A method for estimating the depth of an over-the-horizon target sound source based on shallow sea bottom horizontal array interferometric fringe difference

Abstract

The application discloses a kind of overtop target sound source depth estimation method based on shallow sea bottom horizontal array interference fringe difference, steps include: step 1, signal acquisition and interference spectrum construction;Step 2, CPA interference fringe slice;Step 3, subarray high-precision light and dark fringe positioning;Step 4, CPA slice interference fringe difference modeling;Step 5, double model sound source depth solution;Step 6, multi-fringe weighted least square fusion optimization;Step 7, multi-frequency joint optimization solution.The application adopts interference fringe difference technology and multiple improvements, can eliminate the global phase offset introduced by seabed reflection, avoid the deviation caused by the non-equal amplitude interference between adjacent light and dark fringes, effectively solve the problem of discrete sampling truncation error, balance the calculation efficiency and global solution accuracy, and improve the solution robustness in complex marine environment.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustic signal processing, and in particular, it is a method for estimating the depth of an overhead target sound source based on the differential interferometric fringes of a horizontal array on the shallow seabed. Background Technology

[0002] The horizontal receiving array, deployed on the shallow seabed, possesses natural advantages such as large acoustic aperture, low background noise in the marine environment, and long-term stable array attitude. Data collected from each channel can be transmitted in real time via submarine optical cable to a shore-based processing station for signal processing and parameter calculation. This system primarily serves two core application scenarios in engineering: first, the testing and evaluation of radiated noise from surface / underwater vehicles, estimating motion parameters such as navigation depth, heading, and speed by passively receiving radiated noise from targets, and achieving extrapolation and evaluation at the source level of radiated noise; second, underwater early warning and monitoring, enabling the classification, identification, and threat level assessment of underwater targets through precise estimation of target motion parameters (especially sound source depth estimation).

[0003] When a target passes near the seabed horizontal receiving array, its radiated noise sound field undergoes multiple reflections between the sea surface and the seabed interface, forming a typical Lloyd's mirror interference effect. For each narrowband component, regular interference fringes in both spatial and temporal dimensions can be observed. When the target passes overhead through the seabed horizontal receiving array, closed elliptical interference fringes centered on the time and position of overhead passage can be observed. The spatial distribution characteristics of the fringes are strongly coupled with the sound source depth, forming the core physical basis for target depth inversion in this invention. In addition to traditional discrete hydrophone seabed horizontal arrays, virtual horizontal sensors obtained from distributed acoustic wave sensing via submarine optical cables can also acquire stable spatial-temporal domain interference energy transmission characteristic spectra.

[0004] Existing interferometric bathymetry techniques can be divided into three known schemes: The first is the interferometric fringe template matching scheme, which generates theoretical interferometric copy patterns corresponding to different depths through an acoustic propagation model, and performs global correlation matching and grid optimization with the measured patterns to achieve joint estimation of depth and distance. This is currently the mainstream technology for seabed horizontal array bathymetry. The second is the absolute interferometric order analytical solution scheme, which originated from the study of vertical linear arrays. It solves the depth by interpreting the absolute interferometric brightness and darkness order at the CPA center point and combining it with an approximate model. The third is the broadband frequency characteristic interferometric concave point matching scheme, which relies on the frequency-range domain interferometric characteristics of broadband signals to achieve parameter inversion. This is only applicable to broadband target scenarios.

[0005] The existing technology has the following drawbacks:

[0006] 1. The interpretation of absolute interferometric order contains inherent phase ambiguity and fundamental systematic errors: Under the special deployment conditions of shallow seabed horizontal arrays, the propagation paths of the target's direct wave and the seabed reflected wave completely coincide and have the same path length. After superposition, a globally constant phase shift independent of spatial position is generated, resulting in random shifts in the interferometric state of the CPA center point without a fixed corresponding pattern. Traditional analytical methods relying on the absolute interferometric brightness order of the CPA center point cannot establish a stable interferometric order-depth mapping relationship. The depth solution results are unstable and have large errors. This phase ambiguity problem is an inherent physical defect of the seabed horizontal array scenario and cannot be eliminated by conventional signal processing methods.

[0007] 2. The interferogram template matching method suffers from poor engineering practicality and limited accuracy: Current mainstream seabed horizontal array depth estimation techniques all rely on generating theoretically copied interferograms using acoustic field models. Depth estimation is achieved through global correlation matching with measured spectra and mesh traversal optimization. This method is highly dependent on accurate prior marine environmental parameters, sound velocity profiles, and seabed sediment parameters. Shallow sea environments are time-varying and complex, and parameter mismatch is common, easily leading to strong coupling between distance and depth parameters and the algorithm being prone to getting trapped in local optima. At the same time, global multidimensional mesh traversal computation is large and the running time is high.

[0008] 3. Depth estimation methods based on target passage characteristics are subject to stringent constraints and lack robustness: Existing techniques for calculating CPA horizontal distance by analyzing target energy variation patterns and Doppler frequency variation patterns, and then inverting target depth using geometric relationships, have significant inherent flaws. These methods strictly rely on the assumption of uniform linear motion of the target. In real-world marine scenarios, target maneuvering and variable-speed navigation will cause distortions in the Doppler rate of change and energy fluctuation characteristics, resulting in a sharp decrease in the accuracy of CPA distance calculation.

[0009] 4. Focused beamforming depth sounding method is sensitive to parameters and has a large computational load: The depth sounding technology based on focused beamforming obtains the target azimuth and distance parameters by focusing and scanning the space point by point, and then converts the target depth. The computational load is large. At the same time, this method is sensitive to array element amplitude and phase errors and array distortion. Summary of the Invention

[0010] To address the existing technical problems in estimating the depth of targets passing over shallow seabed horizontal arrays, the present invention aims to provide a method for estimating the depth of sound sources passing over targets based on the differential interferometric fringes of shallow seabed horizontal arrays. This method eliminates the global phase shift introduced by seabed reflection through the differential difference of the relative positions of bright and dark fringes, thus eliminating phase ambiguity system errors at the physical level. It explicitly employs the differential difference of the relative positions of the same bright and dark fringes to avoid deviations caused by non-equal amplitude interference between adjacent bright and dark fringes. It combines sub-array element high-precision fringe positioning technology to solve the discrete sampling truncation error problem. It constructs a dual-model system of fast second-order Taylor approximation and accurate original radical-based solution without approximation, balancing computational efficiency and global solution accuracy. Finally, it improves the robustness of the solution in complex marine environments through multi-fringe, multi-frequency weighted least squares fusion optimization.

[0011] The technical solution of this invention is as follows:

[0012] A method for estimating the depth of an overhead target sound source based on the difference of horizontal interferometric fringes of a shallow seabed array includes:

[0013] Step 1: Signal Acquisition and Interferogram Construction

[0014] The radiation noise signal of the moving target over the shallow sea is collected, and the time domain signal of each channel of the array is transformed into the frequency domain by fast Fourier transform. The power spectrum of each channel is obtained by taking the square of the magnitude of the frequency domain signal, and then the time-frequency power spectrum matrix is ​​constructed.

[0015] From the time-frequency power spectrum, a target stable low-frequency narrowband line spectrum with high signal-to-noise ratio is selected, and the time-series energy data of each array element at the same line spectrum frequency is extracted to construct an array element-time two-dimensional energy passage characteristic interferometric fringe pattern.

[0016] After completing the construction of the interferogram, the target's overpass time is estimated: by using the concentration characteristics of the energy distribution in the interferogram and the maximum point of the rate of change of the line spectrum frequency with time, the closest passing time of the target relative to the array is jointly estimated.

[0017] Step 2, CPA interference fringe section:

[0018] The spatial slice corresponding to the most recent passing time of the target CPA is selected as the solution benchmark, and this slice is the center of symmetry of the interference fringes; narrowband energy-space curves are extracted for the candidate CPA time.

[0019] When the signal-to-noise ratio is low and the single-time slice curve is not smooth enough, a certain time window is selected with the CPA time as the center, and the energy-space curves of each time within the window are averaged in the time domain.

[0020] Step 3: High-precision positioning of bright and dark stripes in subarray elements:

[0021] The method adopted is to first perform coarse positioning at the integer array element level, and then perform fine positioning at the sub-array element level, as follows:

[0022] (1) Coarse localization at the integer array level: First, perform extreme value search on the narrowband energy-space curve intercepted at CPA time, extract the positions of all local maxima and local minima on the curve, and obtain the coarse coordinates of multiple sets of bright fringes and dark fringes at the integer array level.

[0023] (2) Subarray-level fine positioning: For high signal-to-noise ratio scenarios, interpolation methods including parabolic interpolation, cubic spline interpolation, and spatial upsampling interpolation are used; for low signal-to-noise ratio scenarios, a one-dimensional Gaussian envelope model with a baseline term is used, and the LM nonlinear least squares algorithm is used to iteratively fit the cross-sectional data to solve the subarray-level fringe center position.

[0024] (3) By screening high-quality positioning results by fitting goodness and peak signal-to-noise ratio, abnormal stripe coordinates with distortion and noise interference are removed, and the sub-element precision extreme positions of multiple sets of bright and dark stripes are obtained.

[0025] Step 4: Differential modeling of CPA slice interference fringes:

[0026] Multiple sets of adjacent bright or dark fringes are extracted sequentially from the center outwards along the slice. Each set of fringes is determined by the position of the inner fringes. Position of adjacent stripes on the outside The system of equations is constructed by taking multiple pairs of adjacent bright and dark stripes from the center outwards.

[0027] For a set of adjacent stripes of the same light or dark color, the position of the inner stripes is used. Position of outer stripes Constructing information about the depth of the sound source The difference equations are used to completely cancel out the global constant phase shift and the fixed π phase abrupt change through the position difference operation of the same group of bright and dark fringes, thus constructing a pure spatial interference constraint relationship without phase error.

[0028] The core difference equation is as follows:

[0029] ,

[0030] In the formula, D is the depth of the seawater. For the depth of the sound source, The spatial position of the inner stripes. λ represents the spatial position of adjacent bright and dark stripes on the outer side, and λ is the wavelength of sound waves in water.

[0031] Step 5: Solving for the depth of the dual-model sound source:

[0032] Two switchable solution models are constructed. For fast estimation scenarios, a second-order Taylor approximation analytical solution model is used, while for high-precision engineering scenarios, a high-precision solution model is used, as detailed below:

[0033] (1) Second-order Taylor approximate analytical solution model: In the near region of CPA, the root function of path difference is expanded by second-order Taylor truncation. After eliminating the constant term, a quadratic equation with only the fringe position is derived. The closed analytical solution of the sound source depth is obtained by solving the equation.

[0034] (2) Original radical numerical solution model without approximation: No series truncation or model approximation is performed. The original path difference radical expression is completely preserved. The residual function is constructed. The deep solution is completed by bisection method and Newton iteration numerical root finding. There is no model truncation error.

[0035] Step 6: Multi-stripe weighted least squares fusion optimization:

[0036] To address the issue of poor robustness in solving single-group fringes, a global optimization strategy based on weighted least squares in the original path difference residual domain is adopted. The residual squares of all effective bright and dark fringe pairs are weighted and summed to construct a global cost function. The weights are adaptively allocated based on the goodness of fit of each group of fringes and the signal-to-noise ratio, with higher weights for high-quality fringes, automatically suppressing the interference of distortion and noise fringes.

[0037] Meanwhile, for the left and right symmetrical stripes, the position domain absolute value averaging preprocessing is used to reduce noise, and random noise is suppressed in the original observation domain. Finally, the optimal sound source depth is solved by one-dimensional nonlinear optimization iteration.

[0038] Step 7: Multi-frequency joint optimization solution:

[0039] When multiple target narrowband line spectra are extracted, each frequency independently completes fringe localization and residual calculation, constructs a multi-frequency joint weighted cost function, integrates multi-frequency redundant observation information, and uses the single-frequency solution result as the initial value for iteration to jointly optimize and solve the depth of the unique sound source, thereby reducing random errors.

[0040] The beneficial effects of this invention are as follows:

[0041] 1. This invention eliminates the inherent phase ambiguity error under shallow seabed horizontal array conditions from the physical root by using the difference mechanism of bright and dark fringes. It completely gets rid of the dependence on the absolute interference order of the CPA center point and avoids the error introduced by the unequal amplitude interference between adjacent bright and dark fringes, thus solving the fundamental systematic error of traditional analytical methods. At the same time, it abandons the environmentally sensitive and computationally expensive global template matching architecture, which greatly reduces the algorithm's dependence on prior parameters of the marine environment and avoids parameter coupling and local optima problems.

[0042] 2. This invention solves the bottleneck of low-frequency coarse stripe discrete sampling accuracy by subarray element fine fitting and positioning. It relies on a dual-model switching mechanism to balance real-time computing efficiency and global solution accuracy. Through multi-stripe adaptive weighted least squares fusion and multi-frequency joint optimization, it makes full use of redundant observation information, effectively suppresses random errors caused by marine environmental noise and stripe distortion, and significantly improves the robustness and accuracy of depth estimation. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating the workflow of the present invention.

[0044] Figure 2 The distribution of interference fringes over a target in a horizontal array on the shallow seabed under simulation.

[0045] Figure 3 Interference fringe pattern for CPA slices;

[0046] Figure 4 for Figure 3 The relationship between the path difference and the sound source depth after substituting two adjacent bright fringes into the model. Detailed Implementation

[0047] The present invention will be further described below with reference to specific embodiments and accompanying drawings:

[0048] I. Technical Terminology

[0049] 1. Submarine Horizontal Array: A horizontally deployed underwater acoustic signal receiving array, consisting of a traditional discrete hydrophone array and a submarine optical cable DAS equivalent virtual horizontal array, used to collect spatiotemporal data of underwater target acoustic fields.

[0050] 2. Overhead target: A sonic target whose horizontal trajectory crosses the horizontal array.

[0051] 3. CPA (Closest Point of Passage): The horizontal closest position of the moving target relative to the receiving array, which is the center of symmetry of the interference fringes.

[0052] 4. Narrowband energy transmission characteristics: It has a narrowband component with a definite frequency. The target radiated acoustic energy received by the array varies with the spatial position and time of the array elements, and the interference fluctuation characteristics are manifested as two-dimensional interference fringes between array elements and time, which are generated by the coherent superposition of multiple path differences.

[0053] 5. Doppler effect: The signal frequency drift caused by the radial relative motion between the target and the array.

[0054] 6. Interference fringe difference: The signal processing mechanism that uses the spatial position difference of adjacent bright and dark fringes within the same CPA slice to cancel the global constant phase shift also avoids the deviation caused by the spatial position difference of adjacent bright and dark fringes. This is the core original technology of this invention.

[0055] 8. Sub-element localization: Breaking through the limitations of discrete array sampling, it solves for the true extreme positions of fringes between array elements, eliminating sampling truncation errors.

[0056] For the scenario of rapid and robust estimation of the depth of overhead moving underwater acoustic targets under the condition of horizontally deployed linear underwater acoustic receiver arrays in shallow seabeds, this invention provides a method for estimating the depth of overhead target acoustic sources based on the differential interferometric fringe of a horizontal array on the shallow seabed. The flowchart of its workflow is shown below. Figure 1 As shown, the overall process comprises seven steps: signal acquisition and interferogram construction, CPA interferometric fringe slicing, high-precision fringe localization of subarray elements, differential modeling of CPA sliced ​​fringes, dual-model depth solution, multi-fringe weighted least squares fusion, and multi-frequency joint optimization. The specific details of each step are as follows:

[0057] Step 1: Signal Acquisition and Interferogram Construction

[0058] The receiving hardware applicable to this invention includes two types of seabed horizontal arrays: one is a physical horizontal array of discrete hydrophones deployed on the seabed; the other is an equivalent virtual horizontal array obtained by demodulation of a distributed acoustic sensing (DAS) system on a submarine optical cable, where each demodulated spatial channel is equivalent to an independent array element. The radiated noise signal of a uniformly moving target passing overhead in shallow water is collected. The time-domain signal of each channel of the array is subjected to a Fast Fourier Transform (FFT) to the frequency domain. The square of the magnitude of the frequency domain signal is taken to obtain the power spectrum of each channel, thereby constructing a time-frequency power spectrum matrix. Stable narrowband components with high signal-to-noise ratios, including line spectra, are selected from the time-frequency power spectrum. The time-series energy data of each array element at the same frequency is extracted, constructing a two-dimensional energy transmission characteristic interferometric fringe pattern of the array element and time. If necessary, two-dimensional smoothing filtering is performed on the two-dimensional interferogram to suppress ocean random noise and impulse interference, improving the signal-to-noise ratio and discernibility of the fringe features. The interference fringes in the spectrum are symmetrically distributed about the target CPA (Closest Point of Approach), completely preserving the spatial characteristics of the sound field interference.

[0059] After completing the construction of the interferogram, the target overpass time (i.e., CPA time) is further estimated: by using the concentration characteristics of energy distribution in the interferogram and the maximum point of the rate of change of line spectrum frequency with time, the closest passing time of the target relative to the array is jointly estimated, providing an accurate time reference for subsequent CPA spatial slicing.

[0060] Step 2, CPA interference fringe section:

[0061] The spatial slice corresponding to the most recent transit time of the target CPA is selected as the solution benchmark. This slice is the center of symmetry of the interference fringes, where the fringe distribution is most stable and the distortion is minimal. Narrow-band energy-space curves are extracted for the candidate CPA time.

[0062] When the signal-to-noise ratio is low and the single-time slice curve is not smooth enough, a certain time window is selected with the CPA time as the center, and the energy-space curves of each time within the window are averaged in the time domain to improve the smoothness of the curve and the recognizability of the fringe extreme values.

[0063] Step 3: High-precision positioning of bright and dark stripes in subarray elements:

[0064] To address the problem of discrete sampling truncation error in low-frequency coarse fringes, this invention employs a two-level localization scheme combining integer-element level coarse localization and sub-element level fine localization. First, an extreme value search is performed on the narrowband energy-space curve truncated at time CPA, extracting the positions of all local maxima (bright fringes) and local minima (dark fringes) on the curve, thus obtaining multiple sets of integer-element level coarse coordinates for bright and dark fringes.

[0065] Based on coarse localization at the integer array element level, high-precision fine localization at the subarray element level is implemented. To adapt to different signal-to-noise ratio scenarios, two switchable fine localization schemes are set up: for high signal-to-noise ratio scenarios, interpolation methods are preferred, including parabolic interpolation, cubic spline interpolation, and spatial upsampling interpolation, which ensures high computational efficiency while maintaining accuracy; for low signal-to-noise ratio measured scenarios, a one-dimensional Gaussian envelope model with a baseline term is preferred, and the Levenberg-Marquardt (LM) nonlinear least squares algorithm is used to iteratively fit the cross-sectional data to solve for the subarray element level fringe center position, which has excellent noise resistance.

[0066] Finally, high-quality positioning results were selected by goodness of fit and peak signal-to-noise ratio, and abnormal fringe coordinates with distortion and noise interference were removed to obtain the extreme positions of multiple sets of bright and dark fringe subarray elements.

[0067] Step 4: Differential modeling of CPA slice interference fringes:

[0068] Multiple pairs of adjacent bright / dark fringes (either both bright or both dark) are extracted sequentially from the center outwards along the slice. Each pair of fringes is determined by the position of the inner fringes. Position of adjacent stripes on the outside The system of equations is constructed by taking multiple pairs of adjacent bright and dark stripes from the center outwards.

[0069] Based on the multipath interference mechanism of shallow-sea Lloyd's mirrors, the reflected wave from the sea surface exhibits a fixed π-phase abrupt change, while seabed reflection introduces a globally constant phase shift. Both types of phase shifts are constants independent of spatial location. For a set of adjacent bright / dark fringes, the change in path difference between the reflected wave and the direct wave from the inner fringe to the outer fringe is -λ (where λ is the wavelength of the sound wave in the water). Using the position of the inner fringe... Position of outer stripes Constructing information about the depth of the sound source The difference equations, through differential operations on the positions of the same set of bright and dark fringes, can completely cancel out the global constant phase shift and the fixed π phase abrupt change, without relying on the CPA center point being an extreme point. This completely eliminates the phase ambiguity problem unique to seabed horizontal arrays, constructing a pure spatial interferometric constraint relationship without phase error. The core difference equations are as follows:

[0070] ,

[0071] In the formula, D is the depth of the seawater. For the depth of the sound source, The spatial position of the inner stripes. λ represents the spatial position of adjacent bright and dark stripes on the outer side, and λ is the wavelength of sound waves in water.

[0072] The equation eliminates the global constant phase offset term, which is independent of spatial location, by calculating the difference between the inner and outer fringe path differences, and retains only the spatial interference constraint coupled with the depth of the sound source. By taking multiple pairs of adjacent bright and dark fringes from the center outward, an overdetermined set of equations can be constructed, providing an observational basis for subsequent weighted least squares solutions.

[0073] Step 5: Solving for the depth of the dual-model sound source:

[0074] This invention constructs two switchable solution models, covering two types of engineering scenarios: fast estimation and high-precision solution, and is fully adaptable to different stripe distribution ranges:

[0075] (1) Second-order Taylor approximation analytical solution model: A second-order Taylor truncation expansion of the path difference radical function is performed in the near-field region of CPA. After eliminating the constant term, a quadratic equation in one variable that is only related to the fringe position is derived. Solving this equation yields a closed-form analytical solution for the sound source depth. This model is fast, has strong real-time performance, and is suitable for online fast estimation scenarios. This model has the best accuracy only under the condition of small-range fringe in the near-field region of CPA.

[0076] (2) Original radical numerical solution model without approximation: No series truncation or model approximation is performed. The original path difference radical expression is completely preserved. The residual function is constructed. The depth solution is completed by bisection method and Newton iteration numerical root finding. There is no model truncation error. It can be adapted to the full range of stripe distribution scenarios and is the preferred solution for high-precision measurement scenarios.

[0077] Step 6: Multi-stripe weighted least squares fusion optimization:

[0078] To address the issue of poor robustness in solving single-group fringes, this invention abandons the traditional approach of solving each group individually and then arithmetically averaging, instead employing a weighted least squares global optimization strategy based on the original path difference residual domain. A global cost function is constructed by weighted summation of the squared residuals of all valid bright and dark fringe pairs; the weights are adaptively allocated based on the goodness of fit and signal-to-noise ratio of each fringe group, with higher weights for high-quality fringes, automatically suppressing interference from distortion and noise fringes.

[0079] Meanwhile, for the left and right symmetrical stripes, the position domain absolute value averaging preprocessing noise reduction is given priority to suppress random noise in the original observation domain and avoid noise amplification in the depth domain. Finally, the optimal sound source depth is solved by one-dimensional nonlinear optimization iteration.

[0080] Step 7: Multi-frequency joint optimization solution:

[0081] When multiple target narrowband line spectra are extracted, each frequency independently completes stripe localization and residual calculation, constructs a multi-frequency joint weighted cost function, integrates multi-frequency redundant observation information, and uses the single-frequency solution result as the initial value for iteration to jointly optimize the solution of the unique sound source depth, further suppressing random errors and improving the stability and consistency of depth estimation in complex shallow sea environments.

[0082] Simulation experiment: Parameters were set as follows: 128 array elements, 6-meter element spacing, 100-meter sea depth, 40-meter target depth, and 4-meter / second speed. The output showed the distribution of interference fringes of the horizontal array over the target in shallow sea. Figure 2 As shown.

[0083] The CPA interference fringes were sliced ​​and positioned to obtain the CPA slice interference fringe pattern as shown below. Figure 3 As shown, the simulation results with interpolation at three stripe positions are marked.

[0084] Will Figure 3 The relationship between the path difference calculated by substituting the positions of the two bright fringes into the model and the depth of the sound source is as follows: Figure 4 As shown, the intersection point with the wavelength value is 41 meters, and the set sound source error depth is only 1 meter, indicating that the method of the present invention has good estimation accuracy.

[0085] In summary, the present invention has the following characteristics:

[0086] 1. To address the unique global phase shift problem of shallow seabed horizontal arrays, a technical mechanism of CPA time slicing and relative position difference of adjacent bright or dark fringes is adopted to completely cancel the constant phase shift caused by seabed reflection and sea surface reflection. This completely solves the phase ambiguity system error of traditional absolute order interpretation and avoids the adjacent bright and dark spacing shift introduced by the unequal amplitude interference of direct waves and reflected waves.

[0087] 2. Abandoning existing mainstream environmentally sensitive global interferogram template matching schemes, this approach employs a solution architecture combining fringe feature analysis and least-squares fusion. This eliminates the need for precise marine environmental parameters, avoiding drawbacks such as parameter mismatch, parameter coupling, local optima, and high computational cost. Furthermore, the initial values ​​used for interferogram template basis matching can significantly improve efficiency and accuracy.

[0088] 3. Construct a high-precision stripe positioning system for subarray elements. Solve the problem of sampling truncation error of discrete array by solving the extreme value solution of coarse stripe subarray elements through Gaussian fitting nonlinear iteration. At the same time, it is suitable for dual scenarios with high and low signal-to-noise ratios.

[0089] 4. A dual-model switching mechanism is set up, which combines fast analytical solution with second-order Taylor approximation and high-precision numerical solution without approximation of original radical formula, to meet the needs of real-time engineering and high-precision solution across the entire domain, covering all stripe distribution scenarios.

[0090] 5. We adopt a multi-fringe residual domain weighted least squares global fusion optimization, which eliminates the equal weighting defects of arithmetic average and improves noise robustness based on fringe quality adaptive weighting.

[0091] 6. A multi-frequency line spectrum joint weighted optimization mechanism is adopted to further improve the accuracy and stability of depth estimation by utilizing multi-frequency redundant observation information.

[0092] 7. It is compatible with both traditional submarine hydrophone horizontal arrays and submarine optical cable DAS equivalent horizontal arrays.

[0093] It should be noted that the above embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Equivalent modifications made based on the above embodiments are all within the scope of protection of the present invention.

Claims

1. A method for estimating the depth of an overhead target sound source based on the difference of horizontal interferometric fringes of a shallow seabed array, characterized in that, include: Step 1: Signal acquisition and interferogram construction; Step 2: Slice the CPA interference fringes; Step 3: High-precision positioning of bright and dark stripes for subarray elements; Step 4: Differential modeling of CPA slice interference fringes; Step 5: Solve for the depth of the dual-model sound source; Step 6: Multi-stripe weighted least squares fusion optimization; Step 7: Solve the multi-frequency joint optimization problem.

2. The method for estimating the depth of an overhead target sound source based on the differential interferometric fringes of a horizontal array on the shallow seabed, as described in claim 1, is characterized in that... Step 1 includes: The radiation noise signal of the moving target over the shallow sea is collected, and the time domain signal of each channel of the array is transformed into the frequency domain by fast Fourier transform. The power spectrum of each channel is obtained by taking the square of the magnitude of the frequency domain signal, and then the time-frequency power spectrum matrix is ​​constructed. From the time-frequency power spectrum, a target stable low-frequency narrowband line spectrum with high signal-to-noise ratio is selected, and the time-series energy data of each array element at the same line spectrum frequency is extracted to construct an array element-time two-dimensional energy passage characteristic interferometric fringe pattern. After the interferometric pattern is constructed, the time of the target's overhead is estimated.

3. The method for estimating the depth of an overhead target sound source based on the difference of horizontal interferometric fringes of a shallow seabed array, as described in claim 2, is characterized in that: In step 1, the method for estimating the target's overpass time is as follows: by using the concentration characteristics of energy distribution in the interferogram and the maximum point of the rate of change of line spectrum frequency with time, the closest passing time of the target relative to the array is jointly estimated.

4. The method for estimating the depth of an overhead target sound source based on the difference of horizontal interferometric fringes of a shallow seabed array, as described in claim 3, is characterized in that: Step 2 includes: selecting the spatial slice corresponding to the most recent passing time of the target CPA as the solution benchmark, extracting narrowband energy-space curves for candidate CPA times, and when the signal-to-noise ratio is low and the single-time slice curve is not smooth enough, selecting a certain time window centered on the CPA time, and averaging the energy-space curves of each time within the window in the time domain.

5. The method for estimating the depth of an overhead target sound source based on the difference of horizontal interferometric fringes of a shallow seabed array, as described in claim 4, is characterized in that: Step 3 includes: (1) Coarse localization at the integer array level: First, perform extreme value search on the narrowband energy-space curve intercepted at CPA time, extract the positions of all local maxima and local minima on the curve, and obtain the coarse coordinates of multiple sets of bright fringes and dark fringes at the integer array level. (2) Subarray-level fine positioning: For high signal-to-noise ratio scenarios, interpolation methods including parabolic interpolation, cubic spline interpolation, and spatial upsampling interpolation are used; for low signal-to-noise ratio scenarios, a one-dimensional Gaussian envelope model with a baseline term is used, and the LM nonlinear least squares algorithm is used to iteratively fit the cross-sectional data to solve the subarray-level fringe center position. (3) By screening high-quality positioning results by fitting goodness and peak signal-to-noise ratio, abnormal stripe coordinates with distortion and noise interference are eliminated, and the sub-element precision extreme positions of multiple sets of bright and dark stripes are obtained.

6. The method for estimating the depth of an overhead target sound source based on the difference of horizontal interferometric fringes of a shallow seabed array, as described in claim 5, is characterized in that: Step 4 includes: Extract multiple sets of adjacent bright or dark fringes from the center outward along the slice. Each pair of fringes is composed of the inner fringe position and the outer adjacent fringe position. Construct a system of equations by taking multiple pairs of adjacent bright and dark fringes from the center outward. For a set of adjacent bright or dark fringes, a difference equation about the sound source depth is constructed using the positions of the inner and outer fringes. The global constant phase shift and fixed π phase abrupt change are completely canceled by the difference operation of the positions of the same set of bright and dark fringes, thus constructing a pure spatial interference constraint relationship without phase error.

7. The method for estimating the depth of an overhead target sound source based on the difference of horizontal interferometric fringes of a shallow seabed array, as described in claim 6, is characterized in that: The core difference equation in step 4 is: ， In the formula, D is the depth of the seawater. For the depth of the sound source, The spatial position of the inner stripes. λ represents the spatial position of adjacent bright and dark stripes on the outer side, and λ is the wavelength of sound waves in water.

8. The method for estimating the depth of an overhead target sound source based on the difference of horizontal interferometric fringes of a shallow seabed array, as described in claim 7, is characterized in that: Step 5 includes: for fast estimation scenarios, a second-order Taylor approximation analytical solution model is used; for high-precision engineering scenarios, a high-precision solution model is used, as detailed below: (1) Second-order Taylor approximate analytical solution model: In the near region of CPA, the root function of path difference is expanded by second-order Taylor truncation. After eliminating the constant term, a quadratic equation with only the fringe position is derived. The closed analytical solution of the sound source depth is obtained by solving the equation. (2) Original radical numerical solution model without approximation: No series truncation or model approximation is performed. The original path difference radical expression is completely preserved. The residual function is constructed. The deep solution is completed by bisection method and Newton iteration numerical root finding. There is no model truncation error.

9. The method for estimating the depth of an overhead target sound source based on the difference of horizontal interferometric fringes of a shallow seabed array, as described in claim 8, is characterized in that: Step 6 includes: A weighted least squares global optimization strategy based on the original path difference residual domain is adopted; the weighted summation of the residual squares of all effective bright and dark fringe pairs is used to construct a global cost function; the weights are adaptively allocated based on the goodness of fit of each fringe pair's location and the signal-to-noise ratio. Meanwhile, for the left and right symmetrical stripes, the position domain absolute value averaging preprocessing is used to reduce noise, and random noise is suppressed in the original observation domain. Finally, the optimal sound source depth is solved by one-dimensional nonlinear optimization iteration.

10. The method for estimating the depth of an overhead target sound source based on the difference of horizontal interferometric fringes of a shallow seabed array according to claim 9, characterized in that: Step 7 includes: when multiple target narrowband line spectra are extracted, each frequency independently completes stripe localization and residual calculation, constructs a multi-frequency joint weighted cost function, integrates multi-frequency redundant observation information, and uses the single-frequency solution result as the initial value for iteration to jointly optimize and solve the depth of the unique sound source.

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