Underwater target detection and positioning method and system based on passive sonar array

Abstract

The invention discloses an underwater target detection and positioning method and system based on a passive sonar array, and relates to the technical field of underwater acoustic signal processing. Acoustic signals radiated by an underwater target are received and divided into dense subarray data and sparse subarray data; performing a sparse Bayesian learning algorithm on the sparse subarray data, and outputting a high-precision fuzzy value; carrying out azimuth estimation on the dense subarray data in a full-angle range through a dense part to obtain a low-precision unambiguous value; and fusing the high-precision fuzzy value and the low-precision non-fuzzy value through an estimation matching model to obtain an orientation estimation result of the underwater target. According to the method, high-precision azimuth estimation is carried out based on the combination of the ternary co-prime array and the compressed grid sparse Bayesian learning, high-precision (but fuzzy) estimation is carried out by utilizing the sparse part of the TCA array, low-precision (but non-fuzzy) estimation is carried out by utilizing the dense part, and high-precision target azimuth estimation under low operand is realized.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic signal processing technology, and more specifically to a method and system for underwater target detection and localization based on a passive sonar array. Background Technology

[0002] Passive sonar is a key technology for underwater target detection, identification, and localization. Under the far-field assumption, the traditional method to improve the azimuth estimation accuracy of linear arrays is to increase the array aperture. However, conventional half-wavelength-pitch uniform linear arrays (ULAs) are limited by the number of physical array elements, resulting in limited resolution and degrees of freedom (DOFs), and are also costly at large apertures.

[0003] To overcome this limitation, sparse linear arrays (SLAs), such as nested arrays and coprime arrays, have emerged. They achieve larger virtual apertures and degrees of freedom through non-uniform arrangement. However, existing sparse arrays still suffer from strong mutual coupling effects.

[0004] In terms of orientation estimation algorithms, traditional beamforming (CBF) suffers from low resolution, while adaptive methods such as MVDR rely on accurate estimation of the covariance matrix, resulting in significant performance degradation in complex underwater dynamic environments (such as those with a limited number of snapshots). Sparse Bayesian learning (SBL), as an emerging algorithm, performs excellently in low signal-to-noise ratio and coherent source environments. However, SBL faces the "grid mismatch" problem: increasing the grid density can reduce errors but drastically increases computation and leads to numerical instability; while existing off-grid methods are computationally complex. Especially in scenarios with few snapshots, achieving high-precision, unambiguous orientation estimation without changing the physical array structure is a pressing technical challenge.

[0005] Therefore, in view of the shortcomings of the existing technology, how to provide an underwater target detection and localization method and system based on passive sonar array, which increases the degree of freedom while maintaining low mutual coupling, and achieves high-precision and ambiguity-free orientation estimation without changing the physical array structure in scenarios with few snapshots, is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides an underwater target detection and localization method and system based on a passive sonar array, which overcomes the problems of insufficient resolution, high computational complexity, and grating lobe ambiguity in existing technologies with few snapshots and dynamic underwater acoustic environments. It is based on a ternary coprime array (TCA) combined with compressed grid sparse Bayesian learning (CG-SBL) for high-precision azimuth estimation. It utilizes the sparse part of the TCA array for high-precision (but ambiguous) estimation and the dense part for low-precision (but unambiguous) estimation. Through the compressed grid strategy and estimation matching framework, high-precision target azimuth estimation with low computational load is achieved.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: an underwater target detection and localization method based on a passive sonar array, comprising: constructing a ternary coprime array, wherein the ternary coprime array includes a dense part and a sparse part; The acoustic signal radiated by the underwater target is received and divided into dense subarray data and sparse subarray data by a ternary coprime array; The angular ambiguity mechanism of the sparse part is analyzed based on the sampling theorem, and a compressed mesh is constructed. Based on the compressed grid, a sparse Bayesian learning algorithm is run on the sparse subarray data to output a high-precision fuzzy value for orientation estimation. By performing azimuth estimation on the dense subarray data across the entire angular range using the dense part, a low-precision, unambiguous azimuth estimate is obtained. An estimation matching model is constructed, and the high-precision fuzzy value and the low-precision unfuzzy value of the orientation estimation are fused through the estimation matching model to obtain the orientation estimation result of the underwater target.

[0008] Preferably, the dense part adopts a prototype coprime matrix to provide a low-precision, unambiguous estimate of the orientation; The sparse part employs a sparse uniform subarray to provide high-precision fuzzy estimation of the orientation.

[0009] Preferably, the sampling theorem is used to analyze the angular fuzziness mechanism of the sparse part, and a compressed mesh is constructed, including: Calculate the width of the subinterval corresponding to the non-repeating normalized spatial frequency of the sparse subarray data; Divide the sub-interval into grid points.

[0010] Preferably, based on the compressed grid, a sparse Bayesian learning algorithm is run on the sparse subarray data to output a high-precision ambiguity value for orientation estimation, including: Using sparse subarray data as input, a complete dictionary matrix is ​​constructed based on compressed grid. The posterior mean and posterior covariance are calculated through sparse Bayesian learning algorithm, hyperparameters are updated in M ​​steps and iteratively converged, and a high-precision blurred value of the target's true orientation aliasing version is output. Preferably, the ternary coprime array includes a first subarray, a second subarray, and a third subarray; The first subarray comprises M array elements with a spacing of N. d, where d is half the wavelength; The second subarray consists of N array elements with a spacing of M. d; The first subarray and the second subarray constitute a prototype coprime matrix; The third subarray comprises Q array elements with a spacing of L. d, where L = M + N, is the sparse part.

[0011] Preferably, the azimuth estimation of the dense subarray data over the full angular range is performed using a dense part to obtain a low-precision, unambiguous azimuth estimate, including: Build a grid across the entire angular range; Orientation estimation is performed on dense subarray data based on the constructed grid. After the algorithm converges through iteration, it outputs a set of low-precision, unambiguous azimuth estimates; each estimate corresponds to the true range of the underwater target's azimuth.

[0012] Preferably, the underwater target's azimuth estimation result is obtained by fusing the high-precision ambiguity value and the low-precision unambiguity value of the azimuth estimation through the estimation matching model, including: For each low-precision unambiguous value, based on the geometric characteristics of the sparse subarray and the element spacing parameters, and combined with the spatial sampling theorem, the set of all aliasing orientations corresponding to each low-precision unambiguous value is calculated. For each high-precision fuzzy value, calculate the Euclidean distance between each high-precision fuzzy value and each element in the aliasing orientation set; The high-precision fuzzy value with the smallest Euclidean distance is selected as the matching result; Based on the angular aliasing mechanism of the sparse subarray, the matching result is mapped back to the full angular space to obtain the true high-precision orientation after eliminating ambiguity. Integrate all the matching real high-precision bearings to form the final set of underwater target bearing estimation results.

[0013] Preferably, an underwater target detection and localization system based on a passive sonar array includes: a ternary coprime array construction module for constructing a ternary coprime array, wherein the ternary coprime array includes a dense part and a sparse part; The signal receiving module is used to receive acoustic signals radiated by underwater targets and divides the acoustic signals into dense subarray data and sparse subarray data through a ternary coprime array. The analysis module is used to analyze the angular fuzziness mechanism of the sparse part based on the sampling theorem and construct a compressed mesh; A high-precision fuzzy value output module is used to run a sparse Bayesian learning algorithm on the sparse subarray data based on the compressed grid, and output a high-precision fuzzy value for orientation estimation. The low-precision unambiguous value output module is used to perform azimuth estimation on the dense subarray data in the full angular range through the dense part, and obtain the low-precision unambiguous value of the azimuth estimate; The structure fusion output module is used to construct an estimation matching model. The estimation matching model is used to fuse the high-precision fuzzy value and the low-precision unfuzzy value of the azimuth estimation to obtain the azimuth estimation result of the underwater target.

[0014] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method and system for underwater target detection and localization based on a passive sonar array, and the present invention has the following beneficial effects: 1. Balancing high resolution and low computational cost: Traditional SBL methods require extremely dense meshes to improve accuracy, leading to an explosion in computational cost. This invention uses a "compressed mesh" strategy to reduce the search range without increasing the number of meshes (i.e., without increasing computational complexity), significantly improving mesh density and angular resolution.

[0015] 2. Effectively solves the ambiguity problem: It makes full use of the characteristics of the TCA array structure, combines the high precision advantage of sparse subarrays with the anti-ambiguity advantage of dense subarrays, and eliminates the grating lobe ambiguity unique to sparse arrays through matching algorithms.

[0016] 3. Adaptable to environments with few snapshots: This method does not depend on the rank of the covariance matrix, so it can still maintain robust estimation performance under conditions of very few snapshots or even single snapshots, and is suitable for scenarios where the target is moving fast or the environment is non-stationary.

[0017] 4. Array structure advantages: Compared with traditional sparse arrays, TCA arrays have higher degrees of freedom and lower mutual coupling. Combined with the algorithm of this invention, the detection capability under low signal-to-noise ratio is further improved. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of a prototype coprime array structure provided in an embodiment of the present invention.

[0020] Figure 2 This is a schematic diagram of a ternary coprime array structure provided in an embodiment of the present invention.

[0021] Figure 3 A schematic diagram of the Sparse Bayesian Learning (SBL) framework provided in an embodiment of the present invention.

[0022] Figure 4(a) is a schematic diagram of the normalized spatial frequency in the compressed grid provided in the embodiment of the present invention.

[0023] Figure 4(b) is a schematic diagram of the spatial sampling structure in the compressed grid provided in the embodiment of the present invention.

[0024] Figure 4(c) is a schematic diagram of the spectral overlap structure in the compressed grid provided in the embodiment of the present invention.

[0025] Figure 4(d) is a schematic diagram of the compressed grid structure provided in an embodiment of the present invention.

[0026] Figure 5(a) is a schematic diagram of the change of root mean square error with the number of snapshots provided in the embodiment of the present invention.

[0027] Figure 5(b) is a schematic diagram of the root mean square error as a function of signal-to-noise ratio provided in an embodiment of the present invention.

[0028] Figure 5(c) is a schematic diagram of the root mean square error as a function of the number of grids provided in an embodiment of the present invention.

[0029] Figure 5(d) is a schematic diagram of the change of root mean square error with the number of snapshots provided in the embodiment of the present invention.

[0030] Figure 5(e) is a schematic diagram of the root mean square error as a function of signal-to-noise ratio provided in an embodiment of the present invention.

[0031] Figure 5(f) is a schematic diagram of the root mean square error as a function of the number of grids provided in an embodiment of the present invention. Detailed Implementation

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] This invention discloses an underwater target detection and localization method based on a passive sonar array, comprising: constructing a ternary coprime array, wherein the ternary coprime array includes a dense part and a sparse part; The acoustic signal radiated by the underwater target is received and divided into dense subarray data and sparse subarray data by a ternary coprime array; The angular ambiguity mechanism of the sparse part is analyzed based on the sampling theorem, and a compressed mesh is constructed. Based on the compressed grid, a sparse Bayesian learning algorithm is run on the sparse subarray data to output a high-precision fuzzy value for orientation estimation. By performing azimuth estimation on the dense subarray data across the entire angular range using the dense part, a low-precision, unambiguous azimuth estimate is obtained. An estimation matching model is constructed, and the high-precision fuzzy value and the low-precision unfuzzy value of the orientation estimation are fused through the estimation matching model to obtain the orientation estimation result of the underwater target.

[0034] Specifically, the dense part adopts a prototype coprime matrix to provide low-precision, unambiguous estimation of orientation; The sparse part employs a sparse uniform subarray to provide high-precision fuzzy estimation of the orientation.

[0035] Specifically, the sampling theorem is used to analyze the angular fuzziness mechanism of the sparse part, and a compressed mesh is constructed, including: Calculate the width of the subinterval corresponding to the non-repeating normalized spatial frequency of the sparse subarray data; Divide the sub-interval into grid points.

[0036] With the same number of grids, the spacing of the compressed grid is much smaller than that of the full-angle grid, thus significantly improving the angular resolution.

[0037] Specifically, based on the compressed grid, a sparse Bayesian learning algorithm is run on the sparse subarray data to output a high-precision ambiguity value for azimuth estimation, including: Using sparse subarray data as input, a complete dictionary matrix is ​​constructed based on compressed grid. The posterior mean and posterior covariance are calculated through sparse Bayesian learning algorithm, hyperparameters are updated in M ​​steps and iteratively converged, and a high-precision blurred value of the target's true orientation aliasing version is output. Specifically, the basic signal processing model of SLA under the narrowband approximation considers an SLA containing M physical array elements. One element is selected as the origin, and a one-dimensional Cartesian coordinate system is established along the positive direction of the array. Vector This represents the position of the array element along the coordinate axis. Let the narrowband center frequency be f, and the speed of sound in water be... Then the wavelength .Will Divide by The equivalent array configuration vector is obtained and used to describe the geometry of the SLA: (1) Assume K far-field, narrow-band, uncorrelated signals are incident on the array, with the signal source directions being... , At the t-th snapshot time, the received signal of the array can be modeled as: (2) in, For guiding matrix; , As the guiding vector; The source vector of the signal. Indicates the direction of the k-th signal source. The transmitted signal; For array noise, The covariance matrix can be calculated as follows: (3) in, It is a K-order diagonal matrix. The covariance matrix of the signal source is represented. , Let be the power of the k-th signal source; The noise power of the array element; The superscript V denotes the conjugate transpose. For the covariance matrix... After vectorization, we get: (4) in, , , Indicates the Kronecker product. vec( ) represents the vectorization operation of a matrix, where IV is the V-order identity matrix. If the received signal is ergodic, its covariance can be obtained through... Time average estimate: (5) Where T is the number of snapshots.

[0038] From this perspective, equations (3) and (4) are two different mathematical expressions of the same physical quantity. When equation (3) is considered as an observation model, vectorized data... The received signal can be viewed as a virtual array: the steering matrix B of the virtual array acts as the linear observation matrix; while J can be regarded as the incident signal vector. Equation (4) shows that the row rank of B is higher than that of A in Equation (3). This rank advantage is the fundamental reason why the Sparse Linear Array (SLA) can estimate more signal source directions than the Minimum Spacing Uniform Linear Array (ULA) with V physical elements when receiving multiple snapshot signals.

[0039] Specifically, the difference comatrix of the sparse linear array corresponding to P is defined as: (6) Clearly, the number of elements in set D is equal to the row rank of matrix B, which is also known as the degrees of freedom (DOFs) of the SLA.

[0040] There is acoustic mutual coupling between the elements of a hydrophone array, which is usually addressed using a mutual impedance matrix. Description, mutual coupling leakage Used to quantize the degree of mutual coupling of the array: (7) in, Represents the Frobenius norm; Indicates the matrix It is mapped to a diagonal matrix consisting of its diagonal elements; It can be approximated as a symmetric Topulitz matrix with bandwidth G, defined as: (8) The maximum spacing between mutually coupled array elements is usually 1. Mutual coupling coefficient , , ,set up .

[0041] Specifically, the ternary coprime array includes a first subarray, a second subarray, and a third subarray; The first subarray comprises M array elements with a spacing of N. d, where d is half the wavelength; The second subarray consists of N array elements with a spacing of M. d; The first subarray and the second subarray constitute a prototype coprime matrix; The third subarray comprises Q array elements with a spacing of L. d, where L = M + N, is the sparse part.

[0042] Specifically, the Prototype Coprime Array (PCA) consists of two overlapping uniform subarrays whose first elements coincide, and both arrays are aligned along the positive direction of the array axis, such as... Figure 1 As shown. Subarray 1 contains Each array element, subarray 2 contains Each array element, and Coprime, the total number of array elements is Furthermore, the element spacing of subarray 1 is... The element spacing of subarray 2 is The equivalent array configuration vector of the prototype coprime array is: (14) in, This represents the vector formed by sorting the elements of a finite set in ascending order. The difference array of the prototypical coprime array can be represented as: (15) in, The number of distinct elements in the set is also known as the degrees of freedom (DOFs) of the sparse linear array (SLA). When the sparse linear array (SLA) is used to receive multiple snapshot signals, its degrees of freedom (DOFs) determine the row rank of the observation matrix B in equation (4).

[0043] The Type I ternary coprime array (TCA-I) is based on the prototype coprime array, with the addition of a third element containing... A uniform subarray of elements, with element spacing set to... For a type I ternary coprime array, the total number of array elements is... Array structure such as Figure 2 As shown.

[0044] The equivalent array configuration vector for a type I ternary coprime array is: (16) The difference array of a type I ternary coprime array is: (17) The number of elements contained therein can be derived as follows: (18) The Type I ternary coprime array consists of three uniform linear arrays, supporting modular prefabrication; more importantly, equation (18) in This principle remains true even when changes occur, ensuring ease of obtaining degrees of freedom during array expansion. With the same number of physical array elements, the Type I ternary coprime array has significantly more degrees of freedom than the prototype coprime array. It is worth noting that the Type I ternary coprime array is a modular and scalable array, even with changes in the number of elements in the third subarray. Despite the changes, the closed-form expression for the array degrees of freedom is still dominated by equation (18). Equations (14) and (16) give the equivalent array configuration vector of the sparse linear array under the assumption of narrowband, single-frequency incident signal, which can also be interpreted as a pure geometric scale structure independent of any physical background.

[0045] When a sparse linear array (SLA) is applied to a practical broadband underwater acoustic signal, the equivalent array configuration vector P(f) at a specific frequency is... a This can be achieved through a purely geometric proportional structure and the frequency f. a This is obtained by combining. At this point, although P(f) a The elements in the array are no longer presented in integer form as in equations (14) and (16), but the number of elements in the difference array set (i.e., the degrees of freedom (DOFs) of the sparse linear array) is still determined by equations (15) and (17).

[0046] Specifically, the azimuth estimation of the dense subarray data is performed across the entire angular range using a dense part, resulting in a low-precision, unambiguous azimuth estimate, including: Build a grid across the entire angular range; Orientation estimation is performed on dense subarray data based on the constructed grid. After the algorithm converges through iteration, it outputs a set of low-precision, unambiguous azimuth estimates; each estimate corresponds to the true range of the underwater target's azimuth.

[0047] Specifically, by fusing the high-precision ambiguity value and the low-precision unambiguous value of the orientation estimation through the estimation matching model, the orientation estimation result of the underwater target is obtained, including: For each low-precision unambiguous value, based on the geometric characteristics of the sparse subarray and the element spacing parameters, and combined with the spatial sampling theorem, the set of all aliasing orientations corresponding to each low-precision unambiguous value is calculated. For each high-precision fuzzy value, calculate the Euclidean distance between each high-precision fuzzy value and each element in the aliasing orientation set; The high-precision fuzzy value with the smallest Euclidean distance is selected as the matching result; Based on the angular aliasing mechanism of the sparse subarray, the matching result is mapped back to the full angular space to obtain the true high-precision orientation after eliminating ambiguity. Integrate all the matching real high-precision bearings to form the final set of underwater target bearing estimation results.

[0048] In one specific embodiment of the present invention, the basic sparse Bayesian learning for direction-of-arrival estimation includes: Underwater acoustic signal sources exhibit sparsity in the spatial domain, such as... Figure 3 As shown. Based on this, within the framework of Sparse Bayesian Learning (SBL), the spatial range is... Divide the grid into L uniform grids, and denote the grid points as . .

[0049] Each grid corresponds to a potential incident signal direction, and the number of signal sources K is much smaller than L, thus ensuring the sparsity of the azimuth space. Figure 3 middle," "" indicates the actual location of the incident signal source, while " "Indicates that there is no real signal source at the corresponding location.

[0050] Guiding Matrix It is obtained by expanding the original guiding matrix A from K columns to L columns, and can be regarded as an overcomplete dictionary, i.e. The grid resolution increases with increasing L; the larger L is, the finer the azimuth discretization, and the closer the incident signal is to the grid points. When the grid resolution is sufficiently high, .

[0051] Correspondingly, the t-th snapshot of the incident signal is also expanded into an L-dimensional sparse vector, denoted as The vector has K non-zero elements only at the positions corresponding to the actual signal source, and the remaining LK elements are all zero, indicating that there is no signal source in these directions.

[0052] When using a minimum-pitch uniform linear array (ULA) or a sparse linear array (SLA) with a limited number of snapshots, given , Compared with directly observed signals The resulting model is an underdetermined linear system; Sparse Bayesian learning (SBL) aims to find sparse solutions on this model: (19) Wherein, noise vector CN represents a complex Gaussian distribution.

[0053] If the array receives T snapshots, the reception model can be written as: (20) in, For the received signal matrix, For the signal matrix, This is the array noise matrix.

[0054] Clearly, the direction of arrival (DOA) estimation based on the model of equation (20) is essentially maximizing the likelihood function. However, such high-dimensional nonlinear optimizations typically do not have closed-form solutions and cannot guarantee the sparsity of the solutions.

[0055] Therefore, in Sparse Bayesian Learning (SBL), the hypothesis vector The components are independent of each other, and each component It follows the principle of zero mean and variance. The complex Gaussian distribution follows. In other words, for all t, ,in .

[0056] In this hierarchical model, σ and Ω are considered hyperparameters. Given the prior distribution of the hyperparameters, the posterior distribution can be calculated. Then, the expectation is constructed using this posterior distribution. The expectation is maximized in closed-form using the Expectation Maximization (EM) algorithm with respect to σ and Ω. The specific steps are as follows: E-step (calculating the posterior distribution): (twenty one) (twenty two) M-step (update hyperparameters): (twenty three) (twenty four) in, and These are the posterior mean and the posterior covariance, respectively. The trace of the matrix is ​​represented. Equations (23) and (24) are iteratively updated until the maximum number of iterations is reached, or the convergence rate is lower than a preset threshold. This method is called Basic SBL (B-SBL).

[0057] Specifically, compressed mesh sparse Bayesian learning based on ternary coprime arrays includes: In scenarios with a limited number of snapshots, the vectorized SBL (V-SBL) method described above is no longer applicable; and directly applying basic SBL to a ternary coprime array (TCA) cannot fully leverage its structural advantages. Based on the special structure of the TCA, this invention proposes a targeted SBL method called Compressed Grid Sparse Bayesian Learning (CG-SBL), which exhibits superior orientation estimation performance under conditions of few snapshot signals.

[0058] As mentioned above, the element spacing of the third sub-uniform linear array (sub-ULA) of TCA is... As is well known, the signal incident on the array can be considered as spatial sampling; the periodic variation of the signal projected onto the array coordinate axes over a single wavelength distance is defined as the normalized spatial frequency (denoted as ). Then the normalized spatial frequency of the incident signal from direction θ is: As shown in Figure 4(a).

[0059] Therefore, the azimuth range This will be mapped to the normalized spatial frequency range [-1, 1]. To simplify the analysis, the azimuth spatial spectrum is set as a rectangular spectrum per unit height. (U( (This is a unit step function).

[0060] Accordingly, the normalized spatial sampling frequency of the uniform linear array (ULA) is denoted as ,in This represents the normalized value of the element spacing relative to half the wavelength. According to the Nyquist sampling theorem, It is the threshold for aliasing; when When this occurs, the incident azimuth angle of the array will alias, as shown in Figure 4(b). At that time, the entire azimuth space spectrum Overlap will occur, resulting in aliasing at all incident azimuth angles, as shown in Figure 4(c). The sampled azimuth spatial spectrum can be expressed as: (31) Therefore, for the azimuth angle θ, its aliasing azimuth angle The solution can be found using the following equation: (32) Where m is an integer, m∈Z.

[0061] Aliasing is often a problem to be overcome, but it becomes an advantage when combined with mesh-based modeling of sparse Bayesian learning (SBL). According to Equation (32), array sampling means sampling the azimuth spatial spectrum. by The spectrum is repeatedly shifted by the step size, and the shifted spectrum is summed. This value will divide the interval [-1, 1] into... Divide into equal parts.

[0062] As shown in Figure 4(d), when At that time, the interval [-1,1] was sampled and divided into three parts, labeled light blue, blue, and dark blue respectively. After sampling, the sub-intervals [-1,-1 / 3], [-1 / 3,1 / 3], and [1 / 3,1] each contain exactly three color patches of the original spectrum, which means that... The azimuth angle θ within the range will appear once in each of these three sub-intervals, either as its true value or as its aliased value.

[0063] Clearly, for all integers Due to sampling causing the spectrum to shift left and right, within the interval [-1, 1], each width is... Each of the sub-intervals contains exactly one complete set of data. .

[0064] Based on the above analysis, by utilizing the third sub-uniform linear array (sub-ULA) of the ternary coprime array (TCA), the mesh system can be established within the angular domain corresponding to the sub-intervals, rather than covering the entire area. This approach compresses the estimation interval to achieve higher angular resolution, enabling higher azimuth estimation accuracy with the same number of grid cells.

[0065] The proposed Compact Mesh Sparse Bayesian Learning (CG-SBL) typically selects coverage The sub-intervals are used to construct the mesh; for the spacing Its angular range is Divide the interval into L grids evenly, and denote the azimuth set as . Within the compression angle range, K signal directions can be found: However, some of them correspond to overlapping azimuth angles.

[0066] Fortunately, TCA also includes a prototype coprime array (PCA); although its estimation accuracy is lower, it exhibits no aliasing. Next, according to equation (x), calculate... of A superimposed azimuth angle, denoted as , Then, using Euclidean nearest neighbor matching (NN), its corresponding true azimuth angle is identified: (33) in, , Finally, K high-precision estimation results are obtained, denoted as... , where i(k) represents the index i selected for k.

[0067] The second simulation scenario, which addresses the case with few snapshots, verifies the performance of the combined framework of Compressed Grid Sparse Bayesian Learning (CG-SBL) and Type I Triple Coprime Array (TCA-I) under the S-SBL algorithm, compared to Nested Array (NA), Prototype Coprime Array (PCA), and Traditional Uniform Linear Array (ULA).

[0068] Figures 5(a)-5(f) show the root mean square error (RMSE) of the Type I ternary coprime array (TCA-I) and other arrays (c=03): Figure 5(a) RMSE as a function of the number of snapshots (SNR=10, Grid=46); Figure 5(b) RMSE as a function of the signal-to-noise ratio (SNR=10, Grid=46); Figure 5(c) RMSE as a function of the number of grids (SNR=10, Snapshot=10); Figure 5(d) RMSE as a function of the number of snapshots (SNR=10, Grid=46); Figure 5(e) RMSE as a function of the signal-to-noise ratio (SNR=10, Grid=46); Figure 5(f) RMSE as a function of the number of grids (SNR=10, Snapshot=10).

[0069] exist Figures 5(a)-5(c) In this model, the number of array elements is fixed at 10, and the two signal sources are located at 20.5° and 50°, respectively. Table 1 summarizes the corresponding equivalent array configurations, degrees of freedom (DOFs), and mutual coupling leakage. As shown in the figure, the proposed CG-SBL-TCA-I exhibits significant advantages, which stem from two factors: the higher angular resolution provided by the compressed grid, and the significantly reduced mutual coupling effect in the TCA-I sparse subarray.

[0070] In Figure 5(c), the grid numbers 37, 46, 61, and 91 correspond to coarse angular resolutions of 5°, 4°, 3°, and 2° across the omnidirectional range. In this specific case, the element spacing of the sparse subarray of TCA-I is... The established grid sub-intervals are Therefore, even using only 37 grids, it is possible to achieve... It achieves a finer resolution, thus outperforming the angular resolution of the basic SBL (B-SBL) which uses 91 grids.

[0071] Given the inherent scalability of the TCA-I architecture, Figures 5(d)-5(f) The comparison results are shown by adding 5 elements to the sparse subarray of the 10-element TCA-I array. This extension further enhances its relative advantage, corresponding to a lower number of differential co-occurrence elements. and mutual coupling leakage .

[0072] Therefore, TCA-I can be flexibly configured to adapt to complex and dynamic marine environments, effectively balancing the performance requirements of vectorized SBL (V-SBL) and compressed mesh SBL (CG-SBL) algorithms.

[0073] Table 1 Comparison of array performance indicators when the number of array elements is fixed at 10

[0074] A key theoretical contribution of this invention is the Compressed Grid Sparse Bayesian Learning (CG-SBL) algorithm. This method leverages the aliasing ambiguity of sparse subarrays (rather than treating it as a defect) to compress the search space into specific sub-intervals. This approach provides a new perspective on sparse reconstruction, enabling high-resolution estimation in scenarios with few snapshots without altering the hardware architecture.

[0075] In one specific embodiment of the present invention, an embodiment of the present invention provides a location estimation method based on ternary coprime matrix and compressed grid sparse Bayesian learning, comprising the following steps: Step 1: Constructing the Ternary Coprime Array (TCA-I) observation system: Construct a ternary coprime array consisting of three uniform linear subarrays (Sub-ULA). This array can be considered as a prototype coprime array (PCA) plus a large-spaced sparse uniform subarray.

[0076] Concentration Area (PCA section): Used to provide an unambiguous, coarse orientation estimate.

[0077] Sparse part (large-spaced subarray): has a large element spacing, used to provide high-precision azimuth estimation, but will produce periodic angular ambiguity.

[0078] Step Two: Compressed Grid Construction Based on Sparse Subarray Data: The angular ambiguity mechanism of the sparse part is analyzed using the sampling theorem. Since the element spacing of the sparse part is greater than half a wavelength, signals across the entire angular space (-90° to 90°) will alias into specific narrow angular sub-intervals. This embodiment of the invention no longer divides the grid across the entire angular range, but instead constructs a compressed grid: Calculate the width of the subinterval of the non-repeating normalized spatial frequency corresponding to the sparse subarray; Grid points are divided only within sub-intervals of that specific width; According to the spatial sampling theorem, this invention constructs a denser compressed grid in the sub-intervals of the angular domain. With the same number of grids, the spacing of the compressed grid is much smaller than that of the full-angle grid, thereby significantly improving the angular resolution.

[0079] Step 3: Perform Compressed Grid Sparse Bayesian Learning (CG-SBL): Using the limited snapshot data received from the sparse subarray, the sparse Bayesian learning algorithm is run based on the compressed grid constructed in Step 2. Because the grid is compressed within a narrow interval, the algorithm outputs a set of high-precision azimuth estimates Θ^fine. This set of estimates contains a "folded" or "aliased" version of the target's true azimuth, i.e., it contains ambiguity.

[0080] Step 4: Unambiguous coarse estimation based on dense subarray. Using the dense part (i.e. the prototype coprime array PCA part) data in TCA, the traditional SBL algorithm or beamforming method is used to perform azimuth estimation in the full angular range, and obtain a set of unambiguous but low-precision coarse estimates Θ^coarse.

[0081] Step 5: Estimate Matching: Construct an estimate matching framework that integrates the high-precision fuzzy estimation from Step 3 and the low-precision unfuzzy estimation from Step 4. For each coarse estimate θ^c∈Θ^coarse, calculate the theoretically possible set of all aliased orientations based on the geometric properties of the sparse subarray.

[0082] In the high-precision estimation set Θ^fine of the compressed grid output, find the value that is closest to the Euclidean distance of the above aliasing azimuth set.

[0083] The matched high-precision aliasing values ​​are mapped back to the true angle space to obtain the final high-precision, unambiguous target orientation estimation result.

[0084] In this embodiment of the invention, it is assumed that there are multiple far-field narrowband signal sources in the underwater environment.

[0085] 1. Array Configuration: A TCA-I type array configuration is used. The array consists of three subarrays: Subarray 1: Contains M array elements with a spacing of N. d (d is half wavelength).

[0086] Subarray 2: Contains N array elements with a spacing of M. d. Subarray 1 and subarray 2 form a prototype coprime array (PCA) as the "density part".

[0087] Subarray 3: Contains Q array elements with a spacing of L. d (where L=M+N) serves as the "sparse part".

[0088] 2. Compressed Mesh Generation: For subarray 3, the element spacing is L. d. According to the spatial sampling theorem, its unambiguous normalized spatial frequency range is compressed. Define the width of the angular sub-interval as corresponding to the normalized frequency interval 2 / L. Divide this interval into G grid points uniformly. Compared to dividing the entire interval into G points, the resolution is improved by a factor of L / 2.

[0089] 3. Signal processing flow: Step A (Fine Estimation): Input the received data Xsparse from subarray 3; Construct a dictionary matrix Φcompressed based on a compressed grid; The SBL algorithm is used to solve for the sparse vector w, and the peak positions are obtained, denoted as the set Θ^fine. These values ​​are high-precision, but aliased.

[0090] Step B (coarse estimation): Input the received data Xdense of subarray 1 and subarray 2 (PCA); Constructing a standard grid across the full angular range and running SBL or beamforming yields a coarse set of estimates Θ^coarse. These values ​​are unambiguous but have limited accuracy.

[0091] Step C (De-fuzzy matching): Iterate through each angle θ in Θ^coarse. k According to the formula θalias=arcsin(sin(θ) k) +m L2) Calculate all possible aliasing positions of θ in the sparse subarray, where m is an integer. Calculate the distances of these θalias to the elements in Θ^fine, and find the fine estimate θ^best corresponding to the minimum distance. Use the true angle corresponding to θ^best as the final output.

[0092] 4. Experimental Verification: Simulation results show that, with a signal-to-noise ratio (SNR) of 10 dB and only 10 snapshots, the root mean square error (RMSE) of the method in this embodiment (CG-SBL-TCA) is significantly lower than that of the traditional SBL method and methods based on nested matrix (NA) or prototype coprime matrix (PCA). Especially when the number of grid cells is small, this invention still maintains extremely high estimation accuracy, demonstrating the effectiveness of the compressed grid strategy.

[0093] In a specific embodiment of the present invention, an underwater target detection and positioning system based on a passive sonar array includes: a ternary coprime array construction module for constructing a ternary coprime array, wherein the ternary coprime array includes a dense part and a sparse part; The signal receiving module is used to receive acoustic signals radiated by underwater targets and divides the acoustic signals into dense subarray data and sparse subarray data through a ternary coprime array. The analysis module is used to analyze the angular fuzziness mechanism of the sparse part based on the sampling theorem and construct a compressed mesh; A high-precision fuzzy value output module is used to run a sparse Bayesian learning algorithm on the sparse subarray data based on the compressed grid, and output a high-precision fuzzy value for orientation estimation. The low-precision unambiguous value output module is used to perform azimuth estimation on the dense subarray data in the full angular range through the dense part, and obtain the low-precision unambiguous value of the azimuth estimate; The structure fusion output module is used to construct an estimation matching model. The estimation matching model is used to fuse the high-precision fuzzy value and the low-precision unfuzzy value of the azimuth estimation to obtain the azimuth estimation result of the underwater target.

[0094] To improve the performance of underwater acoustic target orientation estimation, this invention proposes a novel scheme integrating a ternary coprime array (TCA) and sparse Bayesian learning (SBL). The TCA consists of three uniform subarrays, offering advantages such as high degrees of freedom (DOFs) and low mutual coupling. Notably, regardless of the number of array elements, the DFOs of this array have closed-form expressions, giving it good modularity and scalability, making it highly suitable for complex and dynamic marine environments. For multi-snapshot scenarios, a vector sparse Bayesian learning algorithm suitable for the TCA is designed. Through comprehensive simulation experiments and sea trial data verification, in both narrowband and wideband scenarios, regardless of changes in signal-to-noise ratio (SNR) and the number of snapshots, the estimation accuracy of this scheme is superior to that of traditional sparse arrays. To address the challenging problem of few snapshots, an innovative compressed grid sparse Bayesian learning strategy limited to specific angular sub-intervals is derived. An estimation matching framework is constructed to fuse the high-precision but aliased estimation results obtained from the sparse subarray with the non-aliased but low-precision estimation results obtained from the dense subarray. Finally, simulation results show that, at the same mesh density, this compressed mesh method has significant performance advantages over existing methods.

[0095] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0096] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for underwater target detection and localization based on a passive sonar array, characterized in that, include: Construct a ternary coprime array, wherein the ternary coprime array includes a dense part and a sparse part; The acoustic signal radiated by the underwater target is received and divided into dense subarray data and sparse subarray data. The angular ambiguity mechanism of the sparse part is analyzed based on the sampling theorem, and a compressed mesh is constructed. Based on the compressed grid, a sparse Bayesian learning algorithm is run on the sparse subarray data to output a high-precision fuzzy value for orientation estimation. By performing azimuth estimation on the dense subarray data across the entire angular range using the dense part, a low-precision, unambiguous azimuth estimate is obtained. An estimation matching model is constructed, and the high-precision fuzzy value and the low-precision unfuzzy value of the orientation estimation are fused through the estimation matching model to obtain the orientation estimation result of the underwater target.

2. The underwater target detection and localization method based on a passive sonar array according to claim 1, characterized in that, The dense part employs a prototype coprime matrix to provide a low-precision, unambiguous estimate of the orientation. The sparse part employs a sparse uniform subarray to provide high-precision fuzzy estimation of the orientation.

3. The underwater target detection and localization method based on a passive sonar array according to claim 1, characterized in that, The angular ambiguity mechanism of the sparsity part is analyzed using the sampling theorem, and a compressed mesh is constructed, including: Calculate the width of the subinterval corresponding to the non-repeating normalized spatial frequency of the sparse subarray data; Divide the sub-interval into grid points.

4. The underwater target detection and localization method based on a passive sonar array according to claim 1, characterized in that, Based on the compressed grid, a sparse Bayesian learning algorithm is run on the sparse subarray data to output a high-precision ambiguity value for orientation estimation, including: Using sparse subarray data as input, a complete dictionary matrix is ​​constructed based on a compressed grid. The posterior mean and posterior covariance are calculated using a sparse Bayesian learning algorithm, the hyperparameters are updated, and the algorithm converges iteratively. The result is a high-precision blurred value of the target's true orientation aliasing.

5. The underwater target detection and localization method based on a passive sonar array according to claim 2, characterized in that, The ternary coprime array consists of a first subarray, a second subarray, and a third subarray; The first subarray comprises M array elements with a spacing of N. d, where d is half the wavelength; The second subarray consists of N array elements with a spacing of M. d; The first subarray and the second subarray constitute a prototype coprime matrix; The third subarray comprises Q array elements with a spacing of L. d, where L = M + N, is the sparse part.

6. The underwater target detection and localization method based on a passive sonar array according to claim 1, characterized in that, By performing azimuth estimation on the dense subarray data across the entire angular range using a dense part, a low-precision, unambiguous azimuth estimate is obtained, including: Build a grid across the entire angular range; Orientation estimation is performed on dense subarray data based on the constructed grid. After the algorithm converges through iteration, it outputs a set of low-precision, unambiguous azimuth estimates; each estimate corresponds to the true range of the underwater target's azimuth.

7. The underwater target detection and localization method based on a passive sonar array according to claim 1, characterized in that, By fusing the high-precision ambiguity value and the low-precision unambiguous value of the bearing estimation using the estimation matching model, the bearing estimation result of the underwater target is obtained, including: For each low-precision unambiguous value, based on the geometric characteristics of the sparse subarray and the element spacing parameters, and combined with the spatial sampling theorem, the set of all aliasing orientations corresponding to each low-precision unambiguous value is calculated. For each high-precision fuzzy value, calculate the Euclidean distance between each high-precision fuzzy value and each element in the aliasing orientation set; The high-precision fuzzy value with the smallest Euclidean distance is selected as the matching result; Based on the angular aliasing mechanism of the sparse subarray, the matching result is mapped back to the full angular space to obtain the true high-precision orientation. Integrate all the matching real high-precision bearings to form the final set of underwater target bearing estimation results.

8. An underwater target detection and localization system based on a passive sonar array, characterized in that, include: A ternary coprime array construction module is used to construct a ternary coprime array, wherein the ternary coprime array includes a dense part and a sparse part; The signal receiving module is used to receive acoustic signals radiated by underwater targets and divides the acoustic signals into dense subarray data and sparse subarray data through a ternary coprime array. The analysis module is used to analyze the angular fuzziness mechanism of the sparse part based on the sampling theorem and construct a compressed mesh; A high-precision fuzzy value output module is used to run a sparse Bayesian learning algorithm on the sparse subarray data based on the compressed grid, and output a high-precision fuzzy value for orientation estimation. The low-precision unambiguous value output module is used to perform azimuth estimation on the dense subarray data in the full angular range through the dense part, and obtain the low-precision unambiguous value of the azimuth estimate; The structure fusion output module is used to construct an estimation matching model. The estimation matching model is used to fuse the high-precision fuzzy value and the low-precision unfuzzy value of the azimuth estimation to obtain the azimuth estimation result of the underwater target.

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