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

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 row near field sources Multiple Parameter Estimation Methods

Technical field

The invention belongs to array signal process technique field, more particularly to the near field sources that a kind of acoustic vector-sensor array is arranged are frequently The method of estimation of rate, two dimensional arrival angles and distance.

Background technology

Acoustic vector sensors are pointed to by a non-direction sound pressure sensor and three are mutually perpendicular with dipole The particle vibration velocity sensor of property is composited, can synchro measure acoustic signals sound pressure and particle vibration velocity information, thus The fields such as radar, sonar, communication, space flight and aviation have obtained increasingly extensive application, when information source falls into the Fresnel of array aperture It is referred to as near field sources during region, the positioning near field sources needs estimated distance and angle of arrival multiple parameters, based on acoustic vector sensing The near-field sound source position positioning of device array has turned into the study hotspot of domestic and foreign scholars.

Array high-resolution method for parameter estimation based on subspace theory has been applied to Near-field sources target positioning, Liu Nan Nanmu is in Jilin University's learned person position scholar's paper (exercise question in 2014：Near field sources multi-parameter inversion based on acoustic vector sensors) middle utilization Two-dimentional Multiple Signal Classification method carries out the estimation of parameters of near field sources under white Gaussian noise background, and the method can suppress Gaussian stationary and make an uproar Sound, but need to do the MUSIC search based on biquaternion, it is necessary to above do three-dimensional search, angle of arrival in two dimensional arrival angles and distance Estimate that the raising of resolution ratio depends on the fine array region of search, thus have the shortcomings that computationally intensive.The present invention is using equal Nicely rounded ideophone spectra of acoustic vector sensor array, it is proposed that the ESPRIT of near field sources angle of arrival, frequency and distance estimates signal ginseng Number (ESPRIT) and Multiple Signal Classification method (MUSIC) method for parameter estimation, the present invention makes full use of acoustic vector sensors first Intrinsic invariable rotary structure itself, parameter Estimation is carried out using ESPRIT algorithms, give near field sources direction of arrival and The rough estimate value of sound source distance, then searched near coarse value using MUSIC algorithms obtain direction of arrival and sound source away from From fine estimation, the method need not in population parameter space three-dimensional search, and Parameter automatic pair；Therefore, amount of calculation Greatly reduce, and in the case where element number of array is limited, improve acoustic vector-sensor array row near field sources under near field sources scene Parameter Estimation Precision.For near-field sound source signal, the direction of phase difference between array element not only with array element spacing and incoming signal has Close and with the distance dependent of sound source to array element, so far field condition has the even linear array of translation invariant structure, uniform L gusts Deng near field without translation invariant structure, so existing document is seldom related to the ESPRIT parameter Estimations of near field sources to calculate Method, the invariable rotary relation that the present invention makes full use of the array of acoustic vector sensors intrinsic carries out parameter Estimation.

The content of the invention

It is many it is an object of the invention to provide a kind of near field sources circle acoustic vector-sensor array row based on ESPRIT and MUSIC Parametric joint method of estimation.

To achieve these goals, the present invention takes following technical solution：

Circular acoustic vector-sensor array row near field sources Multiple Parameter Estimation Methods, K different frequency, orthogonal arrowband, with The steady near-field sound source signal of machine respectively from different directions with different distance (θ_k, φ_k, r_k) incide circular acoustic vector sensing On device array, θ_kIt is the angle of pitch of incoming signal, φ_kIt is the azimuth of incoming signal, r_kIt is k-th signal and origin of coordinates battle array The distance between unit, the circular array is equidistantly spaced from radius for the array element on the circumference of R is constituted, with circumference by M The center of circle is the origin of coordinates and places identical acoustic vector sensors as reference array element in the origin of coordinates, and the array element is by acoustic pressure Sensor and x-axis, y-axis and z-axis direction vibration velocity sensor group into acoustic vector sensors, the respective channel of all the sensors is mutual It is parallel：All of sound pressure sensor is parallel to each other, and all of x-axis direction vibration velocity sensor is parallel to each other, and all of y-axis direction shakes Fast sensor is parallel to each other, and all of z-axis direction vibration velocity sensor is parallel to each other, and x-axis, y-axis and z-axis vibration velocity sensor It is mutually perpendicular to two-by-two；On circular array between adjacent array element at intervals of λ_min/ (8sin (π/M)), λ_minIt is incident acoustic wave signal Meet Near Field between minimum wavelength, and radius of circle R and array element interval and the wavelength of incident acoustic wave signal and the distance of sound source；

The step of near field sources Multiple Parameter Estimation Methods, is as follows：

Step one, the reception data that near field acoustic signals are obtained using circular array；

The n times snapshot data of the circular reception array received signal constitutes direct sampled data Z₁, receiving signal delayed Δ T N times synchronization snapshot data afterwards constitutes time delay sampled data Z₂, by Z₁And Z₂This two groups of data are constituted and receive the total evidence of signalWhereinf_sIt is Nyquist sampling frequency；

Step 2, using receiving the full data acquisition signal subspace of signal and noise subspace；

Estimate full data correlation matrixWherein, A is full data-signal steering vector Matrix, R_s=SS^H/ N is incoming signal correlation matrix, σ²It is the power of white Gaussian noise, I is the unit matrix of 8M × 8M, according to Subspace theory, to data correlation matrix R_ZCarry out feature decomposition and obtain signal subspace U_sWith noise subspace U_N,Wherein, EVD represents feature decomposition, λ_iIt is ith feature value that feature decomposition is obtained, v_iIt is the corresponding ith feature vector of characteristic value, U_s=[v₁..., v_K] it is the corresponding characteristic vector composition of the individual characteristic values greatly of K Signal subspace, U_N=[v_K+1..., v_8M] noise subspace that constitutes for the corresponding characteristic vector of the small characteristic values of 8M-K；

Step 3, estimation signal guide vector matrixAnd signal frequency

By the signal subspace U of 8M × K_sIt is divided into the matrix U of upper and lower two pieces of 4M × K₁And U₂, closed using time invariable rotary Architecture, by U₁And U₂Ψ T=Ω T are obtained by matrix operation, whereinFeature decomposition is carried out to matrix Ψ, it is special Value indicative constitutes matrixCharacteristic vector constitutes matrixWhereinIt is the estimate of Ω,It is the estimate of T, so as to obtain letter The estimation of number steering vector matrix and signal frequency：

Wherein, arg () expressions take argument,Representing matrixThe row k kth column element for taking,U_s =AT, U₁=A₁T, U₂=A₂T, A are exactly the full data array steering vector matrix in step 2, A₁It is direct sampled data array Steering vector matrix, A₂It is time delay sampled data array steering vector matrix, T is the nonsingular matrix of K × K,It is matrix U₁Pseudo inverse matrix,

Step 4, composition and array arrangement according to signal guide vector, obtain k-th x-axis of signal, y-axis vibration velocity and Acoustic pressure obtains the rough estimate value of angle of arrival and sound source distance using normalized vector to the normalized vector of z-axis vibration velocity；

The arrangement form of structure and array according to acoustic vector sensors, by signal guide vector estimateKth (1 ≤ k≤K) row be divided into the corresponding matrix-block of each array element,RepresentKth row,

M-th kth row of array element is represented,X-axis, three components of y-axis direction vibration velocity and acoustic pressure all Normalized vector is obtained compared with the vibration velocity component of z-axis directionK-th signal is averagely obtained by the M normalized vector of array element Normalized vectorDirection of arrival rough estimate value is obtained according to these ratio relationsHarmony Source is apart from rough estimate value

The normalized vector of k-th signal is：

So as to obtain angle of arrival and The estimate of distance：

Wherein,It is the distance between k-th signal and origin of coordinates array element, λ_k It is k-th wavelength of signal, ρ₀It is environment liquid density, c is acoustic wave propagation velocity, Vectorial Γ_k The 1st, 2,4 elements, exp () is to ask exponent arithmetic, tan () and arctan () to represent ask tangent and arc tangent respectively Computing；

Step 5, the fine estimation for searching for direction of arrival and distance near coarse value using MUSIC algorithms；

Using the structure type of circular array, the full data array be given in the zonule near rough estimate value is oriented to arrow AmountUsing MUSIC spectrum peak search methods Search obtains the fine estimation of signal near coarse value；

Wherein,It is the phase difference structure of signal arrival array element m and reference array element Into spatial domain steering vector,For incident sound source is believed Number reach the phase difference of array element m and reference array element, U_nIt is noise subspace that step 2 is obtained, the x-axis of unit energy signal, y The vibration velocity component and acoustic pressure scalar in axle and z-axis direction be：

θ, φ, r are search variables,

WithPoint It is not the rough estimate value at the azimuth, the angle of pitch and distance in step 4, ε_θ、ε_φAnd ε_rIt is respectively intended to set the angle of pitch, orientation Angle and the region of search length of distance；

K=1 ..., K, m=1 ..., M in abovementioned steps, n=1 ..., M, j represent imaginary unit.

The array that the present invention is used is Homogeneous Circular array, and the array element of array is by sound pressure sensor and x-axis, y-axis and z-axis The acoustic vector sensors that the vibration velocity sensor in direction is constituted, and all of sound pressure sensor is parallel to each other, all of x-axis direction Vibration velocity sensor is parallel to each other, and all of y-axis direction vibration velocity sensor is parallel to each other, all of z-axis direction vibration velocity sensor phase It is mutually parallel.

The present invention gives a kind of circular acoustic vector-sensor array row near field sources multi-parameter ESPRIT algorithm for estimating, for one As scalar sensors array such as microphone array cannot utilize ESPRIT algorithm estimation of near field sound-source signals parameter because closely The corrugated of field is spherical wave；Phase between array element it is not only relevant with the direction of array element spacing and incoming signal and also with sound source to battle array The distance dependent of unit, so far field condition has the even linear array of translation invariant structure, uniform L gusts etc., does not have near field Translation invariant structure, it is impossible to utilize ESPRIT algorithms, the present invention makes full use of acoustic vector sensors rotation intrinsic in itself not Structure changes, using ESPRIT algorithms enter line parameter rough estimate and with MUSIC zonules essence search method be combined realize angle of arrival and away from From accurate estimation, compared with existing fourth order statistic and second-order statistic method, the inventive method amount of calculation is small, and has Simple, the easy to use advantage of algorithm.

Brief description of the drawings

In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing The accompanying drawing for having technology to be needed to use in describing does simple introduction, it should be apparent that, drawings in the following description are only the present invention Some embodiments, for those of ordinary skill in the art, on the premise of not paying creative work, can also basis These accompanying drawings obtain other accompanying drawings.

Fig. 1 is the schematic diagram of embodiment of the present invention acoustic vector-sensor array row；

Fig. 2 is the flow chart of the inventive method；

Fig. 3 is the angle-of- arrival estimation scatter diagram of the inventive method of emulation experiment；

Fig. 4 is the orientation angular estimation root-mean-square error of the inventive method with the change curve of signal to noise ratio；

Fig. 5 is the pitching angular estimation root-mean-square error of the inventive method with the change curve of signal to noise ratio；

Fig. 6 is the angle-of- arrival estimation root-mean-square error of the inventive method with the change curve of signal to noise ratio；

Fig. 7 is the distance estimations root-mean-square error of the inventive method with the change curve of signal to noise ratio；

Fig. 8 is the angle-of- arrival estimation probability of success of the inventive method with the change curve of signal to noise ratio.

Specific embodiment

In order to above and other objects of the present invention, feature and advantage can be become apparent from, the embodiment of the present invention cited below particularly, And coordinate appended diagram, it is described below in detail.

Fig. 1 show the schematic diagram of the acoustic vector-sensor array row of the embodiment of the present invention.Acoustic vector sensors of the invention Array is equidistantly spaced from radius for the array element on the circumference of R is constituted by M, and the center of circle with circumference is as the origin of coordinates and in coordinate Origin places identical acoustic vector sensors as reference array element, between the adjacent array element of the circular array at intervals of λ_min/ (8sin (π/M)), the array element of array be by sound pressure sensor and x-axis, y-axis and z-axis direction vibration velocity sensor group into acoustic vector Sensor, wherein, λ_minIt is the minimum wavelength of incoming signal.

The step of reference picture 2, Multiple Parameter Estimation Methods of the invention, is as follows：Circular acoustic vector-sensor array row receive K Different frequency, orthogonal arrowband, random steady near-field sound source signal, K is the quantity of incident sound-source signal, K≤M-1,

Step one, the reception data that near field acoustic signals are obtained using circular array；

The n times snapshot data of the circular reception array received signal constitutes direct sampled data Z₁, receiving signal delayed Δ T N times synchronization snapshot data afterwards constitutes time delay sampled data Z₂, by Z₁And Z₂This two groups of data are constituted and receive the total evidence of signalWhereinf_sIt is Nyquist sampling frequency；

Step 2, using receiving the full data acquisition signal subspace of signal and noise subspace；

Estimate full data correlation matrixWherein, A is full data-signal steering vector Matrix, R_s=SS^H/ N is incoming signal correlation matrix, σ²It is the power of white Gaussian noise, I is the unit matrix of 8M × 8M, according to Subspace theory, to data correlation matrix R_ZCarry out feature decomposition and obtain signal subspace U_sWith noise subspace U_N,Wherein, EVD represents feature decomposition, λ_iIt is ith feature that feature decomposition is obtained Value, v_iIt is the corresponding ith feature vector of characteristic value, U_s=[v₁..., v_K] it is the K corresponding characteristic vector structure of big characteristic value Into signal subspace, U_N=[v_K+1..., v_8M] noise that constitutes for the corresponding characteristic vector of the small characteristic values of 8M-K is empty Between；

Step 3, estimation signal guide vector matrixAnd signal frequency

By the signal subspace U of 8M × K_sIt is divided into the matrix U of upper and lower two pieces of 4M × K₁And U₂, closed using time invariable rotary Architecture, by U₁And U₂Ψ T=Ω T are obtained by matrix operation, whereinFeature decomposition is carried out to matrix Ψ, it is special Value indicative constitutes matrixCharacteristic vector constitutes matrixWhereinIt is the estimate of Ω,It is the estimate of T, so as to obtain letter The estimation of number steering vector matrix and signal frequency：

Wherein, arg () expressions take argument,Representing matrixThe row k kth column element for taking, U_s=AT, U₁=A₁T, U₂=A₂T, A are exactly the full data array steering vector matrix in step 2, A₁It is direct sampled data battle array Row steering vector matrix, A₂It is time delay sampled data array steering vector matrix, T is the nonsingular matrix of K × K,It is matrix U₁Pseudo inverse matrix,

Step 4, composition and array arrangement according to signal guide vector, obtain k-th x-axis of signal, y-axis vibration velocity and Acoustic pressure obtains the rough estimate value of angle of arrival and sound source distance using normalized vector to the normalized vector of z-axis vibration velocity；

The arrangement form of structure and array according to acoustic vector sensors, by signal guide vector estimateKth (1 ≤ k≤K) row be divided into the corresponding matrix-block of each array element,RepresentKth row,

M-th kth row of array element is represented,X-axis, three components of y-axis direction vibration velocity and acoustic pressure all Normalized vector is obtained compared with the vibration velocity component of z-axis directionK-th signal is averagely obtained by the M normalized vector of array element Normalized vectorDirection of arrival rough estimate value is obtained according to these ratio relationsHarmony Source is apart from rough estimate value

The normalized vector of k-th signal is：

So as to obtain angle of arrival and The estimate of distance：

Wherein,It is the distance between k-th signal and origin of coordinates array element, λ_k It is k-th wavelength of signal, ρ₀It is environment liquid density, c is acoustic wave propagation velocity, Vectorial Γ_k The 1st, 2,4 elements, exp () is to ask exponent arithmetic, tan () and arctan () to represent ask tangent and arc tangent respectively Computing；

Step 5, the fine estimation for searching for direction of arrival and distance near coarse value using MUSIC algorithms；

Using the structure type of circular array, the full data array be given in the zonule near rough estimate value is oriented to arrow AmountUsing MUSIC spectrum peak search methods Search obtains the fine estimation of signal near coarse value；

Wherein,It is the phase difference structure of signal arrival array element m and reference array element Into spatial domain steering vector,It is incident sound source Signal reaches the phase difference of array element m and reference array element, U_nIt is noise subspace that step 2 is obtained, the x-axis of unit energy signal, The vibration velocity component and acoustic pressure scalar in y-axis and z-axis direction be：

θ, φ, r are search variables,

WithPoint It is not the rough estimate value at the azimuth, the angle of pitch and distance in step 4, ε_θ、ε_φAnd ε_rIt is respectively intended to set the angle of pitch, orientation Angle and the region of search length of distance；

K=1 ..., K, m=1 ..., M in abovementioned steps, n=1 ..., M, j represent imaginary unit.

The present invention estimates signal array steering vector and letter using the time invariable rotary structure that data before and after time delay have Number frequency, is divided into x-axis, y-axis, four submatrixs of z-axis and acoustic pressure, using the ratio of corresponding element between submatrix by by array steering vector Value relation obtains the rough estimate value of direction of arrival and sound source distance, and MUSIC algorithms are utilized in rough estimate value near zone Precise search is carried out to obtain accurate direction of arrival and range estimation, the algorithm avoids answering for fourth order statistic algorithm The universe three-dimensional search problem of polygamy and simple MUSIC algorithms, combines the having of ESPRIT and MUSIC algorithms and does not need Parameter matches computing.

Effect of the invention can be further illustrated by following simulation result：

Emulation experiment condition is as follows：

Two different frequencies, orthogonal arrowband, random steady near-field sound source signal incide by 9 be equidistantly spaced from Radius for R circumference on array element constitute circular acoustic vector-sensor array row, as shown in figure 1, adjacent array element at intervals of λ_min/ (8sin (π/9)), the parameter of incoming signal is：(θ₁, φ₁20 °, 50 ° of)=(), (θ₂, φ₂30 °, 70 ° of)=(), it is returned One changes frequency for (f₁, f₂)=(0.3,0.4), fast umber of beats is 1024 times, 200 independent experiments.

The simulation experiment result as shown in Figures 3 to 8, Fig. 3 for signal to noise ratio be 15dB when, the inventive method angle-of- arrival estimation Scatter diagram, the as can be seen from Figure 3 smaller range of the azimuth of the inventive method and angle of pitch estimate all near actual value Interior distribution, the angle-of- arrival estimation of the inventive method has Parameter Estimation Precision higher；Present invention side is can be seen that from Fig. 4 and Fig. 7 The root-mean-square error of the azimuth of method, the angle of pitch, angle of arrival and distance estimations is smaller, that is, estimate near true value compared with A small range is disturbed, and the angle of arrival and distance estimations of the inventive method have Parameter Estimation Precision higher, because of the invention Method takes full advantage of acoustic vector sensors invariable rotary structure intrinsic in itself, and it is thick to enter line parameter using ESPRIT algorithms Estimate, and processed by the precise search of MUSIC small areas and improve Parameter Estimation Precision；The angle-of- arrival estimation probability of success is Refer to that the angle of pitch and azimuth estimate meet in 200 independent experimentsExperiment number account for always The percentage of experiment number；Wherein, θ₀And φ₀It is true value,WithRefer to the estimate of i ＆ lt experiment, from figure 8, it is seen that The inventive method has the probability of success higher, and when signal to noise ratio is -10dB, the probability of success of signal one and signal two is respectively 20% and 30%, and signal to noise ratio is when being 0dB, two probability of succesies of signal are all higher than 80%.

The above, is only presently preferred embodiments of the present invention, and any formal limitation is not done to the present invention, though So the present invention is disclosed above with preferred embodiment, but is not limited to the present invention, any to be familiar with this professional technology people Member, without departing from the scope of the present invention, when making a little change or modification using the technology contents of the disclosure above It is the Equivalent embodiments of equivalent variations, as long as being the content without departing from technical solution of the present invention, according to technical spirit of the invention Any simple modification, equivalent variations and the modification made to above example, still fall within the range of technical solution of the present invention.

Claims (1)

1. circular acoustic vector-sensor array row near field sources Multiple Parameter Estimation Methods, it is characterised in that：

The acoustic vector-sensor array is arranged and is equidistantly spaced from radius for the array element on the circumference of R is constituted, with the circle of circumference by M The heart is the origin of coordinates and places identical acoustic vector sensors as reference array element in the origin of coordinates, the circular array it is adjacent Between array element at intervals of λ_min/ (8sin (π/M)), the array element of array is by sound pressure sensor and x-axis, y-axis and z-axis direction vibration velocity The acoustic vector sensors that sensor is constituted, wherein, λ_minIt is the minimum wavelength of incoming signal；

The step of near field sources Multiple Parameter Estimation Methods, is as follows：It is K different frequency of array received, orthogonal arrowband, random steady Near field source signal,

Step one, the reception data that near field acoustic signals are obtained using circular array；

The n times snapshot data of the circular reception array received signal constitutes direct sampled data Z₁, the N after receiving signal delayed Δ T Subsynchronous snapshot data constitutes time delay sampled data Z₂, by Z₁And Z₂This two groups of data are constituted and receive the total evidence of signal Whereinf_sIt is Nyquist sampling frequency；

Step 2, using receiving the full data acquisition signal subspace of signal and noise subspace；

Estimate full data correlation matrixWherein, A is full data-signal steering vector matrix, R_s=SS^H/ N is incoming signal correlation matrix, σ²It is the power of white Gaussian noise, I is the unit matrix of 8M × 8M, according to sub empty Between it is theoretical, to data correlation matrix R_ZCarry out feature decomposition and obtain signal subspace U_sWith noise subspace U_N,Wherein, EVD represents feature decomposition, λ_iIt is ith feature value that feature decomposition is obtained, v_iIt is the corresponding ith feature vector of characteristic value, U_s=[v₁..., v_K] it is the corresponding characteristic vector composition of the individual characteristic values greatly of K Signal subspace, U_N=[v_K+1..., v_8M] noise subspace that constitutes for the corresponding characteristic vector of the small characteristic values of 8M-K；

Step 3, estimation signal guide vector matrixAnd signal frequency

By the signal subspace U of 8M × K_sIt is divided into the matrix U of upper and lower two pieces of 4M × K₁And U₂, using time invariable rotary relation knot Structure, by U₁And U₂Ψ T=Ω T are obtained by matrix operation, whereinFeature decomposition, characteristic value are carried out to matrix Ψ Constitute matrixCharacteristic vector constitutes matrixWhereinIt is the estimate of Ω,It is the estimate of T, is led so as to obtain signal To the estimation of vector matrix and signal frequency：

${\hat{A}}_1=U_1{\hat{T}}^{-1}$

${\hat{f}}_k=\frac{\arg \left(\widehat{\mathrm{\Ω}}\right(k,k\left)\right)}{2\mathrm{\π}\mathrm{\Δ}T};$

Wherein, arg () expressions take argument,Representing matrixThe row k kth column element for taking,U_s= AT, U₁=A₁T, U₂=A₂T, A are exactly the full data array steering vector matrix in step 2, A₁It is that direct sampled data array is led To vector matrix, A₂It is time delay sampled data array steering vector matrix, T is the nonsingular matrix of K × K,It is matrix U₁Pseudo inverse matrix,

Step 4, composition and array arrangement according to signal guide vector, obtain k-th x-axis of signal, y-axis vibration velocity and acoustic pressure To the normalized vector of z-axis vibration velocity, and the rough estimate value of angle of arrival and sound source distance is obtained using normalized vector；

The arrangement form of structure and array according to acoustic vector sensors, by signal guide vector estimateKth (1≤k≤ K) row are divided into the corresponding matrix-block of each array element,RepresentKth row,

${\hat{A}}_1(:,k)=\left[\begin{array}{c}{\hat{A}}_1^1(:,k)\\ .\\ .\\ .\\ {\hat{A}}_1^m(:,k)\\ .\\ .\\ .\\ {\hat{A}}_1^M(:,k)\end{array}\right]$

M-th kth row of array element is represented,X-axis, three components of y-axis direction vibration velocity and acoustic pressure all with z-axis Direction vibration velocity component is compared and obtains normalized vectorK-th normalizing of signal is averagely obtained by the M normalized vector of array element Change vectorDirection of arrival rough estimate value is obtained according to these ratio relationsIt is thick with sound source distance Omit estimate

The normalized vector of k-th signal is：

So as to obtain angle of arrival and distance Estimate：

${\widehat{\mathrm{\θ}}}_k=\arctan \left(\sqrt{{\widehat{\mathrm{\Γ}}}_k^2\left(1\right)+{\widehat{\mathrm{\Γ}}}_k^2\left(2\right)}\right)$

${\widehat{\mathrm{\φ}}}_k=\arctan \left(\frac{{\widehat{\mathrm{\Γ}}}_k\left(2\right)}{{\widehat{\mathrm{\Γ}}}_k\left(1\right)}\right)$

Wherein,It is the distance between k-th signal and origin of coordinates array element, λ_kIt is kth The wavelength of individual signal, ρ₀It is environment liquid density, c is acoustic wave propagation velocity, Vectorial Г_kThe 1st, 2nd, 4 elements, exp () is to ask exponent arithmetic, tan () and arctan () to represent ask tangent and arctangent cp cp operation respectively；

Step 5, the fine estimation for searching for direction of arrival and distance near coarse value using MUSIC algorithms；

Using the structure type of circular array, the full data array steering vector in the zonule near rough estimate value is givenUsing MUSIC spectrum peak search methods Search obtains the fine estimation of signal near coarse value；

Wherein,It is that signal reaches array element m and the phase difference of reference array element is constituted Spatial domain steering vector,For incident sound-source signal is arrived Up to array element m and the phase difference of reference array element, U_nIt is noise subspace that step 2 is obtained, the x-axis of unit energy signal, y-axis and z The vibration velocity component and acoustic pressure scalar of direction of principal axis be：

θ, φ, r are search variables, WithIt is respectively step The rough estimate value at azimuth, the angle of pitch and distance in rapid four, ε_θ、ε_φAnd ε_rBe respectively intended to set the angle of pitch, azimuth and away from From region of search length；

K=1 ..., K, m=1 ..., M in abovementioned steps, n=1 ..., M, j represent imaginary unit.