CN106932087A - Circular acoustic vector-sensor array row near field sources Multiple Parameter Estimation Methods - Google Patents

Circular acoustic vector-sensor array row near field sources Multiple Parameter Estimation Methods Download PDF

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CN106932087A
CN106932087A CN201710171735.4A CN201710171735A CN106932087A CN 106932087 A CN106932087 A CN 106932087A CN 201710171735 A CN201710171735 A CN 201710171735A CN 106932087 A CN106932087 A CN 106932087A
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CN106932087B (en
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王桂宝
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Shenzhen Jingkaisi Technology Co ltd
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Shaanxi University of Technology
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    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
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Abstract

Circular acoustic vector-sensor array row near field sources Multiple Parameter Estimation Methods, step is as follows：Output signal to acoustic vector-sensor array row is sampled,Constituted using direct sampled data and time delay sampled data and receive the total evidence of signal,Signal subspace and noise subspace are obtained by the feature decomposition of data correlation matrix,Estimated using the invariable rotary Relation acquisition signal array steering vector between data before and after time delay and signal frequency,Signal guide vector is divided into four submatrix steering vectors,And the rough estimate value of angle of arrival and sound source distance is obtained using the ratio relation between submatrix steering vector,The fine estimation of direction of arrival and distance is searched in rough estimate value near zone by MUSIC algorithms,The present invention makes full use of acoustic vector sensors invariable rotary structure intrinsic in itself,Rough estimate is carried out using ESPRIT algorithms and be combined the accurate estimation of realizing angle of arrival and distance with MUSIC zonules essence search method,The inventive method has amount of calculation small,Algorithm is simple,Advantage easy to use.

Description

Circular acoustic vector sensor array near-field source multi-parameter estimation method
Technical Field
The invention belongs to the technical field of array signal processing, and particularly relates to a method for estimating near-field source frequency, a two-dimensional arrival angle and a distance of an acoustic vector sensor array.
Background
The acoustic vector sensor is formed by compounding a nondirectional sound pressure sensor and three mutually perpendicular particle vibration velocity sensors with dipole directivity, and can synchronously measure the sound pressure intensity and particle vibration velocity information of a sound wave signal, so that the acoustic vector sensor is increasingly widely applied to the fields of radar, sonar, communication, aerospace, aviation and the like, when a signal source falls into a Fresnel area with an array aperture, the signal source is called a near-field source, a plurality of parameters of distance and arrival angle need to be estimated for positioning the near-field source, and near-field sound source position positioning based on an acoustic vector sensor array becomes a research hotspot of domestic and foreign scholars.
The method for estimating the array high-resolution parameters based on the subspace theory is applied to near-field information source target positioning, near-field source parameter estimation of the Liunan in the 2014 greater university level thesis (title: near-field source multi-parameter estimation based on an acoustic vector sensor) under the Gaussian white noise background is performed by using a two-dimensional multi-signal classification method, Gaussian stationary noise can be inhibited, MUSIC search based on double-quaternion needs to be performed, three-dimensional search needs to be performed on a two-dimensional arrival angle and a two-dimensional distance, and improvement of the arrival angle estimation resolution depends on a fine array search interval, so that the method has the defect of large calculation amount. The invention adopts a uniform circular acoustic vector sensor array, and provides a signal parameter (ESPRIT) and a multi-signal classification Method (MUSIC) parameter estimation method by using a rotation invariant technology of the arrival angle, the frequency and the distance of a near-field source, firstly, the invention fully utilizes the inherent rotation invariant structure of the acoustic vector sensor, utilizes an ESPRIT algorithm to carry out parameter estimation, provides rough estimation values of the arrival angle and the distance of the near-field source signal, and then utilizes the MUSIC algorithm to search near the rough values to obtain the precise estimation values of the arrival angle and the distance of the signal in the full parameter space, and the method does not need three-dimensional search in the full parameter space and the parameters are automatically paired; therefore, the calculation amount is greatly reduced, and the near-field source parameter estimation precision of the acoustic vector sensor array under the condition of the limited number of the array elements is improved. For near-field sound source signals, the phase difference between array elements is not only related to the distance between the array elements and the direction of an incident signal, but also related to the distance from the sound source to the array elements, so that a far-field condition has a uniform linear array, a uniform L array and the like with a translation invariant structure, and for a near field, the translation invariant structure does not exist, so that the existing literature rarely relates to an ESPRIT parameter estimation algorithm of a near-field source.
Disclosure of Invention
The invention aims to provide a near-field source circular acoustic vector sensor array multi-parameter joint estimation method based on ESPRIT and MUSIC.
In order to achieve the purpose, the invention adopts the following technical solutions:
a near-field source multi-parameter estimation method for a circular acoustic vector sensor array is characterized in that K narrow-band random stationary near-field sound source signals with different frequencies and different irrelevantness are respectively from different directions and different distances (theta)k，φk，rk) Incident on an array of circular acoustic vector sensors, thetakIs the pitch angle of the incident signal, phikIs the azimuth angle of the incident signal, rkFor the distance between the kth signal and the array element of the origin of coordinates, the circular array is composed of M array elements which are arranged on the circumference with the radius of R at equal intervals, the circle center of the circumference is used as the origin of coordinates, the same acoustic vector sensor is placed at the origin of coordinates to be used as a reference array element, the array element is an acoustic vector sensor composed of a sound pressure sensor and sensors for the vibration velocity in the directions of the x axis, the y axis and the z axis, and corresponding channels of all the sensors are parallel to each other: all the sound pressure sensors are parallel to each other, all the vibration velocity sensors in the x-axis direction are parallel to each other, all the vibration velocity sensors in the y-axis direction are parallel to each other, all the vibration velocity sensors in the z-axis direction are parallel to each other, and the vibration velocity sensors in the x-axis direction, the vibration velocity sensors in the y-axis direction and the vibration velocity sensors in the z-axis direction are mutually perpendicular to each other in pairs; the interval between adjacent array elements on the circular array is lambdamin/(8sin(π/M))，λminIs the minimum wavelength of the incident acoustic signalAnd the distance between the circle radius R and the array element interval and the wavelength of the incident sound wave signal and the distance of the sound source meet the near field condition;
the near-field source multi-parameter estimation method comprises the following steps:
acquiring receiving data of a near-field acoustic wave signal by using a circular array;
the N times of snapshot data of the round receiving array receiving signal form direct sampling data Z1The N times of synchronous snapshot data after the delay of the received signal is delta T form the delay sampling data Z2From Z1And Z2The two sets of data constitute the full data of the received signalWhereinfsAt the nyquist sampling frequency;
acquiring a signal subspace and a noise subspace by utilizing the received signal full data;
estimating a full data correlation matrixWhere A is the full data signal steering vector matrix, Rs＝SSHN is the incident signal correlation matrix, σ2Is the power of Gaussian white noise, I is an identity matrix of 8M × 8M, and according to the subspace theory, a data correlation matrix R is obtainedZCharacteristic decomposition is carried out to obtain a signal subspace UsSum noise subspace UN，Where EVD represents the eigen decomposition, λiIs the i-th eigenvalue, v, obtained by the feature decompositioniIs the ith feature vector, U, corresponding to the feature values＝[v1，...，vK]Signal subspaces, U, formed for eigenvectors corresponding to K large eigenvaluesN＝[vK+1，...，v8M]A noise subspace formed by the feature vectors corresponding to the 8M-K small feature values;
step three, estimating a signal steering vector matrixSum signal frequency
Signal subspace U of 8M × KsDivided into an upper 4M × K matrix U and a lower matrix U1And U2By using a time-rotation invariant relation structure, composed of U1And U2Obtaining psi T ═ Ω T by matrix operation, whereinPerforming characteristic decomposition on the matrix psi, and forming a matrix by characteristic valuesFeature vector construction matrixWhereinIs an estimate of the value of omega,is an estimate of T, resulting in an estimate of the signal steering vector matrix and signal frequency:
wherein arg (·) represents the argument,representation matrixThe k-th row and k-th column elements are taken,Us＝AT，U1＝A1T，U2＝A2t, A is the full data array steering vector matrix in step two, A1Is a direct sampling data array steering vector matrix, A2Is a time-delay sampling data array guide vector matrix, T is a non-singular matrix of K × K,is a matrix U1The pseudo-inverse matrix of (a) is,
obtaining a normalization vector of the x-axis vibration velocity, the y-axis vibration velocity and the sound pressure of the kth signal to the z-axis vibration velocity according to the composition and array arrangement of the signal guide vector, and obtaining rough estimated values of the arrival angle and the sound source distance by utilizing the normalization vector;
directing signals to vector estimates based on the configuration of the acoustic vector sensor and the array configurationThe K (K is more than or equal to 1 and less than or equal to K) column of the array is divided into matrix blocks corresponding to each array element,to representThe (c) th column of (a),
the kth column representing the mth array element,the three components of the vibration speed in the x-axis direction, the y-axis direction and the sound pressure are compared with the vibration speed component in the z-axis direction to obtain a normalized vectorObtaining the normalized vector of the kth signal by averaging the normalized vectors of M array elementsObtaining a rough estimation value of the arrival angle of the signal according to the ratio relationsRough estimation value of distance to sound source
The normalized vector for the kth signal is:
thus, estimates of angle of arrival and distance are obtained:
wherein,is the distance between the kth signal and the element of the origin of coordinates, λkIs the wavelength of the k-th signal, p0Is the ambient fluid density, c is the acoustic wave propagation velocity, vector quantitykExp (-) is an exponential operation, tan (-) and arctan (-) respectively represent tangent and arctangent operations;
step five, searching accurate estimated values of the arrival angle and the distance of the signal near the rough value by using the MUSIC algorithm;
by using the structural form of a circular array, a full data array guide vector in a small area near a rough estimation value is givenMethod for searching peak by using MUSIC spectrumSearching near the rough value to obtain an accurate estimation value of the signal;
wherein,is a space domain steering vector formed by the phase difference of a signal arrival array element m and a reference array element,for incident sound source signal to reach the phase of array element m and reference array elementDifference, UnAnd 5, in the noise subspace obtained in the step two, the vibration velocity components and the sound pressure scalars in the directions of the x axis, the y axis and the z axis of the unit energy signal are as follows:
theta, phi, r are the search variables,
andrespectively a rough estimate of azimuth angle, pitch angle and distance in step four,θ、φandrthe search interval lengths are respectively used for setting a pitch angle, an azimuth angle and a distance;
in the above steps, K is 1, a., K, M is 1, a., M, n is 1, a.
The array adopted by the invention is a uniform circular array, the array element of the array is an acoustic vector sensor which is composed of a sound pressure sensor and vibration velocity sensors in the directions of an x axis, a y axis and a z axis, all the sound pressure sensors are parallel to each other, all the vibration velocity sensors in the direction of the x axis are parallel to each other, all the vibration velocity sensors in the direction of the y axis are parallel to each other, and all the vibration velocity sensors in the direction of the z axis are parallel to each other.
The invention provides a near-field source multi-parameter ESPRIT estimation algorithm of a circular acoustic vector sensor array, which can not estimate the parameters of a near-field sound source signal by using the ESPRIT algorithm for a general scalar sensor array such as a microphone array, because the wave surface of a near field is spherical wave; the phase between array elements is not only related to the array element spacing and the direction of an incident signal, but also related to the distance from a sound source to the array elements, so that a far field condition has a uniform linear array, a uniform L array and the like with a translation invariant structure, a near field does not have a translation invariant structure, and an ESPRIT algorithm cannot be utilized.
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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 acoustic vector 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 angle of arrival estimates for the method of the present invention of a simulation experiment;
FIG. 4 is a graph of the variation of the RMS error of the azimuth angle estimate with the SNR of the present invention;
FIG. 5 is a graph of the variation of the root mean square error of the pitch angle estimation with the signal to noise ratio according to the method of the present invention;
FIG. 6 is a graph of the variation of the RMS error of the angle of arrival estimate with the signal-to-noise ratio of the method of the present invention;
FIG. 7 is a graph of the RMS error as a function of the signal-to-noise ratio for the method of the present invention;
fig. 8 is a graph of the success probability of angle of arrival estimation as a function of the signal to noise ratio in the method of the present invention.
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 an acoustic vector sensor array according to an embodiment of the present invention. The acoustic vector sensor array is composed of M array elements which are arranged on a circumference with the radius of R at equal intervals, the circle center of the circumference is used as a coordinate origin, the same acoustic vector sensors are placed at the coordinate origin to serve as reference array elements, and the interval between the adjacent array elements of the circular array is lambdamin/(8sin (pi/M)), the array element of the array is an acoustic vector sensor consisting of an acoustic pressure sensor and vibration velocity sensors in the directions of the x axis, the y axis and the z axis, wherein lambda isminIs the minimum wavelength of the incident signal.
Referring to fig. 2, the multi-parameter estimation method of the present invention comprises the following steps: the circular acoustic vector sensor array receives K independent narrow-band random steady near-field acoustic source signals with different frequencies, K is the number of incident acoustic source signals and is less than or equal to M-1,
acquiring receiving data of a near-field acoustic wave signal by using a circular array;
the N times of snapshot data of the round receiving array receiving signal form direct sampling data Z1The N times of synchronous snapshot data after the delay of the received signal is delta T form the delay sampling data Z2From Z1And Z2The two sets of data constitute the full data of the received signalWhereinfsAt the nyquist sampling frequency;
acquiring a signal subspace and a noise subspace by utilizing the received signal full data;
estimating a full data correlation matrixWhere A is the full data signal steering vector matrix, Rs＝SSHN is the incident signal correlation matrix, σ2Is the power of Gaussian white noise, I is an identity matrix of 8M × 8M, and according to the subspace theory, a data correlation matrix R is obtainedZCharacteristic decomposition is carried out to obtain a signal subspace UsSum noise subspace UN，Where EVD represents the eigen decomposition, λiIs the i-th eigenvalue, v, obtained by the feature decompositioniIs the ith feature vector, U, corresponding to the feature values＝[v1，...，vK]Signal subspaces, U, formed for eigenvectors corresponding to K large eigenvaluesN＝[vK+1，...，v8M]A noise subspace formed by the feature vectors corresponding to the 8M-K small feature values;
step three, estimating a signal steering vector matrixSum signal frequency
Signal subspace U of 8M × KsDivided into an upper 4M × K matrix U and a lower matrix U1And U2By using a time-rotation invariant relation structure, composed of U1And U2Obtaining psi T ═ Ω T by matrix operation, whereinPerforming characteristic decomposition on the matrix psi, and forming a matrix by characteristic valuesFeature vector construction matrixWhereinIs an estimate of the value of omega,is an estimate of T, resulting in an estimate of the signal steering vector matrix and signal frequency:
wherein arg (·) represents the argument,representation matrixThe k-th row and k-th column elements are taken,Us＝AT，U1＝A1T，U2＝A2t, A is the full data array steering vector matrix in step two, A1Is a direct sampling data array steering vector matrix, A2Is a time-delay sampling data array guide vector matrix, T is a non-singular matrix of K × K,is a matrix U1The pseudo-inverse matrix of (a) is,
obtaining a normalization vector of the x-axis vibration velocity, the y-axis vibration velocity and the sound pressure of the kth signal to the z-axis vibration velocity according to the composition and array arrangement of the signal guide vector, and obtaining rough estimated values of the arrival angle and the sound source distance by utilizing the normalization vector;
directing signals to vector estimates based on the configuration of the acoustic vector sensor and the array configurationThe K (K is more than or equal to 1 and less than or equal to K) column of the array is divided into matrix blocks corresponding to each array element,to representThe (c) th column of (a),
the kth column representing the mth array element,the three components of the vibration speed in the x-axis direction, the y-axis direction and the sound pressure are compared with the vibration speed component in the z-axis direction to obtain a normalized vectorObtaining the normalized vector of the kth signal by averaging the normalized vectors of M array elementsAccording to the ratio relationshipRough estimation value of signal arrival angleRough estimation value of distance to sound source
The normalized vector for the kth signal is:
thus, estimates of angle of arrival and distance are obtained:
wherein,is the distance between the kth signal and the element of the origin of coordinates, λkIs the wavelength of the k-th signal, p0Is the ambient fluid density, c is the acoustic wave propagation velocity, vector quantitykExp (-) is an exponential operation, tan (-) and arctan (-) respectively represent tangent and arctangent operations;
step five, searching accurate estimated values of the arrival angle and the distance of the signal near the rough value by using the MUSIC algorithm;
by using the structural form of a circular array, a full data array guide vector in a small area near a rough estimation value is givenMethod for searching peak by using MUSIC spectrumSearching near the rough value to obtain an accurate estimation value of the signal;
wherein,is a space domain steering vector formed by the phase difference of a signal arrival array element m and a reference array element,for the phase difference, U, of incident acoustic source signals arriving at array element m and reference array elementnAnd 5, in the noise subspace obtained in the step two, the vibration velocity components and the sound pressure scalars in the directions of the x axis, the y axis and the z axis of the unit energy signal are as follows:
theta, phi, r are the search variables,
andrespectively a rough estimate of azimuth angle, pitch angle and distance in step four,θ、φandrsearch interval lengths for setting pitch angle, azimuth angle and distance, respectively；
In the above steps, K is 1, a., K, M is 1, a., M, n is 1, a.
The invention estimates the signal array guide vector and the signal frequency by using the time rotation invariant structure of the data before and after the delay, divides the array guide vector into four sub-arrays of an x axis, a y axis, a z axis and sound pressure, obtains the rough estimation value of the signal arrival angle and the sound source distance by using the ratio relation of corresponding elements among the sub-arrays, and carries out precise search by using the MUSIC algorithm in the area near the rough estimation value to obtain the precise signal arrival angle and the precise distance estimation value.
The effect of the present invention can be further illustrated by the following simulation results:
the simulation experiment conditions are as follows:
two narrow-band random stationary near-field sound source signals with different frequencies and unrelated to each other are incident to a circular acoustic vector sensor array formed by 9 array elements which are arranged on a circumference with the radius of R at equal intervals, as shown in figure 1, the interval between every two adjacent array elements is lambdamin/(8sin (π/9)), the parameters of the incident signal are: (theta)1，φ1)＝(20°，50°)，(θ2，φ2) As (30 °, 70 °) normalized frequency of (f)1，f2) Fast beat number was 1024 times (0.3, 0.4) and 200 independent experiments.
The simulation experiment results are shown in fig. 3 to 8, fig. 3 is a scatter diagram of the estimation of the arrival angle of the method of the present invention when the signal-to-noise ratio is 15dB, and it can be seen from fig. 3 that the estimation values of the azimuth angle and the pitch angle of the method of the present invention are scattered in a smaller range near the true value, and the estimation of the arrival angle of the method of the present invention has higher parameter estimation accuracy; from fig. 4 and 7, it can be seen that the root mean square error of the azimuth angle, the pitch angle, the arrival angle and the distance estimation of the method of the present invention is small, that is, the estimation value is trueDisturbance in a small range near the value, the arrival angle and distance estimation of the method have higher parameter estimation accuracy, because the method fully utilizes the inherent rotation invariant structure of the acoustic vector sensor, utilizes an ESPRIT algorithm to carry out parameter rough estimation, and improves the parameter estimation accuracy through the accurate search processing of the MUSIC small-area range; the success probability of the arrival angle estimation means that the estimated values of the pitch angle and the azimuth angle meet the requirements in 200 independent testsThe number of experiments of (a) is a percentage of the total number of experiments; wherein, theta0And phi0The true value is true for the time being,andreferring to the estimated value of the ith experiment, as can be seen from fig. 8, the method of the present invention has a high success probability, when the signal-to-noise ratio is-10 dB, the success probabilities of the signal one and the signal two are 20% and 30%, respectively, and when the signal-to-noise ratio is 0dB, the success probabilities of both the signals are higher than 80%.
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 near-field source multi-parameter estimation method of the circular acoustic vector sensor array is characterized by comprising the following steps of:
the acoustic vector sensor array is composed of M array elements which are arranged on a circumference with the radius of R at equal intervals, the circle center of the circumference is used as a coordinate origin, the same acoustic vector sensors are placed at the coordinate origin to serve as reference array elements, and the interval between the adjacent array elements of the circular array is lambdamin/(8sin (pi/M)), the array elements of the array are acoustic vector sensors consisting of acoustic pressure sensors and vibration velocity sensors in the directions of the x axis, the y axis and the z axis, wherein lambda isminFor entering into a letterThe minimum wavelength of the number;
the near-field source multi-parameter estimation method comprises the following steps: the array receives K independent narrow-band random stationary near-field source signals with different frequencies,
acquiring receiving data of a near-field acoustic wave signal by using a circular array;
the N times of snapshot data of the round receiving array receiving signal form direct sampling data Z1The N times of synchronous snapshot data after the delay of the received signal is delta T form the delay sampling data Z2From Z1And Z2The two sets of data constitute the full data of the received signalWhereinfsAt the nyquist sampling frequency;
acquiring a signal subspace and a noise subspace by utilizing the received signal full data;
estimating a full data correlation matrixWhere A is the full data signal steering vector matrix, Rs＝SSHN is the incident signal correlation matrix, σ2Is the power of Gaussian white noise, I is an identity matrix of 8M × 8M, and according to the subspace theory, a data correlation matrix R is obtainedZCharacteristic decomposition is carried out to obtain a signal subspace UsSum noise subspace UN，Where EVD represents the eigen decomposition, λiIs the i-th eigenvalue, v, obtained by the feature decompositioniIs the ith feature vector, U, corresponding to the feature values＝[v1，…，vK]Signal subspaces, U, formed for eigenvectors corresponding to K large eigenvaluesN＝[vK+1，…，v8M]Is 8M-K small characteristic value pairsA noise subspace formed by the corresponding feature vectors;
step three, estimating a signal steering vector matrixSum signal frequency
Signal subspace U of 8M × KsDivided into an upper 4M × K matrix U and a lower matrix U1And U2By using a time-rotation invariant relation structure, composed of U1And U2Obtaining psi T ═ Ω T by matrix operation, whereinPerforming characteristic decomposition on the matrix psi, and forming a matrix by characteristic valuesFeature vector construction matrixWhereinIs an estimate of the value of omega,is an estimate of T, resulting in an estimate of the signal steering vector matrix and signal frequency:
A ^ 1 = U 1 T ^ - 1
f ^ k = arg ( Ω ^ ( k , k ) ) 2 π Δ T ;
wherein arg (·) represents the argument,representation matrixThe k-th row and k-th column elements are taken,Us＝AT，U1＝A1T，U2＝A2t, A is the full data array steering vector matrix in step two, A1Is a direct sampling data array steering vector matrix, A2Is a time-delay sampling data array guide vector matrix, T is a non-singular matrix of K × K,is a matrix U1The pseudo-inverse matrix of (a) is,
obtaining a normalization vector of the x-axis vibration velocity, the y-axis vibration velocity and the sound pressure of the kth signal to the z-axis vibration velocity according to the composition and array arrangement of the signal guide vector, and obtaining rough estimated values of the arrival angle and the sound source distance by utilizing the normalization vector;
directing signals to vector estimates based on the configuration of the acoustic vector sensor and the array configurationThe K (K is more than or equal to 1 and less than or equal to K) column of the array is divided into matrix blocks corresponding to each array element,to representThe (c) th column of (a),
A ^ 1 ( : , k ) = A ^ 1 1 ( : , k ) . . . A ^ 1 m ( : , k ) . . . A ^ 1 M ( : , k )
the kth column representing the mth array element,the three components of the vibration speed in the x-axis direction, the y-axis direction and the sound pressure are compared with the vibration speed component in the z-axis direction to obtain a normalized vectorObtaining the normalized vector of the kth signal by averaging the normalized vectors of M array elementsObtaining a rough estimation value of the arrival angle of the signal according to the ratio relationsRough estimation value of distance to sound source
The normalized vector for the kth signal is:
thus, estimates of angle of arrival and distance are obtained:
θ ^ k = arctan ( Γ ^ k 2 ( 1 ) + Γ ^ k 2 ( 2 ) )
φ ^ k = arctan ( Γ ^ k ( 2 ) Γ ^ k ( 1 ) )
wherein,is the distance between the kth signal and the element of the origin of coordinates, λkIs the wavelength of the k-th signal, p0Is the ambient fluid density, c is the acoustic wave propagation velocity, vector ГkExp (-) is an exponential operation, tan (-) and arctan (-) respectively represent tangent and arctangent operations;
step five, searching accurate estimated values of the arrival angle and the distance of the signal near the rough value by using the MUSIC algorithm;
by using the structural form of a circular array, a full data array guide vector in a small area near a rough estimation value is givenMethod for searching peak by using MUSIC spectrumSearching near the rough value to obtain an accurate estimation value of the signal;
wherein,is a space domain steering vector formed by the phase difference of a signal arrival array element m and a reference array element,for the phase difference, U, of incident acoustic source signals arriving at array element m and reference array elementnAnd 5, in the noise subspace obtained in the step two, the vibration velocity components and the sound pressure scalars in the directions of the x axis, the y axis and the z axis of the unit energy signal are as follows:
theta, phi, r are the search variables, andrespectively a rough estimate of azimuth angle, pitch angle and distance in step four,θ、φandrthe search interval lengths are respectively used for setting a pitch angle, an azimuth angle and a distance;
in the above steps, K is 1, a., K, M is 1, a., M, n is 1, a.
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