Robust high-resolution synthetic aperture method based on deconvolution interference and noise matrix reconstruction and steering vector search, program, equipment and storage medium

Abstract

The invention belongs to the technical field of array signal processing, and particularly relates to a robust high-resolution synthetic aperture method based on deconvolution interference and noise matrix reconstruction and steering vector search, a program, equipment and a storage medium. According to the method, noise and interference matrixes can be reconstructed according to signal changes, steering vectors are accurately searched, effective suppression of interference and accurate capture of target signals are always kept, interference direction deviation can be coped with, expected signal steering vector errors can also be coped with, and the adaptive capacity of an algorithm to the interference environment is enhanced; and the background level of the spatial spectrum can be reduced by using the deconvolution algorithm, so that the width of the main lobe is narrowed, the azimuth estimation is more accurate, and the precision of the azimuth estimation is further improved. According to the invention, the background level of the spatial spectrum can be reduced, and the precision of azimuth estimation can be further improved compared with a single passive synthetic aperture algorithm.

Description

Technical Field

[0001] The present invention belongs to the technical field of array signal processing, and in particular relates to a robust high-resolution synthetic aperture method, program, device and storage medium based on deconvolution-based interference plus noise matrix reconstruction and steering vector search. Background Art

[0002] The emergence of passive synthetic aperture technology has made it possible to achieve improved target signal direction estimation performance using small-aperture hydrophone arrays. The core of this technology lies in leveraging the movement of the small-aperture array to cleverly convert temporal gain into spatial gain, thereby synthesizing a virtual aperture that is much larger than the physical array aperture. This allows the sonar system to achieve better target signal direction estimation performance, regardless of signal frequency or range. Furthermore, by synthesizing a virtual aperture, this technology effectively reduces system manufacturing and maintenance costs, improving the practicality of underwater target direction estimation.

[0003] Scholars have proposed numerous aperture synthesis algorithms for horizontal arrays. Stergiopoulos and Sullivan first proposed the extended towed array of moving (ETAM) synthetic aperture algorithm in 1989 (S. Stergiopoulos, "Extended towed array processing by an overlap correlator," J. Acoust. Soc. Amer., vol. 86, no. 1, pp. 158-171, 1989.). This algorithm performs overlap correlation and phase compensation on two adjacent spatially sampled array received signals in the array element domain, thereby synthesizing a virtual aperture and expanding the array aperture. Yen and Carey also proposed a passive aperture synthesis algorithm based on the beam domain in the same year (NCYen and W.Carey, “Application of synthetic-aperture processing to towed-array data,” J.Acoust.Soc.Amer., vol.86, no.2, pp.754-765, 1989.). The basic principle of this method is to achieve aperture synthesis by phase correction of the relative motion speed between the sound source and the receiving array, and coherent accumulation of the output signal after beamforming. On this basis, Stergiopoulos and Urban optimized this method in 1992 and proposed a synthetic aperture (FFT synthetic aperture processing, FFTSA) algorithm based on fast Fourier transform (S.Stergiopoulos and H.Urban, "A new passive synthetic aperture technique for towed arrays," in IEEE Journal of Oceanic Engineering, vol.17, no.1, pp.16-25, Jan.1992.). The basic principle of this algorithm is to coherently accumulate multiple beam outputs in the beam domain through Fourier transform to achieve the purpose of synthetic aperture.In the same year, Nuttall proposed a synthetic aperture algorithm based on maximum likelihood estimation (ML) (AH Nuttall, "The maximum likelihood estimator for acoustic synthetic aperture processing," in IEEE Journal of Oceanic Engineering, vol. 17, no. 1, pp. 26-29, Jan. 1992.). It has aperture synthesis performance similar to that of the ETAM algorithm, but is computationally complex and has a large amount of computation, so it is rarely used in practice.

[0004] Although passive synthetic aperture sonar technology has made some progress after decades of development, its application is far less successful than radar. This is due to the existence of irresistible factors such as the undulation of the underwater environment medium, the relatively low speed of sound wave propagation in water, and the non-ideal movement of the sonar carrier. Summary of the Invention

[0005] The present invention aims to provide a robust high-resolution synthetic aperture method, program, device, and storage medium for deconvolution-based interference plus noise matrix reconstruction and steering vector search. When strong and weak noise sources coexist, the present invention can cope with interference direction offsets and desired signal steering vector errors, thereby enhancing the algorithm's adaptability to interference environments, reducing spatial spectrum background levels, making azimuth estimation more accurate, and further improving the accuracy of azimuth estimation.

[0006] A robust high-resolution synthetic aperture method based on deconvolution interference plus noise matrix reconstruction and steering vector search includes the following steps:

[0007] The angle domain is divided into three non-overlapping azimuth domains, including the desired signal azimuth distribution range, the interference signal azimuth distribution range, and the noise distribution range; spatial sampling is performed through a uniform linear array to obtain the covariance matrix of the sampled data;

[0008] Calculate the power spectrum according to the covariance matrix of the sampled data, and take the array steering vectors corresponding to all the peaks in the power spectrum as the nominal steering vectors;

[0009] The residual noise is calculated based on the number of sampling points of the uniform linear array within the noise distribution range, the noise power is estimated by the residual noise, and the estimated value of the noise covariance matrix is ​​obtained;

[0010] For each set of nominal steering vectors, discrete sampling is performed around the azimuth angle as the center, and the array steering vectors corresponding to each discrete sampling azimuth are constructed into a hyperplane, and the gradient vector of each nominal steering vector is obtained using the hyperplane;

[0011] For each set of nominal steering vectors, a step factor is introduced. The nominal steering vector and its gradient vector are constructed into an approximate steering vector based on the step factor. The power value is calculated based on the approximate steering vector. The step factor with the largest corresponding power value is taken, and the approximate steering vector corresponding to the step factor is used as the precise steering vector.

[0012] Constructing an interference covariance matrix based on all precise steering vectors and their power values; adding the interference covariance matrix to the noise covariance matrix to obtain an interference plus noise covariance matrix;

[0013] Based on the precise steering vector belonging to the expected signal azimuth distribution range and the interference plus noise covariance matrix, the precise power spectrum is calculated. The deconvolution algorithm is applied to the precise power spectrum and the directivity function of the uniform linear array to obtain the source intensity distribution function with respect to the azimuth angle, and then the signal arrival direction estimation result is obtained.

[0014] Furthermore, the number of array elements in the uniform linear array is M, the spacing between the array elements is d, and spatial sampling is performed through the uniform linear array to obtain the sampling data covariance matrix R xx for:

[0015]

[0016] Among them, N0 represents the number of snapshots, x n Indicates the nth snapshot data.

[0017] Furthermore, the power spectrum is calculated based on the covariance matrix of the sampled data, specifically:

[0018] Using the general Capon algorithm, the power spectrum is calculated as follows:

[0019]

[0020] Where a(θ) is the array steering vector, a(θ)=[1,e b(θ) ,e 2b(θ) ,...,e (M-1)b(θ) ], f c is the center frequency of the uniform linear array sampling signal, c is the speed of sound;

[0021] Take P Capon The azimuth angle θ corresponding to all the peaks in (θ) l , directing its corresponding array to vector a(θ l ) as the nominal steering vector, recorded as l=1,2,...,L, where L is the number of spectral peaks.

[0022] Furthermore, the residual noise is calculated based on the number of sampling points B of the uniform linear array within the noise distribution range.

[0023]

[0024] Where B is the number of sampling points of the uniform linear array within the noise distribution range Θ3;

[0025] Estimation by residual noise Noise power, Estimation results of the noise covariance matrix for:

[0026]

[0027] Where I is the identity matrix.

[0028] Furthermore, for each set of nominal steering vectors Its azimuth angle θ l As the center, around it Δθ l Discrete sampling is performed within the range, and the number of sampling points is set to N-1 to obtain the discrete sampling orientation The array steering vector corresponding to each discrete sampling orientation is constructed as a hyperplane

[0029] Using hyperplane A l Constructing a Hermitian matrix right Perform eigendecomposition:

[0030]

[0031] in, is the eigenvalue, and arranged from large to small, m=1,2,...,N;e lm is the eigenvalue The corresponding eigenvector; E l =[e l1 ,e l2 ,...,e l(N-1) ];

[0032] e lN As the nominal steering vector The gradient vector of .

[0033] Furthermore, for each set of nominal steering vectors Introducing step size factor η l , according to the step size factor η l Nominal Steering Vector With its gradient vector Constructed as an approximate steering vector According to the approximate steering vector Calculating power values

[0034]

[0035] Take the corresponding power value Maximum step size factor η l , the step size factor η l The corresponding approximate steering vector As a precise steering vector And obtain the precise steering vector Corresponding power value

[0036] Furthermore, according to all precise steering vectors and its power value Constructing the interference covariance matrix

[0037]

[0038] The interference covariance matrix and the noise covariance matrix Add together to get the interference plus noise covariance matrix

[0039] From the L group azimuth θ l Filter out the azimuth angle θ that belongs to the expected signal azimuth distribution range Θ1 s , according to the azimuth angle θ s The corresponding precise steering vector and the interference plus noise covariance matrix Calculate the exact power spectrum P IP-ETAM (θ s );

[0040]

[0041] For the exact power spectrum P IP-ETAM (θ s ) and the directivity function of the uniform linear array are applied with the deconvolution algorithm to obtain the source intensity distribution function with respect to the azimuth angle, and then the signal arrival direction estimation result is obtained.

[0042] A computer device / apparatus / system comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the robust high-resolution synthetic aperture method based on deconvolution-based interference plus noise matrix reconstruction and steering vector search.

[0043] A computer-readable storage medium stores a computer program / instruction thereon, which, when executed by a processor, implements the steps of the robust high-resolution synthetic aperture method based on deconvolution-based interference plus noise matrix reconstruction and steering vector search.

[0044] A computer program product includes a computer program / instruction, which, when executed by a processor, implements the steps of the robust high-resolution synthetic aperture method based on deconvolution-based interference plus noise matrix reconstruction and steering vector search.

[0045] The beneficial effects of the present invention are:

[0046] The present invention reconstructs noise and interference matrices based on signal variations and accurately searches for steering vectors, consistently maintaining effective interference suppression and accurate capture of target signals. This approach addresses both interference direction deviations and errors in the desired signal's steering vector, enhancing the algorithm's adaptability to interference environments. The deconvolution algorithm reduces the spatial spectrum background level, narrowing the mainlobe width and thereby making azimuth estimation more accurate, further improving the accuracy of azimuth estimation. This invention can reduce the spatial spectrum background level and further improve the accuracy of azimuth estimation compared to a single passive synthetic aperture algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Schematic diagram of the movement of synthetic aperture sonar.

[0048] Figure 2 It is the overall flow chart of the present invention.

[0049] Figure 3 Model graph for accurate estimation of steering vectors. DETAILED DESCRIPTION

[0050] The present invention will be further described below with reference to the accompanying drawings.

[0051] To enhance the adaptability of passive synthetic aperture (PA) to complex underwater acoustic environments and further improve the accuracy of target direction estimation, this paper proposes a synthetic aperture algorithm based on deconvolution of noise and interference matrices and precise steering vector search. By accurately estimating the steering vector and reconstructing the interference-plus-noise covariance matrix, the algorithm can address both interference direction offsets and desired signal steering vector errors, enhancing its adaptability to interference environments. The deconvolution algorithm reduces the spatial spectral background level and narrows the mainlobe width, further improving the accuracy of direction estimation.

[0052] A robust high-resolution synthetic aperture method based on deconvolution interference plus noise matrix reconstruction and steering vector search includes the following steps:

[0053] Step 1: Divide the angle domain into three non-overlapping azimuth domains, including the desired signal azimuth distribution range Θ1, the interference signal azimuth distribution range Θ2, and the noise distribution range Θ3; perform spatial sampling through a uniform linear array, where the number of array elements is M and the spacing between array elements is d; construct the covariance matrix R based on the sampling data of the uniform linear array xx ;

[0054]

[0055] Among them, N0 represents the number of snapshots, x n Indicates the nth snapshot data;

[0056] Step 2: Estimate the nominal steering vector and noise covariance matrix by the general Capon algorithm;

[0057] Compute the power spectrum of the general Capon algorithm:

[0058]

[0059] Where a(θ) is the array steering vector, a(θ)=[1,e b(θ) ,e 2b(θ) ,...,e (M-1)b(θ) ], f c is the center frequency of the uniform linear array sampling signal, c is the speed of sound;

[0060] According to the power spectrum of the general Capon algorithm, take the azimuth angle θ corresponding to all spectrum peaks l , directing its corresponding array to vector a(θ l ) as the nominal steering vector, recorded as l=1,2,...,L, L is the number of spectral peaks;

[0061] Calculating residual noise

[0062]

[0063] Where B is the number of sampling points of the uniform linear array within the noise distribution range Θ3;

[0064] Estimation of residual noise Noise power, i.e. Estimation results of the noise covariance matrix for:

[0065]

[0066] Where I is the identity matrix;

[0067] Step 3: For each set of nominal steering vectors Its azimuth angle θ l As the center, around it Δθ l Perform discrete sampling within the range and construct hyperplane A l , calculate the gradient vector e lN ;

[0068] For each set of nominal steering vectors Its azimuth angle θ l As the center, around it Δθ l Discrete sampling is performed within the range, and the number of sampling points is set to N-1 to obtain the discrete sampling orientation The array steering vector corresponding to each discrete sampling orientation is constructed as a hyperplane

[0069] Using hyperplane A l Constructing a Hermitian matrix right Perform eigendecomposition:

[0070]

[0071] in, is the eigenvalue, and arranged from large to small, m=1,2,...,N;e lm is the eigenvalue The corresponding eigenvector; E l =[e l1 ,e l2 ,...,e l(N-1) ]; e lN As the nominal steering vector The gradient vector of

[0072] Step 4: For each set of nominal steering vectors Introducing step size factor η l , according to the step size factor η l Nominal Steering Vector With its gradient vector Constructed as an approximate steering vector According to the approximate steering vector Calculating power values Take the corresponding power value Maximum step size factor η l , the step size factor η l The corresponding approximate steering vector As a precise steering vector And obtain the precise steering vector Corresponding power value

[0073]

[0074]

[0075] Step 5: Based on the precise steering vector and its power value Constructing the interference covariance matrix The interference covariance matrix and the noise covariance matrix Add together to get the interference plus noise covariance matrix

[0076]

[0077] Step 6: Set azimuth angle θ from L l Filter out the azimuth angle θ that belongs to the expected signal azimuth distribution range Θ1 s , according to the azimuth angle θ s The corresponding precise steering vector and the interference plus noise covariance matrix Calculate the power spectrum P IP-ETAM (θ s );

[0078]

[0079] Step 7: Power spectrum P IP-ETAM (θ s ) and the directivity function of the uniform linear array are applied with the deconvolution algorithm to obtain the source intensity distribution function with respect to the azimuth angle, and then the signal arrival direction estimation result is obtained.

[0080] Example 1:

[0081] like Figure 1 As shown in the figure, a towed vessel, consisting of a uniform linear array of M hydrophones with a spacing of d, travels along a track at a constant speed v. A far-field sound source impinges on the array at an angle θ. At t = 0, the M-element uniform linear array begins spatial sampling with a sampling interval of Δt. As the uniform linear array moves along the track, a virtual synthetic aperture is formed.

[0082] The present invention can reconstruct the noise and interference matrix according to the signal changes and accurately search for the steering vector, always maintaining effective suppression of interference and accurate capture of the target signal. This is the key guarantee for high-precision direction estimation to ensure that the target direction can be accurately estimated even in complex situations.

[0083] Combine Figure 3, a precise estimation steering vector model is given. The hyperplane is a plane composed of some steering vectors within a small angle range around the estimated signal azimuth. The point where the contour line is tangent to the hyperplane is the estimated signal nominal steering vector. According to the tangent characteristics, it can be approximately determined Figure 3 The gradient vector is perpendicular to the hyperplane, and the search is performed along the gradient direction starting from the tangent point, while the corresponding power value is judged. When the power reaches the maximum value, it corresponds to the true signal steering vector.

[0084] By using the power spectrum value as a measurement standard and searching for the steering vector in the vector space, it is possible to obtain a steering vector estimation result that is closer to the real signal even under the condition of error.

[0085] There are many vectors in the spatial domain that are different from the nominal steering vector, but they have the same power value. Since the power value does not reach the maximum value, they can be regarded as power contours around the true signal steering vector, and the nominal steering vector is also on this contour line.

[0086] The following will compare and verify the spatial spectrum of the robust high-resolution synthetic aperture method based on deconvolution of the interference plus noise matrix reconstruction and steering vector search from the simulation perspective:

[0087] The specific parameters of the simulation environment are:

[0088] Sampling frequency: 10000 Hz; Number of snapshots: 512; Array properties: 16-element hydrophone linear array; Towed array speed: 2 m / s; Speed ​​of sound in water: 1500 m / s; Spatial sampling times: 4; Number of overlapping elements: 8; Element spacing: half the incident signal wavelength; Expected signal angular region: θ1 = [θ d -4°,θ d +4°]; Interference signal angle area: Θ2=[θ j -4°,θ j +4°]; noise region: Θ3 is the rest of the region; input signal-to-noise ratio range: -25dB-10dB, step size is 1dB; number of Monte Carlo experiments at each signal-to-noise ratio: 500;

[0089] Based on the above simulation conditions, the performance of the present invention was analyzed and compared with the Fast Fourier Transform Synthetic Aperture (FFTSA) algorithm and the Extended Towed Mobile Array (ETAM) algorithm. The results show that the output signal-to-noise ratio of the present invention increases with the input signal-to-noise ratio, significantly exceeding that of the FFTSA and ETAM algorithms at the same signal-to-noise ratio. The root mean square error of the azimuth estimation of the present invention is significantly lower than that of the FFTSA and ETAM algorithms at low signal-to-noise ratios, indicating that the algorithm has higher accuracy in azimuth estimation at low signal-to-noise ratios than the FFTSA and ETAM algorithms.

[0090] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A robust high-resolution synthetic aperture method based on deconvolution interference plus noise matrix reconstruction and steering vector search, characterized by: The angle domain is divided into three non-overlapping azimuth domains, including the desired signal azimuth distribution range, the interference signal azimuth distribution range, and the noise distribution range; spatial sampling is performed through a uniform linear array to obtain the covariance matrix of the sampled data; Calculate the power spectrum according to the covariance matrix of the sampled data, and take the array steering vectors corresponding to all the peaks in the power spectrum as the nominal steering vectors; The residual noise is calculated based on the number of sampling points of the uniform linear array within the noise distribution range, the noise power is estimated by the residual noise, and the estimated value of the noise covariance matrix is ​​obtained; For each set of nominal steering vectors, discrete sampling is performed around the azimuth angle as the center, and the array steering vectors corresponding to each discrete sampling azimuth are constructed into a hyperplane, and the gradient vector of each nominal steering vector is obtained using the hyperplane; For each set of nominal steering vectors, a step factor is introduced. The nominal steering vector and its gradient vector are constructed into an approximate steering vector based on the step factor. The power value is calculated based on the approximate steering vector. The step factor with the largest corresponding power value is taken, and the approximate steering vector corresponding to the step factor is used as the precise steering vector. Constructing an interference covariance matrix based on all precise steering vectors and their power values; adding the interference covariance matrix to the noise covariance matrix to obtain an interference plus noise covariance matrix; Based on the precise steering vector belonging to the expected signal azimuth distribution range and the interference plus noise covariance matrix, the precise power spectrum is calculated. The deconvolution algorithm is applied to the precise power spectrum and the directivity function of the uniform linear array to obtain the source intensity distribution function with respect to the azimuth angle, and then the signal arrival direction estimation result is obtained.

2. The robust high-resolution synthetic aperture method based on deconvolution interference plus noise matrix reconstruction and steering vector search according to claim 1, characterized in that: The number of array elements in the uniform linear array is M, the spacing between the array elements is d, and spatial sampling is performed through the uniform linear array to obtain the sampling data covariance matrix R xx for: Among them, N0 represents the number of snapshots, x n Indicates the nth snapshot data.

3. The robust high-resolution synthetic aperture method based on deconvolution interference plus noise matrix reconstruction and steering vector search according to claim 2, characterized in that: The power spectrum is calculated based on the covariance matrix of the sampled data, specifically: Using the general Capon algorithm, the power spectrum is calculated as follows: Where a(θ) is the array steering vector, a(θ)=[1,e b(θ) ,e 2b(θ) ,...,e (M-1)b(θ) ], f c is the center frequency of the uniform linear array sampling signal, c is the speed of sound; Take P Capon The azimuth angle θ corresponding to all the peaks in (θ) l , directing its corresponding array to vector a(θ l ) as the nominal steering vector, recorded as L is the number of spectral peaks.

4. The robust high-resolution synthetic aperture method based on deconvolution interference plus noise matrix reconstruction and steering vector search according to claim 3, characterized in that: The residual noise is calculated based on the number of sampling points B of the uniform linear array within the noise distribution range. Where B is the number of sampling points of the uniform linear array within the noise distribution range Θ3; Estimation of residual noise Noise power, Estimation results of the noise covariance matrix for: Where I is the identity matrix.

5. The robust high-resolution synthetic aperture method based on deconvolution interference plus noise matrix reconstruction and steering vector search according to claim 4, characterized in that: For each set of nominal steering vectors Its azimuth angle θ l As the center, around it Δθ l Discrete sampling is performed within the range, and the number of sampling points is set to N-1 to obtain the discrete sampling orientation The array steering vector corresponding to each discrete sampling orientation is constructed as a hyperplane Using hyperplane A l Constructing a Hermitian matrix right Perform eigendecomposition: in, is the eigenvalue, and arranged from large to small, e lm is the eigenvalue The corresponding eigenvector; E l =[e l1 ,e l2 ,...,e l(N-1) ]; e lN As the nominal steering vector The gradient vector of .

6. The robust high-resolution synthetic aperture method based on deconvolution interference plus noise matrix reconstruction and steering vector search according to claim 5, characterized in that: For each set of nominal steering vectors Introducing step size factor η l , according to the step size factor η l Nominal Steering Vector With its gradient vector Constructed as an approximate steering vector According to the approximate steering vector Calculating power values Take the corresponding power value Maximum step size factor η l , the step size factor η l The corresponding approximate steering vector As a precise steering vector And obtain the precise steering vector Corresponding power value 7. The robust high-resolution synthetic aperture method based on deconvolution interference plus noise matrix reconstruction and steering vector search according to claim 6, characterized in that: According to all precise steering vectors and its power value Constructing the interference covariance matrix The interference covariance matrix and the noise covariance matrix Add together to get the interference plus noise covariance matrix From the L group azimuth θ l Filter out the azimuth angle θ that belongs to the expected signal azimuth distribution range Θ1 s , according to the azimuth angle θ s The corresponding precise steering vector and the interference plus noise covariance matrix Calculate the exact power spectrum P IP-ETAM (θ s ); For the exact power spectrum P IP-ETAM (θ s ) and the directivity function of the uniform linear array are applied with the deconvolution algorithm to obtain the source intensity distribution function with respect to the azimuth angle, and then the signal arrival direction estimation result is obtained.

8. A computer device / apparatus / system comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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