CN109116296A - There are the multi output support vector regression method for parameter estimation of array position error - Google Patents
There are the multi output support vector regression method for parameter estimation of array position error Download PDFInfo
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Abstract
There are the multi output support vector regression method for parameter estimation of array position error, the linear array constituted using N number of sound pressure sensor receives the original training data set that the sound source in M group training interval range generates as receiving array；Data correlation matrix is calculated by original training data set and is taken triangle element thereon and normalizes and obtains data characteristics vector set；Construction gaussian kernel function is gathered by data characteristics vector set harmony source, multi output support vector regression optimum regression parameter is obtained by training；Test data correlation matrix is calculated by original test data；Test nuclear matrix is calculated by test and training data feature vector, and the estimated value of direction of arrival is calculated in the multi output support vector regression optimum regression parameter obtained using training process；Array position error is included in supporting vector optimum regression machine parameter by the method for the present invention by data training, does not need error correction, so that it may obtain high-precision angle-of- arrival estimation result.
Description
Technical field
The invention belongs to the multi outputs under signal processing technology field more particularly to a kind of error condition there are array position
The method of support vector regression parameter Estimation.
Background technique
Array signal angle-of- arrival estimation High Resolution Method requires that array is in perfect condition, i.e. any mistake is not present in array
Difference, but in practice, due to array rotation, antenna orientation error, amplitude phase error and position caused by width phase is inconsistent and position
Set the performance that error has seriously affected subspace class High Resolution Method.Array error is improved as restrictive signal parameter Estimation performance
Bottleneck problem, scholars propose a large amount of error calibration method thus, these methods include source error correction and it is passive
Error correction, these error calibration methods will known error model, the modeling of error is an extremely complex process, especially
Being will be more difficult for the modeling of the composition error in the presence of coupling error and a variety of errors, when error model and array
When true error misfits, the performance of subsequent error calibration method will inevitably be caused to decline.Active error correction side
The performance of method is not only influenced the influence also by sound source parameter precision by error model, when sound source parameter inaccuracy, accidentally
The estimation performance of difference will also be deteriorated, and although passive bearing calibration does not need known sound source, but algorithm complexity is often very high.Such as
Fruit has a kind of method to have high robust to array error, so that it may without error correction, thus avoid array error
The complicated processes of correction directly obtain the accurate estimated result of signal parameter.
Multi output support vector regression method (Multi-output Support Vector Regression, MSVR)
The mapping relations between signal parameter and data correlation matrix, multi output support vector regression method are obtained by data training
It does not need using array information, when array is there are when error, array error is embodied in training data, in data training process
In, the Informational Expression of error is in mapping relations, using there are the available correct signals of mapping relations when array error
Parameter, and MUSIC method, ESPRIT method are needed using array information, when array there are when error according further to no error
Array information construction steering vector carry out parameter Estimation, will obtain mistake source parameter estimate, multi output supporting vector return
Return machine method that there is very high robustness to array position error.The method of the present invention has studied that there are under array position error condition
Multi output support vector regression method for parameter estimation, this method do not need carry out error correction, can directly obtain signal
The estimated value of angle of arrival, and can directly handle coherent signal and not need decorrelation LMS processing.
Summary of the invention
The object of the present invention is to provide the multi output support vector regression ginsengs under a kind of error condition there are array position
Number estimation method.
To achieve the goals above, the present invention takes following technical solution: there are under array position error condition
Multi output support vector regression method for parameter estimation, linear array receive L far field narrow band signal, the array should
It is equidistantly spaced from the uniform linear array constituted in the sound pressure sensor array element in x-axis by N number of, array element interval is dx, dx≤
0.5λmin, λminFor the minimum wavelength of incoming signal, but actually since human factor or natural cause lead to adjacent two array element
Between interval it is unequal, there is location error so as to cause array；
The step of method for parameter estimation, is as follows:
Step 1: the even linear array constituted using N number of sound pressure sensor array element receives M group training center as receiving array
Between [- θ0, θ0] the original training data set Z that generates of the sound source in rangex=[Z1..., Zm..., ZM], sound source set Θ=
[Θ1；Θ2...；Θm...；ΘM]；
Training section [- θ is determined according to the range of incoming wave signal0, θ0] range, 0≤θ0≤ 90 °, first group of sound source Θ1
=[θ11, θ12..., θ1l..., θ1L] be incident on receiving array, array received signal P times sampling obtains first group of original of N × P
Beginning training data Z1, wherein θ1lIndicate the angle of arrival of first of signal source in first group of sound source；Keep the space between sound source with respect to position
Set it is constant, sound source rotate integrally Δ φ as second group of sound source Θ2=[θ21, θ22... θ2l... θ2L], array received signal at this time
P sampling obtains second group of original training data Z of N × P2；Rotation sound source obtains sound source Θ in the same way3,
Θ4..., ΘMWith original training data Z3, Z3..., ZM, to obtain original training data set Zx=[Z1, Z2..., Zm...,
ZM], sound source set Θ=[Θ1；Θ2...；Θm...；ΘM]；Wherein, L is signal source number in one group of sound source；After enhancing
Algorithm Generalization Capability, it is desirable that sound source Θ1..., Θm... ΘMIt is evenly distributed on trained section [- θ0, θ0] in the range of, in order to mention
The angle-of- arrival estimation performance of high algorithm, needs to reduce the value of Δ φ, then trains section [- θ0, θ0] in the range of sound source group number
M will become larger, and determine the numerical value of Δ φ and M according to angle-of- arrival estimation required precision in practice；
Step 2: by original training data set Zx=[Z1, Z2..., Zm..., ZM] obtain data characteristics vector set R=
[R1, R2..., Rm..., RM]；
By first group of training data Z1, obtain data correlation matrix It is the square matrix of N × N, ()HTable
Show and transposed complex conjugate is taken to matrix, extractsLeading diagonal and leading diagonal upper right side element and by row sequence form a line to
AmountIt is rightIt is normalized to obtain data characteristics vectorWherein
According to first group of training data Z1Same processing mode, by Z2..., Zm..., ZMObtain data characteristics vector
R2..., Rm..., RM；To obtain data characteristics vector set R=[R1, R2..., Rm..., RM]；
Step 3: utilizing data characteristics vector set R and sound source set Θ=[Θ1；Θ2...；Θm...；ΘM] training
Obtain multi output support vector regression optimum regression parameter betaomp；
1) by data characteristics vector set R=[R1, R2..., Rm..., RM] bring into gaussian kernel function obtain based on training sample
This nuclear matrix K, wherein Kij=exp (- | | Ri-Rj||2/(2σ2)), σ is the coefficient of gaussian kernel function, KijIndicate nuclear matrix K's
The element of i-th row jth column, RiAnd RjRespectively indicate the ith and jth feature vector of data characteristics vector set R；
2) regression parameter matrix β is initialized0For the full null matrix of a M × L, initial error matrix e0=Θ, according to initial
Error matrix e0Obtain initial LaGrange parameter factor matrixWith initial LaGrange parameter
Coefficient matrixFind u0Middle satisfactionPositionAnd according to it in u0In elder generation
Initial supporting vector matrix is sequentially deposited in afterwardsWith initial supporting vector location matrixAccording toWithCalculate initial abstraction Jacobian matrix
Wherein Indicate e0M row,C is constant penalty factor, and ε is tube wall error, ()TRepresenting matrix takes transposition,
3) kth time circulation, ηk=1, calculate error matrix ek=Θ-K βk-1, according to error matrix ekObtain Lagrangian ginseng
Number factor matrix ukWith LaGrange parameter coefficient matrix αk, find ukSupporting vector matrix in matrixWith corresponding support
Vector position matrixRegression coefficient descent direction matrix P is calculated according to gradient descent methodk, calculate regression parameter matrix βk
With loss function matrixFrom obtaining predetermined optimizing target parameter Lk；
LaGrange parameter factor matrixLaGrange parameter coefficient matrixWhereinIndicate ekM row,Find ukMeet in matrixMatrix elementWith the position of elementAnd according to it in ukIn sequencing deposit in supporting vector matrixWith supporting vector location matrixAccording toWithCalculate loss
Jacobian matrixWhereinRecurrence system is calculated according to gradient descent method
Number descent direction matrix Pk=inv (Gk) Θ, matrix It indicates only to retain
The matrix of element other elements all zero on nuclear matrix K supporting vector position,It indicates only to retain LaGrange parameter
Coefficient matrix αkThe matrix of element other elements all zero on supporting vector position, inv () indicate to matrix inversion,
Diag is the diagonal entry for taking matrix, regression parameter matrix βk=βk-1+pkFurther according to regression parameter matrix βk, nuclear matrix K and
Loss function matrixConstruct optimization object function
Particularly, ukMeet in matrixMatrix element beThen support to
Moment matrixSupporting vector location matrix
4) compare LkAnd Lk-1Size, if Lk> Lk-1, ηk=γ ηk, γ < 1, ηk=γ ηkIt indicates ηkIt is reduced into original
γ times come, according to matrix P, γ and βk-1Obtain current iteration βk=γ pk+(1-γ)βk-1, repeat 3 in step 3)；If
Lk< Lk-1Jump to 5 in step 3)；
5) it verifies whether to meetIfThen k=k+1 continues step 3), wherein k=k+
1 indicates k increasing by 1；If metThen jump to 6 in step 3)；
If 6) metThen training process terminates；β at this timek=βompIt is returned for multi output supporting vector
Return machine optimum regression parameter, εminFor error threshold；
Step 4: by original test data ZcProcessing obtains data correlation matrixIt is tested by data correlation matrix
Input data eigenmatrix Rc；By testing feature vector RcWith training data eigenmatrix R=[R1, R2..., Rm..., RM] bring into
Gaussian kernel function obtains calculating test nuclear matrix Kc, and the optimum regression parameter matrix β obtained using training processomp, according toCarry out sound source angle-of- arrival estimation；
Receiving array receives training section [- θ0, θ0] the irrelevant measuring sound source [θ in K far field narrowband in range1,
θ2..., θ1..., θL], test signal received to array carries out P snap, obtains measuring sound source data Zc, by data ZcIt obtains
Test data correlation matrixThe leading diagonal for extracting test data correlation matrix and master are to line upper right side member
Element simultaneously lines up a column vector by rowWherein
It is rightIt does normalized and obtains testing feature vectorBy testing feature vector RcWith training data spy
Levy matrix R=[R1, R2..., Rm..., RM] bring gaussian kernel function calculating test nuclear matrix K intoc, test nuclear matrix KcIt is 1 × M dimension
Matrix, wherein KCm=exp (- | | RC-Rm||2/(2σ2)) it is nuclear matrix KcM-th of element；Step 3 is obtained how defeated
Support vector regression optimum regression parameter beta outompIt substitutes into, according toEstimate measuring sound source angle of arrival
K=1 ... in abovementioned steps, KXIndicating cycle-index, l=1 ..., L indicate signal source number in one group of sound source,
M=1,2 ..., M indicate sample number；I=1,2 ..., the position of M element in a matrix, j=1,2 ..., M indicate element in matrix
In position, f=1,2 ..., F indicate supporting vector number；
The present invention is based on the far-field signal method for parameter estimation of multi output support vector regression, and this method is to array position
Error has robustness, because array position error has been embodied in supporting vector optimized parameter regression matrix in the training process
In, therefore do not need progress error correction and can be obtained by accurate Direction-of-arrival result；With MUSIC method phase
Compare, the method for the present invention can directly handle coherent signal and not need decorrelation LMS processing.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
Having needs attached drawing to be used to do simple introduction in technical description, it should be apparent that, the accompanying drawings in the following description is only the present invention
Some embodiments for those of ordinary skill in the art without creative efforts, can also basis
These attached drawings obtain other attached drawings.
Fig. 1 is the schematic diagram of sound pressure sensor of embodiment of the present invention array；
Fig. 2 is the flow chart of the method for the present invention；
Fig. 3 is MUSIC method angle-of- arrival estimation scatter diagram；
Fig. 4 is the method for the present invention angle-of- arrival estimation scatter diagram；
Fig. 5 is change curve of the MUSIC method angle-of- arrival estimation root-mean-square error with signal-to-noise ratio；
Fig. 6 is change curve of the method for the present invention angle-of- arrival estimation root-mean-square error with signal-to-noise ratio；
Specific embodiment
In order to above and other objects of the present invention, feature and advantage can be become apparent from, the embodiment of the present invention is cited below particularly,
And cooperate appended diagram, it is described below in detail.
Fig. 1 show the schematic diagram of the sound pressure sensor array of the embodiment of the present invention.Sound pressure sensor array of the invention
The even linear array constituted in the sound pressure sensor in x-axis, array element interval d≤λ should be equidistantly spaced from by N number ofmin/ 2,2minFor
The minimum wavelength of incoming signal, but actually array element, there are location error, actual array position coordinates are X=[d1, d2...,
dn..., dN]；
Referring to Fig. 2, the step of multi output support vector regression method for parameter estimation of the invention is as follows: Homogeneous Pressure is passed
Sensor linear array L far field narrow band signal of reception, quantity of the L for incoming signal, L≤N-1,
Step 1: the even linear array constituted using N number of sound pressure sensor array element receives M group training center as receiving array
Between [- θ0, θ0] the original training data set Z that generates of the sound source in rangex=[Z1..., Zm..., ZM], sound source set Θ=
[Θ1；Θ2...；Θm...；ΘM]；
Training section [- θ is determined according to the range of incoming wave signal0, θ0] range, 0≤θ0≤ 90 °, first group of sound source Θ1
=[θ11, θ12..., θ1l..., θ1L] be incident on receiving array, array received signal P times sampling obtains first group of original of N × P
Beginning training data Z1, wherein θ1lIndicate the angle of arrival of first of signal source in first group of sound source；Keep the space between sound source with respect to position
Set it is constant, sound source rotate integrally Δ φ as second group of sound source Θ2=[θ21, θ22... θ2l... θ2L], array received signal at this time
P sampling obtains second group of original training data Z of N × P2；Rotation sound source obtains sound source Θ in the same way3,
Θ4..., ΘMWith original training data Z3, Z3..., ZM, to obtain original training data set Zx=[Z1, Z2..., Zm...,
ZM], sound source set Θ=[Θ1；Θ2...；Θm...；ΘM]；Wherein, L is signal source number in one group of sound source；After enhancing
Algorithm Generalization Capability, it is desirable that sound source Θ1..., Θm... ΘMIt is evenly distributed on trained section [- θ0, θ0] in the range of, in order to mention
The angle-of- arrival estimation performance of high algorithm, needs to reduce the value of Δ φ, then trains section [- θ0, θ0] in the range of sound source group number
M will become larger, and determine the numerical value of Δ φ and M according to angle-of- arrival estimation required precision in practice；
Step 2: by original training data set Zx=[Z1, Z2..., Zm..., ZM] obtain data characteristics vector set R=
[R1, R2..., Rm..., RM]；
By first group of training data Z1, obtain data correlation matrix It is the square matrix of N × N, ()HTable
Show and transposed complex conjugate is taken to matrix, extractsLeading diagonal and leading diagonal upper right side element and by row sequence form a line to
AmountIt is rightIt is normalized to obtain data characteristics vectorWherein
According to first group of training data Z1Same processing mode, by Z2..., Zm..., ZMObtain data characteristics vector
R2..., Rm..., RM；To obtain data characteristics vector set R=[R1, R2..., Rm..., RM]；
Step 3: utilizing data characteristics vector set R and sound source set Θ=[Θ1；Θ2...；Θm...；ΘM] training
Obtain multi output support vector regression optimum regression parameter betaomp；
1) by data characteristics vector set R=[R1, R2..., Rm..., RM] bring into gaussian kernel function obtain based on training sample
This nuclear matrix K, wherein Kij=exp (- | | Ri-Rj||2/(2σ2)), σ is the coefficient of gaussian kernel function, KijIndicate nuclear matrix K's
The element of i-th row jth column, RiAnd RjRespectively indicate the ith and jth feature vector of data characteristics vector set R；
2) regression parameter matrix β is initialized0For the full null matrix of a M × L, initial error matrix e0=Θ, according to initial
Error matrix e0Obtain initial LaGrange parameter factor matrixWith initial LaGrange parameter
Coefficient matrixFind u0Middle satisfactionPositionAnd according to it in u0In elder generation
Initial supporting vector matrix is sequentially deposited in afterwardsWith initial supporting vector location matrixAccording toWithCalculate initial abstraction Jacobian matrix
WhereinIndicate e0M row,C is constant penalty factor, and ε is tube wall error, ()TRepresenting matrix takes transposition,
3) kth time circulation, ηk=1, calculate error matrix ek=Θ-K βk-1, according to error matrix ekObtain Lagrangian ginseng
Number factor matrix ukWith LaGrange parameter coefficient matrix αk, find ukSupporting vector matrix in matrixWith corresponding support
Vector position matrixRegression coefficient descent direction matrix P is calculated according to gradient descent methodk, calculate regression parameter matrix βk
With loss function matrixFrom obtaining predetermined optimizing target parameter Lk；
LaGrange parameter factor matrixLaGrange parameter coefficient matrixWhereinIndicate ekM row,Find ukMeet in matrixMatrix elementWith the position of elementAnd according to it in ukIn sequencing deposit in supporting vector matrixWith supporting vector location matrixAccording toWithCalculate loss
Jacobian matrixWhereinRecurrence system is calculated according to gradient descent method
Number descent direction matrix Pk=inv (Gk) Θ, matrix It indicates only to retain
The matrix of element other elements all zero on nuclear matrix K supporting vector position,It indicates only to retain LaGrange parameter
Coefficient matrix αkThe matrix of element other elements all zero on supporting vector position, inv () indicate to matrix inversion,
Diag is the diagonal entry for taking matrix, regression parameter matrix βk=βk-1+pkFurther according to regression parameter matrix βk, nuclear matrix K and
Loss function matrixConstruct optimization object function
Particularly, ukMeet in matrixMatrix element beThen support to
Moment matrixSupporting vector location matrix
4) compare LkAnd Lk-1Size, if Lk> Lk-1, ηk=γ ηk, γ < 1, ηk=γ ηkIt indicates ηkIt is reduced into original
γ times come, according to matrix P, γ and βk-1Obtain current iteration βk=γ pk+(1-γ)βk-1, repeat 3 in step 3)；If
Lk< Lk-1Jump to 5 in step 3)；
5) it verifies whether to meetIfThen k=k+1 continues step 3), wherein k=k+
1 indicates k increasing by 1；If metThen jump to 6 in step 3)；
If 6) metThen training process terminates；β at this timek=βompIt is returned for multi output supporting vector
Return machine optimum regression parameter, εminFor error threshold；
Step 4: by original test data ZcProcessing obtains data correlation matrixIt is tested by data correlation matrix
Input data eigenmatrix Rc；By testing feature vector RcWith training data eigenmatrix R=[R1, R2..., Rm..., RM]TBand
Enter gaussian kernel function to obtain calculating test nuclear matrix Kc, and the optimum regression parameter matrix β obtained using training processomp, according toSound source angle angle of arrival is carried out to be estimated；
Receiving array receives training section [- θ0, θ0] the irrelevant measuring sound source [θ in K far field narrowband in range1,
θ2..., θ1..., θL], test signal received to array carries out P snap, obtains measuring sound source data Zc, by data ZcIt obtains
Test data correlation matrixThe leading diagonal for extracting test data correlation matrix and master are to line upper right side member
Element simultaneously lines up a column vector by rowWherein
It is rightIt does normalized and obtains testing feature vectorBy testing feature vector RcAnd training data
Eigenmatrix R=[R1, R2..., Rm..., RM] bring gaussian kernel function calculating test nuclear matrix K intoc, test nuclear matrix KcIt is 1 × M
The matrix of dimension, wherein KCm=exp (- | | RC-Rm||2/(2σ2)) it is nuclear matrix KcM-th of element；Step 3 is obtained more
Export support vector regression optimum regression parameter betaompIt substitutes into, according toEstimate measuring sound source angle of arrival
K=1 ... in abovementioned steps, KXIndicating cycle-index, l=1 ..., L indicate signal source number in one group of sound source,
M=1,2 ..., M indicate sample number；I=1,2 ..., the position of M element in a matrix, j=1,2 ..., M indicate element in matrix
In position, f=1,2 ..., F indicate supporting vector number；
The present invention carries out array parameter estimation using multi output support vector regression method, is trained by data by error
Information is embodied into optimum regression parameter matrix, does not need the complex process of array position error modeling and array error correction；
The method of the present invention does not utilize the prior information of array without utilizing signal subspace and noise subspace yet, so the phase of signal
Dry not influence on the method for the present invention, the method for the present invention can directly handle coherent signal and not need the cumbersome mistake of decorrelation LMS
Journey.
Effect of the invention can be further illustrated by simulation result below:
Emulation experiment condition is as follows: the far field of two different frequencies, narrowband sound-source signal are incident on to be equidistantly spaced from by 9
In the even linear array that the sound pressure sensor array element in x-axis is constituted, as shown in Figure 1, the angle of arrival of incoming signal are as follows: (θ1, θ2)=
(40 °, 60 °), the physical location X=[0.2,1.5,1.7,2.85,4.05,4.5,6.07,7.08,8.7] of array element, unit are half
Wavelength；In -90 ° to O ° of section, data training is carried out to be divided into 20 ° between angle, number of snapshots are 200 times, and 200 times independent real
It tests, the simulation experiment result is as shown in Figures 3 to 6, and Fig. 3 and Fig. 4 are signal-to-noise ratio when being 15dB, MUSIC method and the method for the present invention
The scatter diagram of angle-of- arrival estimation can be seen that MUSIC method estimated value significantly deviates from true value (θ from Fig. 3 and Fig. 41, θ2)
=(40 °, 60 °), the estimated value of the method for the present invention is in true value (θ1, θ240 ° of)=(, 60 °) neighbouring micro- a small range swings, says
Bright multi output support vector regression method for parameter estimation can also provide correct letter there are array position error
Number angle-of- arrival estimation result；It is (how defeated in MUSIC method and MSVR method of the invention that Fig. 5 and Fig. 6 gives signal 1 and signal 2
Support vector regression is referred to as MSVR out) root-mean-square error change curve under different signal-to-noise ratio, it can from Fig. 5 and Fig. 6
Out, array position error has very serious implications to MUSIC method, no matter signal-to-noise ratio how to improve always there are it is biggish partially
Difference is Biased estimator there are MUSIC method when array position error, and the method for the present invention increasingly connects with the raising of signal-to-noise ratio
Nearly true value, even if remaining to obtain very accurate Direction-of-arrival there are array position error as a result, having array position
Set error robustness；
The above described is only a preferred embodiment of the present invention, limitation in any form not is done to the present invention, though
So the present invention has been disclosed as a preferred embodiment, and however, it is not intended to limit the invention, any technology people for being familiar with this profession
Member, without departing from the scope of the present invention, when the technology contents using the disclosure above are modified or are modified
For the equivalent embodiment of equivalent variations, but anything that does not depart from the technical scheme of the invention content, according to the technical essence of the invention
Any simple modification, equivalent change and modification to the above embodiments, all of which are still within the scope of the technical scheme of the invention.
Claims (1)
1. there are the multi output support vector regression method for parameter estimation of array position error, it is characterised in that:
Array of the present invention is linear array, and the linear array should be equidistantly spaced from by N number of in the sound pressure sensor in x-axis
The even linear array of composition, array element interval are dx, dx≤λmin/ 2, λminFor the minimum wavelength of incoming signal, but actually due to people
Cause the interval between adjacent two array element unequal for factor or natural cause, location error occurs so as to cause array；
The step of method for parameter estimation, is as follows:
Step 1: receiving M group using N number of linear array constituted there are the sound pressure sensor of array position error as receiving array
Training section [- θ0, θ0] the original training data set Z that generates of the sound source in rangex=[Z1, Z2..., Zm..., ZM], sound source
Set Θ=[Θ1, Θ2..., Θm..., ΘM]；
The range in training section is [- θ0, θ0], 0≤θ0≤ 90 °, first group of sound source Θ1=[θ11, θ12... θ1L] it is incident on reception
On array, array received signal P times sampling obtains first group of original training data Z of N × P1；Keep the space between sound source opposite
Position is constant, and sound source rotates integrally Δ φ as second group of sound source Θ2=[θ21, θ22... θ2L], array received signal P times at this time
Sampling obtains second group of original training data Z of N × P2；Sound source Θ is obtained in the same way3, Θ4..., ΘMWith it is original
Sampled data Z3..., ZM, to obtain original training data set Zx=[Z1, Z2..., Zm..., ZM], sound source set Θ=
[Θ1；Θ2…；Θm...；ΘM], wherein L is the signal source number in one group of sound source；
Step 2: by original training data set Zx=[Z1, Z2..., Zm..., ZM] obtain data characteristics vector set R=[R1,
R2..., Rm..., RM]；
By first group of training data Z1, obtain data correlation matrix It is the square matrix of N × N, extractsMain pair
It linea angulata and leading diagonal upper right side element and forms a line vector by row sequenceIt is rightIt is normalized and is counted
According to feature vectorWherein (·)HRepresenting matrix takes transposed complex conjugate；
According to first group of data Z1Same processing mode, by Z2..., Zm..., ZMObtain data characteristics vector vector R2,
R3... RM；To obtain data characteristics vector set R=[R1, R2..., Rm..., RM]；
Step 3: it is optimal to obtain multi output support vector regression using data characteristics vector set R and sound source set Θ training
Regression parameter βomp；
1) by training data feature vector set R=[R1, R2..., Rm..., RM] bring into gaussian kernel function obtain based on training sample
This nuclear matrix K.
Wherein Kij=exp (- | | Ri-Rj||2/(2σ2)), wherein σ is the coefficient of gaussian kernel function, KijIndicate the i-th of nuclear matrix K
The element of row jth column, RiAnd RjRespectively indicate the ith and jth feature vector of data characteristics vector set R；
2) regression parameter matrix β is initialized0For the full null matrix of a M × L, initial error matrix e0=Θ, according to initial error
Matrix e0Obtain initial LaGrange parameter factor matrixWith initial LaGrange parameter system
Matrix numberFind u0Middle satisfactionPositionAnd according to it in u0In it is successive
Sequence deposits in initial supporting vector matrixWith initial supporting vector location matrixAccording to
WithCalculate initial abstraction Jacobian matrix
Wherein Indicate e0M row,C
For constant penalty factor, ε is tube wall error, ()TRepresenting matrix takes transposition,
3) kth time circulation, ηk=1, calculate error matrix ek=Θ-K βk-1, according to error matrix ekObtain LaGrange parameter because
Submatrix ukWith LaGrange parameter coefficient matrix αk, find ukSupporting vector matrix in matrixWith corresponding supporting vector
Location matrixRegression coefficient descent direction matrix P is calculated according to gradient descent methodk, calculate regression parameter matrix βkAnd damage
Lose Jacobian matrixFrom obtaining predetermined optimizing target parameter Lk；
LaGrange parameter factor matrixLaGrange parameter coefficient matrixWhereinIndicate ekM row,Find ukMeet in matrixMatrix elementWith the position of elementAnd according to it in ukIn sequencing deposit in supporting vector matrixWith supporting vector location matrixAccording toWithCalculate damage
Lose Jacobian matrixWhereinRecurrence is calculated according to gradient descent method
Coefficient descent direction matrix Pk=inv (Gk) Θ, matrix It indicates only to protect
The matrix of the element other elements all zero on nuclear matrix K supporting vector position is stayed,It indicates only to retain Lagrange
Parameter coefficient matrix αkThe matrix of element other elements all zero on supporting vector position, inv indicate to matrix inversion,
Diag is the diagonal entry for taking matrix, regression parameter matrix βk=βk-1+pkFurther according to regression parameter matrix βk, nuclear matrix K and
Loss function matrixConstruct optimization object function
4) compare LkAnd Lk-1Size, if Lk> Lk-1, ηk=γ ηk, γ < 1 indicates ηkOriginal γ times is narrowed down to, according to
Matrix Pk, γ and βk-1Obtain current iteration βk=γ pk+(1-γ)βk-1, repeat 3 in step 4)；If Lk< Lk-1It jumps to
5 in step 4)；
5) it verifies whether to meetIfThen k=k+1 continues step 3) wherein k=k+1 expression
K is increased by 1；If metThen jump to 6 in step 4)；
If 6) metThen training process terminates；β at this timek=βompMost for multi output support vector regression
Excellent regression parameter, εminFor error threshold；
Step 4: by original test data ZcProcessing obtains data correlation matrixTest input is obtained by data correlation matrix
Data characteristics matrix Rc；By testing feature vector RcWith training data eigenmatrix R=[R1, R2..., Rm..., RM] bring Gauss into
Kernel function obtains test nuclear matrix Kc, and the optimum regression parameter matrix β obtained using training processomp, according to
Obtain sound source angle-of- arrival estimation；
Receiving array receives training section [- θ0, θ0] the irrelevant test signal [θ in K far field narrowband in range1, θ2...,
θ1..., θL], test signal received to array carries out P snap, obtains data test signal Zc, by data ZcIt is tested
Data correlation matrixIt extracts the leading diagonal of test data correlation matrix and leads to line upper right side element simultaneously
A column vector is lined up by rowIt is rightNormalized is done to obtainBy testing feature vector RcAnd training data
Eigenmatrix R=[R1, R2..., Rm..., RM] bring gaussian kernel function calculating test nuclear matrix K intoc, test nuclear matrix KcIt is 1*M,
Wherein KCm=exp (- | | RC-Rm||2/(2σ2))；According toCarry out sound source angle estimationWherein
K=1 in abovementioned steps, 2 ..., KXExpression cycle-index, 1=1 ..., L indicates signal source in one group of sound-source signal
Number, m=1,2 ..., M indicate sample number；I=1,2 ..., M indicates the position of element in a matrix；J=1,
2 ..., the position of M expression element in a matrix, f=1,2 ... the number of .., F expression supporting vector.
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