CN109116296B - Parameter estimation method for multi-output support vector regression machine with array position error - Google Patents

Parameter estimation method for multi-output support vector regression machine with array position error Download PDF

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CN109116296B
CN109116296B CN201810977748.5A CN201810977748A CN109116296B CN 109116296 B CN109116296 B CN 109116296B CN 201810977748 A CN201810977748 A CN 201810977748A CN 109116296 B CN109116296 B CN 109116296B
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CN109116296A (en
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王桂宝
王磊
王兰美
廖桂生
孙长征
张仲鹏
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Xidian University
Shaanxi University of Technology
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Shaanxi University of Technology
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Abstract

The parameter estimation method of the multi-output support vector regression machine with array position errors utilizes a linear array formed by N sound pressure sensors as a receiving array to receive an original training data set generated by a sound source within the range of M groups of training intervals; calculating a data correlation matrix from the original training data set, taking triangular elements on the data correlation matrix, and normalizing the triangular elements to obtain a data characteristic vector set; constructing a Gaussian kernel function by the data feature vector set and the sound source set, and obtaining optimal regression parameters of the multi-output support vector regression machine through training; calculating from the original test data to obtain a test data correlation matrix; calculating a test kernel matrix by using the feature vectors of the test and training data, and calculating an estimated value of a signal arrival angle by using the optimal regression parameters of the multi-output support vector regression machine obtained in the training process; according to the method, the array position errors are contained in the support vector optimal regression parameters through data training, and the high-precision arrival angle estimation result can be obtained without error correction.

Description

Parameter estimation method for multi-output support vector regression machine with array position error
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a method for estimating parameters of a multi-output support vector regression machine under the condition of array position errors.
Background
The array signal arrival angle estimation high-resolution method requires that the array is in an ideal state, i.e. the array does not have any error, but in practice, antenna orientation errors, amplitude-phase errors and position errors caused by array rotation, amplitude-phase inconsistency and position seriously affect the performance of the subspace-like high-resolution method. Array errors become a bottleneck problem restricting the improvement of signal parameter estimation performance, a large number of error correction methods are proposed by the students, and include active error correction and passive error correction, the error correction methods need to be known as error models, and the modeling of errors is a very complex process, especially the modeling of integrated errors in the presence of coupling errors and various errors is more difficult, and when the error models are not matched with the real errors of the array, the performance of the subsequent error correction methods is inevitably reduced. The performance of the active error correction method is affected by the accuracy of the sound source parameter as well as the error model, when the sound source parameter is inaccurate, the estimation performance of the error is also deteriorated, and the passive correction method does not need a known sound source, but the algorithm complexity is high. If one method has high robustness to the array error, the error correction can be omitted, so that the complicated process of the array error correction is avoided, and the accurate estimation result of the signal parameters is directly obtained.
The Multi-output support vector regression method (Multi-output Support Vector Regression, MSVR) obtains the mapping relation between signal parameters and data correlation matrix through data training, the Multi-output support vector regression method does not need to use array information, when an array has errors, the array errors are reflected in training data, in the data training process, the error information is reflected in the mapping relation, correct signal parameters can be obtained by using the mapping relation when the array errors exist, the MUSIC method and the ESPRIT method need to use the array information, when the array has errors, a guide vector is still constructed according to the array information without errors to carry out parameter estimation, and the Multi-output support vector regression method has high robustness to the array position errors. The method researches the parameter estimation method of the multi-output support vector regression machine under the condition of array position errors, the method does not need error correction, can directly obtain the estimated value of the signal arrival angle, and can directly process coherent signals without decoherence processing.
Disclosure of Invention
The invention aims to provide a parameter estimation method of a multi-output support vector regression machine under the condition of array position errors.
In order to achieve the above object, the present invention adopts the following technical solutions: the multi-output support vector regression parameter estimation method under the condition of array position error comprises the steps that a linear array receives L far-field narrowband signals, and the array is a uniform linear array which is formed by N array elements of sound pressure sensors which are arranged on an x axis at equal intervals, wherein the array element intervals are d x ，d x ≤0.5λ min ，λ min Is the minimum wavelength of the incident signal, but actually, the intervals between two adjacent array elements are unequal due to human factors or natural reasons, so that the array has position errors;
the parameter estimation method comprises the following steps:
step one, using a uniform linear array formed by N sound pressure sensor array elements as a receiving array to receive M groups of training intervals [ -theta ] 0 ，θ 0 ]Raw training data set Z generated by sound sources within range x ＝[Z 1 ，…，Z m ，…，Z M ]Sound source set Θ= [ Θ ] 1 ；Θ 2 ，…；Θ m ，…；Θ M ]；
Determining training interval [ -theta ] according to range of incoming wave signal 0 ，θ 0 ]In the range of 0.ltoreq.θ 0 Less than or equal to 90 DEG, a first group of sound sources Θ 1 ＝[θ 11 ，θ 12 ，…，θ 1l ，…，θ 1L ]Incident on a receiving array, the array receives signals P times to obtain N x P first group of original training data Z 1 Wherein θ is 1l Representing the arrival angle of the first signal source in the first group of sound sources; maintaining the relative spatial position between the sound sources unchanged, the overall rotation delta phi of the sound sources as the second group of sound sources theta 2 ＝[θ 21 ，θ 22 ，…θ 2l ，…θ 2L ]At this time, the array receives the signal P times to obtain N×P second set of original training data Z 2 The method comprises the steps of carrying out a first treatment on the surface of the Rotating the sound source in the same way to obtain sound source theta 3 ，Θ 4 ，…，Θ M And raw training data Z 3 ，Z 3 ，…，Z M Thereby obtaining the original training data set Z x ＝[Z 1 ，Z 2 ，…，Z m ，…，Z M ]Sound source set Θ= [ Θ ] 1 ；Θ 2 ，…；Θ m ，…；Θ M ]The method comprises the steps of carrying out a first treatment on the surface of the Wherein L is the number of signal sources in a group of sound sources; in order to enhance post-algorithm generalization performance, a sound source Θ is required 1 ，…，Θ m ，…Θ M Uniformly distributed in training interval [ -theta [ - ] 0 ，θ 0 ]In order to improve the arrival angle estimation performance of the algorithm, the value of delta phi needs to be reduced, and the training interval [ -theta ] is trained 0 ，θ 0 ]The number M of sound source groups in the range of (1) is increased, and the numerical values of delta phi and M are determined according to the accuracy requirement of the arrival angle estimation in practice;
step two, the original training data set Z x ＝[Z 1 ，Z 2 ，…，Z m ，…，Z M ]Obtaining a data characteristic vector set R= [ R ] 1 ，R 2 ，…，R m ，…，R M ]；
From a first set of training data Z 1 Obtaining a data correlation matrix Is an N square matrix, (. Cndot. H Representing transposed complex conjugate of matrix, extracting +.>Main diagonal and upper right element of main diagonal and arranged in a column vector in row order +.>For->Normalization processing is carried out to obtain a data feature vector +.>Wherein the method comprises the steps of
According to the first set of training data Z 1 In the same way, by Z 2 ，…，Z m ，…，Z M Obtaining a data characteristic vector R 2 ，…，R m ，…，R M The method comprises the steps of carrying out a first treatment on the surface of the Thereby obtaining a data characteristic vector set R= [ R ] 1 ，R 2 ，…，R m ，…，R M ]；
Step three, utilizing the data feature vector set R and the sound source set theta= [ theta ] 1 ；Θ 2 ，…；Θ m ，…；Θ M ]Training to obtain optimal regression parameter beta of multi-output support vector regression machine omp ；
1) Set data feature vector r= [ R ] 1 ，R 2 ，…，R m ，…，R M ]Bringing into a Gaussian kernel function yields a training sample-based kernel matrix K, where K ij ＝exp(-||R i -R j || 2 /(2σ 2 ) And sigma is the coefficient of the Gaussian kernel function, K ij Elements representing the ith row and jth column of the kernel matrix K, R i And R is j Respectively representing the ith and jth eigenvectors of the data eigenvector set R;
2) Initializing regression parameter matrix beta 0 Is an MxL all-zero matrix, and the initial error matrix e 0 =Θ, according to the initial error matrix e 0 Obtaining an initial Lagrangian parameter factor matrixAnd an initial Lagrangian parameter coefficient matrix +.>Finding u 0 Is satisfied by->Position->And according to its position in u 0 The order of the sequences is stored in the initial support vector matrix +.>And an initial support vector position matrix->According toAnd->Calculating an initial loss function matrix->
Wherein the method comprises the steps of Representation e 0 Is arranged in the row m of the table (a),c is a constant penalty factor, ε is the pipe wall error, (. Cndot.) T The representation matrix takes the transpose,
3) The kth cycle, eta k =1, calculate error matrix e k ＝Θ-Kβ k-1 According to the error matrix e k Obtaining a Lagrange parameter factor matrix u k And Lagrangian parameter coefficient matrix alpha k Find u k Support vector matrix in matrixAnd corresponding support vector position matrix->Calculating regression coefficient descent direction matrix P according to gradient descent method k Calculating regression parameter matrix beta k And a loss function matrix->From obtaining the optimization target parameter L k ；
Lagrange parameter factor matrixLagrangian parameter coefficient matrixWherein->Representation e k Is arranged in the row m of the table (a),finding u k Satisfy->Matrix elements of (a)And the position of the element->And according to its position in u k Is stored in the support vector matrix according to the sequence of the dataAnd support vector position matrix->According to->And->Calculating a loss function matrix->Wherein->Calculating regression coefficient descent direction matrix P according to gradient descent method k ＝inv(G k ) Θ, matrix-> Representing a matrix which only retains all the elements at the support vector position of the kernel matrix K, the other elements being zero,/->Representing the retention of only the Lagrangian parameter coefficient matrix alpha k Matrix with all the other elements of the elements at the support vector position being zero, inv (·) represents inverting the matrix, diag is the diagonal element of the matrix, and the regression parameter matrix beta k ＝β k-1 +p k Then according to regression parameter matrix beta k A kernel matrix K and a loss function matrix->Constructing an optimized objective function->
In particular, u k The matrix satisfiesMatrix elements of (a)Is->Then support vector matrix +.>Support vector position matrix
4) Comparison L k And L k-1 If L is the size of k ＞L k-1 ，η k ＝γη k ，γ＜1，η k ＝γη k The representation will be eta k Reduced to original gamma times according to the matrix P, gamma and beta k-1 Obtaining the iteration beta k ＝γp k +(1-γ)β k-1 Repeating step 3); if L k ＜L k-1 Jump to step three, 5);
5) Verifying whether or not it satisfiesIf->Then k=k+1 continues with step 3), where k=k+1 means increasing k by 1; if it meets->Jump to step 6) of step three);
6) If it meetsThe training process ends; beta at this time k ＝β omp For the optimal regression parameters of the multi-output support vector regression machine, epsilon min Is an error threshold;
step four, using the original test data Z c Processing to obtain data correlation matrixObtaining a test input data characteristic matrix R from the data correlation matrix c The method comprises the steps of carrying out a first treatment on the surface of the Will test the feature vector R c And training data feature matrix r= [ R 1 ，R 2 ，…，R m ，…，R M ]Carrying out Gaussian kernel function to obtain a calculation test kernel matrix K c And utilizes the optimal regression parameter matrix beta obtained in the training process omp According toEstimating the arrival angle of a sound source;
the receiving array receives the training interval [ -theta ] 0 ，θ 0 ]K far-field narrow-band independent test sound sources [ theta ] in range 1 ，θ 2 ，…，θ 1 ，…，θ L ]Performing P snapshots on the test signals received by the array to obtain test sound source data Z c From data Z c Obtaining a test data correlation matrixExtracting main diagonal of the test data correlation matrix and main diagonal upper right element and row by row into a column vector +.>Wherein the method comprises the steps of
For a pair ofNormalization processing is carried out to obtain a test feature vector +.>Will test the feature vector R c And training data feature matrix r= [ R 1 ，R 2 ，…，R m ，…，R M ]Test kernel matrix K is calculated by taking Gaussian kernel function c Testing nuclear momentArray K c Is a 1 XM dimensional matrix, where K Cm ＝exp(-||R C -R m || 2 /(2σ 2 ) For a nuclear matrix K) c The m-th element of (2); and (3) optimizing regression parameters beta of the multi-output support vector regression machine obtained in the step (III) omp Substitution according to->Estimating the angle of arrival of a test sound source
K=1, …, K in the previous step X The number of loops is represented by l=1, …, L represents the number of signal sources in a group of sound sources, m=1, 2, …, and M represents the number of samples; i=1, 2, …, M element positions in the matrix, j=1, 2, …, M represents element positions in the matrix, f=1, 2, …, F represents the number of support vectors;
the method has robustness to the array position error, and because the array position error is reflected in the support vector optimal parameter regression matrix in the training process, the accurate signal arrival angle estimation result can be obtained without error correction; in contrast to the MUSIC method, the method of the present invention can directly process coherent signals and does not require decoherence processing.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following description will briefly explain the drawings needed in the embodiments or the prior art, and it is obvious that the drawings in the following description are only some embodiments of the present invention and that other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of an acoustic pressure sensor array according to an embodiment of the present invention;
FIG. 2 is a flow chart of the method of the present invention;
FIG. 3 is a scatter diagram of the MUSIC method arrival angle estimation;
FIG. 4 is a scatter plot of the angle of arrival estimate for the method of the present invention;
FIG. 5 is a graph showing the variation of the root mean square error of the MUSIC method arrival angle estimation with the signal to noise ratio;
FIG. 6 is a graph showing the variation of the root mean square error of the angle of arrival estimation with the signal to noise ratio according to the method of the present invention;
Detailed Description
To make the above and other objects, features and advantages of the present invention more apparent, the following detailed description of the embodiments of the present invention will be given with reference to the accompanying drawings.
Fig. 1 is a schematic diagram of an acoustic pressure sensor array according to an embodiment of the present invention. The sound pressure sensor array of the invention is a uniform linear array composed of N sound pressure sensors which are arranged on the x axis at equal intervals, and the array element interval d is less than or equal to lambda min /2，2 min For the minimum wavelength of the incident signal, but in practice there is a position error of the array element, the actual array position coordinate is x= [ d ] 1 ，d 2 ，…，d n ，…，d N ]；
Referring to fig. 2, the multiple output support vector regression parameter estimation method of the present invention comprises the following steps: the uniform sound pressure sensor linear array receives L far-field narrow-band signals, L is the number of incident signals, L is less than or equal to N-1,
step one, using a uniform linear array formed by N sound pressure sensor array elements as a receiving array to receive M groups of training intervals [ -theta ] 0 ，θ 0 ]Raw training data set Z generated by sound sources within range x ＝[Z 1 ，…，Z m ，…，Z M ]Sound source set Θ= [ Θ ] 1 ；Θ 2 ，…；Θ m ，…；Θ M ]；
Determining training interval [ -theta ] according to range of incoming wave signal 0 ，θ 0 ]In the range of 0.ltoreq.θ 0 Less than or equal to 90 DEG, a first group of sound sources Θ 1 ＝[θ 11 ，θ 12 ，…，θ 1l ，…，θ 1L ]Incident on a receiving array, the array receives signals P times to obtain N x P first group of original training data Z 1 Wherein θ is 1l Representing the arrival angle of the first signal source in the first group of sound sources; maintaining the relative spatial position between the sound sources unchanged, the overall rotation delta phi of the sound sources as the second group of sound sources theta 2 ＝[θ 21 ，θ 22 ，…θ 2l ，…θ 2L ]At this time, the array receives the signal P times to obtain N×P second set of original training data Z 2 The method comprises the steps of carrying out a first treatment on the surface of the Rotating the sound source in the same way to obtain sound source theta 3 ，Θ 4 ，…，Θ M And raw training data Z 3 ，Z 3 ，…，Z M Thereby obtaining the original training data set Z x ＝[Z 1 ，Z 2 ，…，Z m ，…，Z M ]Sound source set Θ= [ Θ ] 1 ；Θ 2 ，…；Θ m ，…；Θ M ]The method comprises the steps of carrying out a first treatment on the surface of the Wherein L is the number of signal sources in a group of sound sources; in order to enhance post-algorithm generalization performance, a sound source Θ is required 1 ，…，Θ m ，…Θ M Uniformly distributed in training interval [ -theta [ - ] 0 ，θ 0 ]In order to improve the arrival angle estimation performance of the algorithm, the value of delta phi needs to be reduced, and the training interval [ -theta ] is trained 0 ，θ 0 ]The number M of sound source groups in the range of (1) is increased, and the numerical values of delta phi and M are determined according to the accuracy requirement of the arrival angle estimation in practice;
step two, the original training data set Z x ＝[Z 1 ，Z 2 ，…，Z m ，…，Z M ]Obtaining a data characteristic vector set R= [ R ] 1 ，R 2 ，…，R m ，…，R M ]；
From a first set of training data Z 1 Obtaining a data correlation matrix Is an N square matrix, (. Cndot. H Representing transposed complex conjugate of matrix, extracting +.>Main diagonal and upper right element of main diagonal and arranged in a column vector in row order +.>For->Normalization processing is carried out to obtain a data feature vector +.>Wherein the method comprises the steps of
According to the first set of training data Z 1 In the same way, by Z 2 ，…，Z m ，…，Z M Obtaining a data characteristic vector R 2 ，…，R m ，…，R M The method comprises the steps of carrying out a first treatment on the surface of the Thereby obtaining a data characteristic vector set R= [ R ] 1 ，R 2 ，…，R m ，…，R M ]；
Step three, utilizing the data feature vector set R and the sound source set theta= [ theta ] 1 ；Θ 2 ，…；Θ m ，…；Θ M ]Training to obtain optimal regression parameter beta of multi-output support vector regression machine omp ；
1) Set data feature vector r= [ R ] 1 ，R 2 ，…，R m ，…，R M ]Bringing into a Gaussian kernel function yields a training sample-based kernel matrix K, where K ij ＝exp(-||R i -R j || 2 /(2σ 2 ) And sigma is the coefficient of the Gaussian kernel function, K ij Elements representing the ith row and jth column of the kernel matrix K, R i And R is j Respectively representing the ith and jth eigenvectors of the data eigenvector set R;
2) Initializing regression parameter matrix beta 0 Is an MxL all-zero matrix, and the initial error matrix e 0 =Θ, according to the initial error matrix e 0 Obtaining an initial Lagrangian parameter factor matrixAnd an initial Lagrangian parameter coefficient matrix +.>Finding u 0 Is satisfied by->Position->And according to its position in u 0 The order of the sequences is stored in the initial support vector matrix +.>And an initial support vector position matrix->According toAnd->Calculating an initial loss function matrix->
Wherein the method comprises the steps ofRepresentation e 0 Is arranged in the row m of the table (a),c is a constant penalty factor, ε is the pipe wall error, (. Cndot.) T The representation matrix takes the transpose,
3) The kth cycle, eta k =1, calculate error matrix e k ＝Θ-Kβ k-1 According to the error matrix e k Obtaining a Lagrange parameter factor matrix u k And Lagrangian parameter coefficient matrix alpha k Find u k Support vector matrix in matrixAnd corresponding support vector position matrix->Calculating regression coefficient descent direction matrix P according to gradient descent method k Calculating regression parameter matrix beta k And a loss function matrix->From obtaining the optimization target parameter L k ；
Lagrange parameter factor matrixLagrangian parameter coefficient matrixWherein->Representation e k Is arranged in the row m of the table (a),finding u k Satisfy->Matrix elements of (a)And the position of the element->And according toIt is at u k Is stored in the support vector matrix according to the sequence of the dataAnd support vector position matrix->According to->And->Calculating a loss function matrix->Wherein->Calculating regression coefficient descent direction matrix P according to gradient descent method k ＝inv(G k ) Θ, matrix-> Representing a matrix which only retains all the elements at the support vector position of the kernel matrix K, the other elements being zero,/->Representing the retention of only the Lagrangian parameter coefficient matrix alpha k Matrix with all the other elements of the elements at the support vector position being zero, inv (·) represents inverting the matrix, diag is the diagonal element of the matrix, and the regression parameter matrix beta k ＝β k-1 +p k Then according to regression parameter matrix beta k A kernel matrix K and a loss function matrix->Constructing an optimization targetFunction->
In particular, u k The matrix satisfiesThe matrix element is->Then support vector matrix +.>Support vector position matrix
4) Comparison L k And L k-1 If L is the size of k ＞L k-1 ，η k ＝γη k ，γ＜1，η k ＝γη k The representation will be eta k Reduced to original gamma times according to the matrix P, gamma and beta k-1 Obtaining the iteration beta k ＝γp k +(1-γ)β k-1 Repeating step 3); if L k ＜L k-1 Jump to step three, 5);
5) Verifying whether or not it satisfiesIf->Then k=k+1 continues with step 3), where k=k+1 means increasing k by 1; if it meets->Jump to step 6) of step three);
6) If it meetsThen is trainedEnding the process; beta at this time k ＝β omp For the optimal regression parameters of the multi-output support vector regression machine, epsilon min Is an error threshold;
step four, using the original test data Z c Processing to obtain data correlation matrixObtaining a test input data characteristic matrix R from the data correlation matrix c The method comprises the steps of carrying out a first treatment on the surface of the Will test the feature vector R c And training data feature matrix r= [ R 1 ，R 2 ，…，R m ，…，R M ] T Carrying out Gaussian kernel function to obtain a calculation test kernel matrix K c And utilizes the optimal regression parameter matrix beta obtained in the training process omp According toEstimating the angle of arrival of the sound source;
the receiving array receives the training interval [ -theta ] 0 ，θ 0 ]K far-field narrow-band independent test sound sources [ theta ] in range 1 ，θ 2 ，…，θ 1 ，…，θ L ]Performing P snapshots on the test signals received by the array to obtain test sound source data Z c From data Z c Obtaining a test data correlation matrixExtracting main diagonal of the test data correlation matrix and main diagonal upper right element and row by row into a column vector +.>Wherein the method comprises the steps of
For a pair ofNormalization processing is carried out to obtain a test feature vector +.>Will test the feature vector R c And training data feature matrix r= [ R 1 ，R 2 ，…，R m ，…，R M ]Test kernel matrix K is calculated by taking Gaussian kernel function c Test core matrix K c Is a 1 XM dimensional matrix, where K Cm ＝exp(-||R C -R m || 2 /(2σ 2 ) For a nuclear matrix K) c The m-th element of (2); and (3) optimizing regression parameters beta of the multi-output support vector regression machine obtained in the step (III) omp Substitution according to->Estimating the angle of arrival of a test sound source
K=1, …, K in the previous step X The number of loops is represented by l=1, …, L represents the number of signal sources in a group of sound sources, m=1, 2, …, and M represents the number of samples; i=1, 2, …, M element positions in the matrix, j=1, 2, …, M represents element positions in the matrix, f=1, 2, …, F represents the number of support vectors;
according to the invention, the array parameter estimation is carried out by utilizing a multi-output support vector regression method, error information is reflected into an optimal regression parameter matrix through data training, and complex processes of array position error modeling and array error correction are not required; the method does not use prior information of the array and does not use signal subspace and noise subspace, so that the coherence of the signals has no influence on the method, and the method can directly process coherent signals and does not need a complex process of decoherence.
The effect of the invention can be further illustrated by the following simulation results:
the simulation experiment conditions are as follows: two far-field and narrow-band sound source signals with different frequencies are incident on the two filters which are arranged at equal intervalsAs shown in fig. 1, the arrival angle of the incident signal is: (θ) 1 ，θ 2 ) = (40 °,60 °) the actual position x= [0.2,1.5,1.7,2.85,4.05,4.5,6.07,7.08,8.7 ] of the array element]The unit is half wavelength; in the interval-90 DEG to O DEG, data training is carried out with the angle interval of 20 DEG, the snapshot number is 200 times, 200 independent experiments are carried out, the simulation experiment results are shown in fig. 3 to 6, when the signal to noise ratio is 15dB in fig. 3 and 4, the MUSIC method and the scatter diagram of the arrival angle estimation of the method can be seen from fig. 3 and 4, the estimated value of the MUSIC method is obviously deviated from the true value (theta 1 ，θ 2 ) = (40 °,60 °), the estimation value of the method of the present invention is equal to the true value (θ 1 ，θ 2 ) Swing in a small range near the range of (40 degrees and 60 degrees), which shows that the parameter estimation method of the multi-output support vector regression machine can give a correct signal arrival angle estimation result under the condition of array position errors; fig. 5 and fig. 6 show root mean square error variation curves of the signal 1 and the signal 2 under different signal to noise ratios of the MUSIC method and the MSVR method (multiple output support vector regression machine is called MSVR for short) of the invention, it can be seen from fig. 5 and fig. 6 that the array position error has a very serious influence on the MUSIC method, no matter how the signal to noise ratio is improved, there is always a larger deviation, the MUSIC method is biased estimation when the array position error exists, and the method of the invention is closer to the true value along with the improvement of the signal to noise ratio, even if the array position error exists, the very accurate signal arrival angle estimation result can be obtained, and the robustness of the array position error is provided;
the present invention is not limited to the above-mentioned embodiments, but is not limited to the above-mentioned embodiments, and any simple modification, equivalent changes and modification made to the above-mentioned embodiments according to the technical matters of the present invention can be made by those skilled in the art without departing from the scope of the present invention.

Claims (1)

1. The parameter estimation method of the multi-output support vector regression machine with array position errors is characterized by comprising the following steps of:
the adopted array is a linear array, the linear array is a uniform linear array which is formed by N sound pressure sensors which are equally spaced on the x axis, and the array element intervals are d x ，d x ≤λ min /2，λ min Is the minimum wavelength of the incident signal, but actually, the intervals between two adjacent array elements are unequal due to human factors or natural reasons, so that the array has position errors;
the parameter estimation method comprises the following steps:
step one, receiving M groups of training intervals [ -theta ] by using a linear array formed by N sound pressure sensors with array position errors as a receiving array 0 ，θ 0 ]Raw training data set Z generated by sound sources within range x ＝[Z 1 ，Z 2 ，…，Z m ，…，Z M ]Sound source set Θ= [ Θ ] 1 ，Θ 2 …，Θ m ，…，Θ M ]；
The training interval is within the range of [ -theta [ ] 0 ，θ 0 ]，0≤θ 0 Less than or equal to 90 DEG, a first group of sound sources Θ 1 ＝[θ 11 ，θ 12 ，…θ 1L ]Incident on a receiving array, the array receives signals P times to obtain N x P first group of original training data Z 1 The method comprises the steps of carrying out a first treatment on the surface of the Maintaining the relative spatial position between the sound sources unchanged, the overall rotation delta phi of the sound sources as the second group of sound sources theta 2 ＝[θ 21 ，θ 22 ，…θ 2L ]At this time, the array receives the signal P times to obtain N×P second set of original training data Z 2 The method comprises the steps of carrying out a first treatment on the surface of the The sound source theta is obtained in the same way 3 ，Θ 4 ，…，Θ M And raw sample data Z 3 ，…，Z M Thereby obtaining the original training data set Z x ＝[Z 1 ，Z 2 ，…，Z m ，…，Z M ]Sound source set Θ= [ Θ ] 1 ；Θ 2 …；Θ m ，…；Θ M ]Wherein L is the number of signal sources in a group of sound sources;
step two, the original training data set Z x ＝[Z 1 ，Z 2 ，…，Z m ，…，Z M ]Obtaining a data characteristic vector set R= [ R ] 1 ，R 2 ，…，R m ，…，R M ]；
From a first set of training data Z 1 Obtaining a data correlation matrix Is a square matrix of N×N, extracting +.>Main diagonal and upper right element of main diagonal and arranged in a column vector in row order +.>For->Normalization processing is carried out to obtain a data feature vector +.>Wherein-> (·) H The representation matrix takes the transposed complex conjugate;
according to the first group of data Z 1 In the same way, by Z 2 ，…，Z m ，…，Z M Obtaining a data characteristic vector R 2 ，R 3 ，...R M The method comprises the steps of carrying out a first treatment on the surface of the Thereby obtaining a data characteristic vector set R= [ R ] 1 ，R 2 …，R m ，…，R M ]；
Training by utilizing the data feature vector set R and the sound source set theta to obtain the optimal regression parameter beta of the multi-output support vector regression machine omp ；
1) Training data feature vector set R= [ R ] 1 ，R 2 ，…，R m ，…，R M ]Carrying out Gaussian kernel function to obtain a kernel matrix K based on a training sample;
wherein K is ij ＝exp(-||R i -R j || 2 /(2σ 2 ) Where σ is the coefficient of the gaussian kernel function, K ij Elements representing the ith row and jth column of the kernel matrix K, R i And R is j Respectively representing the ith and jth eigenvectors of the data eigenvector set R;
2) Initializing regression parameter matrix beta 0 Is an MxL all-zero matrix, and the initial error matrix e 0 =Θ, according to the initial error matrix e 0 Obtaining an initial Lagrangian parameter factor matrixAnd an initial Lagrangian parameter coefficient matrix +.>Finding u 0 Is satisfied by->Position->And according to its position in u 0 The order of the sequences is stored in the initial support vector matrix +.>And an initial support vector position matrix->According toAnd->Calculating an initial loss function matrix->
Wherein the method comprises the steps of Representation e 0 M-th row,/->C is a constant penalty factor, ε is the pipe wall error, (. Cndot.) T Representing the matrix transposes,/->
3) The kth cycle, eta k =1, calculate error matrix e k ＝Θ-Kβ k-1 According to the error matrix e k Obtaining a Lagrange parameter factor matrix u k And Lagrangian parameter coefficient matrix alpha k Find u k Support vector matrix in matrixAnd corresponding support vector position matrix->Calculating regression coefficient descent direction matrix P according to gradient descent method k Calculating regression parameter matrix beta k And a loss function matrix->From obtaining the optimization target parameter L k ；
Lagrange parameter factor matrixLagrangian parameter coefficient matrixWherein->Representation e k Is arranged in the row m of the table (a),finding u k Satisfy->Matrix elements of (a)And the position of the element->And according to its position in u k Is stored in the support vector matrix according to the sequence of the dataAnd support vector position matrix->According to->And->Calculating a loss function matrix->Wherein->Calculating regression coefficient according to gradient descent methodDescending direction matrix P k ＝inv(G k ) Θ, matrix-> Representing a matrix which only retains all the elements at the support vector position of the kernel matrix K, the other elements being zero,/->Representing the retention of only the Lagrangian parameter coefficient matrix alpha k Matrix with all the other elements of the elements at the support vector position being zero, inv represents inversion of the matrix, diag is diagonal element of the matrix, regression parameter matrix beta k ＝β k-1 +p k Then according to regression parameter matrix beta k A kernel matrix K and a loss function matrix->Constructing an optimized objective function->
4) Comparison L k And L k-1 If L is the size of k ＞L k-1 ，η k ＝γη k Gamma < 1 means that eta k Reduced to the original gamma times according to the matrix P k Gamma and beta k-1 Obtaining the iteration beta k ＝γp k +(1-γ)β k-1 Repeating step 3) in step four; if L k ＜L k-1 Jump to step 5) of step four;
5) Verifying whether or not it satisfiesIf->Then k=k+1 continues with step 3) where k=k+1 means increasing k by 1; if it meets->Jump to step 6) in step four);
6) If it meetsThe training process ends; beta at this time k ＝β omp For the optimal regression parameters of the multi-output support vector regression machine, epsilon min Is an error threshold;
step four, using the original test data Z c Processing to obtain data correlation matrixObtaining a test input data characteristic matrix R from the data correlation matrix c The method comprises the steps of carrying out a first treatment on the surface of the Will test the feature vector R c And training data feature matrix r= [ R 1 ，R 2 ，…，R m ，…，R M ]Carrying out Gaussian kernel function to obtain a test kernel matrix K c And utilizes the optimal regression parameter matrix beta obtained in the training process omp According to->Obtaining sound source arrival angle estimation;
the receiving array receives the training interval [ -theta ] 0 ，θ 0 ]K far-field narrowband mutually uncorrelated test signals [ theta ] within range 1 ，θ 2 ，…，θ 1 ，…，θ L ]Performing P snapshots on the test signals received by the array to obtain test signal data Z c From data Z c Obtaining a test data correlation matrixExtracting main diagonal of the test data correlation matrix and main diagonal upper right element and row by row into a column vector +.>For->Normalization treatment is carried out to obtain->Will test the feature vector R c And training data feature matrix r= [ R 1 ，R 2 ，…，R m ，…，R M ]Test kernel matrix K is calculated by taking Gaussian kernel function c Test core matrix K c 1*M, where K Cm ＝exp(-||R C -R m || 2 /(2σ 2 ) A) is provided; according to->Sound source angle estimationWherein the method comprises the steps of
K=1, 2 …, K in the previous step X The number of cycles is represented, 1=1, &..l represents the number of signal sources in a set of sound source signals, m=1, 2, &..m represents the number of samples; i=1, 2, i, M represents the position of the element in the matrix; j=1, 2, M represents the position of the element in the matrix, f=1, 2.,. The term, F represents the number of support vectors.
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8648749B1 (en) * 2010-10-20 2014-02-11 L-3 Services, Inc. Estimation of multiple angles of arrival of signals received by an array of antenna elements
CN103901396A (en) * 2014-03-31 2014-07-02 西安电子科技大学 Coherent signal source sub-resolution and super-resolution arrival angle estimation method
CN106997037A (en) * 2017-02-22 2017-08-01 西安电子科技大学 Acoustic vector-sensor array column space rotates decorrelation LMS angle-of- arrival estimation method

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US10386447B2 (en) * 2015-09-16 2019-08-20 Qatar University Method and apparatus for simple angle of arrival estimation

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8648749B1 (en) * 2010-10-20 2014-02-11 L-3 Services, Inc. Estimation of multiple angles of arrival of signals received by an array of antenna elements
CN103901396A (en) * 2014-03-31 2014-07-02 西安电子科技大学 Coherent signal source sub-resolution and super-resolution arrival angle estimation method
CN106997037A (en) * 2017-02-22 2017-08-01 西安电子科技大学 Acoustic vector-sensor array column space rotates decorrelation LMS angle-of- arrival estimation method

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
协方差矩阵输入的DOA估计方法;陶业荣;安新宇;张义军;李鹏飞;;无线电工程(02);全文 *
采用混合核支持向量机的DOA估计;孙菲艳;田雨波;任作琳;;电讯技术(03);全文 *

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