Extrapolation vector estimation method suitable for underwater acoustic uniform linear array

Abstract

The invention discloses an extrapolation vector estimation method suitable for an underwater acoustic uniform linear array. Spatial spectrum information is acquired from an original measurement vector of the array by using a sparse spectrum fitting method. Then, based on initial orientation and power information provided by a spatial spectrum, an extrapolation vector is obtained by solving an atomic norm minimization problem about multi-measurement vector reverse robustness. Spatial spectrum information obtained through a spatial spectrum fitting method is used as prior information of array extrapolation vector estimation, then extrapolation vector estimation is split into sub-extrapolation vector estimation in multiple different orientations, meanwhile, physical constraints are introduced, the precision of extrapolation vector estimation is guaranteed, and therefore target signals are effectively enhanced.

Description

Technical Field

[0001] This invention relates to signal enhancement technology for extrapolation measurement vector estimation applicable to uniform linear arrays of underwater acoustic signals, and belongs to the field of feature extraction and recognition technology for incident noise signals of underwater acoustic targets. Background Technology

[0002] Low-frequency line spectrum signals, as an important acoustic feature, play a crucial role in underwater target detection and identification. Compared to broadband noise, line spectrum signals are typically generated by the periodic motion of underwater vehicles, such as mechanical vibrations and propeller rotation. Their energy is concentrated at specific discrete frequencies, offering advantages such as strong signal energy, long propagation distance, and minimal attenuation from absorption. This makes low-frequency line spectrum signals an effective information source for long-range passive detection, target classification, and identification in complex marine environments.

[0003] With the rapid development of unmanned underwater vehicle (UUV) technology, small-sized arrays have become the mainstream acoustic sensor configuration for UUV platforms. The small size and high mobility of UUVs make them ideal platforms for underwater reconnaissance, patrol, and intelligence gathering missions. However, UUV platforms impose strict limitations on the size and weight of the acoustic arrays they carry, resulting in small array sizes and a limited number of array elements.

[0004] The array aperture is a core parameter determining the array's directivity, spatial gain, and resolution. For small arrays, the spatial gain is limited, making it difficult to effectively suppress isotropic noise and interference from non-target directions. More importantly, the array size is usually proportional to the wavelength of the detected signal. This means that small arrays are severely limited in performance when processing low-frequency, long-wavelength signals, especially when the array size is only 1 to 3 times the signal wavelength. This results in wide beamwidth, poor directivity, and high sidelobe levels, leading to a significant decrease in spatial resolution for low-frequency line spectrum signals.

[0005] This invention proposes an extrapolation measurement vector estimation method suitable for underwater acoustic uniform linear arrays. By fragmenting the received underwater acoustic uniform linear array measurement vector into multiple directions and estimating the extrapolation measurement vector in each direction based on inverse robust atomic norm minimization, a virtual aperture expansion of the underwater acoustic uniform linear array is achieved. Signal enhancement can then be achieved by performing conventional beamforming on the extrapolated measurement vector. Specifically, we first employ a sparse spectrum fitting method to obtain the spatial spectrum information of the sparse signal. Then, using the initial azimuth and power information obtained from the spatial spectrum, the extrapolation measurement vector estimation problem is formulated as an optimization problem based on inverse robust atomic norm minimization. By solving this optimization problem using the interior-point method, an accurate extrapolation measurement vector estimate can be obtained. Finally, conventional beamforming on the extrapolated measurement vector can enhance the target signal. Summary of the Invention

[0006] The purpose of this invention is to address the problem of severe performance degradation of underwater acoustic arrays when processing low-frequency target signals, and to provide an extrapolation measurement vector estimation method suitable for uniform linear underwater acoustic arrays. This method utilizes a sparse spectrum fitting method to obtain spatial spectrum information from the array's original measurement vectors. Subsequently, based on the initial orientation and power information provided by the spatial spectrum, the extrapolated measurement vectors are obtained by solving a problem of minimizing the atomic norm with respect to multiple measurement vectors inversely robust.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] An extrapolation measurement vector estimation method applicable to underwater acoustic uniform linear arrays includes the following steps:

[0009] (1) Read in the underwater acoustic target radiated noise data received by the M-element uniform linear array of underwater acoustic elements, with a sampling frequency of . f s The frequency band range processed [f min , f max The data is segmented, and an L-point discrete Fourier transform is performed on each segment of the signal for each array element. min =⌊f min ×L / f s ⌋, l max =⌊f max ×L / f s ⌋, where ⌊·⌋ represents rounding down, and let l=l min ;

[0010] (2) Extracting frequency point f l =l× f s The discrete Fourier coefficients at / L, if f l > f max Then the estimation process ends; otherwise, the frequency point f is calculated. l The average sample covariance matrix R̂ at point l ;

[0011] (3) Discretize the azimuth space [-90°, 90°] into Q candidate directions, and based on the frequency point f obtained in step (2) l The average sample covariance matrix R̂ at point l The following sparse spectrum fitting semidefinite programming problem is solved using the interior point method to obtain the value at frequency f. l Spatial spectrum v l :

[0012] ;

[0013] in, This is the matrix verticalization operator; and These represent the 1-norm and 2-norm of the vector, respectively; β is the regularization parameter; the matrix... The qth column is , q=1,…,Q, where For θ q The direction corresponds to the guiding vector, where the superscript T indicates the transpose operation, and d s λ is the distance between the two hydrophones. l For frequency point f l The corresponding wavelength, j is the imaginary unit; * and ⊗ represent the conjugate operation and the Kronecker product, respectively; σ is the spatial correlation coefficient of the noise, which can be obtained by expanding the directional distribution in the spatial harmonic domain; 2 Noise power estimated for a semidefinite programming problem;

[0014] (4) For the spatial spectrum v l A peak search was performed, and the azimuth and amplitude of the D peaks obtained were ϕ. d p d , d=1,…,D;

[0015] (5) At frequency point f l At this point, construct an optimization problem for estimating array extrapolation measurement vectors;

[0016] Step (5) specifically includes the following steps:

[0017] (5.1) Construct the Toeplitz matrix for the d-th peak:

[0018] ;

[0019] (5.2) Set the dimension N of the extrapolation measurement vector, and NM is an even number greater than 0; define the extrapolation measurement vector. It is then divided into Z = (NM) / s + 1 sub-measurement vectors, forming a structure about y b (l) Multi-measurement vector matrix:

[0020] ;

[0021] Where s is a positive integer less than M, and (NM) / s is an integer;

[0022] (5.3) Construct the array extrapolation measurement vector estimation optimization problem as shown below:

[0023] ;

[0024] in, This is the extrapolated measurement vector corresponding to the d-th peak; During the extrapolation measurement vector estimation process corresponding to the d-th peak, x b (l) residual amount; Indicates by y b The vector consisting of the first to the (N-1)th elements of (l); P = (NM) / 2 represents the dimensions of the forward and backward extrapolations. Here, λ is the reflection matrix; η, γ are regularization parameters; and δ is the power constraint parameter. Representing matrix inequalities;

[0025] (6) Set λ, η, γ and δ, and use the interior point method to solve the optimization problem in step (5) to obtain the extrapolated measurement vector y after the D peaks are superimposed. b (l);

[0026] Step (6) specifically includes the following steps, and steps (6.1) or (6.2) are performed:

[0027] (6.1) If D=0, execute steps (6.1a)~(6.1b):

[0028] (6.1a) Initialization , Let η = 0;

[0029] (6.1b) Solve the optimization problem in step (5.3) using the interior point method to obtain the following results. ,but .

[0030] (6.2) If D>0, execute steps (6.2a)~(6.2f):

[0031] (6.2a) Initialize y b (l)=0, d=1, ;

[0032] (6.2b) Construct the Toeplitz matrix for the d-th peak based on step (5.1). ;

[0033] (6.2c) Solve the optimization problem in step (5.3) using the interior point method to obtain the result. ;

[0034] (6.2d) Let , d = d + 1;

[0035] (6.2e) Repeat steps (6.2b) to (6.2d) to complete the estimation of the extrapolated measurement vectors corresponding to the D peaks;

[0036] (6.2f) Output y b (l) is the extrapolation measurement vector of the array.

[0037] (7) Set the frequency resolution step size l s Let l = l + l s Return to step (2) and complete the frequency band range [f] sequentially. min ,f max Extrapolation measurement vector estimation for all frequency points within the range;

[0038] Step (7) specifically includes the following steps: Repeat steps (2) to (6) to complete the frequency band range [f] sequentially. min ,f max Extrapolation measurement vector estimation for all frequency points within the range;

[0039] As a further improvement of the present invention, step (1) specifically includes the following steps:

[0040] (1.1) Obtain the time-domain data of underwater target radiated noise received by the uniform linear array of underwater acoustic elements composed of M array elements, and divide the time-domain data into B segments;

[0041] (1.2) Perform an L-point discrete Fourier transform on the B-segment data for each array element to obtain the corresponding data at the l-th frequency point f. l Discrete Fourier coefficients x at point b (l), b=1,…,B.

[0042] As a further improvement of the present invention, step (2) specifically includes the following steps: B segment data at frequency point f l The average sample covariance matrix at point is:

[0043] ;

[0044] The superscript H indicates the conjugate transpose operation.

[0045] Compared with the prior art, the method disclosed in this invention has the following advantages: the spatial spectrum information obtained by the spatial spectrum fitting method is used as the prior information for array extrapolation measurement vector estimation, and then the extrapolation measurement vector estimation is split into multiple sub-extrapolation measurement vector estimations in different orientations. At the same time, physical constraints are introduced to ensure the accuracy of the extrapolation measurement vector estimation, thereby effectively enhancing the target signal. Attached Figure Description

[0046] Figure 1 This is a flowchart illustrating the implementation of the method of the present invention.

[0047] Figure 2 The power spectrum diagram corresponding to the original measurement vector of the 12 array elements is generated by conventional beamforming.

[0048] Figure 3 The power spectrum of the conventional beamforming is generated for the extrapolation measurement vector of the 60-element array. Detailed Implementation

[0049] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments:

[0050] This invention estimates the extrapolated measurement vector of a uniform underwater acoustic linear array by using a sparse spectrum fitting method to estimate the spatial spectrum information of the measurement vector. This spatial spectrum information is then used as a constraint to guide the high-precision estimation of the array's extrapolated measurement vector. A broadband extrapolated measurement matrix can be obtained by estimating the extrapolated measurement vectors corresponding to all frequency points within a set frequency band.

[0051] Example 1:

[0052] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments.

[0053] An extrapolation measurement vector estimation method applicable to underwater acoustic uniform linear arrays, such as As shown, it includes the following steps:

[0054] Step 1 is as follows:

[0055] (1.1) Read in the time-domain data of the radiated noise of the underwater acoustic target from a 12-element uniform linear array underwater acoustic array for 80 seconds, with the element spacing d. s =3.2m, sampling rate f s =4000Hz, this data includes targets located in the -7° direction (containing 36Hz, 47Hz, and 50Hz line spectra), which are divided into 61 segments with an overlap rate of 99% B=61.

[0056] (1.2) Set the FFT point count L = 200000, and the frequency processing range to [49, 71] Hz, corresponding to l min =2450, l max =3550, set the frequency resolution step size l s =5, and let l=l min The divided time-domain signal is transformed to the frequency domain using a discrete Fourier transform. Conventional beamforming is then performed on each frequency point of the original measurement vector in the range [49, 71] Hz, resulting in the following... Figure 2 The power spectrum diagram shown has gray dots and lines representing frequencies of the spectrum. It can be seen that... Figure 2 The 36Hz line spectrum can be observed, but the 47Hz line spectrum is submerged, and the 50Hz line spectrum is not obvious.

[0057] Step 2 is as follows:

[0058] Array at frequency point f lThe discrete Fourier coefficients of the signal at point b are x b (l), b=1,…,B, to obtain the uniform underwater acoustic linear array at frequency point f l The average sample covariance matrix at point is:

[0059] ;

[0060] Step 3 specifically involves:

[0061] The azimuth space [-90, 90]° is discretized into Q candidate directions, and based on the frequency point f obtained in step (2) l The average sample covariance matrix R̂ at point l The following sparse spectrum fitting semidefinite programming problem is solved using the interior point method to obtain the value at frequency f. l Spatial spectrum v l :

[0062] ;

[0063] Step 4 is as follows:

[0064] For spatial spectrum v l A peak search was performed, and the azimuth and amplitude of the D peaks found were ϕ. d p d , d=1,…,D.

[0065] Step 5 specifically involves:

[0066] (5.1) Construct the Toeplitz matrix for the d-th peak:

[0067] ;

[0068] (5.2) Extrapolate the original measurement vector of M=12 dimensions to N=60 dimensions, set s=2, and extrapolate the measurement vector. Divide into multiple sub-measurement vectors to obtain information about y. b (l) Multi-measurement vector matrix:

[0069] ;

[0070] (5.3) Construct the following extrapolation measurement vector estimation optimization problem:

[0071] ;

[0072] Step 6 specifically involves:

[0073] (6.1) Setting , , , , ;

[0074] Execute step (6.2) or (6.3) based on the value of D.

[0075] (6.2) If D=0, execute steps (6.2a)~(6.2b):

[0076] (6.2a) Initialization , Let η = 0;

[0077] (6.2b) Solve the optimization problem in step (5.3) using the interior point method to obtain the following results. ,but .

[0078] (6.3) If D>0, execute steps (6.3a)~(6.3f):

[0079] (6.3a) Initialize y b (l)=0, d=1, ;

[0080] (6.3b) Construct the Toeplitz matrix for the d-th peak based on step (5.1). ;

[0081] (6.3c) Solve the optimization problem in step (5.3) using the interior point method to obtain the result. ;

[0082] (6.3d) Let , d = d + 1;

[0083] (6.3e) Repeat steps (6.2b) to (6.2d) to complete the estimation of the extrapolated measurement vectors corresponding to the D peaks;

[0084] (6.3f) Output y b (l) is the extrapolation measurement vector of the array.

[0085] Step 7 specifically includes:

[0086] Let l = l + l s Return to step (2), and repeat steps (2) to (6) to sequentially complete the extrapolation measurement vector estimation for all frequency points within the [49,71] Hz frequency band. Perform conventional beamforming on the extrapolated measurement vectors at each frequency point within the [49,71] Hz frequency band to obtain the following results: Figure 3 The power spectrum shown shows that the background is well suppressed, and the 36Hz, 47Hz, and 50Hz line spectra can be clearly observed.

[0087] The above embodiments demonstrate that by using the method of the present invention to estimate the extrapolation measurement vector of a uniform underwater acoustic linear array, and combining it with conventional beamforming, the target line spectrum signal can be significantly enhanced. This shows that the proposed "extrapolation measurement vector estimation method suitable for uniform underwater acoustic linear arrays" can effectively increase the virtual aperture of the array.

[0088] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A method for extrapolating measurement vector estimation applicable to underwater acoustic uniform linear arrays, characterized in that, Includes the following steps: (1) Read in the underwater acoustic target radiated noise data received by the M-element uniform linear array of underwater acoustic elements, with a sampling frequency of . f s The frequency band range processed [f min , f max The data is segmented, and an L-point discrete Fourier transform is performed on each segment of the signal for each array element. min =⌊f min ×L / f s ⌋, l max =⌊f max ×L / f s ⌋, where ⌊·⌋ represents rounding down, and let l=l min ; (2) Extracting frequency point f l =l× f s The discrete Fourier coefficients at / L, if f l > f max Then the estimation process ends; otherwise, the frequency point f is calculated. l The average sample covariance matrix R̂ at point l ; (3) Discretize the azimuth space [-90°, 90°] into Q candidate directions, and based on the frequency point f obtained in step (2) l The average sample covariance matrix R̂ at point l The following sparse spectrum fitting semidefinite programming problem is solved using the interior point method to obtain the value at frequency f. l Spatial spectrum v l : ； in, This is the matrix verticalization operator; and These represent the 1-norm and 2-norm of the vector, respectively; β is the regularization parameter; the matrix... The qth column is , q=1,…,Q, where For θ q The direction corresponds to the guiding vector, where the superscript T indicates the transpose operation, and d s λ is the distance between the two hydrophones. l For frequency point f l The corresponding wavelength, j is the imaginary unit; * and ⊗ represent the conjugate operation and the Kronecker product, respectively; σ is the spatial correlation coefficient of noise, which is obtained by expanding the directional distribution in the spatial harmonic domain; 2 Noise power estimated for a semidefinite programming problem; (4) For the spatial spectrum v l A peak search was performed, and the azimuth and amplitude of the D peaks obtained were ϕ. d p d , d=1,…,D; (5) At frequency point f l At this point, construct an optimization problem for estimating array extrapolation measurement vectors; (6) Set λ, η, γ and δ, and use the interior point method to solve the optimization problem in step (5) to obtain the extrapolated measurement vector y after the D peaks are superimposed. b (l); (7) Set the frequency resolution step size l s Let l = l + l s Return to step (2) and repeat steps (2) to (6) to complete the frequency band range [f] sequentially. min , f max Extrapolation measurement vector estimation for all frequency points within the range.

2. The extrapolation measurement vector estimation method applicable to underwater acoustic uniform linear arrays according to claim 1, characterized in that, Step (1) specifically includes the following steps: (1.1) Obtain the time-domain data of underwater target radiated noise received by the uniform linear array of underwater acoustic elements composed of M array elements, and divide the time-domain data into B segments; (1.2) Perform an L-point discrete Fourier transform on the B-segment data for each array element to obtain the corresponding data at the l-th frequency point f. l Discrete Fourier coefficients x at point b (l), b=1,…,B.

3. The extrapolation measurement vector estimation method applicable to underwater acoustic uniform linear arrays according to claim 2, characterized in that, In step (2), the B segment data is at frequency point f l The average sample covariance matrix at point is: ； The superscript H indicates the conjugate transpose operation.

4. The extrapolation measurement vector estimation method applicable to underwater acoustic uniform linear arrays according to claim 3, characterized in that, Step (5) specifically includes the following steps: (5.1) Construct the Toeplitz matrix for the d-th peak: ； (5.2) Set the dimension N of the extrapolation measurement vector, and NM is an even number greater than 0; define the extrapolation measurement vector. It is then divided into Z = (NM) / s + 1 sub-measurement vectors, forming a structure about y b (l) Multi-measurement vector matrix: ； Where s is a positive integer less than M, and (NM) / s is an integer; (5.3) Construct the array extrapolation measurement vector estimation optimization problem as shown below: ； in, This is the extrapolated measurement vector corresponding to the d-th peak; During the extrapolation measurement vector estimation process corresponding to the d-th peak, x b (l) residual amount; Indicates by y b The vector consisting of the first to the (N-1)th elements of (l); P = (NM) / 2 represents the dimensions of the forward and backward extrapolations. Here, λ is the reflection matrix; η, γ are regularization parameters; and δ is the power constraint parameter. This represents a matrix inequality.

5. The method for estimating the external inference vector of a uniform underwater acoustic linear array according to claim 4, characterized in that, Step (6) specifically includes the following steps, and steps (6.1) or (6.2) are performed: (6.1) If D=0, execute steps (6.1a)~(6.1b): (6.1a) Initialization , Let η = 0; (6.1b) Solve the optimization problem in step (5.3) using the interior point method to obtain the following results. ,but ; (6.2) If D>0, execute steps (6.2a)~(6.2f): (6.2a) Initialize y b (l)=0, d=1, ; (6.2b) Construct the Toeplitz matrix for the d-th peak based on step (5.1). ; (6.2c) Solve the optimization problem in step (5.3) using the interior point method to obtain the result. ; (6.2d) Let , d = d + 1; (6.2e) Repeat steps (6.2b) to (6.2d) to complete the estimation of the extrapolated measurement vectors corresponding to the D peaks; (6.2f) Output y b (l) is the extrapolation measurement vector of the array.

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