A method for correcting underwater acoustic spectrum based on Doppler compensation and deformable convolution
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HARBIN ENG UNIV
- Filing Date
- 2026-05-14
- Publication Date
- 2026-08-04
AI Technical Summary
[0006]为了解决现有水声信号处理方法在面对机动目标与浅海多径效应耦合时，无法有效修复水声线谱的展宽、畸变以及断裂现象的问题，本发明提供一种基于多普勒补偿与可变形卷积的水声线谱修正方法
[0029] (1) This invention effectively solves the problem of insufficient compensation caused by ignoring multipath effects in traditional Doppler compensation, and makes up for the deficiency of poor generalization due to lack of physical constraints in pure deep learning models.
Smart Images
Figure CN122511267A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of signal processing technology, and specifically to a method for underwater acoustic line spectrum correction based on Doppler compensation and deformable convolution. Background Technology
[0002] In underwater passive detection, the radiated noise line spectrum of a target is a key feature for target identification and parameter estimation. However, in complex shallow marine environments, extremely low signal-to-noise ratios often lead to dispersion or even masking of the radiated noise line spectrum. In recent years, deep learning has become an important approach to solving the problem of underwater acoustic line spectrum enhancement in complex shallow marine environments. Yu Xueyang et al. (Yu Xueyang, Chi Cheng, Li Shuqiu, et al. Joint line spectrum enhancement and deep neural network for underwater acoustic target recognition [J]. Acta Acustica, 2024, 49(04): 656-663.) verified from both theoretical and experimental perspectives the important role of underwater acoustic line spectrum enhancement in improving the target recognition rate of deep neural networks under low signal-to-noise ratio conditions. Meanwhile, F. Wang-xuan et al. (F. Wang-xuan, L. Qi-yu, H. Juan, S. Hao-tong and C. Miao, "Line Enhancement Algorithm Based on Unsupervised Deep Learning in Underwater Unmanned Vehicle," 2024 OES ChinaOcean Acoustics (COA), Harbin, China, 2024, pp. 1-6, doi: 10.1109 / COA58979.2024.10723599.) also demonstrated that data-driven networks have certain advantages over traditional physical adaptive line spectrum enhancers in underwater acoustic line spectrum enhancement with low signal-to-noise ratio. Despite significant progress in deep neural networks, Y. Pak et al. (Y. Pak, Y. Shin, Y. Guk Kim and C. Chun, "Adversarial Representation Learning for Underwater Acoustic Noise Suppression in LOFARgram Space," in IEEE Access, vol. 14, pp. 15869-15882, 2026, doi: 10.1109 / ACCESS.2026.3658888.) pointed out that in the process of processing LOFAR time-frequency spectra, how to completely preserve the key structural and geometric features of the underwater acoustic line spectrum while reducing noise remains a major challenge.
[0003] One of the main reasons for the degradation of underwater acoustic line spectrum structure features is the coupling effect between target maneuvering and underwater acoustic physical propagation mechanism. In actual shallow sea waveguide environments, target maneuvering will produce Doppler frequency shift. Han, Y, et al. (Han, Y., Han, S., Zhao, H., Hu, Y., Xu, J., & Yang, G. (2024). Dopplercompensation techniques for M-ary sequence spread spectrum signals based on correlation cost factors in mobile underwater acoustic communication. Journal of Marine Science and Engineering, 12(12), 2151. doi:https: / / doi.org / 10.3390 / jmse12122151.) pointed out that the Doppler distortion caused by the time-varying marine environment and target maneuvering will destroy the energy concentration of the signal. Therefore, it is necessary to perform macroscopic frequency offset correction before feature extraction. In addition, the sound waves form a complex multipath propagation structure after multiple reflections from the sea surface and seabed. Traditional Doppler compensation methods typically resample based on a single radial velocity assumption, which often fails to adequately account for the varying time delays and phase distortions introduced by differences in acoustic path lengths along different propagation paths. This results in the compensated underwater acoustic line spectrum still potentially retaining a certain degree of energy dissipation and sidelobe interference in the time-frequency plane.
[0004] On the other hand, while existing deep learning-based image inpainting methods possess strong nonlinear fitting capabilities, most focus on end-to-end data-driven models and rarely incorporate the physical mechanisms of underwater acoustic propagation as prior constraints into the network structure. When faced with non-rigid bending and fracturing of underwater acoustic line spectra on the time-frequency plane due to the time-varying velocity of the target, conventional regular convolutional kernels have limitations in extracting such dynamic deformation features. For non-rigid deformation problems, deformable convolutional network (DCN) technology in computer vision provides a new approach to processing time-frequency spectra. S. Li et al. ("A Novel Method of Bearing Fault Diagnosis in Time-Frequency Graphs Using InceptionResnet and Deformable Convolution Networks," in IEEE Access, vol. 8, pp. 92743-92753, 2020, doi: 10.1109 / ACCESS.2020.2995198.) demonstrated that introducing deformable convolution can dynamically adapt to non-rigid geometric distortions in time-frequency graphs. Y. Zhang et al. (Y. Zhang, H. Yu and Z. Ma, "Speaker Verification System Based on Deformable CNN and Time-FrequencyAttention," 2020 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC), Auckland, New Zealand, 2020, pp.1689-1692.) further demonstrated that by learning the two-dimensional offset field on the time-frequency spectrum, the sampling points of the convolution kernel can be adaptively adjusted, thereby better focusing on the curvature and abrupt changes of acoustic features.
[0005] Therefore, how to effectively integrate the underwater acoustic physics propagation mechanism with a deep learning network that has deformation adaptability to overcome multipath interference in complex shallow marine environments and restore underwater acoustic line spectrum distortion with high fidelity is a technical problem that urgently needs to be solved in this field. Summary of the Invention
[0006] To address the problem that existing underwater acoustic signal processing methods cannot effectively repair the broadening, distortion, and breakage of underwater acoustic line spectra when faced with the coupling of maneuvering targets and shallow sea multipath effects, this invention provides an underwater acoustic line spectrum correction method based on Doppler compensation and deformable convolution.
[0007] This invention provides an underwater acoustic line spectrum correction method based on Doppler compensation and deformable convolution. It is a correction network and line spectrum morphology restoration method combining Doppler and deformable convolution for maneuvering underwater targets. By designing a hierarchical line spectrum restoration architecture that integrates tandemly driven physical compensation and data-driven geometric correction, this invention effectively suppresses channel multipath interference and improves the continuity and focus of the underwater acoustic line spectrum.
[0008] The technical solution adopted by this invention to solve the technical problem is as follows:
[0009] This invention provides a method for correcting underwater acoustic line spectra based on Doppler compensation and deformable convolution, comprising the following steps:
[0010] Step 1: Acquisition, preprocessing, and time-frequency representation of the raw underwater acoustic time-domain signal;
[0011] Step 2: Calculate the multipath phase compensation function using the Bellhop sound field calculation model;
[0012] Step 3: Construct a multipath sensing Doppler scaling transform kernel function, perform an integral transform on the underwater acoustic time-domain signal, and obtain a preliminary time-frequency spectrum for suppressing multipath energy dispersion;
[0013] Step 4: Construct a geometrically perceptive deformable convolutional network. Input the time-frequency spectrum, which has been initially suppressed for multipath energy dispersion, into the geometrically perceptive deformable convolutional network, extract the displacement parameters of each pixel in the time-frequency spectrum in the frequency axis and time axis directions, and generate a two-dimensional offset field.
[0014] Step 5: Use the two-dimensional offset field as the driving force for redefining the sampling position of the multi-scale deformable convolutional module. Perform irregular displacement sampling on multiple deformable convolutional branches with different dilation rates. Output the final repaired continuous focused line spectrum through the channel splicing and feature fusion network.
[0015] Furthermore, in step one, a hydrophone is used to collect the original underwater acoustic time-domain signal.
[0016] Furthermore, in step one, the acquired raw underwater acoustic time-domain signal is bandpass filtered, and automatic gain control is performed to balance the signal amplitude.
[0017] Furthermore, in step one, the preprocessed original underwater acoustic time-domain signal is converted into an initial time-frequency analysis spectrum through short-time Fourier transform or continuous wavelet transform.
[0018] Furthermore, in step two, the sound velocity profile information, the target's rough motion state parameters, and the receiver's geometric configuration information are input into the Bellhop sound field calculation model. The Bellhop sound field calculation model is used to simulate the sound propagation path in the layered medium, extract the direct path delay and multipath path delay, extract the delay difference between the multipath path and the direct path by solving the sound wave equation, and calculate the multipath phase compensation function.
[0019] Furthermore, the specific calculation formula for the multipath phase compensation function is as follows:
[0020] ;
[0021] in, This is a multipath phase compensation function. The center frequency of the signal. For direct path delay, This represents the multipath delay.
[0022] Furthermore, the multipath sensing Doppler scale transformation kernel function integrates the scale factor, Doppler frequency shift, and multipath phase compensation term corresponding to the target radial velocity.
[0023] Furthermore, the mathematical expression for the integral transform is as follows:
[0024] ;
[0025] in, For time delay, As a scale factor, Here is the multipath phase compensation function, and x(t) is the input signal. For the mother wavelet function, superscript Indicates complex conjugation. This is the Doppler frequency shift.
[0026] Furthermore, the geometry-aware deformable convolutional network includes an offset regression module and a multi-scale deformable convolutional module; the offset regression module is implemented by a lightweight convolutional sub-network, and the multi-scale deformable convolutional module consists of three parallel deformable convolutional branches and fused convolutional layers; the lightweight convolutional sub-network adopts a three-layer cascaded architecture: the first two layers are configured as follows: Convolution; the final output layer uses no activation function. Convolution and regression generate a number of channels. The two-dimensional offset field feature map; the dilation rates of the three parallel deformable convolution branches are 1, 3, and 5, respectively: the deformable convolution branch with a dilation rate of 1, combined with the offset field, focuses and aggregates the fine spikes and local dispersions of the underwater acoustic line spectrum; the deformable convolution branch with a dilation rate of 3, combined with the offset field, tracks and fits the curved trajectory of the underwater acoustic line spectrum caused by the medium-scale Doppler nonlinear deformation; the deformable convolution branch with a dilation rate of 5, combined with the offset field, spans a large time rate interval and reconnects the broken parts of the underwater acoustic line spectrum caused by the large fading of the channel.
[0027] Furthermore, step six is included: constructing a training set based on simulation and measured data, and using a composite loss function that includes mean square error and structural similarity to perform end-to-end backpropagation training on the geometrically aware deformable convolutional network.
[0028] Compared with the prior art, the beneficial effects of the present invention are:
[0029] (1) This invention effectively solves the problem of insufficient compensation caused by ignoring multipath effects in traditional Doppler compensation, and makes up for the deficiency of poor generalization due to lack of physical constraints in pure deep learning models.
[0030] (2) This invention achieves joint correction of motion frequency shift and multipath phase mismatch by introducing a multipath phase compensation term driven in real time by the Bellhop sound field calculation model in the scale transformation, thereby converging the line spectrum energy divergence from a physical level.
[0031] (3) The geometrically perceptive deformable convolutional network (GA-DCN) constructed in this invention learns the spatial distribution of residual distortion, dynamically adjusts the position of the receptive field, focuses on details with a small dilation rate, and breaks the connection with a large dilation rate, which can accurately correct any nonlinear distortion geometrically.
[0032] (4) The line spectrum processed by the method proposed in this invention has high sharpness and continuity, which can serve the subsequent target identification of edge computing modules such as shore-based processing systems and autonomous underwater vehicles. Attached Figure Description
[0033] Figure 1 A general flowchart of an underwater acoustic line spectrum correction method based on Doppler compensation and deformable convolution provided by the present invention is given.
[0034] Figure 2 A schematic diagram of the architecture of the Geometry-Aware Deformable Convolutional Network (GA-DCN) is presented.
[0035] Figure 3Performance metrics curves for the network training process in this embodiment of the invention are provided. In the figure, A is the Joint Loss curve; B is the Peak Signal-to-Noise Ratio (PSNR) curve; and C is the Structural Similarity (SSIM) curve.
[0036] Figure 4 A time-frequency comparison diagram of the underwater acoustic line spectrum restoration effect according to an embodiment of the present invention is provided. In the diagram, A represents stage one: the physical-driven joint compensation output; B represents stage two: the data-driven geometric correction output; and C represents the basic target. Detailed Implementation
[0037] The present invention will be further described in detail below with reference to the accompanying drawings.
[0038] like Figure 1 As shown, the present invention provides a method for underwater acoustic line spectrum correction based on Doppler compensation and deformable convolution, which mainly includes a physics-driven joint compensation stage and a data-driven geometric correction stage. Its specific implementation process is as follows:
[0039] Step 1: Signal acquisition, preprocessing, and time-frequency representation;
[0040] The raw underwater acoustic time-domain signal acquired by the hydrophone is preprocessed by filtering and gain control, and then an initial time-frequency analysis spectrum is generated using short-time Fourier transform or continuous wavelet transform; the specific implementation process is as follows:
[0041] Step S101: First, the original underwater acoustic time-domain signal under the real physical ocean environment is acquired by the hydrophone. ;
[0042] Step S102: Then, bandpass filtering is performed to remove out-of-band noise, and automatic gain control is performed to balance the signal amplitude;
[0043] Step S103: Finally, convert it into an initial time-frequency analysis spectrum through short-time Fourier transform or continuous wavelet transform to provide a time-frequency reference for subsequent physical compensation.
[0044] Step 2: Calculate the multipath phase compensation function using the Bellhop sound field calculation model;
[0045] The sound velocity profile information, the target's rough motion state parameters, and the receiver's geometric configuration information are input into the Bellhop sound field calculation model to calculate the multipath phase compensation function; the specific implementation process is as follows:
[0046] Step S201: Obtain the rough motion state parameters of the target;
[0047] Preliminary coarse motion state parameters of the target can be obtained by using navigation systems, multi-source sensor-assisted detection, or traditional Doppler estimation methods.
[0048] Step S202: Calculate the multipath phase compensation function;
[0049] The sound velocity profile information, the target's approximate motion state parameters, and the receiver's geometric configuration information are input into the Bellhop sound field calculation model. The Bellhop sound field calculation model is then used to simulate the sound propagation path in the layered medium. Based on the input water depth parameters, bottom sediment parameters, and target approximate motion state parameters, the direct path delay is extracted. and multipath delay The time delay difference between the multipath path and the direct path is extracted by solving the acoustic wave equation, and the multipath phase compensation function is calculated. The specific calculation formula is as follows:
[0050] ;
[0051] in, This is a multipath phase compensation function. The multipath phase compensation function is the signal center frequency. Used to quantitatively characterize time delay and phase distortion caused by the channel.
[0052] Step 3: Construct a multipath sensing Doppler scaling transform kernel function, perform an integral transform on the underwater acoustic time-domain signal, and obtain a preliminary time-frequency spectrum for suppressing multipath energy dispersion;
[0053] Construct a multipath sensing Doppler scaling transform kernel function that integrates the scale factor corresponding to the target radial velocity, Doppler frequency shift, and multipath phase compensation term, and perform the following integral transform:
[0054] ;
[0055] in, For time delay, As a scale factor, Here is the multipath phase compensation function, and x(t) is the input signal. For the mother wavelet function, superscript Indicates complex conjugation. For Doppler frequency shift. Multipath phase compensation function. This primarily characterizes the time delay difference between different propagation paths. Solving through this physical process outputs a two-dimensional time-frequency feature map that has undergone preliminary phase correction and energy convergence. This third step aims to reduce the learning burden on deep learning networks by utilizing physical priors, transforming non-rigid deformations into residual distortions that the network can handle.
[0056] Step 4: Generate a two-dimensional offset field;
[0057] Step S401: Construct a geometry-aware deformable convolutional network (GA-DCN).
[0058] like Figure 2 As shown, the geometry-aware deformable convolutional network (GA-DCN) constructed in this invention mainly consists of an offset regression module and a multi-scale deformable convolutional module. The offset regression module is mainly implemented by a lightweight convolutional sub-network, and the multi-scale deformable convolutional module mainly consists of three parallel deformable convolutional branches and a fused convolutional layer.
[0059] The time-frequency spectrum obtained in step 3, which initially suppresses multipath energy dispersion, is input into the offset regression module of the geometrically aware deformable convolutional network (GA-DCN). The displacement parameters of each pixel in the time-frequency spectrum in the frequency axis and time axis are extracted using a lightweight convolutional sub-network to generate a two-dimensional offset field.
[0060] Specifically, the lightweight convolutional subnetwork adopts a three-layer cascaded architecture: the first two layers are configured as follows: Convolution (64 channels, Leaky ReLU activation); the final output layer uses no activation function. Convolution and regression generate a number of channels. ( This is a two-dimensional offset field feature map (where the number of sampling points is 1). This offset field feature map accurately characterizes the underwater acoustic line spectrum pixels along the frequency axis. and timeline The amount of geometric distortion.
[0061] Step 5: Perform deformable convolution to output the final repaired line spectrum.
[0062] The two-dimensional offset field obtained in step four is used as the driving force for redefining the sampling position of the multi-scale deformable convolutional module. Irregular displacement sampling is performed on multiple deformable convolutional branches with different dilation rates. Then, the final repaired continuous focused line spectrum is output through a channel splicing and feature fusion network.
[0063] Specifically, this invention utilizes the two-dimensional offset field obtained in step four to drive a multi-scale deformable convolution module. The multi-scale deformable convolution module deploys three parallel deformable convolution branches with dilation rates d of 1, 3, and 5, respectively. The small dilation rate (d=1), combined with the offset field, aggregates and focuses on subtle spikes and local dispersions in the underwater acoustic spectrum; the medium dilation rate (d=3), combined with the offset field, tracks and fits the curved trajectory of the underwater acoustic spectrum caused by medium-scale Doppler nonlinear deformation; the large dilation rate (d=5), combined with the offset field, spans a large time rate interval, reconnecting the broken parts of the underwater acoustic spectrum caused by large channel fading. Finally, the feature maps output by the three parallel deformable convolution branches are concatenated along the channel dimension, and the fused features are then processed via 1... The standard convolutional layer (fusion convolutional layer) is integrated to output the final repaired continuous focused line spectrum.
[0064] Step 6: Construct a training set based on simulation and measured data, and use a composite loss function that includes mean square error and structural similarity to perform end-to-end backpropagation training on the entire Geometrically Aware Deformable Convolutional Network (GA-DCN);
[0065] This invention constructs a physics simulation-driven dataset and employs a composite loss function. Perform backpropagation to update the weights. (Composite loss function) Combining mean squared error and structural similarity, its mathematical expression is as follows:
[0066] ;
[0067] in, Mean square error, It is a structural similarity index. The weights are calculated by backpropagating the difference between the output line spectrum and the true undistorted line spectrum.
[0068] By executing the above steps in sequence, this invention effectively improves the extraction quality of underwater acoustic line spectra of moving targets in complex shallow marine environments, and has important value for military exploration and civilian marine research.
[0069] The effectiveness of the present invention will be verified below with reference to specific embodiments.
[0070] In this embodiment, the parameters are set as follows:
[0071] Set the center frequency of the transmitted signal for This generates a Doppler frequency-modulated signal with a linear frequency change, where the Doppler rate of change is... to The values are randomly selected from the given range and superimposed with random Gaussian noise to simulate a real hydrological background. A sparse channel impulse response is constructed by setting discrete multipath delays and attenuation coefficients. Finally, the transmitted signal is convolved with this channel impulse response to generate the original underwater acoustic time-domain signal with significant multipath fading and phase distortion. .
[0072] Model training uses a composite loss function Composite loss function It combines mean squared error and structural similarity, and uses the Adam optimizer for parameter updates, setting the initial learning rate to be... Momentum parameters , The model training process consisted of 30 epochs with a batch size of 4, and a learning rate warm-up strategy was introduced in the first 5 epochs. Peak signal-to-noise ratio (PSNR) and structural similarity were used as quantitative metrics for evaluation.
[0073] Combination Figure 3 The performance index curves of the network training process and the quantitative evaluation data in Table 1 show that the present invention exhibits excellent convergence performance throughout the entire training cycle. In the first 5 epochs of training, due to the introduction of the learning rate warm-up strategy, the composite loss function... The loss value rapidly decreased to 0.37911, exhibiting a significant downward trend. This phenomenon indicates that the Geometrically Aware Deformable Convolutional Network (GA-DCN) can quickly escape its initial random state and initially establish a feature mapping to the geometric distribution of the line spectrum. As the training process progresses, by the 30th epoch, the model's peak signal-to-noise ratio steadily increased from the initial 14.27 dB to 26.37 dB, while the structural similarity also rapidly increased from 0.1084 and stabilized at 0.9502. The high level of convergence of the above quantitative indicators mathematically verifies the accuracy of the Geometrically Aware Deformable Convolutional Network (GA-DCN) on the offset field regression task, demonstrating that this invention can achieve a high degree of fitting to the features of complex underwater acoustic signals with relatively low computational overhead.
[0074] Table 1. Quantitative Evaluation and Analysis of the Network with Iteration Number
[0075] [05 / 30] 0.37911 14.27 0.1084 [10 / 30] 0.09786 20.63 0.7684 [15 / 30] 0.03995 23.77 0.9065 [20 / 30] 0.03112 24.76 0.9272 [25 / 30] 0.02594 25.69 0.9393 [30 / 30] 0.02134 26.37 0.9502
[0076] Further integration Figure 4 Visual feature verification was performed using a time-frequency comparison of the underwater acoustic line spectrum restoration effect. In the output stage of joint compensation driven only by physical means, although the basic outline of the underwater acoustic line spectrum in the image was revealed, it still exhibited significant energy dispersion, geometric curvature, and local breaks caused by deep channel fading due to complex multipath effects. In contrast, in the output image after deep processing in the data-driven geometric correction output stage, background environmental noise was well suppressed, and the originally blurred and broken underwater acoustic line spectrum was reshaped into a smooth and continuous trajectory. The energy distribution showed a highly focused state, and the overall visual features were highly consistent with the pure line spectrum under ideal conditions. This comparison result confirms the effectiveness of multi-scale deformable convolutional branch collaborative processing. The deformable convolutional branch with an expansion rate of 1 effectively filtered out local spikes and dispersion, the deformable convolutional branch with an expansion rate of 3 accurately corrected the Doppler nonlinear bending trajectory, and the deformable convolutional branch with an expansion rate of 5 successfully crossed the time axis interval, completing the feature-level bridging of the broken underwater acoustic line spectrum.
[0077] Based on the above quantitative and qualitative analyses, this invention can effectively overcome multipath interference in shallow seas and robustly restore diffuse and distorted underwater acoustic line spectra to a continuously focused, high-fidelity form, demonstrating significant technological advancement and engineering practical value.
[0078] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for correcting underwater acoustic line spectra based on Doppler compensation and deformable convolution, characterized in that, Includes the following steps: Step 1: Acquisition, preprocessing, and time-frequency representation of the raw underwater acoustic time-domain signal; Step 2: Calculate the multipath phase compensation function using the Bellhop sound field calculation model; Step 3: Construct a multipath sensing Doppler scaling transform kernel function, perform an integral transform on the underwater acoustic time-domain signal, and obtain a preliminary time-frequency spectrum for suppressing multipath energy dispersion; Step 4: Construct a geometrically perceptive deformable convolutional network. Input the time-frequency spectrum, which has been initially suppressed for multipath energy dispersion, into the geometrically perceptive deformable convolutional network, extract the displacement parameters of each pixel in the time-frequency spectrum in the frequency axis and time axis directions, and generate a two-dimensional offset field. Step 5: Use the two-dimensional offset field as the driving force for redefining the sampling position of the multi-scale deformable convolutional module. Perform irregular displacement sampling on multiple deformable convolutional branches with different dilation rates. Output the final repaired continuous focused line spectrum through the channel splicing and feature fusion network.
2. The underwater acoustic line spectrum correction method based on Doppler compensation and deformable convolution according to claim 1, characterized in that, In step one, a hydrophone is used to collect the raw underwater acoustic time-domain signal.
3. The underwater acoustic line spectrum correction method based on Doppler compensation and deformable convolution according to claim 1, characterized in that, In step one, the acquired raw underwater acoustic time-domain signal is bandpass filtered, and automatic gain control is used to balance the signal amplitude.
4. The underwater acoustic line spectrum correction method based on Doppler compensation and deformable convolution according to claim 1, characterized in that, In step one, the preprocessed original underwater acoustic time-domain signal is converted into an initial time-frequency analysis spectrum by short-time Fourier transform or continuous wavelet transform.
5. The underwater acoustic line spectrum correction method based on Doppler compensation and deformable convolution according to claim 1, characterized in that, In step two, the sound velocity profile information, the target's rough motion state parameters, and the receiver's geometric configuration information are input into the Bellhop sound field calculation model. The Bellhop sound field calculation model is used to simulate the sound propagation path in the layered medium, extract the direct path delay and multipath path delay, extract the delay difference between the multipath path and the direct path by solving the sound wave equation, and calculate the multipath phase compensation function.
6. The underwater acoustic line spectrum correction method based on Doppler compensation and deformable convolution according to claim 1, characterized in that, The multipath phase compensation function is calculated using the following formula: ； in, This is a multipath phase compensation function. The center frequency of the signal. For direct path delay, This refers to the multipath delay.
7. The underwater acoustic line spectrum correction method based on Doppler compensation and deformable convolution according to claim 1, characterized in that, The multipath sensing Doppler scaling transformation kernel function integrates the scaling factor, Doppler frequency shift, and multipath phase compensation term corresponding to the target radial velocity.
8. The underwater acoustic line spectrum correction method based on Doppler compensation and deformable convolution according to claim 1, characterized in that, The mathematical expression for the integral transform is as follows: ； in, For time delay, As a scale factor, Here is the multipath phase compensation function, and x(t) is the input signal. For the mother wavelet function, superscript Indicates complex conjugation. This is due to the Doppler frequency shift.
9. The underwater acoustic line spectrum correction method based on Doppler compensation and deformable convolution according to claim 1, characterized in that, The geometry-aware deformable convolutional network includes an offset regression module and a multi-scale deformable convolutional module. The offset regression module is implemented by a lightweight convolutional sub-network, and the multi-scale deformable convolutional module consists of three parallel deformable convolutional branches and a fused convolutional layer. The lightweight convolutional sub-network adopts a three-layer cascaded architecture: the first two layers are configured as follows: Convolution; the final output layer uses no activation function. Convolution and regression generate a number of channels. The two-dimensional offset field feature map; the dilation rates of the three parallel deformable convolution branches are 1, 3, and 5, respectively: the deformable convolution branch with a dilation rate of 1, combined with the offset field, focuses and aggregates the fine spikes and local dispersions of the underwater acoustic line spectrum; the deformable convolution branch with a dilation rate of 3, combined with the offset field, tracks and fits the curved trajectory of the underwater acoustic line spectrum caused by the medium-scale Doppler nonlinear deformation; the deformable convolution branch with a dilation rate of 5, combined with the offset field, spans a large time rate interval and reconnects the broken parts of the underwater acoustic line spectrum caused by the large fading of the channel.
10. The underwater acoustic line spectrum correction method based on Doppler compensation and deformable convolution according to claim 1, characterized in that, It also includes step six: constructing a training set based on simulation and measured data, and using a composite loss function that includes mean square error and structural similarity to perform end-to-end backpropagation training on the geometrically aware deformable convolutional network.