CN108364659A - Frequency domain convolution Blind Signal Separation method based on multiple-objection optimization - Google Patents
Frequency domain convolution Blind Signal Separation method based on multiple-objection optimization Download PDFInfo
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Abstract
The present invention proposes a kind of frequency domain convolution Blind Signal Separation method based on multiple-objection optimization, for solving the problems, such as existing in the prior art to be easy to converge to degenerate solution, and can realize that source signal is less than the frequency domain convolution Blind Signal Separation of observation signal quantity, realize that step is：Obtain objective matrix set；Construct diagonalizable matrix B (ωk)；Construct non-orthogonal joint diagonalization Model for Multi-Objective Optimization；Using non-orthogonal joint diagonalization Model for Multi-Objective Optimization, to objective matrix setSeparation matrix W (ω on each frequency pointk) estimated；Obtain the estimated value of time domain source signal.The reliability of the present invention is high, has a wide range of application, and can be applied to the blind separation of the convolution mixed signals such as voice signal, signal of communication under the conditions of overdetermination.
Description
Technical field
The invention belongs to blind signal processing technology fields, are related to a kind of frequency domain convolution Blind Signal Separation method, and in particular to
A kind of frequency domain convolution Blind Signal Separation method based on multiple-objection optimization Joint diagonalization, voice is believed under the conditions of can be applied to overdetermination
Number, the blind separations of the convolution mixed signals such as signal of communication.
Background technology
Objective optimisation problems refer to just usually the optimum solution that object function is obtained by certain optimization algorithm.When excellent
The object function of change be one when referred to as single object optimization (Single-objective Optimization Problem,
SOP).When the object function of optimization there are two or it is more than two when referred to as multiple-objection optimization (Multi-objective
Optimization Problem,MOP).Solution different from single object optimization is finite solution, and the solution of multiple-objection optimization is typically one
Group equilibrium solution.
In the signal processing problems such as wireless communication, radar, sonar, often there is the recovery resource from multiple observation signals and believe
Number the problem of, blind signal separation technology provides potential solution for these problems.Blind Signal Separation problem early stage is studied
Relatively simple instantaneous mixed scenario is concentrated on, but in practical applications, such as " cocktail party " problem, it is contemplated that sound transmission
Multipath effect, the mixing voice signal observed are actually convolved mixtures voice signal.
The blind separating method of existing convolved mixtures voice signal is broadly divided into two class of frequency domain method and time domain, general in time domain
Carry out the method that joint block-diagonalization estimates separation matrix using to correlation matrix, the deficiency of this method be it is computationally intensive and
Often cause to become difficult to count under higher-dimension joint block-diagonalization problem, such as high-order convolved mixtures (serious reverberant ambiance)
It calculates.
On frequency domain generally the method that Joint diagonalization estimates separation matrix, this side are carried out using to power spectral density matrix
There is the problems such as being easy to converge to degenerate solution, hybrid matrix is required to be square formation, sequence is indefinite in rule.This greatly limits this
Application of the method in convolution Blind Signal Separation.Joint diagonalization algorithm is divided into as orthogonal Joint diagonalization algorithm and nonopiate
Diagonalization algorithm is closed, orthogonal Joint diagonalization algorithm requires separation matrix to be necessary for orthogonal matrix, although many times can be with
By whitening processing so that separation matrix meets orthogonality condition, but whitening processing can introduce extra error, lead to separating property
It is deteriorated.To avoid being deteriorated since whitening processing introduces separating property caused by error, now mostly using not requiring the separation matrix to be
The non-orthogonal joint diagonalization algorithm of orthogonal matrix.
The application study of non-orthogonal joint diagonalization algorithm is still in the junior stage, existing NOODLES methods, QDIAG
Method and ACDC methods all there are problems that being easy to converge to degenerate solution, and the reliability of separation is poor.J-Di methods, the side FFDIAG
Although method and Jacobilike methods avoid the problem of being easy to converge to degenerate solution, but all exist because limitation separation matrix is
Square formation causes the frequency domain convolution Blind Signal Separation that can only realize that source signal is equal with observation signal quantity, application range limited.
Invention content
It is an object of the invention to overcome above-mentioned the shortcomings of the prior art, it is proposed that a kind of based on multiple-objection optimization
Frequency domain convolution Blind Signal Separation method, for solve the problems, such as it is existing in the prior art be easy to converge to degenerate solution, and can
Realize that source signal is less than the frequency domain convolution Blind Signal Separation of observation signal quantity.
The present invention technical thought be：The convolution mixed signal of observation is transformed to the instantaneous mixing model of frequency domain,
The separation matrix that each frequency point is estimated using multiple-objection optimization non-orthogonal joint diagonalization algorithm, it is extensive in frequency domain using separation matrix
Multiple source signal, obtains source signal time domain waveform, specific implementation step is as follows after Fourier inversion：
(1) objective matrix set is obtained
(1a) M sensor receives the observation signal x from N number of source signal sensorm(t), observation signal vector x is formed
(t), x (t)=[x1(t),…,xM(t)]T, wherein N >=1, and M >=N, m indicate sensor serial number, m=1 ..., M；
(1b) divides x (t), obtains Q observation signal subvector, and calculate by each observation signal subvector
Objective matrix obtains the objective matrix set of Q × K objective matrix composition
Wherein, R (k, q) indicates the objective matrix on observation signal subvector q k-th of frequency point of section, k each observation signal of expression to
The objective matrix serial number calculated is measured, q indicates that observation signal subvector serial number, K indicate the mesh that each observation signal subvector calculates
Mark matrix number；
(2) construction diagonalizable matrix B (ωk)：
Construct the diagonalizable matrix B (ω that dimension is M × Nk), wherein ωkIndicate objective matrix setK-th of frequency point；
(3) non-orthogonal joint diagonalization Model for Multi-Objective Optimization is constructed：
Utilize R (k, q) and B (ωk) construction non-orthogonal joint diagonalization Model for Multi-Objective Optimization：
Wherein, bnIndicate diagonalizable matrix B (ωk) n-component column vector, min expression take minimum operate, max expression take
Maximum operation, Off () indicate the diagonal line operation of pulverised matrix, ()HExpression takes complex conjugate operation, det to matrix
() expression asks matrix determinant to operate；
(4) non-orthogonal joint diagonalization Model for Multi-Objective Optimization is utilized, to objective matrix setPoint on each frequency point
From matrix W (ωk) estimated：
Objective matrix set is arranged in (4a)The initial value of the diagonalizable matrix of first frequency point is B (ω1)=[I, 0]TIf
It is ψ to set conditional number threshold value, and setting iteration stopping condition threshold is λ, enables k=1, wherein I indicates N × N-dimensional unit matrix, []T
The transposition of representing matrix operates；
(4b) is to objective matrix setSeparation matrix W (ω on k-th of frequency pointk) estimated：
(4b.1) enables n=1；
(4b.2) calculates Hessian matrix QnAnd orthogonal intersection cast shadow matrix
Wherein, BnIndicate diagonalizable matrix B (ωk) matrix that remaining column vector is constituted after arranging of deletion n-th, I expression unit squares
Battle array, []-1The inversion operation of representing matrix；
(4b.3) calculates Hessian matrix QnConditional number κ (Qn), and judge κ (Qn) whether ＞ ψ true, if so, executing step
(4b.5), it is no to then follow the steps (4b.4)；
(4b.4) calculating matrix pairGeneralized eigenvalue decomposition, and by the corresponding feature of maximum generalized characteristic value
Vector is used as diagonalizable matrix B (ωk) the n-th row, and execute step (4b.7)；
(4b.5) calculates intermediary matrix C：
Wherein, U0Representing matrix QnThe corresponding eigenvectors matrix of MN+1 minimal eigenvalue；
(4b.6) calculates diagonalizable matrix B (ωk) the n-th column vector bnVector value：
bn=U0w
Wherein, w indicates the corresponding feature vector of maximum eigenvalue of intermediary matrix C；
(4b.7) enables n=n+1, and judges whether n≤N is true, if so, step (4b.2) is executed, it is no to then follow the steps
(4b.8)；
(4b.8) calculates cost function J (B (ωk)), and judge | J (B (ωk))J(B(ωk-1)) | whether ＞ λ are true, if
It is to execute step (4b.1), it is no to then follow the steps (4b.9)；
(4b.9) is to diagonalizable matrix B (ωk) complex conjugate is taken, obtain separation matrix W (ωk)；
(4c) enables k=k+1, and judges whether k≤K is true, if so, enabling B (ωk)=WH(ωk-1), and execute step
(4b), it is no to then follow the steps (5)；
(5) estimated value of time domain source signal is obtained：
(5a) calculates the source signal vector estimated value on q k-th of frequency point of section
Wherein, x (k, q) indicates the observation signal vector on q k-th of frequency point of section, W (ωk) indicate separation matrix；
(5b) is rightFourier inversion is carried out, time domain source signal estimated value is obtained, is realized to frequency domain convolution fanaticism number
Separation.
Compared with prior art, the present invention having following advantages：
(1) present invention is when estimating separation matrix, using multiple-objection optimization non-orthogonal joint diagonalization model, it is contemplated that right
The conditional number of diagonalized matrix avoids the problem of being easy to converge to degenerate solution, compared with prior art, improves convolution fanaticism number
The reliability of separation.
(2) constraint of diagonalizable matrix is become the conjugate transposition and diagonalizable matrix product to diagonalizable matrix by the present invention
Constraint, eliminate separation matrix be square formation limitation, can realize source signal be less than or equal to observation signal quantity frequency domain roll up
Product Blind Signal Separation, compared with prior art, application range is wider while avoiding being easy to converge to degenerate solution.
Description of the drawings
Fig. 1 is the implementation flow chart of the present invention；
Fig. 2 is right in the present inventionSeparation matrix W (ω on each frequency pointk) flow chart estimated；
Fig. 3 (a) is the oscillogram for 3 source signals that present invention emulation uses；
Fig. 3 (b) is the signal waveforms restored with NOODLES methods；
Fig. 3 (c) is the signal waveforms restored with ACDC methods；
Fig. 3 (d) is the signal waveforms restored with the method for the present invention.
Specific implementation mode
In the following with reference to the drawings and specific embodiments, present invention is further described in detail：
The present embodiment is based on a cocktail party scene, in the talk of three people received from 4 microphone sensors
Hold, the conversational speech of three people is isolated using the present invention.In this embodiment, sensor is microphone, the volume received
Product aliasing signal is voice signal.
Referring to Fig.1, a kind of frequency domain convolution Blind Signal Separation method based on multiple-objection optimization, includes the following steps：
Step 1) obtains objective matrix set
(1a) M electric signal sensor receives the observation signal x from N number of source signal sensorm(t), observation letter is formed
Number vector x (t), x (t)=[x1(t),…,xM(t)]T, wherein N >=1, and M >=N, m expression sensor serial number, m=1 ..., M,
In this embodiment, M=4, N=3；
(1b) divides x (t), obtains Q observation signal subvector, and calculate by each observation signal subvector
Objective matrix obtains the objective matrix set of Q × K objective matrix composition
Wherein, R (k, q) indicates the objective matrix on observation signal subvector q k-th of frequency point of section, k each observation signal of expression to
The objective matrix serial number calculated is measured, q indicates that observation signal subvector serial number, K indicate the mesh that each observation signal subvector calculates
X (t) is divided into Q=20 observation signal subvector by mark matrix number in this embodiment：
(1b.1) is to observation signal xm(t) Short Time Fourier Transform is carried out, frequency domain mixed signal vector x (k, q) is obtained,
In, k indicates that the objective matrix serial number that each observation signal subvector calculates, q indicate observation signal subvector serial number, and k=
1 ..., K, q=1 ..., Q, K indicate Fourier transformation frequency point number, the target square that value is calculated with each observation signal subvector
Battle array number is equal, in this embodiment, Fourier transformation frequency point number K=256：
(1b.11) calculates the discrete adding window Fourier transformation of K points：
Wherein, subscript i indicates that frame number, subscript m indicate to carry out Fourier transformation to the roads m observation signal,It indicates
Q sections of the roads m observation signal, window function length K, window function are slided along positive, and consecutive frame sliding distance is d=(1- μ)
K, μ are the overlap factor of adjacent two frame, and μ generally takes 50%；
Each frame frequency spectrum of the roads m mixed signal is merged into vector by (1b.12)Its
In, I indicates the frame number of q sections of discrete adding window Fourier transformations；
(1b.13) utilizes vector xm(k, q) constructs frequency domain mixed signal vector x (k, q)=[x1(k,q),...,xM(k,
q)]T；
(1b.2) calculates power spectral density matrix Rx(k,q)：
Rx(k, q)=E [x (k, q) xH(k,q)]；
(1b.3) estimates noise variance σ with principal component method2；
Objective matrix R (k, q), R (k, q)=R on (1b.4) calculating observation signal subvector q k-th of frequency point of sectionx
(k,q)-σ2I, wherein I indicates unit matrix.
Step 2) constructs diagonalizable matrix B (ωk)：
Construct the diagonalizable matrix B (ω that dimension is M × Nk), wherein ωkIndicate objective matrix setK-th of frequency point；
Step 3) constructs non-orthogonal joint diagonalization Model for Multi-Objective Optimization：
Utilize R (k, q) and B (ωk) construction non-orthogonal joint diagonalization Model for Multi-Objective Optimization：
Wherein, bnIndicate diagonalizable matrix B (ωk) n-component column vector, min expression take minimum operate, max expression take
Maximum operation, Off () indicate the diagonal line operation of pulverised matrix, ()HExpression takes complex conjugate operation, det to matrix
() expression asks matrix determinant to operate；
Step 4) utilizes non-orthogonal joint diagonalization Model for Multi-Objective Optimization, to objective matrix setOn each frequency point
Separation matrix W (ωk) estimated, the realization process of estimation is as shown in Figure 2：
Objective matrix set is arranged in (4a)The initial value of the diagonalizable matrix of first frequency point is B (ω1)=[I, 0]TIf
It is ψ to set conditional number threshold value, and the order of magnitude of ψ is generally 103, setting iteration stopping condition threshold be λ, the order of magnitude be generally 10-2,
Enable k=1, wherein I indicates N × N-dimensional unit matrix, []TThe transposition of representing matrix operates；
(4b) is to objective matrix setSeparation matrix W (ω on k-th of frequency pointk) estimated：
(4b.1) enables n=1；
(4b.2) calculates Hessian matrix QnAnd orthogonal intersection cast shadow matrix
Wherein, BnIndicate diagonalizable matrix B (ωk) matrix that remaining column vector is constituted after arranging of deletion n-th, I expression unit squares
Battle array, []-1The inversion operation of representing matrix；
(4b.3) calculates Hessian matrix QnConditional number κ (Qn), and judge κ (Qn) whether ＞ ψ true, if so, the gloomy square in sea
Battle array QnIt is ill, executes step 4b.5), no to then follow the steps 4b.4), Hessian matrix QnConditional number κ (Qn) calculate as the following formula
It carries out：
Wherein, []-1The inversion operation of representing matrix, | | | | expression asks norm to operate；
(4b.4) calculating matrix pairGeneralized eigenvalue decomposition, and by the corresponding feature of maximum generalized characteristic value
Vector is used as diagonalizable matrix B (ωk) n-th row, and execute step 4b.7), wherein the corresponding feature of maximum generalized characteristic value
Vector, obtaining step are：
To matrix pairGeneralized eigenvalue decomposition is carried out, matrix pair is obtainedGeneralized eigenvalue constitute
The matrix V that diagonal matrix D and the corresponding feature vector of generalized eigenvalue are constituted, and using the first row of V as matrix pair
The corresponding feature vector of maximum generalized eigenvalue, generalized eigenvalue decomposition formula are：
Wherein, eig () indicates generalized eigenvalue decomposition operation；
(4b.5) calculates intermediary matrix C：
Wherein, U0Representing matrix QnThe corresponding eigenvectors matrix of M-N1 minimal eigenvalue；
(4b.6) calculates diagonalizable matrix B (ωk) the n-th column vector bnVector value：
bn=U0w
Wherein, w indicates the corresponding feature vector of maximum eigenvalue of intermediary matrix C；
(4b.7) enables n=n+1, and judges whether n≤N is true, if so, step (4b.2) is executed, it is no to then follow the steps
(4b.8)；
(4b.8) calculates cost function J (B (ωk)), and judge | J (B (ωk))J(B(ωk-1)) whether ＞ λ true, if
It is to execute step (4b.1), it is no to then follow the steps (4b.9), wherein thinking B (w in first time iteration0) it is null matrix；
(4b.9) is to diagonalizable matrix B (wk) complex conjugate is taken, obtain separation matrix W (wk)；
(4c) enables k=k+1, and judges whether k≤K is true, if so, enabling B (ωk)=WH(ωk-1), and execute step
(4b), no to then follow the steps (5), B (wk)=WH(ωk-1)=B (ωk-1) be using diagonalizable matrix B current iteration results as under
An iteration initial value, the purpose of this step are that solving frequency domain detaches the sequencing problem that will appear；
Step 5) obtains the estimated value of time domain source signal：
(5a) calculates the source signal vector estimated value on q k-th of frequency point of section
Wherein, x (k, q) indicates the observation signal vector on q k-th of frequency point of section, W (ωk) indicate separation matrix；
(5b) is rightFourier inversion is carried out, time domain source signal estimated value is obtained, is realized to frequency domain convolution fanaticism number
Separation.
Below by way of emulation experiment, the technique effect of the present invention is described further.
1. simulated conditions and content：
Simulated conditions：MATLAB (R2013a), Intel (R) Core (TM) i7-2600CPU 6503.40GHz, Window
7Professional。
Emulation content：Source signal is the sinusoidal signal of N=3 different frequency, is superimposed white Gaussian noise, sets signal-to-noise ratio
SNR=10dB establishes convolved mixtures model using 8 tap FIR filters.These three source signals acquire 20000 sample points,
Mixed signal is acquired using M=4 receiving sensor, the element of wherein hybrid matrix A randomly generates, and obeys standard normal
Distribution.The performance of Blind Signal Separation method is weighed by signal-to-noise ratio SIR, and SIR is bigger, and blind separation performance is better, SIR definition
For：
Wherein, G (ωk)=W (ωk)A(ωk) it is frequency domain global change matrix,gnj(ωk)
For matrix G (ωk) line n j column elements.
2. simulation result：
Shown in the oscillogram such as Fig. 3 (a) for 3 source signals that present invention emulation uses.Now by the method for the present invention (JD-NS) with
Other two methods are compared, wherein method one be based on alternate column update diagonalization (ACDC) method, method two be it is non-just
Jacobi's approximately joint diagonalization (NOODLES) method of friendship.Restore source signal such as Fig. 3 with three that NOODLES methods are isolated
(b) shown in, restored shown in source signal such as Fig. 3 (c) with three that ACDC methods are isolated.
As can be seen that using ACDC methods restore three signals with second source signal phase in source signal oscillogram
Seemingly, this illustrates that ACDC methods have in fact converged to degenerate solution.The method of the present invention can effectively restore institute's active signal, and
The source signal recovered is free of the ingredient of other source signals, and this demonstrate preferably separating effects.
When table 1 summarizes SNR=10dB, 100 independent experiments, the method for the present invention and NOODLES method recovery resources are carried out
The SIR performances of signal.It can be seen that the SIR aspect of performance that the method for the present invention restores source signal at three is better than NOODLES methods,
Than the convolution Blind Signal Separation reliability higher of NOODLES method.
Table 1
Claims (4)
1. a kind of frequency domain convolution Blind Signal Separation method based on multiple-objection optimization, it is characterised in that include the following steps：
(1) objective matrix set is obtained
(1a) M sensor receives the observation signal x from N number of source signal sensorm(t), observation signal vector x (t), x are formed
(t)=[x1(t),...,xM(t)]T, wherein N >=1, and M >=N, m indicate sensor serial number, m=1 ..., M；
(1b) divides x (t), obtains Q observation signal subvector, and calculate target by each observation signal subvector
Matrix obtains the objective matrix set of Q × K objective matrix composition
Wherein,Indicate the objective matrix on observation signal subvector q k-th of frequency point of section, k each observation signal of expression to
The objective matrix serial number calculated is measured, q indicates that observation signal subvector serial number, K indicate the mesh that each observation signal subvector calculates
Mark matrix number；
(2) construction diagonalizable matrix B (ωk)：
Construct the diagonalizable matrix B (ω that dimension is M × Nk), wherein ωkIndicate objective matrix setK-th of frequency point；
(3) non-orthogonal joint diagonalization Model for Multi-Objective Optimization is constructed：
Utilize R (k, q) and B (ωk) construction non-orthogonal joint diagonalization Model for Multi-Objective Optimization：
Wherein, bnIndicate diagonalizable matrix B (ωk) n-component column vector, min expression take minimum operate, max expression take maximum
Change operation, Off () indicates the diagonal line operation of pulverised matrix, ()HExpression takes complex conjugate operation, det () table to matrix
Show and matrix determinant is asked to operate；
(4) non-orthogonal joint diagonalization Model for Multi-Objective Optimization is utilized, to objective matrix setSeparation square on each frequency point
Battle array W (ωk) estimated：
Objective matrix set is arranged in (4a)The initial value of the diagonalizable matrix of first frequency point is B (ω1)=[I, 0]T, item is set
Number of packages threshold value is ψ, and setting iteration stopping condition threshold is λ, enables k=1, wherein I indicates N × N-dimensional unit matrix, []TIt indicates
The transposition of matrix operates；
(4b) is to objective matrix setSeparation matrix W (ω on k-th of frequency pointk) estimated：
(4b.1) enables n=1；
(4b.2) calculates Hessian matrix QnAnd orthogonal intersection cast shadow matrix
Wherein, BnIndicate diagonalizable matrix B (ωk) matrix that remaining column vector is constituted after arranging of deletion n-th, I expression unit matrixs,
[·]-1The inversion operation of representing matrix；
(4b.3) calculates Hessian matrix QnConditional number κ (Qn), and judge κ (Qn) whether ＞ ψ true, if so, executing step
4b.5), no to then follow the steps 4b.4)；
(4b.4) calculating matrix pairGeneralized eigenvalue decomposition, and the corresponding feature vector of maximum generalized characteristic value is made
For diagonalizable matrix B (ωk) n-th row, and execute step 4b.7)；
(4b.5) calculates intermediary matrix C：
Wherein, U0Representing matrix QnThe corresponding eigenvectors matrix of M-N+1 minimal eigenvalue；
(4b.6) calculates diagonalizable matrix B (ωk) the n-th column vector bnVector value：
bn=U0w
Wherein, w indicates the corresponding feature vector of maximum eigenvalue of intermediary matrix C；
(4b.7) enables n=n+1, and judges whether n≤N is true, if so, step (4b.2) is executed, it is no to then follow the steps (4b.8)；
(4b.8) calculates cost function J (B (ωk)), and judge | J (B (ωk))-J(B(ωk-1)) | whether ＞ λ are true, if so,
Step (4b.1) is executed, it is no to then follow the steps (4b.9)；
(4b.9) is to diagonalizable matrix B (ωk) complex conjugate is taken, obtain separation matrix W (ωk)；
(4c) enables k=k+1, and judges whether k≤K is true, if so, enabling B (ωk)=WH(ωk-1), and step (4b) is executed, it is no
It thens follow the steps (5)；
(5) estimated value of time domain source signal is obtained：
(5a) calculates the source signal vector estimated value on q k-th of frequency point of section
Wherein, x (k, q) indicates the observation signal vector on q k-th of frequency point of section, W (ωk) indicate separation matrix；
(5b) is rightFourier inversion is carried out, time domain source signal estimated value is obtained, is realized to frequency domain convolution fanaticism number point
From.
2. the frequency domain convolution Blind Signal Separation method according to claim 1 based on multiple-objection optimization, which is characterized in that step
Suddenly the R (k, q) described in (1b), calculating step is：
(1b.1) is to observation signal xm(t) Short Time Fourier Transform is carried out, obtains frequency domain mixed signal vector x (k, q), wherein k
Indicate the objective matrix serial number that each observation signal subvector calculates, q indicates observation signal subvector serial number, and k=1 ...,
K, q=1 ..., Q, K indicate Fourier transformation frequency point number, the objective matrix number that value is calculated with each observation signal subvector
It is equal；
(1b.2) calculates power spectral density matrix Rx(k,q)：
Rx(k, q)=E [x (k, q) xH(k,q)]；
(1b.3) estimates noise variance σ with principal component method2；
Objective matrix R (k, q), R (k, q)=R on (1b.4) calculating observation signal subvector q k-th of frequency point of sectionx(k,q)-
σ2I, wherein I indicates unit matrix.
3. the frequency domain convolution Blind Signal Separation method according to claim 1 based on multiple-objection optimization, which is characterized in that step
Suddenly the calculating Hessian matrix Q described in (4b.3)nConditional number κ (Qn), calculating following formula is：
Wherein, []-1The inversion operation of representing matrix, | | | | expression asks norm to operate.
4. the frequency domain convolution Blind Signal Separation method according to claim 1 based on multiple-objection optimization, which is characterized in that step
Suddenly the corresponding feature vector of maximum generalized characteristic value described in (4b.4), obtaining step are：
To matrix pairGeneralized eigenvalue decomposition is carried out, matrix pair is obtainedGeneralized eigenvalue constitute it is diagonal
The matrix V that matrix D and the corresponding feature vector of generalized eigenvalue are constituted, and using the first row of V as matrix pairIt is maximum
The corresponding feature vector of generalized eigenvalue, generalized eigenvalue decomposition formula is：
Wherein, eig () indicates generalized eigenvalue decomposition operation.
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| CN110890098A (en) * | 2018-09-07 | 2020-03-17 | 南京地平线机器人技术有限公司 | Blind signal separation method and device and electronic equipment |
| CN111106866A (en) * | 2019-12-13 | 2020-05-05 | 南京理工大学 | Satellite-borne AIS/ADS-B collision signal separation method based on hessian matrix pre-estimation |
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| CN116866123A (en) * | 2023-07-13 | 2023-10-10 | 中国人民解放军战略支援部队航天工程大学 | Convolution blind separation method without orthogonal limitation |
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| CN110890098B (en) * | 2018-09-07 | 2022-05-10 | 南京地平线机器人技术有限公司 | Blind signal separation method and device and electronic equipment |
| CN110890098A (en) * | 2018-09-07 | 2020-03-17 | 南京地平线机器人技术有限公司 | Blind signal separation method and device and electronic equipment |
| CN109616138A (en) * | 2018-12-27 | 2019-04-12 | 山东大学 | Voice signal blind separating method and ears hearing assistance system based on segmentation frequency point selection |
| CN110236589A (en) * | 2019-06-03 | 2019-09-17 | 苏州美糯爱医疗科技有限公司 | A kind of real-time heart and lung sounds automatic separation method of electronic auscultation device |
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| TWI809390B (en) * | 2021-03-01 | 2023-07-21 | 新加坡商台達電子國際（新加坡）私人有限公司 | Method and audio processing system for blind source separation without sampling rate mismatch estimation |
| CN115372902A (en) * | 2022-08-05 | 2022-11-22 | 中国人民解放军战略支援部队信息工程大学 | TDOA offset reduction positioning method based on underwater multi-base sonar |
| CN115372902B (en) * | 2022-08-05 | 2023-12-01 | 中国人民解放军战略支援部队信息工程大学 | TDOA bias reduction positioning method based on underwater multi-base sonar |
| CN116866116A (en) * | 2023-07-13 | 2023-10-10 | 中国人民解放军战略支援部队航天工程大学 | Time-delay mixed linear blind separation method |
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| CN116866116B (en) * | 2023-07-13 | 2024-02-27 | 中国人民解放军战略支援部队航天工程大学 | Time-delay mixed linear blind separation method |
| CN116866123B (en) * | 2023-07-13 | 2024-04-30 | 中国人民解放军战略支援部队航天工程大学 | Convolution blind separation method without orthogonal limitation |
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