CN110082712B - Acoustic vector circular array coherent target azimuth estimation method - Google Patents

Abstract

The invention provides an acoustic vector circular array coherent target direction estimation method. Construction of sound pressure P (t) and vibration velocity V _x (t)、V _y (t) cross covariance matrix R _x And R _y Two are combinedThe cross covariance matrix stack obtains a new matrix R _xy ＝[R _x ，R _y ] ^T (ii) a Will matrix R _xy Singular value decomposition is carried out to obtain a left singular vector u corresponding to the maximum singular value ₁ (ii) a Discretizing the plane of the space azimuth angle to obtain a space angle set theta, constructing an overcomplete basis B (theta), and establishing a sparse solving framework min | | Σ | survival ₁ +ε||u ₁ ‑B(Θ)∑|| ₂ And obtaining a space spectrum through the solved sigma, and estimating the target azimuth through the position of a spectrum peak. Simulation analysis and test results show that the method can effectively solve the orientation estimation problem under the conditions of large correlation or coherence of incident signals, small angle interval of targets in spatial orientation, large environmental noise and the like. In addition, the method does not need to estimate the noise power or the signal number, provides an effective method for the remote passive direction finding problem of the acoustic vector circular array coherent target, and has good application prospect.

Description

Acoustic vector circular array coherent target azimuth estimation method

Technical Field

The invention relates to an acoustic vector signal processing method, in particular to an acoustic vector circular array coherent target direction estimation method.

Background

Underwater target orientation estimation is an important topic in the field of underwater signal processing. Compared to a sound pressure sensor, an acoustic vector sensor can measure more sound field information, i.e., two or three mutually orthogonal vibration velocity components. Compared with area arrays and linear arrays in other shapes, the uniform circular array has the characteristics of simple structure, capability of acquiring 360-degree omnidirectional unambiguous range information, approximately same angular resolution and the like. These advantages make the circular array composed of acoustic vector sensors attract a wide attention in the aspect of underwater target orientation estimation. Due to the existence of various reflection surfaces (such as mountains, sea surfaces and the like) under water, the situation that the target signal is subjected to multipath propagation cannot be avoided. Therefore, the acoustic vector circular array faces the challenge of separating and detecting coherent targets from ambient noise.

Conventional Beamforming (CBF) is the first proposed method of position of arrival (DOA) estimation in the field of array Signal processing (Krim, H., viberg, M., two detectors of array Signal processing research: the parameter adaptive approach. IEEE Signal processing. Mag.1996,13, (4), 67-94.). The method can be used for estimating the azimuth of a coherent signal, but the angular resolution of the CBF is limited by Rayleigh limit, and two targets with smaller angle intervals cannot be distinguished. Subsequently, a Minimum Variance Distortionless Response (MVDR) with High resolution was proposed (Capon, J., high-resolution frequency-wave number spread analysis. Procedings of the IEEE 1969,57, (8), 1408-1418.) and a subspace decomposition type orientation estimation method (Schmidt, R., multiple identity and signal estimation 276. IEEE transaction. Extensions Propag.1986,34, (3), 280.) as represented by a Multiple signal classification Method (MUSIC). However, when the incident signal is highly correlated or coherent, the MVDR and subspace-like approaches will fail. In order to make these high-resolution orientation estimation methods able to resolve coherent targets, a series of solution coherent orientation estimation methods such as Spatial smoothing algorithms (Tran, j.m. q.d.; hodgkiss, w.s., spatial smoothing and minimum variance estimation methods are proposed, e.g., transmit, j.m. q.d.; hodgkiss, w.s., ieee j.objective en.1993, 18, (1), 15-24.), forward and backward Spatial smoothing algorithms (choice, y.h., on-contrast for the forward/backward Spatial smoothing. Ieee ns.on Signal processes.2002, 50, (11), 2900-2901.), toe matrix reconstruction methods (Fang-Ming, h.; like-Da, z-estimate, prior-correlation, etc., wiener-443, etc. are proposed. However, these de-coherent methods have some drawbacks: on one hand, in order to apply the solution coherent method to the circular array, they need to use a phase mode transformation method as a preprocessing technology, which increases the difficulty of the algorithm; on the other hand, these de-coherent methods recover the rank of the signal covariance matrix at the expense of the array aperture, reducing both the performance of the azimuth estimator and the number of resolvable coherent targets.

In recent years, the sparse representation technique provides a new view angle in the field of direction of arrival estimation due to sparsity of sound sources in spatial azimuth distribution, and has attracted much attention due to its characteristics of ultra-high angular resolution and estimation accuracy. To our knowledge, sparse representation algorithms mainly comprise two main classes. One type of the method is a singular value decomposition method (Fang-Ming, h.; xian-Da, z., an ESPRIT-like algorithm for coherent DOA estimation, ieee extensions Wireless prop. Lett.2005,4, 443-446.) for directly and sparsely representing the received data of a matrix, and a compressed sensing beam forming technique (Shi, j.; yang, d.; shi, s.; hu, b.; zhu, z., compressed focused beam forming based on vector sensor array. Acta physics Sinica 2016,65, (2), 02430201-02430211., etc.). However, these algorithms cannot effectively eliminate noise, and their estimation performance is difficult to guarantee under relatively noisy environments. Another class is achieved by exploiting second order statistics of the output data of the sensor array. The literature (Yin, J.H.; chen, T.Q., direction-of-Arrival Estimation Using a spark repetition of Array covariane vectors IEEE transactions on Signal Process.2011,59, (9), 4489-4493, wang, X.P., wang, W.; li, X., liu, J., real-Valued Covariance Vector space-indicative DOA Estimation for a monomeric MIMO radar. Sensors 201515, (11), 28271-28286) estimates the target azimuth by finding the sparsest parameters of the Array Covariance matrix or Vector from the virtual overcomplete. The literature (Hu, N.; ye, Z.F.; xu, D.Y.; cao, S.H., A space recovery algorithm for DOA estimation using weighted subspace fixing. Signal Process.2012,92, (10), 2566-2570.) realizes target position estimation by solving the sparsest parameters of weighted signal feature vectors in an overcomplete basis. However, the second type of sparse DOA estimation method has some disadvantages, such as the need to estimate the noise power, accurately know the number of signal sources, and being unable to estimate the coherent target. And the probability of signal subspace to noise subspace interchange is high when the signal-to-noise ratio is low, the literature ((Hu, n.; the orientation estimation method in A spark orientation for DOA estimation using weighted direction estimation, cao, S.H., A spark orientation process, 2012,92, (10), 2566-2570.) to reduce the effect of isotropic noise on direction of arrival estimation, the direction of arrival estimation method based on acoustic vector sensors is a relatively convenient and feasible method. Furthermore, the literature (white Xingxu, yandson, zhao Chunhui. Acoustic vector array coherent signal subspace approach based on a joint processing of sound pressure and vibration velocity. Acoustics. 2006,31 (5): 410-417.) constructs a cross covariance matrix by projecting two acoustic particle velocities into the observation direction. Improper viewing directions can severely reduce the amplitude of some incident signals, causing spectral peaks corresponding to those incident signals to be buried in the background spectrum.

Disclosure of Invention

The invention aims to provide an acoustic vector circular array coherent target direction estimation method which can realize direction estimation of a coherent target under the conditions of low signal-to-noise ratio and low snapshot number without estimating noise power and signal source number.

The invention is realized by the following steps:

the method comprises the following steps: the sound vector circular array collects sound pressure channel and two vibration speed channel signals along x and y axes, which are respectively marked as P (t) and V _x (t) and V _y (t)；

Step two: respectively constructing sound pressure P (t) and vibration velocity V _x (t)、V _y (t) cross covariance matrix R _x And R _y Stacking two cross covariance matrices to obtain a new matrix R _xy ＝[R _x ，R _y ] ^T ，(·) ^T Representing a transpose operation;

step three: combining the matrix R in the second step _xy Singular values are respectively carried out to obtain a left singular vector u corresponding to the maximum singular value ₁ ；

Step four: discretizing the plane of the space azimuth angle to obtain a space angle set theta, constructing an overcomplete basis B (theta), and sparsely representing a left singular vector u ₁ = B (theta) | Σ, so that a sparse solution framework min | | | Σ | u is established ₁ +ε||u ₁ -B(Θ)∑|| ₂ And obtaining a spatial spectrum through the solved sigma, and obtaining a target azimuth through the spectrum peak position, wherein epsilon represents a regularization parameter.

The present invention may further comprise:

1. the second step specifically comprises:

sound pressure P (t) and vibration velocity V _x (t)、V _y (t) cross covariance matrix R _x And R _y Expressed as:

wherein, A _p 、A _x And A _y Respectively is a guide vector matrix of sound pressure, x and y vibration velocity channels of the acoustic vector circular array; (.) ^H Represents a conjugate transpose operation; r is _s ＝E{S(t)S ^H (t) } denotes a signal covariance matrix, where S (t) = [ S ] ₁ (t)，…，s _Q (t)] ^T Is a signal vector, s _q (t)＝β _q s ₁ (t) is the Q-th signal, Q is the number of coherent signals, β _q Is complex constant, Q =1, \8230, Q, R _nx 、R _ny Respectively representing a noise cross covariance matrix, wherein in an isotropic noise field, sound pressure and vibration velocity measured at the same point are irrelevant, and noise received by any two acoustic vector sensors is also irrelevant, so that the matrix R _nx 、R _ny Are respectively equal to

In the formula (I), the compound is shown in the specification,

and N _y，m (t) represents sound pressure received by mth array element, noise of x and y vibration velocity channels, M, n =1, \ 8230; (M, M represents array element number of sound vector circular array, 0 _M×M Representing an M x M dimensional zero matrix and, therefore,

by using cooperative partiesDifference matrix R _x 、R _y To obtain a new matrix

In the formula, A _xy ＝[A _x ，A _y ] ^T 。

2. The third step specifically comprises:

(1) Will matrix R _xy Singular value decomposition is carried out to obtain a left singular vector u corresponding to the maximum singular value ₁ ：

In the formula, mu _m ，u _m And d _m Respectively representing singular values, 2M × 1-dimensional left singular vectors and M × 1-dimensional right singular vectors, M =1, \8230;, M;

using right singular vectors d ₁ Left-multiplying by the above equation to obtain:

when the sources are coherent, the matrix R _xy As follows:

in the formula, a _xy (θ _q ) Is a matrix A _xy The (c) th column (q) of (c),

is the signal s ₁ Power of (t) to obtain

Wherein z = [ alpha ] ₁ ，…，α _q ，…，α _Q ] ^T ，α _q Is a scalar that is not zero.

3. The fourth step specifically comprises:

sampling the azimuth plane to obtain a spatially discrete azimuth set theta = [ theta = ₁ ，…，Θ _N ]Wherein N represents the number of grids divided by the azimuth plane, and an overcomplete basis B (theta) is constructed:

B(Θ)＝[a _xy (Θ ₁ )，…，a _xy (Θ _N )]

in the formula (I), the compound is shown in the specification,

wherein phi ₁ ，…，φ _M Representing an angle of the M-element acoustic vector sensor from the x-axis;

left singular vector u ₁ The sparseness is represented as:

u ₁ ＝B(Θ)∑

in the formula, zero elements of the vector sigma represent that the direction has no target, and non-zero elements represent that the direction has a target;

establishing a sparse solving frame, solving unknown number sigma through the following formula to obtain a spatial spectrum, estimating a target direction through the position of a spectrum peak,

min||∑|| ₁ +ε||u ₁ -B(Θ)∑|| ₂

in the formula, ε represents a regularization parameter.

The invention provides a coherent signal azimuth estimation method based on left singular vector sparse representation, which does not need phase mode transformation, projection of vibration velocity components and estimation of coherent target number, and has lower sidelobe, higher spectral peak, higher azimuth estimation precision and angle resolution.

The invention has the beneficial effects that: the invention organically combines the good anti-noise capability of acoustic vector signal processing with the ultrahigh angle resolution of the sparse reconstruction technology, and solves the orientation estimation problems of large incident signal correlation or coherence, small angle interval of a target in a space orientation, large environmental noise and the like. In addition, the method does not need to estimate the noise power or the signal number, provides an effective method for the remote passive direction finding problem of the acoustic vector circular array coherent target, and has a good application background.

Drawings

FIG. 1 is a flow chart of the acoustic vector circular array coherent source orientation estimation method based on left singular vector sparse representation.

Fig. 2 is a schematic diagram of acoustic vector circular array layout.

Fig. 3 (a) -fig. 3 (c) are comparative analysis of spatial spectra under different signal-to-noise ratios, fig. 3 (a) signal-to-noise ratio SNR = -5dB; fig. 3 (b) signal to noise ratio SNR = -10dB; fig. 3 (c) signal to noise ratio SNR = -15dB.

FIG. 4 is a comparative analysis of root mean square error curves for coherent object orientation estimation for different algorithms.

FIG. 5 is an angular resolution contrast analysis of coherent object orientation estimation for different algorithms.

Fig. 6 (a) -6 (c) are experimental results of coherent dual acoustic sources with an incident angle of 205 ° and 254 ° under different signal-to-noise ratios, fig. 6 (a) signal-to-noise ratio SNR =0dB; fig. 6 (b) signal to noise ratio SNR = -6dB; fig. 6 (c) signal to noise ratio SNR = -12dB.

FIG. 7 shows the experimental results of the coherent dual sound source with the incident angle of 205 ° and the incident angle of 225 ° under the condition of 0 dB.

Fig. 8 shows experimental results of coherent dual acoustic sources with an incident angle of 205 deg. and an incident angle of 254 deg., wherein the projection angle is 293 deg..

Detailed Description

The present invention is further explained with reference to the drawings and examples, wherein a signal processing flow chart of the present invention is shown in fig. 1, and the specific embodiment is as follows:

firstly, collecting signals of a sound pressure channel of the acoustic vector circular array and two vibration velocity channels along x and y axes, and respectively marking the signals as P (t) and V _x (t) and V _y (t)。

As shown in FIG. 2, the acoustic vector circular array with the array element number of M is positioned in the xoy plane, the radius is r, and the vibration velocity component x and y channel positive axis square of the acoustic vector sensorTo radial and tangential directions along the circular array, respectively, assume Q coherent signals s ₁ (t)，…，s _Q (t) from θ respectively ₁ ，…，θ _Q Incident to the acoustic vector circular array, signals and noise are independent. With the circle center as a reference point, the data collected by the acoustic vector circular array at time t can be expressed as:

wherein S (t) = [ S ] ₁ (t)，…，s _Q (t)] ^T Is a Qx 1 dimensional signal vector, where s _q (t)＝β _q s ₁ (t)，β _q Is a complex constant, (.) ^T Representing a transpose operation. P (t) represents data acquired by the acoustic pressure channel. Similarly, V _x (t)，V _y (t) represents data collected along the x and y axis velocity channels, respectively. N is a radical of _p (t)，N _x (t)，N _y And (t) is a noise vector received by a sound pressure and vibration velocity channel. A. The _p ，A _x ，A _y Array manifold matrixes respectively representing sound pressure, x and y vibration velocity are respectively as follows:

wherein, a _p (θ _q )，a _x (θ _q )＝a _p (θ _q )cosθ _q ，a _y (θ _q )＝a _p (θ _q )sinθ _q Respectively representing the guide vectors of the sound pressure and vibration velocity channels corresponding to the q-th signal, a _p (θ _q ) Is equal to

a _p (θ _q )＝[a _p，1 (θ _q )，…，a _p，m (θ _q )，…，a _p，M (θ _q )] ^T (3)

In the formula (I), the compound is shown in the specification,

φ _m =2 π (M-1)/M stands forThe mth sensor forms an angle with the x-axis. k =2 pi f/c denotes a beam, f denotes a signal frequency, c denotes a sound velocity,

denotes imaginary unit, M =1, \8230;, M, Q =1, \8230;, Q.

Secondly, respectively constructing sound pressure P (t) and vibration velocity V according to the sound pressure and vibration velocity combined processing idea _x (t)、V _y (t) cross covariance matrix R _x And R _y Further, two cross covariance matrixes are stacked to obtain a new cross covariance matrix Rx _y ＝[R _x ，R _y ] ^T ，(·) ^T The transposition operation is represented, and the specific steps are as follows:

respectively constructing cross covariance R of sound pressure and x and y vibration velocities by using sound pressure and vibration velocity combined processing idea _x And R _y ：

In the formula (DEG) ^H Representing a conjugate transpose operation. R _s ＝E{S(t)S ^H (t) } denotes a signal covariance matrix. R _nx 、R _ny Respectively, represent the noise cross-covariance matrix. In an isotropic noise field, sound pressure and vibration velocity measured at the same point are mutually irrelevant, and meanwhile, the noise received by any two acoustic vector sensors is also supposed to be irrelevant, so that the matrix R _nx 、R _ny Are respectively equal to

In the formula (I), the compound is shown in the specification,

and N _y，m And (t) respectively represents sound pressure received by the mth element acoustic vector sensor, and noise of x and y vibration velocity channels, wherein M, n =1, \ 8230;, M.0 _M×M Representing an M x M dimensional zero matrix.

Substituting the formula (5) into the formula (4) can obtain

Using a cross-covariance matrix R _x 、R _y To obtain a new matrix

In the formula, A _xy ＝[A _x ，A _y ] ^T 。

Thirdly, the matrix R in the second step is processed _xy Singular values are respectively carried out to obtain a left singular vector u corresponding to the maximum singular value ₁ 。

In the formula, mu _m ，u _m And d _m Respectively representing singular values (in descending order), a 2M × 1-dimensional left singular vector and an M × 1-dimensional right singular vector, M =1, \ 8230, M. Using right singular vectors d ₁ By left-multiplying equation (8), we can get:

when the sources are coherent, the matrix R _xy Can be represented as follows:

in the formula, a _xy (θ _q )＝[a _x (θ _q )，a _y (θ _q )] ^T Is a matrix A _xy The q-th column of (1).

Is the signal s ₁ (t) power.

Substituting equation (10) into equation (9) yields:

wherein z = [ alpha ] ₁ ，…，α _q ，…，α _Q ] ^T ，α _q Is a scalar that is not zero. It can be seen that the left singular vector u ₁ Containing the orientation information of all signals.

Fourthly, discretizing the space azimuth plane to obtain a space angle set theta, constructing an overcomplete basis B (theta), and sparsely representing a left singular vector u ₁ = B (theta) | Σ, so that a sparse solution framework min | | | Σ | u is established ₁ +ε||u ₁ -B(Θ)∑|| ₂ Obtaining a space spectrum through the solved sigma, estimating the target azimuth through the spectrum peak position, wherein epsilon represents a regularization parameter, and the concrete steps are as follows:

let Θ = [ Θ ₁ ，…，Θ _N ]Is a set obtained by sampling the spatial azimuth plane, N is the number of meshes of division of the spatial azimuth plane, and it is assumed that the incident angle of the target is also included in the azimuth set Θ. The corresponding overcomplete basis may be expressed as:

B(Θ)＝[a _xy (Θ ₁ )，…，a _xy (Θ _N )] (12)

thus, the left singular vector u ₁ Sparsely representable as:

u ₁ ＝B(Θ)∑ (13)

where zero elements of the vector sigma indicate that the direction is not targeted and non-zero elements indicate that the direction is targeted.

The solution to the sparse vector Σ can be expressed as:

min||∑|| ₁ +ε|lu ₁ -B(Θ)∑|| ₂ (14)

in the formula, | \ | non-counting ₁ And | · | non-counting ₂ Sub-table representation l ₁ And l ₂ And (4) norm. ε represents the regularization parameter and is used to controll ₁ Norm terms and ₂ norm term. The above equation can be solved with the optimization toolkit sedimi or CVX.

The foregoing describes embodiments of various aspects of the present disclosure. The following further describes the present invention by way of simulation examples and test examples.

Simulation example: the simulation adopts an acoustic vector circular array with 8 array elements uniformly distributed, and the radius of the circular array is 0.35m; the signals of two coherent sound sources are respectively s ₁ (t)，s ₂ (t) in which s ₂ (t)＝e ^jπ/8 s ₁ (t) the signal frequency is 2000Hz. Two-phase dry signals are respectively incident to the acoustic vector circular array from 100 degrees and 140 degrees, the sampling frequency is 30000Hz, and the fast beat number is 5000. The azimuth plane is divided into 360 grids from 0 ° to 360 ° at 1 ° intervals, i.e., N =360. The noise is isotropic.

For simplicity, the MVDR and MUISC based on the forward and backward term spatial smoothing are abbreviated as FBSS-MVDR and FBSS-MUSIC, respectively, wherein the cross covariance matrix is

Psi is the angle of projection and,

is a sound pressure, x and y vibration speed channel signal after mode conversion. The orientations in the literature (Yin, J.H.; chen, T.Q., direction-of-Arrival Estimation uses a spark Estimation of array Covariance vectors IEEE trans. On Signal Process.2011,59, (9), 4489-4493.) are abbreviated as l ₁ -SRCCV, wherein the cross covariance matrix used in the method is

FIGS. 3 (a) to 3 (c) are views of the present inventionMethod and FBSS-MVDR, FBSS-MUSIC, l ₁ Spatial spectral contrast results of SRCCV at different signal-to-noise ratios, where the regularization parameter in the proposed method is set to 1.7. Fig. 3 (a) is SNR = -5dB, fig. 3 (b) is SNR = -10dB, and fig. 3 (c) is SNR = -15dB. As can be seen from comparative analysis, the FBSS-MVDR method cannot distinguish two coherent sources; the FBSS-MUSIC approach can resolve two coherent objects at SNR = -5dB, but the approach has not been able to resolve two coherent sources at SNR = -10dB and-15 dB. l. the ₁ SRCCV can effectively resolve two coherent targets when SNR = -5dB and SNR = -10dB, but the method fails when SNR = -15dB, failing to resolve two coherent targets. In contrast, the method can still effectively separate two coherent targets when the SNR is reduced to-15 dB, which shows that the method has stronger capability of detecting the coherent targets.

Fig. 4 shows the root mean square error curves of the orientation estimates of two coherent sources at different signal-to-noise ratios, where the two target incidence angles are 100 ° and 145 °, respectively, and the regularization parameter of the proposed method is equal to 1.7. It can be seen from fig. 4 that the root mean square error of the orientation estimate decreases for all methods as the signal-to-noise ratio increases. And the method is characterized in that the estimation error ratios FBSS-MVDR, FBSS-MUSIC and l ₁ The SRCCV is small, especially under low signal-to-noise ratio conditions. The result shows that the method provided by the patent is superior to other methods in the aspect of the position estimation precision and is more suitable for passive detection of a remote coherent target.

Fig. 5 shows the resolution probability curves for two coherent targets at different angular intervals, where the signal-to-noise ratio SNR = -5dB. When the two signals satisfy the inequality

The two signals are considered to be successfully resolved, wherein

And

for estimating the azimuth angles, theta, of two coherent objects ₁ And theta ₂ Are the angles of incidence of two coherent objects. The resolution probability is defined as the ratio of the number of trials to successfully resolve the two targets to the total number of trials. As can be seen from fig. 5, the FBSS-MVDR under this condition still cannot resolve two coherent targets when the angular separation reaches 46 °. The FBSS-MUSIC method can successfully resolve two objects when the angular interval is greater than or equal to 42 °. l. the ₁ The SRCCV method allows to fully resolve two coherent objects when the angular separation is equal to or greater than 18 °. In contrast, the proposed method allows to fully resolve two coherent targets when the angular separation is equal to or greater than 8 °. Therefore, the method has stronger angle resolution capability.

Test examples:

and carrying out experimental study on coherent target azimuth estimation of the acoustic vector circular array in the silencing water pool, and verifying the feasibility and effectiveness of the algorithm. The experiment adopts an 8-element uniformly distributed vector circular array, the radius of a basic array is 0.35m, and the vibration speeds x and y of the acoustic vector sensor are respectively superposed with the radial direction and the tangential direction of the circular array. And projecting the two vibration velocity directions to x and y axes to obtain vibration velocity components along the x and y axes. The coherent target signal of the experiment is a single-frequency signal which is transmitted by a transmitting transducer and then transmitted by two sets of transmitting systems (comprising a power amplifier and the transmitting transducer). The background noise and the target signal are acquired and recorded in the experiment, and the acoustic vector circular array receiving data under the conditions of different signal-to-noise ratios are obtained by adjusting the size of the background noise and mixing the background noise into the measured target signal.

Fig. 6 (a) -6 (c) show experimental results for coherent acoustic sources incident from 205 ° and 254 ° under different signal-to-noise ratios. Fig. 6 (a) SNR =0dB, fig. 6 (b) SNR = -6dB, and fig. 6 (c) SNR = -12dB. The signal frequency was 2500Hz and the number of fast beats used was 15000. The regularization parameters of the proposed method are set to 1.7,1.5 and 1.2 in fig. 6 (a), (b) and (c), respectively. In FBSS-MVDR, FBSS-MUSIC and l ₁ -projection angle ψ =230 ° in the SRCCV method. The FBSS-MVDR, FBSS-MUSIC methods can resolve two coherent objects when SNR =0dB, but the FBSS-MVDR and FBSS-MUSIC methods have been unable to effectively separate the two coherent objects when the signal-to-noise ratios SNR = -6dB and-12 dB. At SNR =0dB and-6 dB,/ ₁ The SRCCV method has two higher spectral peaks than the FBSS-MVDR, FBSS-MUSIC methods, but the method has failed when SNR = -12dB. Compared with the prior art, the method has stronger detection capability, can successfully distinguish two coherent targets when the signal-to-noise ratio is reduced to-12 dB, and has higher position estimation precision.

Fig. 7 shows the experimental results of a coherent dual source with an incident angle of 205 deg., 225 deg. under the 0dB condition. The number of snapshots used for the test procedure was 8000. The signal frequency was 5000Hz. The regularization parameter in the proposed method is set to 1.75 ₁ -projection angle ψ =215 ° in the SRCCV method. As can be seen from the figure, the presence of grating lobes in the FBSS-MUSIC and FBSS-MVDR methods does not give the orientation of the two coherent objects. The reason is that the two methods need phase modal change as a preprocessing method, when the signal frequency is equal to 5000Hz, the number of virtual array elements generated by mode space transformation exceeds the number of array elements of a circular array, the space Nyquist sampling law is not satisfied, and therefore higher grating lobes are generated. In FIG. 7,/ ₁ The SRCCV method can resolve two coherent objects, but the position estimation error of the method is large. In contrast, the method has two higher spectral peaks, can successfully distinguish two coherent targets, and has higher positioning accuracy.

FIG. 8 shows the experimental results of coherent dual acoustic sources with an incident angle of 205 DEG, 254 DEG, where the results are shown in FBSS-MVDR, FBSS-MUSIC and l ₁ -projection angle ψ =293 ° in the SRCCV method. The regularization parameter of the proposed method is 1.75. The signal-to-noise ratio is equal to 0dB, and the number of fast beats used in the test is 15000. In FBSS-MVDR, FBSS-MUSIC and l ₁ Combined velocities obtained by projection in the SRCCV method

And V _c (t) may be represented by

V _c (t)＝A _p Ψ _v S(t)+n _c (t) wherein the matrix Ψ _v ＝diag(cos(ψ-θ ₁ )，cos(ψ-θ ₂ ))(θ ₁ ＝205°，θ ₂ =254 °). Cos (ψ - θ) when ψ =293 ° ₁ ) About 0.03, severely attenuates the angle of incidence theta ₁ Corresponding signal s ₁ (t) in turn such that the signal covariance matrix R _s Neutralization s ₁ (t) the corresponding elements are extremely small, resulting in FBSS-MVDR, FBSS-MUSIC and l ₁ -no theta in the space spectrum of the SRCCV method ₁ The spectral peak of the direction cannot effectively estimate the two target orientations. In contrast, the proposed method does not require projection to calculate the cross-covariance matrix, and can effectively estimate the incoming wave direction.

Claims (3)

1. An acoustic vector circular array coherent target direction estimation method is characterized in that:

the method comprises the following steps: an acoustic vector circular array collects sound pressure channel signals and two vibration velocity channel signals along x and y axes, and the signals are respectively marked as P (t) and V _x (t) and V _y (t)；

Step two: respectively constructing sound pressure P (t) and vibration velocity V _x (t)、V _y (t) cross covariance matrix R _x And R _y Two cross covariance matrices are stacked to obtain a new matrix R _xy ＝[R _x ,R _y ] ^T ,(·) ^T Representing a transpose operation;

step three: combining the matrix R in the second step _xy Singular value decomposition is carried out to obtain a left singular vector u corresponding to the maximum singular value ₁ ；

Will matrix R _xy Singular value decomposition is carried out to obtain a left singular vector u corresponding to the maximum singular value ₁ ：

In the formula, mu _m ，u _m And d _m Respectively representing singular values, 2 mx 1-dimensional left singular vectors and mx 1-dimensional right singular vectors, M =1, \ 8230;, M;

using right singular vector d ₁ Left-multiplying by the above equation to obtain:

when the sound sources are coherent, the matrix R _xy As follows:

in the formula, a _xy (θ _q ) Is a matrix A _xy The (c) th column (q) of (c),

is the signal s ₁ (t) power, to obtain

Wherein z = [ alpha ] ₁ ,…,α _q ,…,α _Q ] ^T ，α _q Is a scalar that is not zero;

step four: discretizing the plane of the space azimuth angle to obtain a space angle set theta, constructing an overcomplete basis B (theta), and sparsely representing a left singular vector u ₁ = B (Θ) Σ, thereby establishing a sparse solution framework min | ∑ iil ₁ +ε‖u ₁ -B(Θ)∑‖ ₂ And obtaining a spatial spectrum through the solved sigma, and obtaining a target azimuth through the spectrum peak position, wherein epsilon represents a regularization parameter.

2. The acoustic vector circular array coherent target direction estimation method as claimed in claim 1, wherein the second step specifically comprises:

sound pressure P (t) and vibration velocity V _x (t)、V _y (t) cross covariance matrix R _x And R _y Expressed as:

wherein A is _p 、A _x And A _y Respectively is a guide vector matrix of sound pressure, x and y vibration velocity channels of the acoustic vector circular array; (.) ^H Represents a conjugate transpose operation; r _s ＝E{S(t)S ^H (t) } denotes a signal covariance matrix, where S (t) = [ S ] ₁ (t),…,s _Q (t)] ^T Is a signal vector, s _q (t)＝β _q s ₁ (t) is the Q-th signal, Q is the number of coherent signals, β _q Is complex constant, Q =1, \8230, Q, R _nx 、R _ny Respectively representing a noise cross covariance matrix, wherein in an isotropic noise field, sound pressure and vibration velocity measured at the same point are irrelevant, and noise received by any two acoustic vector sensors is also irrelevant, so that the matrix R _nx 、R _ny Are respectively equal to

In the formula (I), the compound is shown in the specification,

N _x,m (t) and N _y,m (t) represents sound pressure received by mth array element, noise of x and y vibration velocity channels, M, n =1, \ 8230; (M, M represents array element number of sound vector circular array, 0 _M×M Representing an M x M dimensional zero matrix and, therefore,

using a cross-covariance matrix R _x 、R _y To obtain a new matrix

In the formula, A _xy ＝[A _x ,A _y ] ^T 。

3. The acoustic vector circular array coherent target direction estimation method as claimed in claim 2, wherein the fourth step specifically comprises:

sampling an azimuth plane to obtain a spatially discrete azimuth set theta = [ theta ] ₁ ,…,Θ _N ]Wherein N represents the number of grids divided by the azimuth plane, and an overcomplete basis B (theta) is constructed:

B(Θ)＝[a _xy (Θ ₁ ),…,a _xy (Θ _N )]

in the formula, a _xy (Θ _n )＝[a _x (Θ _n ),a _y (Θ _n )] ^T ,

Wherein phi ₁ ,…,φ _M Representing the angle of the M-element acoustic vector sensor from the x-axis;

left singular vector u ₁ The sparse representation is:

u ₁ ＝B(Θ)∑

in the formula, zero elements of the vector sigma represent that the direction has no target, and non-zero elements represent that the direction has a target;

establishing a sparse solving frame, solving unknown number sigma through the following formula to obtain a spatial spectrum, estimating a target direction through the position of a spectrum peak,

min‖∑‖ ₁ +ε‖u ₁ -B(Θ)∑‖ ₂

in the formula, ε represents a regularization parameter.

Images