A two-dimensional DOA estimation method for non-uniform sampling of an underwater mobile observation platform

Abstract

The application discloses a kind of underwater mobile observation platform non-uniform sampling two-dimensional DOA estimation method.The method is through the phase compensation factor to the original multiple fast shot signal and concatenation splicing are filled, constructs equivalent observation matrix;After being combined with physical array position and non-uniform displacement amount, over-complete dictionary matrix is constructed;Finally, norm minimization reconstruction model is established, and sparse signal matrix is reconstructed by convex optimization algorithm, and the energy peak value mapping is searched to obtain the super-resolution joint estimation of target azimuth and pitch angle.The application combines platform motion characteristics and non-uniform space-time sampling sequence, synthesizes equivalent virtual spatial aperture, effectively breaks through the constraint of array gain in underwater physical space, can enhance the perception ability of system in complex underwater environment, shows extremely high robustness in the harsh underwater condition of low signal-to-noise ratio and few fast shots, and has significant marine engineering application value.

Description

Technical Field

[0001] This invention belongs to the field of information and marine science and technology, specifically relating to a two-dimensional DOA estimation method for non-uniform sampling of underwater mobile observation platforms. By combining the motion characteristics of the marine observation platform with a non-uniform spatiotemporal sampling sequence, and processing the observation data using a sparse reconstruction algorithm, the joint estimation of the azimuth and elevation angles of underwater signal targets is achieved. Background Technology

[0002] In complex marine acoustic detection missions, the estimation of two-dimensional direction of arrival (2D-DOA) for the azimuth and pitch angles of underwater acoustic targets is a core technology for marine mobile observation platforms to perform remote early warning, underwater situational awareness, and fine target identification. Its accuracy directly determines the system's tracking and identification performance of underwater acoustic targets.

[0003] Traditional underwater acoustic engineering relies on physical two-dimensional arrays for DOA estimation, such as cross-linear arrays, planar arrays, or cylindrical arrays. However, due to the elongated cylindrical structure and payload space of underwater unmanned vehicles or deep-sea observation platforms, it is difficult for these platforms to accommodate large-sized physical planar arrays. Most observation platforms can only carry one-dimensional lateral linear arrays arranged along the axis, which leads to severe "cone ambiguity" problems during static observations. Furthermore, the spatial resolution is constrained by the Rayleigh limit, making it difficult to meet the high-precision positioning requirements of modern oceanographic exploration.

[0004] To overcome the limitations of physical aperture and achieve dimensional expansion, synthetic aperture processing utilizing the motion characteristics of marine observation platforms has become a research hotspot in the field of marine technology. Taking a large underwater acoustic monitoring vessel as an example, by effectively utilizing the vessel's navigation displacement, the flank linear array, which originally only had one-dimensional orientation sensing capabilities, can be equivalently synthesized into a two-dimensional virtual planar array in the spatiotemporal dimension. When the platform moves at a constant speed, the one-dimensional data collected at different times is equivalently concatenated through spatiotemporal displacement. This not only allows for the synthesis of an equivalent large aperture in the mathematical model to improve resolution, but also fundamentally breaks the angular ambiguity problem of a single linear array, achieving two-dimensional joint estimation of azimuth and pitch angles.

[0005] However, existing motion array synthesis techniques mostly employ uniform sampling patterns with equal intervals. This generates massive amounts of redundant echo data during long-endurance detection, significantly increasing the storage pressure and computational overhead of airborne or shipborne systems. Furthermore, most existing motion detection schemes still rely on traditional subspace algorithms, failing to effectively utilize the spatial sparsity of signals and lacking methods for deeply integrating motion synthesis logic with sparse reconstruction algorithms. This results in the system struggling to fully exploit the resolution gain brought by the synthetic aperture under low signal-to-noise ratio or limited sampling points.

[0006] This application proposes a two-dimensional DOA estimation method for underwater mobile observation platforms using non-uniform sampling. Compared to traditional methods, this method not only effectively suppresses data redundancy through non-uniform sampling but also fundamentally overcomes the limitations of physical aperture. Furthermore, by combining phase compensation with sparse reconstruction depth, this method significantly improves the estimation accuracy of azimuth and pitch angles. This application maintains good performance under low signal-to-noise ratio conditions and can be widely applied to various complex underwater environments. In summary, this application has low computational overhead and high engineering application value. Summary of the Invention

[0007] This application addresses the limitations of traditional two-dimensional DOA estimation methods on marine observation platforms, such as physical aperture constraints and severe data redundancy caused by uniform sampling. It proposes a non-uniform sampling method for two-dimensional DOA estimation on a mobile underwater observation platform. This method combines non-uniform spatiotemporal sampling sequences, phase compensation factors, cascaded equivalent observation matrices, and a sparse reconstruction algorithm. During the mobile detection process of the marine observation platform, it utilizes a non-uniform sampling set to sparsely acquire echo data, reducing system storage and computational overhead. This mechanism enables the algorithm to achieve high-resolution two-dimensional joint estimation of target azimuth and elevation angles using only a one-dimensional hull-side physical linear array. Furthermore, by combining motion synthesis logic with sparse reconstruction, it effectively overcomes the constraints of physical aperture on spatial resolution, improving the accuracy of marine signal detection.

[0008] A two-dimensional DOA estimation method based on non-uniform sampling of an underwater mobile observation platform is proposed. This method is applicable to a one-dimensional coprime array mounted on an underwater mobile platform, the array comprising... Each array element, array element along The axis is distributed, and its position vector is denoted as . The array is mounted on a mobile platform, and moves along the platform along a path perpendicular to the array's axis. Axial direction at a constant speed The system moves according to a pre-set non-uniform sampling sequence set. exist Echo data were collected at discrete spatiotemporal sampling points, among which The reference element spacing, The signal wavelength is [wavelength]; the method is characterized by the following steps: a two-dimensional DOA estimation method based on non-uniform sampling from an underwater mobile observation platform.

[0009] Step 1: Calculate the first... Propagation delay of each displacement point relative to its initial position According to the formula Construct the phase compensation factor for this sampling point, where The center frequency of the signal. , This represents the total number of steps in the non-uniform sampling sequence. The imaginary unit;

[0010] Step 2: Use the phase compensation factor obtained in Step 1 to analyze the original multi-shot received signal matrix at each sampling displacement point. Phase completion is performed, and the data is vertically concatenated and stitched according to the spatial sampling order to construct an equivalent observation matrix. ;

[0011] Step 3: Determine the azimuth of the target spatial region and pitch angle Divided into Discrete grid points For each grid point, calculate its corresponding direction cosine variable. and ;

[0012] Step 4: Combine the physical array element positions With non-uniform displacement Construct the two-dimensional spatial guide vector corresponding to each grid point. ,in ;

[0013] Step 5: Guide the two-dimensional space to a vector After normalization, the matrices are concatenated column-wise to construct an overcomplete dictionary matrix. ;

[0014] Step 6: Calculate the observation matrix The Frobenius norm, combined with the signal-to-noise ratio (SNR) and a preset adjustment coefficient. Set error tolerance ,in Denotes the Frobenius norm of a matrix;

[0015] Step 7: Establish a system based on and The joint sparse reconstruction model, taking the input signal, utilizes the shared sparse structure of the signal on the spatial grid to construct the matrix of the signal to be recovered. For a multi-measurement vector optimization problem with multiple variables, a joint sparse signal matrix on a two-dimensional spatial grid is reconstructed using a convex optimization algorithm. ;

[0016] Step 8: Calculate the sparse signal matrix all sectors Norm, generating spatial energy distribution vector ,search The highest energy level in the front The grid index corresponding to each peak is mapped back to a preset angle grid to obtain the final azimuth estimate of the target. With pitch angle estimate ,in This represents the number of signal sources.

[0017] Furthermore, a two-dimensional DOA estimation method for non-uniform sampling of an underwater mobile observation platform is provided, wherein the one-dimensional coprime array is composed of two uniform linear subarrays, subarray one and subarray two, wherein subarray one contains There are 1 physical array elements, with an element spacing of 1. Subarray 2 contains There are 1 physical array elements, with an element spacing of 1. The physical element position vector is constructed by taking the union of the position vectors of the two subarray elements. ,in and They are coprime positive integers.

[0018] Furthermore, a two-dimensional DOA estimation method for non-uniform sampling of an underwater mobile observation platform is proposed, in which an equivalent observation matrix is ​​constructed in step two. The specific process is as follows:

[0019] A1: For all The displacement points are determined according to the formula. The compensated signal matrix is ​​calculated. ;

[0020] A2: Will The samples are longitudinally cascaded and stitched together according to the order of spatial sampling displacements, forming a dimension of... Equivalent observation matrix ,in This represents the number of snapshots.

[0021] Furthermore, a two-dimensional DOA estimation method for non-uniform sampling of an underwater mobile observation platform is proposed, in which an overcomplete dictionary is constructed in step five. The specific process is as follows:

[0022] B1: Guiding vector in two-dimensional space Perform a normalization operation to obtain the normalized two-dimensional spatial steering vector. ,in Representing vectors Norm;

[0023] B2: All The normalized column vector of grid points The matrices are horizontally joined sequentially according to the grid division order to form the overcomplete dictionary matrix used for sparse reconstruction. .

[0024] Furthermore, a two-dimensional DOA estimation method for non-uniform sampling of an underwater mobile observation platform is proposed, in which step seven involves reconstructing the joint sparse signal matrix. The specific process is as follows:

[0025] An optimization problem based on a multi-measurement vector framework is constructed to recover the signal matrix. To optimize the variables, a minimization reconstruction model is established, which includes data fidelity terms and row sparsity constraints: The model is iteratively solved using a convex optimization algorithm to reconstruct the joint sparse signal matrix on a two-dimensional spatial angular grid. ,in This is the regularization function.

[0026] Furthermore, a two-dimensional DOA estimation method for non-uniform sampling of an underwater mobile observation platform is proposed, in which step eight generates a spatial energy distribution vector. The specific process for extracting the final angle estimate is as follows:

[0027] C1: The sparse signal matrix obtained in step seven. Calculate the value of each row vector Norms, constituting lengths of Spatial energy distribution column vector , its first element ;

[0028] C2: Column vector of spatial energy distribution All elements are sorted in descending order of numerical value, before extraction The grid index value corresponding to each peak point;

[0029] C3: Extract the above Each grid index value is back-mapped to the pre-divided two-dimensional spatial angle discrete grid sequence in step three, and the corresponding value is found. The azimuth and elevation angle values ​​are combined and used as the final two-dimensional DOA joint estimation result for the target signal source.

[0030] Compared with the prior art, the technical solution of the present invention has the following technical effects:

[0031] 1. This method utilizes the navigation displacement characteristics of a mobile observation platform to synthesize an equivalent huge virtual airspace aperture in the time domain, solving the problem that the side array is limited by the load space of the cylinder and cannot be extended indefinitely. Without increasing the number of underwater acoustic sensor array elements, it greatly improves the resolution of targets.

[0032] 2. This method uses a pre-set non-uniform sampling sequence set to sparsely collect echo data, which reduces the data scale generated during long-term cruise from the source, effectively alleviates the storage pressure and computing burden of the mobile observation platform during continuous detection, and improves the real-time data processing performance of the system in complex and dynamic marine environments.

[0033] 3. By combining the phase compensation mechanism generated by the motion displacement of the observation platform with the depth construction of the two-dimensional spatial steering vector, the algorithm can complete the high-resolution two-dimensional joint estimation of the target azimuth and elevation angles using only a one-dimensional physical linear array.

[0034] 4. This method deeply integrates motion synthesis logic with sparse reconstruction algorithm, utilizes norm minimization to reconstruct the model and introduces adjustable error tolerance, which can effectively cope with harsh underwater conditions such as low signal-to-noise ratio and few snapshots, and improve the reliability of marine signal detection and identification. Attached Figure Description

[0035] Figure 1 This is the structure of the 2D DOA estimation model used in this invention;

[0036] Figure 2 This is a diagram showing the DOA estimation results of the signal processing method of the present invention;

[0037] Figure 3 This is a curve showing the relationship between the root mean square error of the azimuth angle and the signal-to-noise ratio in the signal processing method of this invention.

[0038] Figure 4 This is a curve showing the relationship between the root mean square error of the azimuth angle and the number of snapshots in the signal processing method of this invention.

[0039] Figure 5 This is the relationship curve between the root mean square error of the elevation angle and the signal-to-noise ratio in the signal processing method of this invention;

[0040] Figure 6 This is a curve showing the relationship between the root mean square error of the pitch angle and the number of snapshots in the signal processing method of this invention. Detailed Implementation

[0041] The present invention will now be further described in conjunction with the embodiments and accompanying drawings:

[0042] Example 1: Figure 1 The structure of the 2D DOA estimation model based on a mobile synthetic virtual array used in this invention is presented. The receiving array adopts a structure consisting of... A one-dimensional coprime array composed of physical array elements. This array is composed of two uniform linear subarrays: subarray one contains There are 1 physical array elements, with an element spacing of 1. Subarray 2 contains There are 1 physical array elements, with an element spacing of 1. The physical element position vector is constructed by taking the union of the position vectors of the two subarray elements. The reference spacing between each array element is The moving platform travels at a constant speed along a direction perpendicular to the array axis. Uniform motion.

[0043] It has An uncorrelated far-field narrowband signal source is incident on the array, and its azimuth angle They are respectively and Pitch angle They are respectively and signal carrier frequency for speed of sound The system employs a non-uniform moving sampling sequence. ,exist Echo data were collected at discrete spatiotemporal sampling points. System snapshot count. Signal-to-noise ratio During the reconstruction phase, the azimuth search range is set to... The pitch angle search range is set to Error tolerance adjustment coefficient Set to 1.2.

[0044] The DOA estimation is performed under the above conditions, and the specific implementation process is as follows:

[0045] Step 1: Calculate the first... Propagation delay of each displacement point relative to its initial position According to the formula Construct the phase compensation factor for this sampling point, where The center frequency of the signal. , This represents the total number of steps in the non-uniform sampling sequence. The imaginary unit;

[0046] Step 2: Use the phase compensation factor obtained in Step 1 to analyze the original multi-shot received signal matrix at each sampling displacement point. Phase completion is performed, and the data is vertically concatenated and stitched according to the spatial sampling order to construct an equivalent observation matrix. ;

[0047] Step 3: Determine the azimuth of the target spatial region and pitch angle Divided into Discrete grid points For each grid point, calculate its corresponding direction cosine variable. and ;

[0048] Step 4: Combine the physical array element positions With non-uniform displacement Construct the two-dimensional spatial guide vector corresponding to each grid point. ,in ;

[0049] Step 5: Guide the two-dimensional space to a vector After normalization, the matrices are concatenated column-wise to construct an overcomplete dictionary matrix. ;

[0050] Step 6: Calculate the observation matrix The Frobenius norm, combined with the signal-to-noise ratio (SNR) and a preset adjustment coefficient. Set error tolerance ,in Denotes the Frobenius norm of a matrix;

[0051] Step 7: Establish a system based on and The joint sparse reconstruction model, taking the input signal, utilizes the shared sparse structure of the signal on the spatial grid to construct the matrix of the signal to be recovered. For a multi-measurement vector optimization problem with multiple variables, a joint sparse signal matrix on a two-dimensional spatial grid is reconstructed using a convex optimization algorithm. ;

[0052] Step 8: Calculate the sparse signal matrix all sectors Norm, generating spatial energy distribution vector ,search The highest energy level in the front The grid index corresponding to each peak is mapped back to a preset angle grid to obtain the final azimuth estimate of the target. With pitch angle estimate ,in This represents the number of signal sources.

[0053] Furthermore, a two-dimensional DOA estimation method for non-uniform sampling of an underwater mobile observation platform is provided, wherein the one-dimensional coprime array is composed of two uniform linear subarrays, subarray one and subarray two, wherein subarray one contains There are 1 physical array elements, with an element spacing of 1. Subarray 2 contains There are 1 physical array elements, with an element spacing of 1. The physical element position vector is constructed by taking the union of the position vectors of the two subarray elements. ,in and They are coprime positive integers.

[0054] Furthermore, a two-dimensional DOA estimation method for non-uniform sampling of an underwater mobile observation platform is proposed, in which an equivalent observation matrix is ​​constructed in step two. The specific process is as follows:

[0055] A1: For all The displacement points are determined according to the formula. The compensated signal matrix is ​​calculated. ;

[0056] A2: Will The samples are longitudinally cascaded and stitched together according to the order of spatial sampling displacements, forming a dimension of... Equivalent observation matrix ,in This represents the number of snapshots.

[0057] Furthermore, a two-dimensional DOA estimation method for non-uniform sampling of an underwater mobile observation platform is proposed, in which an overcomplete dictionary is constructed in step five. The specific process is as follows:

[0058] B1: Guiding vector in two-dimensional space Perform a normalization operation to obtain the normalized two-dimensional spatial steering vector. ,in Representing vectors Norm;

[0059] B2: All The normalized column vector of grid points The matrices are horizontally joined sequentially according to the grid division order to form the overcomplete dictionary matrix used for sparse reconstruction. .

[0060] Furthermore, a two-dimensional DOA estimation method for non-uniform sampling of an underwater mobile observation platform is proposed, in which step seven involves reconstructing the joint sparse signal matrix. The specific process is as follows:

[0061] An optimization problem based on a multi-measurement vector framework is constructed to recover the signal matrix. To optimize the variables, a minimization reconstruction model is established, which includes data fidelity terms and row sparsity constraints: The model is iteratively solved using a convex optimization algorithm to reconstruct the joint sparse signal matrix on a two-dimensional spatial angular grid. ,in This is the regularization function.

[0062] Furthermore, a two-dimensional DOA estimation method for non-uniform sampling of an underwater mobile observation platform is proposed, in which step eight generates a spatial energy distribution vector. The specific process for extracting the final angle estimate is as follows:

[0063] C1: The sparse signal matrix obtained in step seven. Calculate the value of each row vector Norms, constituting lengths of Spatial energy distribution column vector , its first element ;

[0064] C2: Column vector of spatial energy distribution All elements are sorted in descending order of numerical value, before extraction The grid index value corresponding to each peak point;

[0065] C3: Extract the above Each grid index value is back-mapped to the pre-divided two-dimensional spatial angle discrete grid sequence in step three, and the corresponding value is found. The azimuth and elevation angle values ​​are combined and used as the final two-dimensional DOA joint estimation result for the target signal source.

[0066] The method of the present invention based on the above conditions was simulated using MATLAB simulation software, and the DOA estimation results of the method of the present invention are as follows. Figure 2 As shown, the estimated angle point almost completely overlaps with the actual angle point, indicating that this invention, through the combination of phase compensation and sparse reconstruction depth, can effectively eliminate the spatiotemporal deviation introduced during motion, achieving accurate capture of underwater acoustic targets. Using only 8 physical elements, this method, through the synthesis of a huge virtual spatial aperture via non-uniform sampling, exhibits super-resolution characteristics in both azimuth and pitch angle dimensions. Even with limited snapshot data, it can still clearly distinguish between two targets.

[0067] Second embodiment: The relationship between RMSE and signal-to-noise ratio of azimuth angle estimation in the signal processing method of the present invention is studied, and the resulting effect is shown in the figure. Figure 3 As shown, comparison methods 1 (uniform sampling of a moving coprime matrix), 2 (non-uniform sampling of a moving uniform matrix), and 3 (static 8) are also presented. Comparison curves of the physical array (2). The application conditions of the method of this invention are as follows:

[0068] The method of this invention is based on a moving coprime array, the physical structure of which is as follows: Figure 1 As shown, there are A far-field narrowband signal source is incident on the array, with azimuth and elevation angles of respectively. System carrier frequency 12 kHz, speed of sound Take 1500 m / s as the moving platform speed. =5 m / s, non-uniform sampling sequence set to ,exist Echo data were collected at discrete spatiotemporal sampling points, and the number of snapshots was [number missing]. =10. The SNR starts from -10 dB and increases to 20 dB in 5 dB steps. 200 Monte Carlo simulation experiments are performed at different SNRs each time, and the simulation is carried out using MATLAB software.

[0069] analyze Figure 3 It can be seen that the RMSE of all four methods gradually decreases as the signal-to-noise ratio increases. Across the entire SNR range, the azimuth RMSE of the method in this invention is consistently lower than the other three comparative methods, with a particularly pronounced advantage in low SNR scenarios, demonstrating the strong robustness of the combination of sparse reconstruction and non-uniform sampling.

[0070] Third embodiment: The relationship between the RMSE of azimuth angle estimation and the number of snapshots in the signal processing method of the present invention is studied, and the resulting effect is shown in the figure. Figure 4 As shown, comparison methods 1 (uniform sampling of a moving coprime matrix), 2 (non-uniform sampling of a moving uniform matrix), and 3 (static 8) are also presented. Comparison curves of the physical array (2). The application conditions of the method of this invention are as follows:

[0071] The method of this invention is based on a moving coprime array, the physical structure of which is as follows: Figure 1 As shown, there are A far-field narrowband signal source is incident on the array, with azimuth and elevation angles of respectively. System carrier frequency 12 kHz, speed of sound Take 1500 m / s as the moving platform speed. =5 m / s, non-uniform sampling sequence set to ,exist Echo data were collected at discrete spatiotemporal sampling points with a signal-to-noise ratio (SNR) of 10. The number of snapshots started at 10 and increased to 250 in steps of 40. Monte Carlo simulation experiments were conducted 200 times at different snapshot numbers each time, using MATLAB software.

[0072] analyze Figure 4 It can be seen that the estimation accuracy of all four methods gradually improves with the increase of the number of snapshots. In scenarios with few snapshots, the RMSE of the method in this invention is approximately 0.07. The error rate is significantly lower than that of the comparison method; as the number of snapshots increases, the method still maintains the lowest error level, which fully verifies the robust estimation capability of the method of the present invention.

[0073] Fourth embodiment: The relationship between the RMSE of pitch angle estimation and the fast signal-to-noise ratio of the signal processing method of the present invention is studied, and the resulting effect is shown in the figure. Figure 5 As shown, comparison methods 1 (uniform sampling of a moving coprime matrix), 2 (non-uniform sampling of a moving uniform matrix), and 3 (static 8) are also presented. Comparison curves of the physical array (2). The application conditions of the method of this invention are as follows:

[0074] The method of this invention is based on a moving coprime array, the physical structure of which is as follows: Figure 1 As shown, there are A far-field narrowband signal source is incident on the array, with azimuth and elevation angles of respectively. System carrier frequency 12 kHz, speed of sound Take 1500 m / s as the moving platform speed. =5 m / s, non-uniform sampling sequence set to ,exist Echo data were collected at discrete spatiotemporal sampling points, and the number of snapshots was [number missing]. =10. The SNR starts from -10 dB and increases to 20 dB in 5 dB steps. 200 Monte Carlo simulation experiments are performed at different SNRs each time, and the simulation is carried out using MATLAB software.

[0075] analyze Figure 5 It can be seen that the pitch angle RMSE of all four methods gradually decreases as the signal-to-noise ratio increases. Across the entire SNR range, the pitch angle RMSE of the method in this invention is consistently lower than that of the other three comparative methods, with a particularly prominent advantage in low SNR scenarios, demonstrating the strong robustness of the combination of sparse reconstruction and non-uniform sampling.

[0076] Fifth embodiment: The relationship between the RMSE of pitch angle estimation and the number of snapshots in the signal processing method of the present invention is studied, and the resulting effect is shown in the figure. Figure 6 As shown, comparison methods 1 (uniform sampling of a moving coprime matrix), 2 (non-uniform sampling of a moving uniform matrix), and 3 (static 8) are also presented. Comparison curves of the physical array (2). The application conditions of the method of this invention are as follows:

[0077] The method of this invention is based on a moving coprime array, the physical structure of which is as follows: Figure 1 As shown, there are A far-field narrowband signal source is incident on the array, with azimuth and elevation angles of respectively. System carrier frequency 12 kHz, speed of sound Take 1500 m / s as the moving platform speed. =5 m / s, non-uniform sampling sequence set to ,exist Echo data were collected at discrete spatiotemporal sampling points with a signal-to-noise ratio (SNR) of 10. The number of snapshots started at 10 and increased to 250 in steps of 40. Monte Carlo simulation experiments were conducted 200 times at different snapshot numbers each time, using MATLAB software.

[0078] analyze Figure 6 As can be seen, the estimation accuracy of all four methods gradually improves with the increase of the number of snapshots. In scenarios with few snapshots, the RMSE of the method in this invention is significantly lower than that of the comparative methods; as the number of snapshots increases, this method still maintains the lowest error level, fully verifying the robust estimation capability of the method in this invention.

[0079] The specific examples described in this patent are merely illustrative of the invention. Those skilled in the art to which this invention pertains may make various modifications, additions, or similar substitutions to the described specific examples, without departing from the invention or exceeding the scope defined by the claims.

Claims

1. A two-dimensional DOA estimation method for non-uniform sampling of an underwater mobile observation platform, the method employing... A one-dimensional coprime array composed of physical array elements serves as the receiving array, with the array elements along... The axis is distributed, and its position vector is denoted as . The array is mounted on a mobile platform, and moves along the axis perpendicular to the array's axis. Axial direction at a constant speed The system moves according to a pre-set non-uniform sampling sequence set. exist Echo data were collected at discrete spatiotemporal sampling points, among which The reference element spacing, The signal wavelength; characterized in that: The two-dimensional DOA estimation method based on non-uniform sampling from an underwater mobile observation platform includes the following steps: Step 1: Calculate the first... Propagation delay of each displacement point relative to its initial position According to the formula Construct the phase compensation factor for this sampling point, where The center frequency of the signal. , This represents the total number of steps in the non-uniform sampling sequence. The imaginary unit; Step 2: Use the phase compensation factor obtained in Step 1 to analyze the original multi-shot received signal matrix at each sampling displacement point. Phase completion is performed, and the data is vertically concatenated and stitched according to the spatial sampling order to construct an equivalent observation matrix. ; Step 3: Determine the azimuth of the target spatial region and pitch angle Divided into Discrete grid points For each grid point, calculate its corresponding direction cosine variable. and ; Step 4: Combine the physical array element positions With non-uniform displacement Construct the two-dimensional spatial guide vector corresponding to each grid point. ,in ; Step 5: Guide the two-dimensional space to a vector After normalization, the matrices are concatenated column-wise to construct an overcomplete dictionary matrix. ; Step 6: Calculate the observation matrix The Frobenius norm, combined with the signal-to-noise ratio (SNR) and a preset adjustment coefficient. Set error tolerance ,in Denotes the Frobenius norm of a matrix; Step 7: Establish a system based on and The joint sparse reconstruction model, taking the input signal, utilizes the shared sparse structure of the signal on the spatial grid to construct the matrix of the signal to be recovered. For a multi-measurement vector optimization problem with multiple variables, a joint sparse signal matrix on a two-dimensional spatial grid is reconstructed using a convex optimization algorithm. ; Step 8: Calculate the sparse signal matrix all sectors Norm, generating spatial energy distribution vector ,search The highest energy level in the front The grid index corresponding to each peak is mapped back to a preset angle grid to obtain the final azimuth estimate of the target. With pitch angle estimate ,in This represents the number of signal sources.

2. The two-dimensional DOA estimation method for non-uniform sampling of an underwater mobile observation platform as described in claim 1, characterized in that: The one-dimensional coprime array is composed of two uniform linear subarrays, subarray one and subarray two, wherein subarray one contains There are 1 physical array elements, with an element spacing of 1. Subarray 2 contains There are 1 physical array elements, with an element spacing of 1. The physical element position vector is constructed by taking the union of the position vectors of the two subarray elements. ,in and They are coprime positive integers.

3. The two-dimensional DOA estimation method for non-uniform sampling of an underwater mobile observation platform as described in claim 1, characterized in that: In step two, construct the equivalent observation matrix. The specific process is as follows: A1: For all The displacement points are determined according to the formula. The compensated signal matrix is ​​calculated. ; A2: Will The samples are longitudinally cascaded and stitched together according to the order of spatial sampling displacements, forming a dimension of... Equivalent observation matrix ,in This represents the number of snapshots.

4. The two-dimensional DOA estimation method for non-uniform sampling of an underwater mobile observation platform as described in claim 1, characterized in that: In step five, a complete dictionary is constructed. The specific process is as follows: B1: Guiding vector in two-dimensional space Perform a normalization operation to obtain the normalized two-dimensional spatial steering vector. ,in Representing vectors Norm; B2: All The normalized column vector of grid points The matrices are horizontally joined sequentially according to the grid division order to form the overcomplete dictionary matrix used for sparse reconstruction. .

5. The two-dimensional DOA estimation method for non-uniform sampling of an underwater mobile observation platform as described in claim 1, characterized in that: Reconstructing the joint sparse signal matrix in step seven The specific process is as follows: An optimization problem based on a multi-measurement vector framework is constructed to recover the signal matrix. To optimize the variables, a minimization reconstruction model is established, which includes data fidelity terms and row sparsity constraints: The model is iteratively solved using a convex optimization algorithm to reconstruct the joint sparse signal matrix on a two-dimensional spatial angular grid. ,in This is the regularization function.

6. The two-dimensional DOA estimation method for non-uniform sampling of an underwater mobile observation platform as described in claim 1, characterized in that: Step eight generates the spatial energy distribution vector. The specific process for extracting the final angle estimate is as follows: C1: The sparse signal matrix obtained in step seven. Calculate the value of each row vector Norms, constituting lengths of Spatial energy distribution column vector , its first element ; C2: Column vector of spatial energy distribution All elements are sorted in descending order of numerical value, before extraction The grid index value corresponding to each peak point; C3: Extract the above Each grid index value is back-mapped to the pre-divided two-dimensional spatial angle discrete grid sequence in step three, and the corresponding value is found. The azimuth and elevation angle values ​​are combined and used as the final two-dimensional DOA joint estimation result for the target signal source.

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