CN110927663A - Three-dimensional compressed sensing dimension reduction method for near-field sound source parameter estimation - Google Patents

Three-dimensional compressed sensing dimension reduction method for near-field sound source parameter estimation Download PDF

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CN110927663A
CN110927663A CN201910428387.3A CN201910428387A CN110927663A CN 110927663 A CN110927663 A CN 110927663A CN 201910428387 A CN201910428387 A CN 201910428387A CN 110927663 A CN110927663 A CN 110927663A
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matrix
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array
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compressed sensing
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王新宽
王桂宝
王兰美
廖桂生
孙长征
张仲鹏
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Shaanxi University of Technology
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Shaanxi University of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/80—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using ultrasonic, sonic or infrasonic waves
    • G01S3/802—Systems for determining direction or deviation from predetermined direction
    • G01S3/8027—By vectorial composition of signals received by plural, differently-oriented transducers
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S11/00—Systems for determining distance or velocity not using reflection or reradiation
    • G01S11/14—Systems for determining distance or velocity not using reflection or reradiation using ultrasonic, sonic, or infrasonic waves
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/80—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using ultrasonic, sonic or infrasonic waves
    • G01S3/802—Systems for determining direction or deviation from predetermined direction
    • G01S3/803—Systems for determining direction or deviation from predetermined direction using amplitude comparison of signals derived from receiving transducers or transducer systems having differently-oriented directivity characteristics

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Abstract

A three-dimensional compressed sensing dimension reduction method for near-field sound source parameter estimation is characterized in that symmetrical subarrays of uniformly simplified acoustic vector sensors distributed in the z-axis direction are utilized, distance factors are eliminated by calculating a data correlation matrix of vibration velocity sensors in the z-axis direction of symmetrical array elements, a data correlation matrix only containing a pitch angle is obtained, and an estimation value of the pitch angle is obtained through compressed sensing; singular value decomposition is carried out on sound pressure sensor subarray received data, a pitch angle estimation value is substituted into a constructed distance sparse dictionary, and distance estimation is obtained through compressed sensing; singular value decomposition is carried out on received data of a vibration velocity sensor in the z-axis direction of a uniform simplified acoustic vector sensor subarray arranged in the x-axis direction, a pitch angle and a distance are substituted into a constructed azimuth dimension sparse dictionary, and an optimization constraint equation is solved through a compressed sensing method to obtain estimation of an azimuth angle; the method greatly reduces the calculation amount and effectively solves the problem that compressed sensing is used for multi-parameter estimation.

Description

Three-dimensional compressed sensing dimension reduction method for near-field sound source parameter estimation
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a three-dimensional compressed sensing dimension reduction method for near-field sound source parameter estimation.
Background
The compressed sensing parameter estimation method can directly process coherent signals, single snapshot data has good parameter estimation precision, the parameter estimation performance under low signal-to-noise ratio is obviously superior to that of an MUSIC algorithm, the compressed sensing parameter estimation method has the advantages that compressed sensing is widely applied in recent years, but with the increase of parameters, a compressed sensing dictionary increases exponentially, a high-dimensional dictionary brings large calculation amount, a near-field sound source signal is a three-dimensional function of an azimuth angle, a pitch angle and a distance, a three-dimensional sparse dictionary is very huge, and the calculation amount is greatly reduced if the decoupling of multiple parameters can be realized through corresponding data processing by utilizing the structural characteristics of an array and data. The method utilizes the characteristics of the symmetrical structure of the uniformly symmetrical simplified acoustic vector sensor array distributed in the z-axis direction and the particularity of the vibration velocity sensor in the z-axis direction, realizes the decoupling of the azimuth angle, the pitch angle and the distance, changes the three-dimensional compressed sensing into three one-dimensional compressed sensing, and greatly reduces the calculated amount, and is called as a three-step compressed sensing method. The method has the advantages that parameters are automatically paired, extra parameter pairing operation is not needed, coherent signals can be processed, the array aperture loss does not exist, the resolution and the resolution precision of the array are kept, the dimension of a compressed sensing signal matrix is reduced on the premise of improving the signal-to-noise ratio by utilizing multiple times of snapshot data and singular value decomposition, and the parameter estimation precision is improved; the three-step MUSIC method is a dimension reduction method for obtaining three-dimensional parameter estimation by decomposing the characteristics of three groups of different data and respectively searching through spectral peaks.
Disclosure of Invention
The invention aims to provide a method for estimating three-dimensional parameters of a near-field narrow-band incoherent source.
In order to achieve the purpose, the invention adopts the following technical solutions:
the three-dimensional compressed sensing dimensionality reduction method for near-field sound source parameter estimation comprises the steps that a receiving array is a uniform symmetric subarray formed by L2P +1 symmetric array elements which are uniformly distributed on two sides of a z-axis coordinate origin and a uniform orthogonal array formed by P uniform subarrays which are distributed on an x-axis positive half shaft, the array element interval is d, the array element is a simplified acoustic vector sensor formed by a sound pressure sensor and a z-axis sound velocity sensor, and the array element interval is less than or equal to one quarter of the minimum wavelength of an incident signal;
the three-dimensional compressed sensing dimension reduction method for near-field sound source parameter estimation comprises the following steps:
step one, the uniform symmetric orthogonal array is used as a receiving array to receive K incoherent, near-field and narrow-band signals, and M times of snapshot data of L uniform symmetric sub-arrays distributed along the z-axis direction form a z-axis direction vibration velocity sensor sub-array receiving data matrix
Figure BSA0000183524890000021
Receiving data matrix of sound pressure sensor sub-array
Figure BSA0000183524890000022
P vibration velocity sensor subarrays distributed along the x-axis direction and in the z-axis direction of the uniform symmetrical subarrays
Figure BSA0000183524890000023
Step two, receiving a data matrix by a vibration velocity sensor subarray in the z-axis direction
Figure BSA0000183524890000024
Method for solving correlation matrix of symmetric array element data
Figure BSA0000183524890000025
Wherein the content of the first and second substances,
Figure BSA0000183524890000026
is a correlation matrix of the data received by the vibration velocity sensors in the z-axis directions of the-p and the p array elementsHRepresenting the transposed complex conjugate of the matrix,
Figure BSA0000183524890000027
λkis the wavelength of the k-th signal, θkThe angle between the incident direction of the kth signal and the positive direction of the z-axis is called pitch angle,
Figure BSA0000183524890000028
is the variance of the k-th signal,
Figure BSA0000183524890000029
is the variance of the noise; delta (-2p) is the unit impact function; l × K dimensional matrix a ═ a (θ)1)，a(θ2)，...，a(θk)，...，a(θK)]The array steering vector matrix of L x 1 dimension corresponding to the k signal and the signal array steering vector matrix corresponding to the correlation matrix of the symmetric array elements
Figure BSA0000183524890000031
A column vector matrix formed for the K signal powers,
Figure BSA0000183524890000032
in order to select the matrix, the matrix is selected,
Figure BSA0000183524890000033
zero matrix representing dimension 1 × P;
thirdly, constructing an ultra-complete pitch angle sparse dictionary according to the structural form of the signal array steering vector matrix A corresponding to the symmetric array element data correlation matrix in the second step
Figure BSA0000183524890000034
Solving optimization constraint equations by a compressed sensing method
Figure BSA0000183524890000035
Thereby obtaining an estimate of pitch angle
Figure BSA0000183524890000036
Wherein the sparse dictionary
Figure BSA0000183524890000037
Is a signal steering vector matrix of potential signals, NθAs to the number of potential signals,
Figure BSA0000183524890000038
represents the value of x 'that makes the expression take the minimum value, | x' | luminance1Represents the 1 norm of x' | · | | non-woven phosphor2Representing a column vector formed by taking the 2 norm, x 'being the variance of the potential signal, x' being a sparse structure having K non-zero values, the position of each non-zero value corresponding to the elevation angle of the source signal, and Nθ＞＞K，Nθ> L, ε is the error threshold;
step four: forming a received data matrix by utilizing M times of snapshot data of sound pressure sensor subarrays distributed on a z-axis
Figure BSA0000183524890000039
To the received data matrix Z[f]Performing singular value decomposition, Z[f]＝UΣVH，Z[f]Is an L × M matrix, and retains a data matrix corresponding to L × K signal subspaces
Figure BSA00001835248900000310
Wherein Ssv＝SVDk，Nsv＝NVDkObtaining the reduced-dimension sound pressure sensor subarray receiving data matrix distributed on the z axis
Figure BSA00001835248900000311
Wherein
Figure BSA00001835248900000312
A vector matrix is directed to the signal array corresponding to the original data,
Figure BSA00001835248900000313
steering the vector, r, for the kth signal arraykThe distance of the kth signal from the origin of coordinates,
Figure BSA00001835248900000314
u is Z[f]Matrix formed by left eigenvector subjected to singular value decomposition, sigma being Z[f]Diagonal matrix of singular values of singular value decomposition, VHIs Z[f]A matrix formed by right eigenvectors subjected to singular value decomposition, S is a signal matrix formed by M times of snapshot data of the signal, N is a noise matrix received by the sound pressure sensor in the z-axis direction,
Figure BSA0000183524890000041
IKis a unit array of K multiplied by K,
Figure BSA0000183524890000042
is a zero matrix of K (M-K);
step five, obtaining the pitch angle estimated value in the step three
Figure BSA0000183524890000043
Substituting, according to step four original array signal steering vector matrix
Figure BSA0000183524890000044
Constructing distance sparse dictionaries
Figure BSA0000183524890000045
Solving optimization equations by using compressed sensing method
Figure BSA0000183524890000046
Obtaining an estimate of distance
Figure BSA0000183524890000047
Wherein
Figure BSA0000183524890000048
In order to be a distance sparse dictionary,
Figure BSA0000183524890000049
is Frobenius norm, parameter
Figure BSA00001835248900000410
In order to regularize the parameters of the process,
Figure BSA00001835248900000411
represents the matrix SsvThe sum of the squares of the elements in each row constitutes a column vector, min (-) indicates the minimum;
Figure BSA00001835248900000412
Nrthe number of potential signals in the azimuth dimension;
sixthly, utilizing the vibration velocity sensor subarrays of the L uniform symmetrical subarrays distributed along the x-axis direction and in the z-axis direction to perform M times of snapshot data matrix
Figure BSA00001835248900000413
To X[z]Performing singular value decomposition, X[z]＝Ux∑xVx HPreserving the L x K dimensional signal subspace matrix
Figure BSA00001835248900000414
The vibration velocity sensor subarray receiving data matrix of the simplified acoustic vector sensor array distributed along the x-axis direction after dimension reduction in the z-axis direction can be obtained
Figure BSA00001835248900000415
Wherein the content of the first and second substances,
Figure BSA00001835248900000416
Nxnoise matrix, U, received for the x-axis direction of the oscillation velocity sub-arrayxIs X[z]Matrix of left eigenvectors, sigma, subjected to singular value decompositionxIs X[z]The singular values of the singular value decomposition constitute a diagonal matrix,
Figure BSA00001835248900000417
is X[z]Matrix of right eigenvectors subjected to singular value decomposition, and
Figure BSA00001835248900000418
B＝[b(θ1，φ1，r1)，b(θ2，φ2，r2)，…，b(θk，φk，rk)，…，b(θK，φK，rK)]an original steering vector matrix phi of the x-axis direction vibration velocity sub-matrixkThe included angle between the incident direction of the kth signal and the positive direction of the x axis is called azimuth angle, and the array steering vector corresponding to the kth signal is
Figure BSA00001835248900000420
Figure BSA0000183524890000051
Step seven, the angle estimation value obtained in the step three is used
Figure BSA0000183524890000052
And the distance estimation obtained in the fifth step
Figure BSA0000183524890000053
Substituting step six original array signal steering vector matrix B to construct azimuth dimension sparse dictionary
Figure BSA0000183524890000054
Solving optimization equations by using compressed sensing method
Figure BSA0000183524890000055
Obtaining an estimate of the azimuth angle
Figure BSA0000183524890000056
Figure BSA0000183524890000057
As an azimuthal sparse dictionary, NfFor the number of potential signals in the azimuth dimension,
Figure BSA0000183524890000058
to be submergedIn an L x K dimensional matrix of signals,
Figure BSA0000183524890000059
for a sparse matrix with K non-zero rows, the position of each non-zero row corresponds to the azimuth of the source signal,
Figure BSA00001835248900000510
is composed of
Figure BSA00001835248900000511
A column vector obtained by summing the squares of the elements in each row;
k in the previous step is 1, wherein K is a signal number, and n is a signal numberθ＝1，...，NθP is the array element number, and j is the virtual unit vector.
The invention provides a three-dimensional compressed sensing dimension reduction method for near-field sound source parameter estimation, when an incident signal contains three parameters, a three-dimensional sparse dictionary is very huge, the method utilizes the phase characteristics of symmetrical array elements of a z-axis direction vibration velocity sensor subarray of a uniformly symmetrical simplified sound vector sensor subarray distributed on a z axis to realize the separation of a distance and a pitch angle, so that the pitch angle and the distance estimation are obtained through two-step compressed sensing, and finally, the azimuth angle estimation is obtained through compressed sensing by utilizing the z-axis direction vibration velocity sensor subarray of the uniformly simplified sound vector sensor subarray distributed on an x axis.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic diagram of an array structure according to the present invention;
FIG. 2 is a flow chart of the method of the present invention;
FIG. 3 is a spatial spectrum of pitch angle for the method of the present invention at a signal-to-noise ratio of 10 dB;
FIG. 4 is a distance space spectrum of the method of the present invention at a signal-to-noise ratio of 10 dB;
FIG. 5 is a comparison of the pitch angle RMS of the present invention method and a three step MUSIC;
FIG. 6 is a comparison of the azimuthal RMS of the method of the present invention and three-step MUSIC.
Detailed Description
In order to make the aforementioned and other objects, features and advantages of the present invention more apparent, embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
Fig. 1 is a schematic diagram of a receiving array of the present invention, where L ═ 2P +1 symmetric array elements uniformly arranged on both sides of a z-axis coordinate origin constitute a uniform symmetric subarray and P uniform subarrays arranged on an x-axis positive half axis constitute an orthogonal array, the array element interval is d, the array elements are simplified acoustic vector sensors constituted by acoustic pressure sensors and acoustic velocity sensors in x and z directions, and the array element interval is less than or equal to one quarter of the minimum wavelength of an incident signal.
Referring to fig. 2, the near-field narrowband incoherent sound source parameter estimation method of the present invention comprises the following steps: k incoherent near-field narrow-band signals are incident on the receiving array, K is the number of incident sound source signals and is less than or equal to L,
step one, the uniform symmetric orthogonal array is used as a receiving array to receive K incoherent, near-field and narrow-band signals, and M times of snapshot data of L uniform symmetric sub-arrays distributed along the z-axis direction form a z-axis direction vibration velocity sensor sub-array receiving data matrix
Figure BSA0000183524890000061
Receiving data matrix of sound pressure sensor sub-array
Figure BSA0000183524890000062
Z-axis direction of P uniform symmetrical subarrays distributed along x-axis directionThe vibration velocity sensor subarray receives the data matrix
Figure BSA0000183524890000063
Step two, receiving a data matrix by a vibration velocity sensor subarray in the z-axis direction
Figure BSA0000183524890000064
Method for solving correlation matrix of symmetric array element data
Figure BSA0000183524890000065
Wherein the content of the first and second substances,
Figure BSA0000183524890000071
is a correlation matrix of the data received by the vibration velocity sensors in the z-axis directions of the-p and the p array elementsHRepresenting the transposed complex conjugate of the matrix,
Figure BSA0000183524890000072
λkis the wavelength of the k-th signal, θkThe angle between the incident direction of the kth signal and the positive direction of the z-axis is called pitch angle,
Figure BSA0000183524890000073
is the variance of the k-th signal,
Figure BSA0000183524890000074
is the variance of the noise; delta (-2p) is the unit impact function; l × K dimensional matrix a ═ a (θ)1)，a(θ2)，...，a(θk)，...，a(θK)]The array steering vector matrix of L x 1 dimension corresponding to the k signal and the signal array steering vector matrix corresponding to the correlation matrix of the symmetric array elements
Figure BSA0000183524890000075
A column vector matrix formed for the K signal powers,
Figure BSA0000183524890000076
in order to select the matrix, the matrix is selected,
Figure BSA0000183524890000077
zero matrix representing dimension 1 × P;
thirdly, constructing an ultra-complete pitch angle sparse dictionary according to the structural form of the signal array steering vector matrix A corresponding to the symmetric array element data correlation matrix in the second step
Figure BSA0000183524890000078
Solving optimization constraint equations by a compressed sensing method
Figure BSA0000183524890000079
Thereby obtaining an estimate of pitch angle
Figure BSA00001835248900000710
Wherein the sparse dictionary
Figure BSA00001835248900000711
Is a signal steering vector matrix of potential signals, NθAs to the number of potential signals,
Figure BSA00001835248900000712
represents the value of x 'that makes the expression take the minimum value, | x' | luminance1Represents the 1 norm of x' | · | | non-woven phosphor2Representing a column vector formed by taking the 2 norm, x 'being the variance of the potential signal, x' being a sparse structure having K non-zero values, the position of each non-zero value corresponding to the elevation angle of the source signal, and Nθ＞＞K，Nθ> L, ε is the error threshold;
step four: forming a received data matrix by utilizing M times of snapshot data of sound pressure sensor subarrays distributed on a z-axis
Figure BSA00001835248900000713
To the received data matrix Z[f]Performing singular value decomposition, Z[f]＝U∑VH，Z[f]Is an L × M matrix, and retains a data matrix corresponding to L × K signal subspaces
Figure BSA00001835248900000714
Wherein Ssv＝SVDk，Nsv＝NVDkObtaining the reduced-dimension sound pressure sensor subarray receiving data matrix distributed on the z axis
Figure BSA0000183524890000081
Wherein
Figure BSA0000183524890000082
A vector matrix is directed to the signal array corresponding to the original data,
Figure BSA0000183524890000083
steering the vector, r, for the kth signal arraykThe distance of the kth signal from the origin of coordinates,
Figure BSA0000183524890000084
u is Z[f]Matrix formed by left eigenvector subjected to singular value decomposition, sigma being Z[f]Diagonal matrix of singular values of singular value decomposition, VHIs Z[f]A matrix formed by right eigenvectors subjected to singular value decomposition, S is a signal matrix formed by M times of snapshot data of the signal, N is a noise matrix received by the sound pressure sensor in the z-axis direction,
Figure BSA0000183524890000085
IKis a unit array of K multiplied by K,
Figure BSA0000183524890000086
is a zero matrix of K (M-K);
step five, obtaining the pitch angle estimated value in the step three
Figure BSA0000183524890000087
Substituting, according to step four original array signal steering vector matrix
Figure BSA0000183524890000088
Constructing distance sparse dictionaries
Figure BSA0000183524890000089
Solving optimization equations by using compressed sensing method
Figure BSA00001835248900000810
Obtaining an estimate of distance
Figure BSA00001835248900000811
Wherein
Figure BSA00001835248900000812
In order to be a distance sparse dictionary,
Figure BSA00001835248900000813
is Frobenius norm, parameter
Figure BSA00001835248900000814
In order to regularize the parameters of the process,
Figure BSA00001835248900000815
represents the matrix SsvThe sum of the squares of the elements in each row constitutes a column vector, min (-) indicates the minimum;
Figure BSA00001835248900000816
Nrthe number of potential signals in the azimuth dimension;
sixthly, utilizing the vibration velocity sensor subarrays of the L uniform symmetrical subarrays distributed along the x-axis direction and in the z-axis direction to perform M times of snapshot data matrix
Figure BSA00001835248900000817
To X[z]Performing singular value decomposition, X[z]＝Ux∑xVx HPreserving the L x K dimensional signal subspace matrix
Figure BSA00001835248900000818
Can obtain the distribution along the x-axis direction after dimension reductionThe vibration velocity sensor subarray in the z-axis direction of the simplified acoustic vector sensor array receives the data matrix
Figure BSA00001835248900000819
Wherein the content of the first and second substances,
Figure BSA0000183524890000091
Nxnoise matrix, U, received for the x-axis direction of the oscillation velocity sub-arrayxIs X[z]Matrix of left eigenvectors, sigma, subjected to singular value decompositionxIs X[z]The singular values of the singular value decomposition constitute a diagonal matrix,
Figure BSA0000183524890000092
is X[z]Matrix of right eigenvectors subjected to singular value decomposition, and
Figure BSA0000183524890000093
B＝[b(θ1，φ1，r1)，b(θ2，φ2，r2)，…，b(θk，φk，rk)，…，b(θK，φK，rK)]an original steering vector matrix phi of the x-axis direction vibration velocity sub-matrixkThe included angle between the incident direction of the kth signal and the positive direction of the x axis is called azimuth angle, and the array steering vector corresponding to the kth signal is
Figure BSA0000183524890000094
Figure BSA0000183524890000095
Step seven, the angle estimation value obtained in the step three is used
Figure BSA0000183524890000096
And the distance estimation obtained in the fifth step
Figure BSA0000183524890000097
Substituting step six original arrayMethod for constructing azimuth dimension sparse dictionary by column signal steering vector matrix B
Figure BSA0000183524890000098
Solving optimization equations by using compressed sensing method
Figure BSA0000183524890000099
Obtaining an estimate of the azimuth angle
Figure BSA00001835248900000910
Figure BSA00001835248900000911
As an azimuthal sparse dictionary, NfFor the number of potential signals in the azimuth dimension,
Figure BSA00001835248900000912
an L x K dimensional matrix constructed for the underlying signals,
Figure BSA00001835248900000913
for a sparse matrix with K non-zero rows, the position of each non-zero row corresponds to the azimuth of the source signal,
Figure BSA00001835248900000914
is composed of
Figure BSA00001835248900000915
A column vector obtained by summing the squares of the elements in each row;
k in the previous step is 1, wherein K is a signal number, and n is a signal numberθ＝1，...，NθP is the array element number, and j is the virtual unit vector.
The method of the invention utilizes an orthogonal array formed by symmetrical subarrays of simplified acoustic vector sensors distributed in the z-axis direction and uniform subarrays distributed in the x-axis positive semi-axis, three-step compressed sensing is used for estimating three-dimensional parameters of a pitch angle, an azimuth angle and a distance of a near-field source, and a three-dimensional sparse dictionary is reduced into three one-dimensional sparse dictionaries;
the effect of the present invention can be further illustrated by the following simulation results:
the simulation experiment conditions are as follows:
the number L of the array elements of the Z-axis symmetric subarray is 13, the number P of the array elements of the x-axis uniform subarray is 6, and the interval between the adjacent array elements is d lambdaminAnd 4, setting the parameters of two incoherent near-field sound sources to be (theta)1，φ1，r1)＝(-10°，30°，5λmin) And (theta)2，φ2，r2)＝(30°，60°，10λmin) The fast african number is 100, the Monte Carlo experiment number is 100, and the noise is white Gaussian noise. At [0 °, 360 ° ]]In azimuth space, divided by a grid of 0.1 degree intervals in distance space [0, 15 lambda ]min]At 0.1 lambdaminThe grid division is carried out, the information source parameters are estimated at 10dB, fig. 3 is a power spectrogram for estimating the pitch angle by the method, the peak value of the spectrogram is very sharp as can be seen from fig. 3, and the position where the peak value appears is at the position of a real signal source, which shows that the method can accurately estimate the pitch angle of the near-field sound source. Fig. 4 is a distance estimation power spectrum of the method of the present invention, and it can be seen from fig. 4 that the method of the present invention can obtain the estimation of the distance very accurately. FIG. 5 and FIG. 6 show the comparison graphs of root mean square error of pitch angle and azimuth angle estimation under 20 times of snapshots for the method and the three-step MUSIC method, and it can be seen from FIG. 5 and FIG. 6 that the performance of the method of the present invention is obviously superior to that of the three-step MUSIC method when the signal-to-noise ratio is-5 dB, the method of the present invention is superior to that of the three-step MUSIC method under low snapshots and low signal-to-noise ratios, the performance of the MUSIC algorithm is rapidly improved along with the increase of the signal-to-noise ratio and the number of snapshots, and the three-step compressive sensing method is particularlyAnd (6) estimating.
Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (1)

1. The three-dimensional compressed sensing dimension reduction method for near-field sound source parameter estimation is characterized by comprising the following steps of:
the receiving array used by the method is an orthogonal array formed by L-2P +1 symmetrical array elements which are uniformly arranged at two sides of a z-axis coordinate origin to form a uniform symmetrical subarray and P uniform subarrays which are arranged at an x-axis positive half shaft, the intervals of the array elements are d respectively, and the d is not less than lambdamin/4，λminIs the minimum wavelength of the incident signal;
the three-dimensional compressed sensing dimension reduction method for near-field sound source parameter estimation comprises the following steps: the array receives K near-field, narrow-band, incoherent signals,
step one, the uniform symmetric orthogonal array is used as a receiving array to receive K incoherent, near-field and narrow-band signals, and M times of snapshot data of L uniform symmetric sub-arrays distributed along the z-axis direction form a z-axis direction vibration velocity sensor sub-array receiving data matrix
Figure FSA0000183524880000011
Receiving data matrix of sound pressure sensor sub-array
Figure FSA0000183524880000012
P vibration velocity sensor subarrays distributed along the x-axis direction and in the z-axis direction of the uniform symmetrical subarrays
Figure FSA0000183524880000013
Step two, receiving a data matrix by a vibration velocity sensor subarray in the z-axis direction
Figure FSA0000183524880000014
Method for solving correlation matrix of symmetric array element data
Figure FSA0000183524880000015
Wherein the content of the first and second substances,
Figure FSA0000183524880000016
is a correlation matrix of the data received by the vibration velocity sensors in the z-axis directions of the-p and the p array elementsHRepresenting the transposed complex conjugate of the matrix,
Figure FSA0000183524880000017
λkis the wavelength of the k-th signal, θkThe angle between the incident direction of the kth signal and the positive direction of the z-axis is called pitch angle,
Figure FSA0000183524880000018
is the variance of the k-th signal,
Figure FSA0000183524880000019
is the variance of the noise; delta (-2p) is the unit impact function; l × K dimensional matrix a ═ a (θ)1)，a(θ2)，...，a(θk)，...，a(θK)]The array steering vector matrix of L x 1 dimension corresponding to the k signal and the signal array steering vector matrix corresponding to the correlation matrix of the symmetric array elements
Figure FSA0000183524880000021
A column vector matrix formed for the K signal powers,
Figure FSA0000183524880000022
in order to select the matrix, the matrix is selected,
Figure FSA0000183524880000023
zero matrix representing dimension 1 × P;
thirdly, constructing an ultra-complete pitch angle sparse dictionary according to the structural form of the signal array steering vector matrix A corresponding to the symmetric array element data correlation matrix in the second step
Figure FSA0000183524880000024
Solving optimization constraint equations by a compressed sensing method
Figure FSA0000183524880000025
Thereby obtaining an estimate of pitch angle
Figure FSA0000183524880000026
Wherein the sparse dictionary
Figure FSA0000183524880000027
Is a signal steering vector matrix of potential signals, NθAs to the number of potential signals,
Figure FSA0000183524880000028
represents the value of x 'that makes the expression take the minimum value, | x' | luminance1Represents the 1 norm of x' | · | | non-woven phosphor2Representing a column vector formed by taking the 2 norm, x 'being the variance of the potential signal, x' being a sparse structure having K non-zero values, the position of each non-zero value corresponding to the elevation angle of the source signal, and Nθ＞＞K，Nθ> L, ε is the error threshold;
step four: forming a received data matrix by utilizing M times of snapshot data of sound pressure sensor subarrays distributed on a z-axis
Figure FSA0000183524880000029
To the received data matrix Z[f]Performing singular value decomposition, Z[f]＝U∑VH，Z[f]Is L-M matrix, retaining data matrix corresponding to L × K signal subspace
Figure FSA00001835248800000210
Wherein Ssv＝SVDk，Nsv＝NVDkObtaining the reduced-dimension sound pressure sensor subarray receiving data matrix distributed on the z axis
Figure FSA00001835248800000211
Wherein
Figure FSA00001835248800000212
A vector matrix is directed to the signal array corresponding to the original data,
Figure FSA00001835248800000213
steering the vector, r, for the kth signal arraykThe distance of the kth signal from the origin of coordinates,
Figure FSA00001835248800000214
u is Z[f]Matrix formed by left eigenvector subjected to singular value decomposition, sigma being Z[f]Diagonal matrix of singular values of singular value decomposition, VHIs Z[f]A matrix formed by right eigenvectors subjected to singular value decomposition, S is a signal matrix formed by M times of snapshot data of the signal, N is a noise matrix received by the sound pressure sensor in the z-axis direction,
Figure FSA0000183524880000031
IKis a unit array of K multiplied by K,
Figure FSA0000183524880000032
is a zero matrix of K (M-K);
step five, obtaining the pitch angle estimated value in the step three
Figure FSA0000183524880000033
Substituting, according to step four original array signal steering vector matrix
Figure FSA0000183524880000034
Constructing distance sparse dictionaries
Figure FSA0000183524880000035
Solving optimization equations by using compressed sensing method
Figure FSA0000183524880000036
Obtaining an estimate of distance
Figure FSA0000183524880000037
Wherein
Figure FSA0000183524880000038
In order to be a distance sparse dictionary,
Figure FSA0000183524880000039
is Frobenius norm, parameter
Figure FSA00001835248800000310
In order to regularize the parameters of the process,
Figure FSA00001835248800000311
represents the matrix SsvThe sum of the squares of the elements in each row constitutes a column vector, min (-) indicates the minimum;
Figure FSA00001835248800000312
Nrthe number of potential signals in the azimuth dimension;
sixthly, utilizing the vibration velocity sensor subarrays of the L uniform symmetrical subarrays distributed along the x-axis direction and in the z-axis direction to perform M times of snapshot data matrix
Figure FSA00001835248800000313
To X[z]Performing singular value decomposition, X[z]＝Ux∑xVx HPreserving the L x K dimensional signal subspace matrix
Figure FSA00001835248800000314
The vibration velocity sensor subarray receiving data matrix of the simplified acoustic vector sensor array distributed along the x-axis direction after dimension reduction in the z-axis direction can be obtained
Figure FSA00001835248800000315
Wherein the content of the first and second substances,
Figure FSA00001835248800000316
Nxnoise matrix, U, received for the x-axis direction of the oscillation velocity sub-arrayxIs X[z]Matrix of left eigenvectors, sigma, subjected to singular value decompositionxIs X[z]The singular values of the singular value decomposition constitute a diagonal matrix,
Figure FSA00001835248800000317
is X[z]Matrix of right eigenvectors subjected to singular value decomposition, and
Figure FSA00001835248800000318
B＝[b(θ1，φ1，r1)，b(θ2，φ2，r2)，…，b(θk，φk，rk)，…，b(θK，φK，rK)]an original steering vector matrix phi of the x-axis direction vibration velocity sub-matrixkThe included angle between the incident direction of the kth signal and the positive direction of the x axis is called azimuth angle, and the array steering vector corresponding to the kth signal is
Figure FSA00001835248800000319
Figure FSA0000183524880000041
Step seven, the angle estimation value obtained in the step three is used
Figure FSA0000183524880000042
And the distance estimation obtained in the fifth step
Figure FSA0000183524880000043
Substituting step six original array signal steering vector matrix B to construct azimuth dimension sparse dictionary
Figure FSA0000183524880000044
Solving optimization equations by using compressed sensing method
Figure FSA0000183524880000045
Obtaining an estimate of the azimuth angle
Figure FSA0000183524880000046
Figure FSA0000183524880000047
As an azimuthal sparse dictionary, NfFor the number of potential signals in the azimuth dimension,
Figure FSA0000183524880000048
an L x K dimensional matrix constructed for the underlying signals,
Figure FSA0000183524880000049
for a sparse matrix with K non-zero rows, the position of each non-zero row corresponds to the azimuth of the source signal,
Figure FSA00001835248800000410
is composed of
Figure FSA00001835248800000411
A column vector obtained by summing the squares of the elements in each row;
k in the previous step is 1, wherein K is a signal number, and n is a signal numberθ＝1，...，NθP is the array element number, and j is the virtual unit vector.
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