A passive synthetic aperture method based on r-l deconvolution beam domain processing

Abstract

The application discloses a passive synthetic aperture method and device based on R-L deconvolution beam domain processing, a medium and equipment. Through constructing an array shape distortion model under disturbance of a towed array, the absolute coordinates of each array element are obtained by processing the discretized array shape distortion model by using a Kalman filter. Based on a sound pressure expression and the absolute coordinates, the time domain solution of the received signal of each array element is determined. Based on an ETAM algorithm, the beam outputs of overlapping sub-arrays in adjacent time samples are obtained, and R-L iteration is performed on the beam outputs to obtain a phase compensation factor. The phase compensation is performed on the beam outputs based on the phase compensation factor to obtain each phase corrected beam and the beam output of the synthetic aperture. The passive synthetic aperture algorithm is effectively combined with the R-L deconvolution beam forming technology, the accuracy of the phase compensation factor after the array shape distortion is maximally improved, and the algorithm still provides high-precision target positioning in the case that the ETAM algorithm fails.

Description

Technical Field

[0001] This application relates to the field of signal processing technology, and more specifically to a passive synthetic aperture method, apparatus, medium, and device based on RL deconvolution beam domain processing. Background Technology

[0002] Shipborne hull-mounted sonar has long been the primary equipment for underwater acoustic detection. However, due to the limitations of the platform's internal space, hull-mounted sonar suffers from problems such as limited array aperture and severe interference from ship self-noise and radiated noise, resulting in a significant decrease in detection performance in complex hydrological environments. Some existing technologies indicate that towed array sonar effectively improves the detection capability of low-frequency and even very low-frequency sound sources by increasing the number of hydrophones and the array aperture. Its adjustable operating depth allows the system to select the optimal acoustic environment according to different hydrological conditions, overcoming sound wave propagation barriers such as thermoclines, thereby extending the detection range. Conventional beamforming (CBF) algorithms are one of the most basic array signal processing methods. However, since the Rayleigh resolution of a linear array is proportional to the ratio of the incident signal wavelength to the array aperture, a long array with a large aperture is required to detect weak signals. But due to engineering implementation and system cost issues, it is impossible to use excessively long hydrophone arrays.

[0003] To address this issue, existing Extended Towed Array Measurement (ETAM) algorithms use an overlap correlator to cross-correlate the received signals of overlapping array elements in consecutive measurement samples, using this cross-correlation as a least-squares estimate of the phase correction factor. This is then used to perform phase compensation on non-overlapping array elements, thereby extending the effective aperture of the towed array. Other existing technologies require prior knowledge of the relative velocities of the sound source and the receiving array for phase correction to achieve coherent accumulation of the beam output. Existing technologies also propose the Fast Fourier Transform Synthetic Aperture (FFTSA) algorithm, which coherently superimposes the beam outputs in the beam domain using FFT to achieve the synthetic aperture, eliminating the need for prior knowledge of the relative velocities of the sound source and the receiving array.

[0004] However, in practical applications, due to the motion of the towed platform, changes in ocean currents, and other environmental factors, the towed array formation often becomes distorted, making it difficult to maintain an ideal straight shape. This distortion severely affects the performance of the synthetic aperture, leading to a decrease in the accuracy of target positioning. Summary of the Invention

[0005] This application aims to at least address one of the technical problems existing in the prior art. To this end, the first aspect of this application proposes a passive synthetic aperture method based on RL deconvolution beam domain processing, comprising: constructing a towed array distortion model under disturbance based on the Padoussis equation of a flexible cable; using a Kalman filter to process the discretized array distortion model to obtain the absolute coordinates of each array element in the towed array; determining the time-domain solution of the received signal of each array element based on the sound pressure expression and absolute coordinates of the array elements in the towed array; sampling the time-domain solution of the received signal at adjacent time moments based on the ETAM algorithm to obtain the beam output of the overlapping subarray in the samples at adjacent time moments, and performing RL iteration on the beam output to obtain a phase compensation factor; performing phase compensation on the beam output based on the phase compensation factor to obtain each phase-corrected beam; and obtaining the beam output of the synthetic aperture based on the coherently summed phase-corrected beams.

[0006] Optionally, the Paidoussis equation based on the flexible cable is used to construct the array distortion model of the towed array under disturbance, which includes: obtaining a simplified expression of the Paidoussis equation of the flexible cable in an ideal fluid under preset conditions; determining the small-diameter Paidoussis equation of the flexible cable based on the simplified expression; discarding the higher-order components of the small-diameter Paidoussis equation to obtain the hydrodynamic model of the flexible cable; and rewriting the parameters in the hydrodynamic model using the preset disturbance expression to obtain the array distortion model.

[0007] Optionally, determining the frequency domain solution of the received signal of each array element based on the sound pressure expression and absolute coordinates of the array elements in the towed array includes: calculating the sound pressure expression of the position of the sound source at the array element position in the towed array; determining the time domain solution of the received signal of the array element based on the sound pressure expression; and determining the time domain solution of the received signal of other array elements in the towed array according to the absolute coordinates of each array element.

[0008] Optionally, determining the frequency domain solution of the received signal of the array elements based on sound pressure includes: under far-field conditions, replacing the two-dimensional Fourier transform in the sound pressure expression with the Hankel transform of the horizontal wavenumber to obtain a new sound pressure expression; and simplifying the new sound pressure expression with the Green's function of the discrete spectrum of the normal mode wave to obtain the time domain solution of the received signal of the towed array elements.

[0009] Optionally, the step of sampling the time-domain solutions of the received signals at adjacent time points based on the ETAM algorithm to obtain the beam output of the overlapping subarray in the adjacent time point samples includes: obtaining the (m-1)th sampling result based on the time-domain solution of the received signal of the (n+q)th array element at time t, and obtaining the m-th sampling result based on the time-domain solution of the received signal of the nth array element at time t+τ; performing frequency-domain beamforming based on the (m-1)th sampling result to obtain the first beam output of the overlapping subarray; performing frequency-domain beamforming based on the m-th sampling result to obtain the second beam output of the overlapping subarray, and determining the beam output of the overlapping subarray in the adjacent time point samples based on the first beam output and the second beam output.

[0010] Optionally, the step of performing RL iteration on the beam output to obtain the phase compensation factor includes: deconvolving the (m-1)th sample to obtain a first separation signal; deconvolving the mth sample to obtain a second separation signal; calculating the first point scattering function and the second point scattering function corresponding to the first and second separation signals, respectively; constructing a first iterative expression based on the first separation signal and the first point scattering function, and iterating the first iterative expression according to a preset number of RL deconvolutions to obtain a first phase factor; constructing a second iterative expression based on the second separation signal and the second point scattering function, and iterating the second iterative expression according to a preset number of RL deconvolutions to obtain a second phase factor; and processing the first phase factor and the second phase factor based on a preset formula to obtain the phase compensation factor.

[0011] Optionally, the step of performing phase compensation on the beam output based on the phase compensation factor to obtain each phase-corrected beam includes: using the phase compensation factor to phase-shift the second beam output to obtain the phase-corrected beam of the m-th sample; calculating the phase compensation factor of all beam outputs, and performing phase shift on the corresponding beam output according to the phase compensation factor to obtain each phase-corrected beam.

[0012] To achieve the above objectives, this application also provides a passive synthetic aperture device based on RL deconvolution beam domain processing, comprising: an array modeling module for constructing an array distortion model of a towed array under disturbance based on the Padoussis equation of a flexible cable, and obtaining the absolute coordinates of each array element in the towed array by processing the discretized array distortion model using a Kalman filter; a received signal determination module for determining the frequency domain solution of the received signal of each array element based on the sound pressure expression and absolute coordinates of the array elements in the towed array; a phase compensation module for sampling the time domain solution of the received signal at adjacent time moments based on the ETAM algorithm to obtain the beam output of the overlapping subarray in the samples at adjacent time moments, and performing RL iteration on the beam output to obtain a phase compensation factor; and a synthesis module for performing phase compensation on the beam output based on the phase compensation factor to obtain each phase-corrected beam, and obtaining the beam output of the synthetic aperture based on the coherently summed phase-corrected beams.

[0013] To achieve the above objectives, this application also provides an electronic device, which includes a processor and a memory. The memory stores at least one instruction, at least one program, a code set, or an instruction set. The at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by the processor to implement the passive synthetic aperture method based on RL deconvolution beam domain processing provided in the preceding claims.

[0014] To achieve the above objectives, this application also provides a computer-readable storage medium storing at least one instruction, at least one program, code set, or instruction set, wherein the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by a processor to implement the passive synthetic aperture method based on RL deconvolution beam domain processing provided in the preceding claims.

[0015] This application provides a passive synthetic aperture method, apparatus, medium, and device based on RL deconvolution beam domain processing. Compared with the prior art, the beneficial effects of the method are as follows: A towed array distortion model under disturbance is constructed based on the Padousse equation of the flexible cable; the absolute coordinates of each array element in the towed array are obtained by processing the discretized array distortion model using a Kalman filter; the time-domain solution of the received signal of each array element is determined based on the sound pressure expression and absolute coordinates of the array elements in the towed array; the time-domain solution of the received signal at adjacent time points is sampled based on the ETAM algorithm to obtain the beam output of the overlapping subarray in the samples at adjacent time points, and RL iteration is performed on the beam output to obtain the phase compensation factor; the beam output is then processed based on the phase compensation factor. Phase compensation is performed to obtain each phase-corrected beam. Based on the coherent summation of each phase-corrected beam, the beam output of the synthetic aperture is obtained. This application uses a hydrodynamic model to construct the array shape model of the towed array under external disturbances, and uses a Kalman filter to obtain the accurate coordinate position based on the distortion, thereby generating the corresponding received signal expression. The passive synthetic aperture algorithm is effectively combined with RL deconvolution beamforming technology to maximize the accuracy of the phase compensation factor after generating array distortion. The RL deconvolution algorithm replaces the method of obtaining the phase correction factor by conjugate multiplication of overlapping array element signals in the traditional passive synthetic aperture algorithm, so that the algorithm of this application is still effective when the ETAM algorithm fails. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of this application, the accompanying drawings used in the description of the embodiments or prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0017] Figure 1 A flowchart illustrating a passive synthetic aperture method based on RL deconvolution beam domain processing provided in this application embodiment;

[0018] Figure 2 A towed array pattern at time t provided for a passive synthetic aperture method based on RL deconvolution beam domain processing in an embodiment of this application;

[0019] Figure 3 A diagram showing the azimuth variation of drag point perturbation in a passive synthetic aperture method based on RL deconvolution beam domain processing, provided in an embodiment of this application.

[0020] Figure 4 An array variation diagram of a passive synthetic aperture method based on RL deconvolution beam domain processing provided in this application embodiment;

[0021] Figure 5 A towed array pattern at time t provided for a passive synthetic aperture method based on RL deconvolution beam domain processing in an embodiment of this application;

[0022] Figure 6 The images show the single-objective DOA estimation spatial spectrum of the algorithm designed in this application, the CBF algorithm, and the FFTSA algorithm. (a) and (b) are schematic diagrams of the spectrum obtained after 10 and 20 samplings, respectively.

[0023] Figure 7 The variation of RMSE estimated by each algorithm of a passive synthetic aperture method based on RL deconvolution beam domain processing provided in this application embodiment is shown as a function of synthetic aperture distance.

[0024] Figure 8 The RMSE estimated by each algorithm of the passive synthetic aperture method based on RL deconvolution beam domain processing provided in the embodiments of this application varies with the signal-to-noise ratio. Detailed Implementation

[0025] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0026] This specification provides the operational steps for the methods described in the embodiments or flowcharts, but may include more or fewer operational steps based on conventional or non-inventive labor. In actual system or server product execution, the methods shown in the embodiments or drawings may be executed sequentially or in parallel (e.g., in a parallel processor or multi-threaded processing environment).

[0027] refer to Figure 1 , Figure 1 A passive synthetic aperture method based on RL deconvolution beam domain processing is provided in one embodiment of this application. This algorithm can be executed by a processor, which can be located in a shipborne hull-mounted sonar system. The algorithm may include:

[0028] S10. Based on the Padoussis equation of the flexible cable, construct the array distortion model of the towed array under disturbance, and use the Kalman filter to process the discretized array distortion model to obtain the absolute coordinates of each array element in the towed array.

[0029] Among them, constructing a model of array distortion of a towed array under perturbation based on the Padoussis equations of flexible cables can include:

[0030] A simplified expression of the Padoussis equation in an ideal fluid based on a flexible cable under preset conditions;

[0031] The Paidoussis equation for the small diameter flexible cable is determined based on a simplified expression.

[0032] By discarding the higher-order components of the small-diameter Paidoussis equation, a hydrodynamic model for the flexible cable is obtained.

[0033] By rewriting the parameters in the hydrodynamic model using a pre-defined perturbation expression, a morphological distortion model is obtained.

[0034] In the specific execution process, the motion of the flexible cable in an ideal fluid can be expressed by the Padoussis equation:

[0035]

[0036] Taking the opposite direction of array movement as the positive x-axis, y = y(x,t) corresponds to the lateral displacement deviation of the array elements. When the array moves along the negative x-axis, and the platform's dragging speed is much greater than the ocean current speed, we have:

[0037]

[0038] Where M represents the fluid mass per unit length of cable, U represents the velocity of the array, L represents the length of the array, d represents the diameter of the flexible cable, and c T and c N c′ represents the tangential and normal drag coefficients, respectively. T This represents the coefficient of drag force at the tail of the array. Generally, the cable length is much greater than its diameter and deformation amplitude, and the effect of the array restoring force is ignored, i.e., B = 0. If the tangential viscous drag acts in the x-axis direction, rather than the tangential direction of the array, the Paidoussis equation can be simplified to:

[0039]

[0040] When the tail of the array is in a free state, c′ T The value is zero. Through spatial and temporal variations, the Paidoussis equation for the slender cable becomes:

[0041]

[0042] Typically, the length of the tow cable is much greater than its diameter (L >> d), so we can assume ε -1 ≈0, the above equation can be simplified to the Small-Diameter Paidoussis equation:

[0043]

[0044] If the acceleration of the array in the drag direction is very small, then the Paidoussis equation for small diameters... This can be ignored; after simplification, the equations can be obtained as the hydrodynamic model equations:

[0045]

[0046] make

[0047] The array distortion model is obtained:

[0048]

[0049] It should be noted that the above formula ignores the change in velocity over a short period of time and approximates the disturbance applied to the drag point as propagating along the array at a velocity of ρU.

[0050] The processor discretizes the above equation and uses a Kalman filter to generate the array expression for the flexible cable:

[0051] η(t+1)=Fη(t)+b(t)+w(t)

[0052] F = (1-μ)I + μL,

[0053] η(t) represents a linear approximation of the actual array configuration, where t = 1, 2, ..., T represents time intervals, b(t) represents the disturbance applied to the towing point, and w(t) represents Gaussian white noise with a mean of 0 and a variance of Q. μ is a given parameter. When a value of ΔT is selected such that ρ = 1, then F = αL, where α represents the damping factor, which varies along the cable length.

[0054] After the processor sets the array distortion to an interval of d between adjacent array elements (with the tow cable approximately maintaining a straight line within the interval between adjacent array elements), the absolute coordinates of the nth array element can be calculated:

[0055]

[0056] in, η represents the coordinates of the first element. t (l) represents the heading value of the l-th array element. t =[r t 1 ,…,r t N It contains the coordinate information of all array elements.

[0057] S20. Based on the sound pressure expression and absolute coordinates of the array elements in the towed array, determine the time-domain solution of the received signal of each array element.

[0058] In one embodiment of this application, step S20 may include the following execution process:

[0059] S201. Calculate the sound pressure expression of the sound source at the position of the array element in the towed array;

[0060] Specifically, assuming the seawater medium is horizontally stratified and the environmental parameters are independent of distance, the depth of the array elements is fixed at z. r Assume it is moving at a constant velocity v in the horizontal direction. r At time t0, the distance between the sound source and the array is r0. The angles between the velocity vectors of the sound source and the array elements and the lines connecting their positions in the horizontal plane are θ. s and θ r According to the uniform linear motion, the distance at time t is r. t =r0+v r If t is the sound pressure level of the sound source at the position of the array element in the towed array at time t, then the expression for the sound pressure level is:

[0061]

[0062] In the above formula, G is the frequency ω+k. r ·v s The Green's function for deep separation, S(Ω) k ) is the power spectrum of the sound source, Ω k The sound source frequency Ω after Doppler correction k =ω-k r ·(v s cosθ s -v r cosθ r ).

[0063] S202. Determine the time-domain solution of the received signal of the array element based on the sound pressure expression;

[0064] In one embodiment of this application, step S202 may include the following execution process:

[0065] S2021. Under far-field conditions, a new sound pressure expression is obtained by replacing the two-dimensional Fourier transform in the sound pressure expression with the Hankel transform of the horizontal wavenumber.

[0066] S2022. Using the Green's function of the discrete spectrum of normal modes to simplify the new sound pressure expression, the time-domain solution of the received signal of the towed array element is obtained.

[0067] S203. Based on the absolute coordinates of each array element, determine the time-domain solution of the received signal of other array elements in the towed array.

[0068] In the far-field condition, the processor replaces the two-dimensional Fourier transform in the sound pressure expression with the Hankel transform of the horizontal wavenumber, and simplifies the above equation according to the Green's function of the discrete spectrum of the normal mode wave to obtain the time-domain solution of the signal received by the towed array element:

[0069]

[0070] In the formula, Ψ(z) s ) and Ψ(z r ) is the depth mode function corresponding to the sound source and the array. v mg It is the group velocity of the m-th mode.

[0071] When the towed array undergoes array distortion, assuming the array shape at time t is obtained from the hydrodynamic model as follows: Figure 2 As shown. Where (x n,t ,y n,t Let (x') be the position coordinates of the nth element of the towed array without any array distortion. n,t ,y′ n,t Let be the position coordinates of the nth array element during array distortion. Based on the absolute coordinates of each array element calculated previously, the time-domain solution of the received signal after array distortion can be obtained as follows:

[0072]

[0073] S30. Based on the ETAM algorithm, the time-domain solutions of the received signals at adjacent time moments are sampled to obtain the beam output of the overlapping subarray in the samples at adjacent time moments, and the beam output is subjected to RL iteration to obtain the phase compensation factor.

[0074] Specifically, the time-domain solutions of the received signals at adjacent time points are sampled based on the ETAM algorithm to obtain the beam output of the overlapping subarray in the samples at adjacent time points, including:

[0075] Based on the time-domain solution of the received signal of the (n+q)th array element at time t, the (m-1)th sampling result is obtained; and based on the time-domain solution of the received signal of the nth array element at time t+τ, the mth sampling result is obtained.

[0076] Based on the m-1th sampling result, frequency domain beamforming is performed to obtain the first beam output of the overlapping subarray;

[0077] Frequency domain beamforming is performed based on the m-th sampling result to obtain the second beam output of the overlapping subarray. The beam output of the overlapping subarray in adjacent time-time samples is then determined based on the first and second beam outputs.

[0078] In this embodiment, the processor's signal acquisition process is the same as the classic ETAM algorithm. First, the processor obtains the received signal of the (n+q)th array element at time t and the received signal of the nth array element at time t+τ, where τ is the time interval between adjacent samples. Then, the (m-1)th sampling result is:

[0079]

[0080] The result of the m-th sampling is:

[0081]

[0082] Assuming these two samplings are the (m-1)th and m-th samplings, the expression for the beam output of the overlapping subarray of the (m-1)th and m-th samples, that is, the first beam output of the overlapping subarray in samples at adjacent time points, is:

[0083]

[0084] The expression for the second beam output in the beam output of the overlapping subarray in adjacent time-series samples is:

[0085]

[0086] In one embodiment of this application, the step of performing RL iteration on the beam output to obtain the phase compensation factor includes:

[0087] The first separation signal is obtained by deconvolving the sampled m-1th sample.

[0088] The second separation signal is obtained by deconvolving the m-th sample.

[0089] Calculate the first point scattering function and the second point scattering function corresponding to the first separation signal and the second separation signal, respectively;

[0090] A first iterative expression is constructed based on the first separation signal and the first point scattering function. The first iterative expression is iterated according to the preset number of RL deconvolution steps to obtain the first phase factor.

[0091] A second iterative expression is constructed based on the second separation signal and the second point scattering function. The second iterative expression is iterated according to the preset number of RL deconvolutions to obtain the second phase factor.

[0092] The first phase factor and the second phase factor are processed based on a preset formula to obtain the phase compensation factor.

[0093] In actual execution, the processor calculates the first point scattering function h of the deconvolution of the m-th and (m-1)-th segments of the sample according to the following formula. m (θs ) and second point scattering to construct h m-1 (θ s ).

[0094] The preset number of deconvolution iterations is I. RL deconvolution is performed on the frequency domain beam outputs of the (m-1)th and m-th overlapping subarrays, respectively. The iterative formula for the deconvolution beam outputs of the (m-1)th and m-th overlapping subarrays is, in other words, the first iteration expression:

[0095]

[0096] Second iteration expression:

[0097]

[0098] The final iteration results are denoted as the first phase factor Π. m (θ s ) I Second phase factor Π m-1 (θ s ) I The processor calculates the phase compensation factor according to the following formula:

[0099]

[0100] S40. Perform phase compensation on the beam output based on the phase compensation factor to obtain each phase-corrected beam. Based on each phase-corrected beam after coherent summation, obtain the beam output of the synthetic aperture.

[0101] The step of performing phase compensation on the beam output based on the phase compensation factor to obtain each phase-corrected beam may include:

[0102] By using a phase compensation factor to shift the phase of the second beam output, the phase-corrected beam of the m-th sample is obtained;

[0103] Calculate the phase compensation factor for all beam outputs, and phase-shift the corresponding beam outputs according to the phase compensation factor to obtain each phase-corrected beam.

[0104] In this embodiment of the application, the processor performs phase compensation on the continuously sampled beam output using a phase compensation factor:

[0105]

[0106] Where b m (f0,θ s ) represents the beam output result of the m-th sampled data. This represents the frequency domain output of the nth array element, where N is the total number of array elements, f0 represents the frequency, c represents the underwater sound speed, d represents the element spacing, and θ represents the frequency. s This indicates the scanning angle of beamforming.

[0107] The expression for the phase-corrected beam of the m-th sampled data after phase compensation is as follows:

[0108]

[0109] Where b′ m (f0,θ s The expression represents the result after phase compensation of the output of the m-th beam segment. This represents the phase compensation term corresponding to the p-th segment, used to correct phase differences between multiple segments (m segments in total) of data caused by time or motion.

[0110] Finally, the processor coherently sums the phase-corrected beams to obtain the beam output of the virtual array, which is the beam output of the synthetic aperture. The expression for the beam output of the synthetic aperture is:

[0111]

[0112] The actual effect of this application can be illustrated by the following simulation:

[0113] 1. Simulation conditions:

[0114] Assume a towed linear array consists of 12 elements with a spacing of 1m, moving away from a sound source at a relative speed of 3m / s, with a sampling frequency of 1kHz and a sampling time of 1s for each sample. Apply the following to the towed point: Figure 3 The disturbances shown correspond to changes in the formation as follows: Figure 4 As shown.

[0115] 2. Simulation content and results:

[0116] Simulation 1: Assuming the signal is incident from direction θ = 0°, the source frequency is 200Hz, and the signal-to-noise ratio of the received signal in a single array element is set to 10dB. The number of consecutive samplings is 10 and 20 (i.e., the number of synthetic apertures is 9 and 19 respectively). The simulation results of the CBF algorithm, FFTSA algorithm, and the proposed method are as follows: Figure 5 As shown in (a) and 5(b).

[0117] Simulation 2: Assume two uncorrelated signals of equal power are incident on the array from directions [θ1, θ2] = [0°, 20°]. The number of consecutive samplings is 10 and 20 (i.e., the number of synthetic apertures is 9 and 19 respectively). The simulation results of the CBF algorithm, FFTSA algorithm, and the proposed method are as follows: Figure 6As shown in (a) and 6(b).

[0118] Figure 5 and Figure 6 Experimental results show that the proposed algorithm has approximately the same beamwidth as the FFTSA algorithm, but the proposed algorithm has lower sidelobes. As the synthetic aperture number increases, the main lobe width of the proposed algorithm narrows and the sidelobes decrease, demonstrating better azimuth estimation accuracy.

[0119] Simulation 3: The source conditions are the same as in Simulation 1, but the signal-to-noise ratio is set to -10dB. The distance of the synthetic aperture is increased from 18m to 100m. The root mean square error of azimuth estimation as a function of the synthetic aperture distance is shown below. Figure 7 As shown.

[0120] Figure 7 Simulation results show that the ETAM algorithm has a positioning error of approximately 4° at a synthetic aperture distance of 18m. However, the performance of the ETAM algorithm drops sharply as the synthetic aperture distance increases, indicating poor synthetic aperture performance under array distortion. In contrast, the root mean square error (RMSE) of both the FFTSA algorithm and the proposed algorithm gradually decreases with increasing synthetic aperture distance, and approaches 0° as the aperture expands. Among these two algorithms, the RMS error curve of the proposed algorithm is consistently lower than that of the FFTSA algorithm, indicating that the D-ETAM algorithm performs better at the same synthetic aperture distance.

[0121] Simulation 4: The source conditions are the same as in Simulation 1, but the number of synthesized apertures is 4 and 9 respectively. The signal-to-noise ratio (SNR) increases from -20dB to 20dB. The root mean square error of azimuth estimation as a function of SNR is shown below. Figure 8 As shown.

[0122] Figure 8 Simulation results show that the root mean square error (RMSE) of CBF gradually decreases with increasing signal-to-noise ratio (SNR), approaching zero after 0 dB. The RMSE of several passive synthetic aperture algorithms does not change with SNR. ETAM RMSE FFTSA RMSE D-ETAM The root mean square error (RMSE) of the ETAM algorithm remained around 10.1° and 13.6° at 5 and 10 sampling times, respectively, further verifying the failure of the ETAM algorithm under distortion conditions. At sufficient synthetic aperture distances, the proposed algorithm outperforms the CBF algorithm at low signal-to-noise ratios, and the performance gap between the proposed algorithm and CBF gradually decreases at high signal-to-noise ratios as the synthetic aperture distance increases.

[0123] In another embodiment provided in this application, a passive synthetic aperture device based on RL deconvolution beam domain processing is also provided. The device may include: an array modeling module for constructing an array distortion model of the towed array under disturbance based on the Padoussis equation of the flexible cable, and using a Kalman filter to process the discretized array distortion model to obtain the absolute coordinates of each array element in the towed array; a received signal determination module for determining the received signal time-domain solution of each array element based on the sound pressure expression and absolute coordinates of the array elements in the towed array; a phase compensation module for sampling the time-domain solution of the received signal at adjacent time moments based on the ETAM algorithm to obtain the beam output of the overlapping subarray in the samples at adjacent time moments, and performing RL iteration on the beam output to obtain the phase compensation factor; and a synthesis module for performing phase compensation on the beam output based on the phase compensation factor to obtain each phase-corrected beam, and obtaining the beam output of the synthetic aperture based on the coherently summed phase-corrected beams.

[0124] In another embodiment provided in this application, an apparatus is also provided, the apparatus including a processor and a memory, the memory storing at least one instruction, at least one program, code set or instruction set, the at least one instruction, the at least one program, the code set or instruction set being loaded and executed by the processor to implement the passive synthetic aperture method based on RL deconvolution beam domain processing described in the embodiments of this application.

[0125] In another embodiment provided in this application, a computer-readable storage medium is also provided, wherein at least one instruction, at least one program, code set or instruction set is stored in the storage medium, wherein the at least one instruction, the at least one program, the code set or instruction set is loaded and executed by a processor to implement the passive synthetic aperture method based on RL deconvolution beam domain processing described in the embodiments of this application.

[0126] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes multiple computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates multiple available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0127] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0128] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0129] The above description is merely a preferred embodiment of this application and is not intended to limit the scope of protection of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application are included within the scope of protection of this application.

Claims

1. A passive synthetic aperture method based on RL deconvolution beam domain processing, characterized in that, include: The Padoussis equation based on flexible cable is used to construct the array distortion model of the towed array under disturbance. The Kalman filter is used to process the discretized array distortion model to obtain the absolute coordinates of each array element in the towed array. Based on the sound pressure expression and absolute coordinates of the array elements in the towed array, the time-domain solution of the received signal of each array element is determined. Based on the ETAM algorithm, the time-domain solution of the received signal at adjacent time moments is sampled to obtain the beam output of the overlapping subarray in the samples at adjacent time moments, and the beam output is subjected to RL iteration to obtain the phase compensation factor. Phase compensation is performed on the continuously sampled beam output based on the phase compensation factor to obtain each phase-corrected beam. Coherent summation is then performed on the corrected beam output results to obtain the beam output of the synthetic aperture.

2. The passive synthetic aperture method based on RL deconvolution beam domain processing as described in claim 1, characterized in that, The Paddosis equation based on flexible cables is used to construct a model of the array distortion of the towed array under perturbation, including: A simplified expression of the Padoussis equation in an ideal fluid based on a flexible cable under preset conditions; The Paidoussis equation for the small diameter flexible cable is determined based on a simplified expression. By discarding the higher-order components of the small-diameter Paidoussis equation, a hydrodynamic model for the flexible cable is obtained. By rewriting the parameters in the hydrodynamic model using a pre-defined perturbation expression, a morphological distortion model is obtained.

3. The passive synthetic aperture method based on RL deconvolution beam domain processing as described in claim 1, characterized in that, The determination of the received signal frequency domain solution for each array element based on the sound pressure expression and absolute coordinates of the array elements in the towed array includes: Calculate the sound pressure expression for the position of the sound source at the base element position in the towed array; The time-domain solution of the received signal of the array element is determined based on the sound pressure expression; Based on the absolute coordinates of each array element, determine the time-domain solution of the received signal of other array elements in the towed array.

4. The passive synthetic aperture method based on RL deconvolution beam domain processing as described in claim 3, characterized in that, The time-domain solution of the received signal based on sound pressure to determine the array elements includes: Under far-field conditions, a new sound pressure expression is obtained by replacing the two-dimensional Fourier transform in the sound pressure expression with the Hankel transform of the horizontal wavenumber. By simplifying the new sound pressure expression using the Green's function of the discrete spectrum of normal modes, the time-domain solution of the received signal of the towed array element is obtained.

5. The passive synthetic aperture method based on RL deconvolution beam domain processing as described in claim 1, characterized in that, The method of sampling the time-domain solution of the received signals at adjacent time points based on the ETAM algorithm to obtain the beam output of the overlapping subarray in the samples at adjacent time points includes: Based on the time-domain solution of the received signal of the (n+q)th array element at time t, the (m-1)th sampling result is obtained; and based on the time-domain solution of the received signal of the nth array element at time t+τ, the mth sampling result is obtained. Based on the m-1th sampling result, frequency domain beamforming is performed to obtain the first beam output of the overlapping subarray; Frequency domain beamforming is performed based on the m-th sampling result to obtain the second beam output of the overlapping subarray, and the beam output of the overlapping subarray in adjacent time samples is determined based on the first beam output and the second beam output.

6. The passive synthetic aperture method based on RL deconvolution beam domain processing as described in claim 1, characterized in that, The beam output is then subjected to RL iteration to obtain the phase compensation factor, including: The first separation signal is obtained by deconvolving the sampled m-1th sample. The second separation signal is obtained by deconvolving the m-th sample. Calculate the first point scattering function and the second point scattering function corresponding to the first separation signal and the second separation signal, respectively; A first iterative expression is constructed based on the first separation signal and the first point scattering function. The first iterative expression is iterated according to the preset number of RL deconvolution steps to obtain the first phase factor. A second iterative expression is constructed based on the second separation signal and the second point scattering function. The second iterative expression is iterated according to the preset number of RL deconvolutions to obtain the second phase factor. The first phase factor and the second phase factor are processed based on a preset formula to obtain the phase compensation factor.

7. The passive synthetic aperture method based on RL deconvolution beam domain processing as described in claim 1, characterized in that, The step of performing phase compensation on the beam output based on the phase compensation factor to obtain each phase-corrected beam includes: By using a phase compensation factor to phase-shift the output of the second beam, a phase-corrected beam for the m-th sample is obtained. Calculate the phase compensation factor for all beam outputs, and phase-shift the corresponding beam outputs according to the phase compensation factor to obtain each phase-corrected beam.

8. A passive synthetic aperture device based on RL deconvolution beam domain processing, characterized in that, include: The array modeling module is used to construct the array distortion model of the towed array under disturbance based on the Padousse equation of the flexible cable. The Kalman filter is used to process the discretized array distortion model to obtain the absolute coordinates of each array element in the towed array. The received signal determination module is used to determine the time-domain solution of the received signal of each array element based on the sound pressure expression and absolute coordinates of the array elements in the towed array. The phase compensation module is used to sample the time-domain solution of the received signal at adjacent time points based on the ETAM algorithm, obtain the beam output of the overlapping subarray in the samples at adjacent time points, and perform RL iteration on the beam output to obtain the phase compensation factor. The synthesis module is used to perform phase compensation on the beam output based on the phase compensation factor to obtain each phase-corrected beam, and to obtain the beam output of the synthesized aperture based on each phase-corrected beam after coherent summation.

9. An electronic device, characterized in that, The electronic device includes a processor and a memory, wherein the memory stores at least one instruction, at least one program, code set, or instruction set, and the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by the processor to implement the passive synthetic aperture method based on RL deconvolution beam domain processing as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The storage medium stores at least one instruction, at least one program, code set, or instruction set, wherein the at least one instruction, the at least one program, the code set, or instruction set is loaded and executed by a processor to implement the passive synthetic aperture method based on RL deconvolution beam domain processing as described in any one of claims 1-7.

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