CN106680762A - Sound vector array orientation estimation method based on cross covariance sparse reconstruction - Google Patents

Abstract

The invention relates to a method for estimating the direction of an acoustic vector array based on the sparse reconstruction of mutual covariance. The present invention includes: (a) obtaining the receiving data of the sound vector array, generating a sparse representation of the vector array space domain about the sound source signal in the space Θ of interest; (b) generating M×M at each azimuth angle θ _k dimensional sound pressure-vibration velocity cross-covariance matrix R ^(p+vc) (θ _k ); (c) make full use of the uncorrelation between signal and noise and the relationship between signal and signal in joint processing of sound pressure-vibration velocity , the independence between noise and noise, transform Φ ^(vc) (θ _k ) in the cross-covariance matrix into a K×K dimensional diagonal matrix, etc. The present invention constructs a new sparse representation form of the sound source signal. This form is different from treating the vibration velocity channel in the vector array as the same scalar quantity as the sound pressure channel in the past, but makes full use of the sound pressure-vibration velocity channel. The advantage of joint processing greatly improves the noise suppression ability of array signal processing.

Description

A Method of Acoustic Vector Array Orientation Estimation Based on Cross-covariance Sparse Reconstruction

technical field

The invention relates to a method for estimating the direction of an acoustic vector array based on the sparse reconstruction of mutual covariance.

Background technique

The biggest advantage of the acoustic vector array signal processing technology is that it organically combines the anti-noise ability of the vector sensor with the spatial resolution performance of the array, so it has higher azimuth estimation performance than the single acoustic pressure array processing. However, the existing acoustic vector array signal processing technology is basically based on the Nehorai theoretical framework, and its essence is to process the vibration velocity information of the acoustic vector array as the same independent array element information as the sound pressure, and does not make full use of the "sound pressure- Vibration velocity" joint information processing, so the signal-to-noise ratio threshold is higher. In fact, the sound pressure and vibration velocity of coherent source (signal source with limited scale) signal are coherent in the remote sound field, but the sound pressure and vibration velocity of the noise in the isotropic noise field are irrelevant, so based on the acoustic The pressure-vibration-velocity joint information processing technology will inevitably have a stronger ability to suppress isotropic noise. Based on this, Bai Xingyu et al. proposed a joint signal processing method of sound pressure and vibration velocity, which organically combined the high-resolution capability of subspace methods and the anti-noise capability of vector hydrophones, and realized long-range high-resolution DOA estimation (1 Bai Xingyu, based on Acoustic Vector Direction Finding Technology Based on Joint Information Processing, Doctoral Dissertation in Engineering, Harbin Engineering University, 2006). Its core technology is to decompose the sound pressure and vibration velocity cross-covariance matrix into subspace, so as to extend the subspace-like high-resolution spatial spectrum method to vector array signal processing.

Angeliki Xenaki and others proposed the concept of compressed sensing beamforming, using the spatial sparsity of the array received data for sound source reconstruction (2 Angeliki Xenaki, Peter Gerstoft, KlausMosegaard.Compressive beamforming.J.Acoust.Soc.Am.2014,136( 1): 260-271). In the study of using array covariance matrix sparse reconstruction for target orientation estimation, Siyang Zhong et al. proposed a compressive sensing beamforming method based on the covariance matrix of sound pressure array data (3 Siyang Zhong, Qingkai Wei, XunHuang. Compressive sensing beamforming based on covariance for acoustic imaging with noisy measurements, J.Acoust.Soc.Am.2013, 134(5), 445-451), transforming the problem of sound source waveform estimation into the problem of sound source power estimation. Ning Chu et al proposed a sound source power and position estimation method based on sparse reconstruction (4 Ning Chu, José Picheral, Ali Mohammad-djafari, Nicolas Gac. A robust super-resolution approach with sparsity constraint in acoustic imaging). However, the above method only utilizes the prior information that the sound sources are independent of each other, and its disadvantage is the same as that of the traditional sound pressure array processing, which cannot reduce the threshold of the signal-to-noise ratio. Shi Jie and others proposed a vector array focus positioning method based on compressed sensing (5 Shi Jie, Yang Desen, Shi Shengguo, Hu Bo, Zhu Zhongrui. Vector array focus positioning method based on compressed sensing. Acta Phys. 2016, 65(2) :024302,1-11), making full use of the spatial sparsity of the sound source, constructing a sparse signal model for vector array near-field positioning, and using the l1 norm regularization method to solve it, and realizing the accurate sound source localization in the snapshot. Although this technology uses vector array processing, it overcomes the difficulty of coherent sound source resolution, the contribution evaluation is not accurate, the performance of the algorithm is seriously degraded in practical applications, the calculation results rely on large snapshots for data covariance estimation, and the iterative processing of the algorithm has a huge amount of calculation. However, it still treats the sound pressure and vibration velocity as an independent channel for processing, and cannot give full play to the advantages of sound pressure-vibration velocity joint processing.

Inspired by the above physical mechanism and processing method, this patent focuses on the spatial sparsity of the sound pressure and vibration velocity cross-covariance matrix, and invents a compressive sensing beamforming method based on the cross-covariance matrix, which can simultaneously obtain acoustic Source power and azimuth estimation results.

Contents of the invention

The purpose of the present invention is to make full use of the advantages of vector array sound pressure-vibration velocity joint processing to provide an enhanced noise suppression capability, realize the reconstruction of sound source energy in a sparse space, and simultaneously obtain sound source power and orientation estimation results based on mutual Acoustic Vector Array Orientation Estimation Method Based on Covariance Sparse Reconstruction.

The purpose of the present invention is achieved like this:

(a) Obtain the received data of the acoustic vector array, and generate a spatial sparse representation of the vector array about the sound source signal in the space of interest.

(b) At each azimuth angle θ _k , generate an M×M dimensional sound pressure-vibration velocity cross-covariance matrix R ^(p+vc) (θ _k ).

(c) Make full use of the uncorrelation between signal and noise and the independence between signal and signal and between noise and noise in the joint processing of sound pressure and vibration velocity, and convert Φ ^(vc) in the cross-covariance matrix (θ _k ) into a K×K dimensional diagonal matrix.

(d) Transform the M×M dimensional cross-covariance matrix R ^(p+vc) (θ _k ) to generate a new M ² ×1-dimensional cross-covariance column vector

(e) get the signal power sparse representation of .

(f) Using the obtained vector matrix cross-covariance column vector and overcomplete GΦ ^(vc) (θ _k ) to reconstruct the sparse signal matrix

(g) Traverse all azimuth angles θ _k (k=1, 2,..., K), repeat steps (b) to (f), and obtain the power estimation result of the sound source signal at each angle θ _k .

(h) Draw an azimuth spectrogram based on the estimated power of the sound source signal at all azimuth angles.

(i) Simultaneously determine the azimuth and relative power of the sound source through the spectral peak position and intensity of the spatial spectrum.

The beneficial effects of the present invention are:

1) A new sparse representation of the sound source signal is constructed. This form is different from the previous treatment of the vibration velocity channel in the vector array as the same scalar as the sound pressure channel, but makes full use of the sound pressure-vibration velocity The advantage of joint processing greatly improves the noise suppression ability of array signal processing.

2) Utilizing the spatial compression characteristics of the sound source information received by the vector array, the array signal processing is no longer directly obtained the azimuth estimation result (that is, only the estimated value of the azimuth angle can be obtained), but can simultaneously obtain the sound source azimuth and power The result of the joint estimate.

3) The fuzzy resolution ability of the vector array to starboard and starboard is fully utilized, and the fuzzy information is completely suppressed in the sparsely reconstructed spatial spectrum.

4) It naturally exhibits extremely high spatial high-resolution performance in the spatial spectrum, and only shows the power value of the sound source in the direction where the sound source is located, while there is no power leakage at all in adjacent directions.

5) An ideal orientation estimation effect can still be obtained with a small number of snapshots.

Description of drawings

Fig. 1 is a schematic diagram of vector array sparse signal;

Figure 2 is the comparison result of azimuth spectrum;

Fig. 3 is the variation curve of power estimation error with signal-to-noise ratio;

Fig. 4 is the change curve of the orientation estimation error with the signal-to-noise ratio.

detailed description

The present invention will be further described below in conjunction with the accompanying drawings.

This method takes full advantage of the joint processing of sound pressure and vibration velocity of the vector array, utilizes the sparsity of the sound source in the spatial orientation, and constructs a novel sparse representation of the cross-covariance vector of the acoustic vector array to effectively enhance the performance of the acoustic vector array orientation estimation.

(a) Obtain the received data of the acoustic vector array, and generate a spatial sparse representation of the vector array about the sound source signal in the space of interest.

Considering that a single far-field single-frequency point sound source signal is incident on an M-element uniform two-dimensional acoustic vector linear array, the array element spacing d is generally selected as half the acoustic wave wavelength (Figure 1 shows a schematic diagram of a vector array sparse signal). The matrix form of the vector array sparse signal generated at multiple times is as follows:

Y ^(p) = AS + N ^(p) (1a)

Y ^(vx) = AΦ ^(vx) S+N ^(vx) (1b)

Y ^(vy) = AΦ ^(vy) S+N ^(vy) (1c)

The above formula can be expanded to express as:

Among them, S is the K×L dimensional source signal matrix, K is the number of all azimuth angles in the space Θ, L is the number of snapshots, s _k is the 1×L dimensional signal vector corresponding to the kth incoming wave direction; A is a regular linear array steering vector matrix, where the elements (m=1,2,...,M, k=1,2,...,K) is the steering vector element corresponding to the arrival of the signal in the direction of the kth incoming wave to the mth array element, and d is Array element spacing, f is the frequency of the sound wave, c is the speed of sound in water; the superscripts (.) ^(p) , (.) ^(vx) and (.) ^(vy) represent the corresponding sound pressure, x-direction vibration velocity and y-direction Variable, vector, or matrix of vibration velocities. Φ ^(vx) and Φ ^(vy) are unit vector matrices corresponding to the x-direction vibration velocity and y-direction vibration velocity channels, respectively, and both are K×K dimensional diagonal matrices. Considering background noise interference, N ^(p) , N ^(vx) and N ^(vy) are M×L dimensional sound pressure, x-direction vibration velocity and y-direction vibration velocity channel noise matrices, respectively. with are the sound pressure, x-direction vibration velocity, and y-direction vibration velocity channel 1×L-dimensional noise data vector of the m-th hydrophone, respectively. Y ^(p) , Y ^(vx) and Y ^(vy) are M×L dimensional sound pressure, x-direction vibration velocity and y-direction vibration velocity data matrices, respectively, with are the sound pressure, x-direction vibration velocity, and y-direction vibration velocity of the mth array element, respectively, 1×L-dimensional data vectors.

The physical meaning of the sparse signal model is shown in Figure 1. Divide the azimuth space domain Θ where the sound source is located into K equal-spaced uniform azimuth angles {θ ₁ , θ ₂ ,...,θ _k ,...,θ _K }, then each spatial orientation θ _k and The directions of the sound sources are in one-to-one correspondence, and because there are only N real sound sources (N<<K) in the space. On Θ, only N azimuth angles have signals, that is, in the constructed K×L-dimensional signal matrix S, there are only waveform data of corresponding N rows of non-zero elements. y ^(p) , y ^(vx) and y ^{( vy)} are essentially sparse representations of S, and the reconstruction of signal S is realized by using the new method of sound pressure-vibration velocity combination.

(b) At each azimuth angle θ _k , generate an M×M dimensional sound pressure-vibration velocity cross-covariance matrix R ^(p+vc) (θ _k ).

On θ _k , construct the combined vibration velocity signal Y ^(vc) (θ _k )=cosθ _k Y ^(vx) +sinθ _k Y ^(vy) . Then the M×M dimensional sound pressure-velocity cross-covariance matrix is generated:

R ^(p+vc) (θ _k )＝E{Y ^(p) (Y ^(vc) (θ _k )) ^* }＝E{Y(cosθ _k Y ^(vx) + sinθ _k Y ^(vy) ) ^* } (3)

Among them, E{·} is the mathematical expectation, and ^* is the conjugate transposition operator.

(c) Make full use of the uncorrelation between signal and noise and the independence between signal and signal and between noise and noise in the joint processing of sound pressure and vibration velocity, and convert Φ ^(vc) in the cross-covariance matrix (θ _k ) into a K×K dimensional diagonal matrix.

Taking advantage of the uncorrelation between signal and noise, the operation property satisfies (i=1,2,...,K, j=1,2,...,K), and the independence between signal and signal, noise and noise with (i≠j is required at this time), then Φ ^(vc) (θ _k ) in the cross-covariance matrix can be transformed into a K×K dimensional diagonal matrix.

have:

(d) Transform the M×M dimensional cross-covariance matrix R ^(p+vc) (θ _k ) to generate a new M ² ×1-dimensional cross-covariance column vector

The M×M-dimensional cross-covariance matrix R ^(p+vc) can be further reorganized according to the following formula to generate an M ² ×1-dimensional cross-covariance column vector

(e) Get the signal power sparse representation of .

Wherein, G is an M ² ×K dimensional reconstruction transformation matrix. Reconstruct signal matrix for K×1 dimension, its physical meaning represents the power of sparse signal. is an M ² ×1-dimensional reconstruction noise matrix.

(f) Using the obtained vector matrix cross-covariance column vector and overcomplete GΦ ^(vc) (θ _k ) to reconstruct the sparse signal matrix

Express the sparse signal processing procedure as the following optimization solution:

Where ε is the noise constraint parameter, ||.|| ₁ means the l ₁ norm, ||.|| ₂ means the l ₁ norm, and min means take the minimum value. The meaning of st is to minimize the l ₁ norm of the left side of the formula under the constraints of the right side of the formula. The above formula is an underdetermined equation, which can recover the source signal power from the cross-covariance column vector of the vector matrix, and thus indirectly obtain the signal power estimation result in the θ _k direction. This sparse linear regression problem can be efficiently solved by using the CVX toolbox to regularize the second-order error by using a low-order norm.

(g) Traverse all azimuth angles θ _k (k=1, 2,..., K), repeat steps (b) to (f), and obtain the power estimation result of the sound source signal at each angle θ _k .

(h) Draw an azimuth spectrogram based on the estimated power of the sound source signal at all azimuth angles.

(i) Simultaneously determine the azimuth and relative power of the sound source through the spectral peak position and intensity of the spatial spectrum.

The specific implementation of each part of the content of the invention has been described above. The new method makes full use of the advantages of vector array sound pressure-vibration velocity joint processing, enhances the noise suppression ability, realizes the reconstruction of sound source energy in a sparse space, and can obtain the sound source power and orientation estimation results at the same time. The simulation example is analyzed below.

Example 1: Comparative Analysis of Azimuth Spectrum

The example parameters are set as follows: the frequency of a single single-frequency sound source is 1kHz, and its incident azimuth angle is 45°. For the convenience of analysis, the sound source power is taken as 1. The number of vector array elements is 7, and the distance between the array elements is selected as 0.75m of the half-wavelength of the incident sound wave. The system sampling rate is 10kHz. The speed of sound in water is taken as 1480m/s. The azimuth scanning range is 0° to 360°, and the scanning step is 1°. In the simulation, the new method using the sparse reconstruction of the cross-covariance matrix in this patent and the method using the sparse reconstruction of the auto-covariance matrix in the literature [3] are compared and analyzed. The azimuth spectrogram contrast result of two kinds of methods is as shown in Figure 2, among the figure (a) represents the calculation result of document [3] method, (b) represents the calculation result of the present invention, and abscissa among the figure represents azimuth angle, and vertical Coordinates represent estimated powers.

Example 2: Error Analysis of Amplitude Estimation and Azimuth Estimation under Different Signal-to-Noise Ratio

The simulation parameters remain unchanged, and the error analysis of amplitude estimation and azimuth estimation under different signal-to-noise ratios, the signal-to-noise ratio ranges from -5dB to 20dB. Figure 3 shows the variation curve of the power estimation error with the signal-to-noise ratio. Figure 4 shows the variation curve of the orientation estimation error with the signal-to-noise ratio.

From the simulation results in the comprehensive example, it can be seen that the new method in the present invention has the advantages of the joint processing of sound pressure and vibration velocity, and has the ability to resist port and starboard ambiguity, especially when the signal-to-noise ratio is low, the azimuth estimation performance is significantly improved . Because the method reconstructs the power of the sound source, the background fluctuation suppression ability can be significantly improved.

Claims (1)

1. a kind of acoustic vector sensor array direction estimation method based on the sparse reconstruct of cross covariance, it is characterised in that the method is included such as Lower step：

A () obtains acoustic vector sensor array and receives data, the vector array spatial domain on sound-source signal is generated in space Θ interested dilute Thinization is represented；

B () is in each azimuth angle theta_kOn, generation M × M dimensions acoustic pressure-vibration velocity Cross-covariance R^(p+vc)(θ_k)；

C () is made full use of in acoustic pressure-vibration velocity Combined Treatment, the irrelevance and signal and signal between signal and noise it Between, the independence between noise and noise, by the Φ in Cross-covariance^(vc)(θ_k) turn to K × K dimension diagonal matrix；

D () is to M × M dimension Cross-covariances R^(p+vc)(θ_k) deformed, generate new M²× 1 dimension cross covariance column vector

E () is obtained on signal powerRarefaction representation；

F () is using the vector array cross covariance column vector for having obtainedWith super complete G Φ^(vc)(θ_k) dilute to reconstruct Dredge signal matrix

The whole azimuth angle thetas of (g) traversal_k(k=1,2 ..., K), repeat step (b) to (f) obtains each angle, θ_kOn sound Source signal power estimated result；

H () draws orientation spectrogram according to all azimuthal sound-source signal power estimation values；

I () determines sound source incoming wave orientation and power relative size simultaneously by the spectrum peak position and intensity of spatial spectrum.