[y\left(t\right)\]\stackrel{\mathrm{\Δ}}{=}E\[|y\left(t\right){|}^4\]-2{\{E\[|y\left(t\right){|}^2\]\}}^2-|E\[y{\left(t\right)}^2\]{|}^2\\ =E\left\{{\[y\left(t\right)y{\left(t\right)}^{*}\]}^2\right\}-2E{\[y\left(t\right)y{\left(t\right)}^{*}\]}^2\\ -E\[y\left(t\right)y\left(t\right)\]E\[y^{*}\left(t\right)y^{*}\left(t\right)\]\end{array}$

${{\▿}^{*}}_{w}J=2\{E\[|y\left(t\right){|}^{2}y{\left(t\right)}^{*}z\left(t\right)\]-2E\[y{\left(t\right)}^{*}z\left(t\right)\]-E\[y{\left(t\right)}^{*2}\]E\[y\left(t\right)z\left(t\right)\]\}$

H₁J=4{E [| y (t) |²z(t)z(t)^H]-E[y(t)^*z(t)]E[y(t)z(t)^*]^T-E[y(t)z(t)]E[y(t)^*z (t)^*]^T-I}

H₂J=2{E [y (t)^*2z(t)z(t)^T]-2E[y(t)^*z(t)]E[y(t)^*z(t)]^T-2E[y(t)^*2]E[z(t)z(t)^T]}

Y (t)=w (t) z (t)；Wherein, w (t) is that t makes W (t)^HThe optimal solution of A (t)=I mixes a m dimension of matrix W (t) Column vector；

$w(t+1)=sign\{K\[y\left(t\right)\]\}\[-{{\▿}^{*}}_{w}J+H_{1}Jw\left(t\right)+H_{2}Jw{\left(t\right)}^{*}\]$

$E\[\·\left(t\right)\]=\frac{t-1}{t}E\[\·(t-1)\]+\frac{1}{t}\·\left(t\right)$

CalculateIndividual new explanation w₊；

Wherein, w (t+1) represents the new explanation after iteration, i.e. the t+1 moment makes W (t+1)^HThe optimal solution of A (t+1)=I is mixed in matrix I-th column vector；K [y (t)] represents the kurtosis of y (t)；E is for asking expectation computing to accord with, and E [(t)] expression finds a function (t) Expected value, this expectation computing symbol represents the function expression following computing of execution in expectation computing symbol:

According to formula

$w_i\left(t\right)=\frac{w_i\left(t\right)}{\left|\right|w_i\left(t\right)\left|\right|},$

Remove m new explanation w_iDependency between (t)；

According to formulaIt is calculated the value of source signal

Wherein, W (t)=[w₁(t)^H w₂(t)^H L w_m(t)^H]。