Adaptive fourier and mamba sea clutter prediction method, system, and media

Abstract

The present application belongs to the technical field of sea clutter prediction, and particularly relates to an adaptive Fourier and Mamba sea clutter prediction method, system and medium, which comprises the following steps: obtaining original radar echo data, and performing input preprocessing of time-space enhancement; performing frequency domain transformation through Fourier, introducing learnable frequency band parameters, adaptively separating frequency bands, performing feature transformation and enhancement on the separated frequency bands, and obtaining time domain features through inverse Fourier transformation; the time domain features are activated to enter two parallel paths, are processed through Mamba blocks, and are fused through cross modulation and enhancement to obtain a final feature tensor; after layer normalization, the feature tensor extracts global context representation, and a multilayer perception machine is used to map the converged context representation to amplitude prediction values of future k time steps; the stability of prediction and the adaptability to sudden events are significantly improved, and prediction bias is overcome.

Description

Technical Field

[0001] This invention belongs to the field of sea clutter prediction technology, specifically relating to adaptive Fourier and Mamba sea clutter prediction methods, systems, and media. Background Technology

[0002] Sea clutter is the backscattered echo generated by scatterers on the sea surface and changes in the marine environment after radar illumination of the sea surface. The radar echo contains both target echoes and non-target sea clutter caused by wind, waves, and tides. In rough sea conditions or when target echoes are weak, sea clutter can easily obscure target information, leading to increased false alarm rates and decreased detection sensitivity, thus limiting the reliability of applications such as maritime surveillance. Therefore, developing efficient and accurate sea clutter amplitude prediction methods is of great significance for improving radar target detection capabilities under complex sea conditions.

[0003] In recent years, deep learning has driven the development of sea clutter prediction, with recurrent neural networks and their improved structures showing significant results: GF-RNN achieves temporal feature extraction through cascaded multi-layer GRUs and fully connected layers; LSTM addresses the gradient vanishing problem through gating mechanisms, and combining it with generative adversarial networks can improve prediction accuracy; SCPNet employs a sequence-to-sequence architecture and self-attention modules, mitigating the decay of long sequence information through k-step advance prediction. However, all of the above methods are limited to temporal modeling. Recent models combining self-attention mechanisms and ConvLSTM, while improving accuracy by mining spatiotemporal correlations, still have many shortcomings.

[0004] First, most methods only consider the temporal correlation of sea clutter and ignore the spatial correlation of adjacent gate clutter, making it difficult to fully grasp the evolution of sea surface scattering and limiting prediction performance in complex scenarios. Second, the spectrum of sea clutter changes dynamically over time, and existing methods lack frequency domain analysis, are sensitive to noise, and cannot effectively separate key prediction components. Third, the self-attention mechanism fails to fully model multi-scale dependencies and has high computational complexity, affecting application effectiveness. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides an adaptive Fourier and Mamba sea clutter prediction method, system, and medium. First, this invention constructs a multi-channel input tensor that integrates spatial context information from adjacent distance gates using a spatiotemporally enhanced input preprocessing module, generating initial features. Second, an adaptive Fourier filtering module transforms the initial features to the frequency domain, adaptively separating low-frequency trends, high-frequency details, and noise using learnable frequency band parameters, and enhancing key frequency bands. Then, a dual-path Mamba module extracts and fuses local detail features and long-term trend features in parallel with linear computational complexity. Finally, a prediction head outputs predicted sea clutter amplitude values ​​for multiple future time steps. This invention effectively suppresses non-stationary noise while achieving efficient multi-scale time-dependent modeling and adaptive fusion, improving computational efficiency while maintaining prediction accuracy.

[0006] To achieve the above objectives, the first aspect of this invention proposes an adaptive Fourier and Mamba sea clutter prediction method, comprising: S1. Input preprocessing for spatiotemporal augmentation: Raw sea clutter radar echo data is acquired and converted into amplitude data. Based on the amplitude data, spatial correlation calculation is performed to select the center range gate to be predicted and the historical temporal amplitude data of the adjacent range gates before and after the center range gate to construct a multi-channel input tensor. The input tensor is normalized and linearly mapped to obtain the projection features. Based on the projection features Construct a joint coding mechanism to generate initial features ; S2, Adaptive Fourier Filtering: The initial features Adaptive frequency band separation is achieved by performing a Fourier transform in the frequency domain and introducing learnable frequency band parameters. The separated frequency bands are then subjected to frequency-point feature transformation and enhancement using a learnable multilayer perceptron. The enhanced features are then reconstructed in the time domain by calculating the mixed spectrum and performing an inverse Fourier transform to obtain the time-domain features. ; S3, Dual-path Mamba time series modeling: The time-domain features Activate to obtain shared context Shared context The process involves two parallel paths, each processed using Mamba blocks to output local detail features. Long-term trend characteristics The local detail features With the aforementioned long-term trend characteristics The output features are obtained by cross-modulation and enhancement fusion through a cross-gating fusion mechanism. ; S4. Output predicted value: The output features The final feature tensor is obtained after stacking adaptive Fourier filtering and dual-path Mamba temporal modeling. The feature tensor Global contextual representations are extracted from the normalized sequence, and a multilayer perceptron is used as the prediction head to map the converged contextual representations into predicted sea clutter amplitude values ​​for the next k time steps.

[0007] Furthermore, based on the amplitude data, through spatial correlation calculation, the temporal amplitude sequences of the center distance gate to be predicted and the adjacent distance gates before and after the center distance gate are selected to construct a multi-channel input tensor, including: S1.1: Based on the amplitude data, calculate the mean-free space autocorrelation function for a single radar pulse echo; S1.2: Averaging the mean-free spatial autocorrelation function across all impulse dimensions yields a curve characterizing the overall spatial correlation; the distance lag index corresponding to the first time the average spatial autocorrelation function value falls below a preset threshold is then calculated. The spatial decorrelation point is determined; the temporal amplitude sequence of the center distance gate to be predicted and the temporal amplitude sequences of the adjacent distance gates before and after the center distance gate are selected through the spatial decorrelation point to construct a multi-channel input tensor; The input tensor is normalized and linearly mapped to obtain the projection features. Based on projection features Construct a joint coding mechanism to generate initial features ,include: S1.3: Perform global minimum-maximum normalization on the input tensor to obtain the normalized tensor S; S1.4: The normalized tensor S is linearly projected through a fully connected layer to obtain the projection features. ; S1.5: Based on projection features Add learnable time codes to each time step of the time-series amplitude sequence. Spatial codes are generated based on the relative spatial positions of multiple input distance gates. and encode the space Replication expansion is performed along the length dimension of the temporal amplitude sequence, using a learnable scaling factor. Encoding the space The contribution is adaptively adjusted and combined with time coding. and projection features Add them together to generate the initial features. .

[0008] Furthermore, the initial features Adaptive frequency band separation is achieved by performing frequency domain transform using Fourier transform and introducing learnable frequency band parameters, including: S2.1: The initial feature Performing a Fast Fourier Transform independently along the time dimension yields the spectrum. That is, frequency domain representation; S2.2: Frequency points based on Fourier transform Calculate the normalized frequency vector ; S2.3: Introduce two learnable frequency band parameters With frequency band parameters Based on normalized frequency vector Generate low-frequency and high-frequency masks, represented as: ; ; in, For low-frequency masking, For high-frequency mask, For the Sigmoid function, Choose the smoothness of the boundary for the temperature coefficient control frequency; S2.4: The low-frequency mask and the high-frequency mask respectively affect the spectrum. Adaptive frequency band separation is performed to obtain the separated low-frequency spectrum and the separated high-frequency spectrum.

[0009] Furthermore, the separated frequency bands are the separated low-frequency spectrum and the separated high-frequency spectrum. The separated frequency bands are subjected to frequency-point feature transformation and enhancement through a learnable multilayer perceptron. The enhanced features are then reconstructed in the time domain by calculating the mixed spectrum and inverse Fourier transform to obtain the time-domain features. ,include: S2.5: Apply a learnable frequency-point filter to both the separated low-frequency spectrum and the separated high-frequency spectrum, wherein the filter applies a filter to each frequency point. Linear transformation and nonlinear activation are performed on the channel vectors to obtain enhanced features, namely enhanced low-frequency spectral features and enhanced high-frequency spectral features; S2.6: The original spectrum and the enhanced features are fused using residuals to obtain a mixed spectrum; S2.7: Perform inverse Fourier transform on the mixed spectrum to obtain the enhanced and denoised time-domain features. .

[0010] Furthermore, the shared context The process involves two parallel paths, each processed using Mamba blocks to output local detail features. Long-term trend characteristics ,include: Shared Context The system enters two parallel paths: one is a local path, which uses a small convolutional kernel to extract local contextual features, and the other is a global path, which uses a large convolutional kernel to extract global contextual features under a large receptive field. Subsequently, the two paths are modeled temporally using their respective Mamba blocks. The Mamba block for the local path, based on its internal discretized state-space model and selective scanning mechanism, performs state recursion and feature updates along the time dimension on the local context features extracted from the local path, outputting local detail features. The Mamba block of the global path, based on its internal discretized state-space model and selective scanning mechanism, performs state recursion and feature updates along the time dimension on the global context features extracted from the global path, outputting long-term trend features. .

[0011] Furthermore, the Mamba blocks of the local path, based on an internal discretized state-space model and a selective scanning mechanism, perform state recursion and feature updates along the time dimension on the local context features extracted from the local path, outputting local detail features. The Mamba block of the global path, based on its internal discretized state-space model and selective scanning mechanism, performs state recursion and feature updates along the time dimension on the global context features extracted from the global path, outputting long-term trend features. ,include: For any time step The Mamba blocks for local and global paths dynamically generate relevant parameters of the state-space model based on the input features at the current time step, including the discretized state transition matrix. Discretized input projection matrix Output projection matrix and skip connection matrix ; Based on the above state space model parameters, the Mamba block recursively calculates the hidden state of the current time step and outputs the output features of the current time step through the hidden state of the current time step. The Mamba block of the local path sequentially performs the above state recursion and feature output on the features of each time step in the local path, and arranges the output features of all time steps in chronological order to form local detail features. The Mamba block of the global path sequentially performs the above state recursion and feature output on the features of each time step in the global path, and arranges the output features of all time steps in chronological order to form long-term trend features. .

[0012] Furthermore, the local detail features Long-term trend characteristics The output features are obtained through cross-modulation and enhancement fusion using a cross-gating fusion mechanism. ,include: Local detail features Long-term trend characteristics Nonlinear transformation and regularization are performed respectively to generate the first gated signal and the second gated signal for modulation; The first gating signal and the second gating signal are respectively related to long-term trend characteristics. Local details and the shared context Cross modulation is achieved through a triple Hadamard product; The output features after cross-modulation are summed, and the channel dimension is adjusted through a linear projection layer to obtain the aggregated features of multi-scale sea clutter. The aggregated features, after undergoing random deep regularization, are combined with the initial input temporal features. Residual connections yield output features .

[0013] Furthermore, the feature tensor Global context representations are extracted from the normalized sequence, and a multilayer perceptron is used as the prediction head to map the converged global context representations to predicted sea clutter amplitudes for the next k time steps, including: S4.1: Feature Tensor Global context representations are extracted using layer normalization, and a multilayer perceptron is used as the prediction head. The converged global context representations are projected onto a higher-dimensional hidden space, and nonlinearity is introduced through the GELU activation function to obtain hidden features. ; S4.2: During the training phase, the activated hidden features... By applying the Dropout operation, the output of some neurons is randomly set to zero to obtain regularized hidden features. S4.3: Projecting the regularized hidden features into the output space yields the predicted sea clutter amplitude values ​​for the next k time steps, expressed as: ; in, This represents the predicted sea clutter amplitude at k time steps. This represents the bias term of the second-layer perceptron. This represents the weight matrix of the second-layer perceptron.

[0014] A second aspect of this invention proposes an adaptive Fourier and Mamba sea clutter prediction system, comprising: The spatiotemporal augmentation input preprocessing module is used for input preprocessing of spatiotemporal augmentation: acquiring raw sea clutter radar echo data and converting it into amplitude data; based on the amplitude data, through spatial correlation calculation, selecting the center range gate to be predicted and the temporal amplitude sequences of the adjacent range gates before and after the center range gate to construct a multi-channel input tensor, and obtaining projection features. Based on the projection features Construct a joint coding mechanism to generate initial features ; An adaptive Fourier filter module is used for adaptive Fourier filtering: the initial features Adaptive frequency band separation is achieved by performing a Fourier transform in the frequency domain and introducing learnable frequency band parameters. The separated frequency bands are then subjected to frequency-point feature transformation and enhancement using a learnable multilayer perceptron. The enhanced features are then reconstructed in the time domain by calculating the mixed spectrum and performing an inverse Fourier transform to obtain the time-domain features. ; The dual-path Mamba module is used for dual-path Mamba time series modeling: the time-domain features Activate to obtain shared context Shared context The process involves two parallel paths, each processed using Mamba blocks to output local detail features. Long-term trend characteristics The local detail features With the aforementioned long-term trend characteristics The output features are obtained by cross-modulation and enhancement fusion through a cross-gating fusion mechanism. ; Output module, used to output predicted values: the output features The final feature tensor is obtained after stacking adaptive Fourier filtering and dual-path Mamba temporal modeling. The feature tensor Global context representations are extracted from the normalized sequence, and a multilayer perceptron is used as the prediction head to map the converged global context representations into predicted sea clutter amplitude values ​​for the next k time steps.

[0015] A third aspect of the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, is used to implement the adaptive Fourier and Mamba sea clutter prediction method as described above.

[0016] Compared with the prior art, the advantages of this invention are: (1) By using spatiotemporally enhanced input preprocessing, the spatial correlation of sea clutter is fully utilized, thereby improving the robustness and accuracy of the prediction.

[0017] Most existing deep learning-based sea clutter prediction methods only model time-series echo data for a single range gate, failing to fully utilize the inherent spatial dependence of sea clutter in the range dimension. To address this limitation, this invention constructs a spatiotemporally enhanced input preprocessing module. It explicitly uses the time-series amplitude data of the range gate to be predicted and its adjacent range gates as multi-channel joint input, and adaptively fuses temporal evolution information and spatial context information through a learnable spatiotemporal joint coding mechanism. This invention can more completely perceive the continuous dynamic characteristics of the local sea surface scattering field, thus enabling inference based on richer spatial constraints when amplitude changes drastically or in complex sea conditions. This significantly improves prediction stability and adaptability to sudden events, overcoming prediction bias caused by insufficient utilization of spatial information.

[0018] (2) By using the adaptive Fourier filter module, frequency domain information is extracted and non-stationary noise is suppressed, which enhances the model's ability to represent complex sea clutter signals.

[0019] Existing methods mostly perform direct modeling in the time domain, lacking sufficient information mining in the frequency domain. This makes it difficult to separate the components of sea clutter dominated by different physical processes (such as large-scale wave motion and micro-scale breaking waves) at the spectral level, and also fails to effectively suppress non-stationary noise. To address this problem, this invention designs an adaptive Fourier filter module, innovatively transforming features to the frequency domain. A smoothing mask is generated using two learnable frequency band parameters, adaptively separating the spectrum into low-frequency trends, high-frequency details, and noise. The low-frequency component corresponds to the slowly varying trends dominated by large-scale wave motion, while the high-frequency component contains rapid fluctuations caused by micro-scale processes. Subsequently, the module utilizes a lightweight network to specifically enhance key frequency bands and preserves the global structure through residual connections. This intelligently preserves and strengthens core spectral information closely related to amplitude evolution prediction, while significantly suppressing irrelevant noise interference, improving noise robustness under complex sea conditions.

[0020] (3) By using the dual-path Mamba module, multi-scale temporal dependencies are efficiently modeled with linear computational complexity, thus overcoming the computational efficiency bottleneck of the self-attention mechanism.

[0021] To simultaneously capture both local rapid fluctuations and long-term slow trends in sea clutter, and to avoid the computational efficiency issues inherent in self-attention mechanisms, this invention introduces a dual-path Mamba module based on a selective state-space model. This architecture uses two parallel paths, each employing different receptive fields to extract local details and global trends, and leverages the selective state-space model to efficiently model long sequences with linear computational complexity. Furthermore, a cross-gating fusion mechanism enables deep interaction and adaptive fusion of information from both paths. Therefore, this invention significantly reduces computational overhead while ensuring accurate modeling of multi-scale temporal dependencies in sea clutter and fusing local details and global trends, achieving a better balance between prediction accuracy and computational efficiency. Attached Figure Description

[0022] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This is a flowchart of the adaptive Fourier and Mamba sea clutter prediction method in this embodiment; Figure 2 This is a diagram of the architecture of the adaptive Fourier and Mamba sea clutter prediction system in this embodiment. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions in the embodiments will be clearly and completely described below with reference to the accompanying drawings. The following embodiments are used to illustrate this application, but are not intended to limit the scope of this application.

[0025] Example 1: See Figure 1 , Figure 2 This embodiment provides an adaptive Fourier and Mamba sea clutter prediction method, which specifically includes the following steps: S1. Input preprocessing for spatiotemporal augmentation: Raw sea clutter radar echo data is acquired and converted into amplitude data. Based on the amplitude data, spatial correlation is calculated, and the historical temporal amplitude sequences of the center range gate to be predicted and the adjacent range gates before and after the center range gate are selected to construct a multi-channel input tensor. The input tensor is normalized and linearly mapped to obtain the projection features. Based on projection features Construct a joint coding mechanism to generate initial features ; S2, Adaptive Fourier Filtering: Initial features Adaptive frequency band separation is achieved by performing a Fourier transform in the frequency domain and introducing learnable frequency band parameters. The separated frequency bands are then subjected to frequency-point feature transformation and enhancement using a learnable multilayer perceptron. The enhanced features are then reconstructed in the time domain by calculating the mixed spectrum and performing an inverse Fourier transform to obtain the time-domain features. ; S3, Dual-path Mamba time series modeling: Temporal characteristics Activate to obtain shared context Shared context The process involves two parallel paths, each processed using Mamba blocks to output local detail features. Long-term trend characteristics The local detail features With the aforementioned long-term trend characteristics The output features are obtained by cross-modulation and enhancement fusion through a cross-gating fusion mechanism. ; S4. Output and Optimization: Output features The final feature tensor is obtained after stacking adaptive Fourier filtering and dual-path Mamba temporal modeling. Feature tensor Global context representations are extracted from the normalized sequence, and a multilayer perceptron is used as the prediction head to map the converged global context representations into predicted sea clutter amplitude values ​​for the next k time steps.

[0026] In step S1 of this embodiment, based on amplitude data, spatial correlation calculation is performed to select the historical temporal amplitude sequences of the center distance gate to be predicted and the adjacent distance gates before and after the center distance gate, and a multi-channel input tensor is constructed, including: Raw sea clutter radar echo data was obtained from the Sea-detecting X-band Radar and Data Acquisition Program database and converted into amplitude data.

[0027] S1.1: Based on amplitude data, the mean-free spatial autocorrelation function is calculated for a single radar pulse echo, expressed as: ; in, This represents the mean-space autocorrelation function. This indicates the total number of range gates contained in a single radar pulse echo. This represents the average of all amplitude data. This indicates a distance lag index, which is a spatially correlated point. In a single radar pulse echo, the first... The timing amplitude of each distance gate.

[0028] S1.2: Averaging the mean-free spatial autocorrelation function across all impulse dimensions yields a curve characterizing the overall spatial correlation. The distance lag index corresponding to the first time the average spatial autocorrelation function value falls below the threshold ε is then calculated. The spatial decorrelation point is determined, and the temporal amplitude sequence of the center distance gate to be predicted and the temporal amplitude sequences of the j adjacent distance gates before and after the center distance gate are selected through the spatial decorrelation point to construct the multi-channel input tensor, where the threshold ε is 1 / e.

[0029] In step S1 of this embodiment, the input tensor is normalized and linearly mapped to obtain the projection features. Based on projection features Construct a joint coding mechanism to generate initial features Specifically: S1.3: Perform global minimum-maximum normalization on all data of the input tensor to obtain the normalized tensor S. The normalization parameters are calculated only from the training set and are expressed as: ; in, This represents a single normalized magnitude value in the input tensor. This represents a single raw magnitude value in the input tensor. and These are the minimum and maximum amplitude values ​​of the entire training set, respectively. This is a small constant used for numerical stability.

[0030] S1.4: The normalized tensor S is linearly projected through a fully connected layer to obtain the projection features. This involves mapping from the original multi-channel model to a higher-dimensional feature space to enhance the model's representational power, expressed as: ; in, Indicates linear projection. Indicates projection features, This represents the normalized tensor.

[0031] S1.5: Based on projection features Add learnable temporal codes to each time step of the temporal amplitude sequence of each of the j range gates before and after. Spatial codes are generated based on the relative spatial positions of multiple input distance gates. and spatial encoding The temporal amplitude sequence length dimension broadcast to each of the j distance gates before and after is passed through a learnable scaling factor. Encoding the space The contribution is adaptively adjusted and combined with time coding. and projection features Adding them together generates initial features that possess both temporal evolution and spatial context. The calculation formula is as follows: .

[0032] In step S2 of this embodiment, the initial feature Adaptive frequency band separation is achieved by performing a Fourier transform in the frequency domain and introducing learnable frequency band parameters, specifically as follows: S2.1: The initial feature Performing a Fast Fourier Transform independently along the time dimension yields the spectrum. That is, frequency domain representation, expressed as: ; in, Indicates the total number of frequency points. Indicates frequency point, Indicates Fourier transform; S2.2: Frequency points based on Fourier transform Calculate the normalized frequency vector , is represented as: ; S2.3: Introduce two learnable frequency band parameters With frequency band parameters Based on normalized frequency vector Generate low-frequency and high-frequency masks, represented as: ; ; in, For low-frequency masking, For high-frequency mask, For the Sigmoid function, Select the smoothness of the boundary for the temperature coefficient control frequency; S2.4: Low-frequency mask and high-frequency mask respectively affect the spectrum Adaptive frequency band separation is performed to obtain the separated low-frequency spectrum and the separated high-frequency spectrum, which are represented as follows: ; ; in, Indicates a low-frequency mask. Represents a high-frequency mask; ⊙ represents element-wise broadcast product. This represents the low-frequency spectrum after separation. This represents the high-frequency spectrum after separation.

[0033] In step S2 of this embodiment, the separated frequency bands are the separated low-frequency spectrum and the separated high-frequency spectrum. The separated frequency bands are subjected to frequency-point feature transformation and enhancement through a learnable multilayer perceptron. The enhanced features are obtained by reconstructing the time domain features through the calculation of the mixed spectrum and inverse Fourier transform. Specifically: S2.5: Apply a learnable frequency-by-frequency filter to the separated low-frequency and high-frequency spectra respectively. See [link to relevant documentation]. Figure 2 Learnable low-frequency filters and learnable high-frequency filters in Figure 1 Learnable low-pass mask filtering and learnable high-pass mask filtering; frequency-point-by-frequency filter for each frequency point For linear transformations and nonlinear activations of the channel vectors, see [link to relevant documentation]. Figure 2 The linear layer in the model yields enhanced features, namely the enhanced low-frequency spectral features and the enhanced high-frequency spectral features. (See [link to relevant documentation]). Figure 2 The low-frequency and high-frequency features in the data are represented as follows: ; ; in, This represents a learnable low-frequency filter in a frequency-point-by-frequency filter. This represents a learnable high-frequency filter in a frequency-point-by-frequency filter. This indicates the enhanced low-frequency spectral characteristics. This indicates the enhanced high-frequency spectral characteristics; S2.6: To ensure the stability of the module and preserve the global spectral shape of the input signal, the original spectrum and the enhanced features are fused using residuals to obtain a mixed spectrum, expressed as: ; in, Indicates a mixed spectrum. This represents the original spectrum, i.e., the frequency domain representation; S2.7: Perform inverse Fourier transform on the mixed spectrum to obtain the enhanced and denoised time-domain features. While suppressing irrelevant noise and interference, it enhanced key features in sea clutter related to evolution trends and local abrupt changes, as shown below: ; in, This represents the inverse Fourier transform.

[0034] Sea clutter is a composite echo generated by sea surface motion and surface microstructure at different scales. In the lower frequency band, it is mainly dominated by large-scale wave motion, while in the higher frequency band, it is more contributed by micro-scale processes of the sea surface (such as capillary waves, turbulence, and wind-driven scattering). The electromagnetic scattering physical processes of waves driven by wind and ocean currents are difficult to observe in the time domain. To address the non-stationary characteristics of sea clutter in the time domain and suppress redundant noise unrelated to prediction, an adaptive Fourier dual-band Fourier filter is used. In the frequency domain, it intelligently decouples and enhances the core physical spectrum components related to prediction, while suppressing irrelevant or interfering spectrum bands, thereby improving the input quality of subsequent time series modeling.

[0035] Changes in sea clutter simultaneously contain transient fluctuations caused by wave breaking and long-term trends driven by wind fields and tidal currents. To effectively model this cross-scale dependency relationship from local rapid disturbances to long-term slow evolution without high computational complexity, a dual-path temporal modeling mechanism is adopted. This mechanism can adaptively capture and fuse local detailed features and global trend information in sea clutter with linear computational complexity, thereby providing a deep temporal representation foundation for accurate prediction.

[0036] Specifically, the time-domain features in step S3 of this embodiment Activate to obtain shared context Shared context The process involves two parallel paths, each processed using Mamba blocks to output local detail features. Long-term trend characteristics ,include: Temporal characteristics The shared context is obtained by activation via the SiLU function. , is represented as: ; Shared Context The system enters two parallel paths: one is a local path, which uses one-dimensional convolution with a small kernel to extract local contextual features to capture local details and short-term fluctuations of sea clutter; the other is a global path, which uses one-dimensional convolution with a large kernel to extract global contextual features under a large receptive field to characterize the long-term evolution trend of sea clutter.

[0037] Subsequently, the two paths are modeled temporally using their respective Mamba blocks. Specifically, the Mamba block for the local path, based on its internal discretized state-space model and selective scanning mechanism, performs state recursion and feature updates along the time dimension on the local context features extracted from the local path, outputting local detail features. The Mamba block of the global path, based on its internal discretized state-space model and selective scanning mechanism, performs state recursion and feature updates along the time dimension on the global context features extracted from the global path, outputting long-term trend features. , is represented as: ; ; in, Mamba blocks representing local paths Mamba blocks representing global paths, This indicates the shared context obtained through activation. This represents the local detail features output by the local path. This represents the long-term trend characteristics of the global path output. The Mamba block contains a discretized state-space model, a process for generating input-related parameters, and a selective scanning mechanism, which models sequence features by recursively probing the hidden states along the time dimension.

[0038] Specifically, in step S3 of this embodiment, for any time step Mamba blocks for local and global paths are determined based on the input features at the current time step. Dynamically generate relevant parameters for the state-space model, including the discretized state transition matrix. Discretized input projection matrix Output projection matrix and skip connection matrix The state-space model is used to describe the recursive evolution of the hidden state over time, while the selective scanning mechanism is used to efficiently recursively calculate the hidden state along the time dimension and output the features of each time step.

[0039] Based on the parameters of the state-space model mentioned above, the Mamba block recursively calculates the hidden state at the current time step and outputs the output features at the current time step using the hidden state at the current time step. , is represented as: ; ; in, This represents the feature input to the Mamba block at the current time step. This indicates the hidden state at the current time step. This indicates the hidden state of the previous time step. This represents the output feature at the current time step. , , and This represents the state-space model parameters dynamically generated from the current input features.

[0040] The Mamba block of the local path sequentially performs the above state recursion and feature output on the features of each time step in the local path, and arranges the output features of all time steps in chronological order to form local detail features. The Mamba block of the global path sequentially performs the above state recursion and feature output on the features of each time step in the global path, and arranges the output features of all time steps in chronological order to form long-term trend features. Therefore, local paths focus on representing local fluctuations on a short timescale, while global paths focus on representing evolutionary trends on a longer timescale.

[0041] In step S3 of this embodiment, local detailed features Long-term trend characteristics The output features are obtained through cross-gating and enhancement fusion using a cross-gating fusion mechanism. Specifically: Local detail features Long-term trend characteristics After performing nonlinear transformation and regularization, the first gate signal and the second gate signal for modulation are generated, as follows: ; ; in, Indicates regularization, Represents a nonlinear transformation. This represents the first gating signal generated from local detail features. This represents the second gating signal generated from long-term trend characteristics; The first and second gating signals are respectively related to long-term trend characteristics. Local details and the shared context Cross-modulation is achieved through a triple Hadamard product, represented as: ; ; in, This indicates the shared context obtained through activation. This represents the output characteristics of a local path after cross-modulation. This represents the output characteristics of the global path after cross-modulation; The output features after cross-modulation are summed, and the channel dimensions are adjusted through a linear projection layer to obtain the aggregated features of multi-scale sea clutter, expressed as: ; in, Indicates linear projection. This indicates the aggregation characteristics of multi-scale sea clutter; The aggregated features, after being processed by random deep regularization, are combined with the initial input temporal features. Residual connections yield output features , is represented as: ; in, This indicates random depth regularization.

[0042] In step S4 of this embodiment, the output feature is... The final feature tensor is obtained after stacking N layers of adaptive Fourier filtering and dual-path Mamba temporal modeling. .

[0043] Specifically, feature tensor Global contextual representations are extracted from the normalized sequence, and a two-layer multilayer perceptron is used as the prediction head to map the converged contextual representations to predicted sea clutter amplitudes for the next k time steps, including: S4.1: For the characteristic tensor Perform layer normalization to obtain the normalized feature tensor. The normalized feature tensor Preserve the time dimension and extract the feature vector from the last time step as a global context representation. A multilayer perceptron is used as the prediction head to project the global context representation into a higher-dimensional hidden space. Nonlinearity is introduced through the GELU activation function to obtain hidden features. , is represented as: ; ; in, Representation layer normalization, Represents the normalized feature tensor. As a global context representation, This is the bias term for the first-layer perceptron. This represents the weight matrix of the first-layer perceptron; S4.2: During the training phase, the activated hidden features... By applying the Dropout operation, the outputs of some neurons are randomly set to zero, resulting in regularized hidden features. To prevent the model from overfitting, it is expressed as: ; S4.3: Project the regularized hidden features into the output space to obtain the predicted sea clutter amplitude values ​​for the next k time steps. See [link to relevant documentation]. Figure 1 The k-step pulse amplitude value is expressed as: ; in, This represents the predicted sea clutter amplitude at k time steps. This represents the bias term of the second-layer perceptron. This represents the weight matrix of the second-layer perceptron.

[0044] Loss function: Mean squared error (MSE) is selected as the loss function to measure the difference between the sea clutter amplitude sequence predicted by the model and the actual amplitude sequence. The loss function is defined as follows: ; in, For the size of the training batch, This is the predicted value for sea clutter amplitude. This represents the true value of the corresponding sea clutter amplitude.

[0045] Experimental verification: As an application example, this embodiment uses sea clutter amplitude prediction as an example, employing measured sea clutter data from the Sea-detecting X-band Radar and Data Acquisition Program database as the training and testing dataset. This dataset provides high-resolution sea clutter echo data acquired by shore-based X-band radar for sea detection, offering information on sea surface scattering in a real marine environment. Many researchers have used this dataset to train and evaluate deep learning models for various applications, including sea clutter prediction, target detection, and marine remote sensing, due to its reliable data quality and realistic sea conditions.

[0046] Specifically, this embodiment focuses on radar staring observation data from the northern sea area of ​​City A. The radar operates in T2 mode (linear frequency modulated pulse, bandwidth 25 MHz, pulse width 3 μs), and the sea state during the observation period is level 3-4. The dataset contains a total of 6940 pulses, 4346 range sampling units, a range resolution of 6 meters, and a sampling interval of 2.5 meters. The first 1280 range gates were selected for experimental verification. The input sequence length is 64 time steps, and a multi-channel spatial input is constructed using the current range gate and two adjacent range gates before and after it (a total of 5 range gates).

[0047] This invention uses 70% of the samples as the training set, 10% as the validation set, and the remaining 20% ​​as the test set. All data is divided in chronological order to meet the requirements of time series prediction. The model is evaluated using mean squared error (MSE), mean absolute error (MAE), and coefficient of determination (R²), all of which are commonly used evaluation metrics in this field. Mean squared error (MSE) measures the squared deviation between the predicted and actual values; a smaller value indicates higher prediction accuracy. Mean absolute error (MAE) is the average of the absolute errors between the predicted and actual values. The coefficient of determination (R²) represents the model's ability to explain changes in actual data.

[0048] The model receives a sea clutter amplitude sequence as a joint input from multiple range gates. It achieves accurate multi-step prediction of sea clutter amplitudes through spatiotemporally enhanced input preprocessing, adaptive Fourier filtering, dual-path Mamba temporal modeling, and a lightweight output module. Experiments were conducted on an NVIDIA 4080 GPU, with the network trained for 80 epochs using the AdamW optimizer and a minimum batch size of 256. The learning rate was initialized to 5 × 10⁻⁻⁻⁴ during training. 4 It adopts an adaptive learning rate decay strategy based on the validation set MSE (ReduceLROnPlateau, patience value of 5, decay factor of 0.5), and introduces an early stopping mechanism and gradient clipping (threshold of 0.5) to prevent overfitting and gradient explosion.

[0049] To demonstrate the effectiveness of this invention, LSTM (Long Short-Term Memory), GF-RNN (Gated Fusion Recurrent Neural Network), and Transformer were selected for comparative experiments with the proposed method STF-Mamba (Spatio-Temporal Enhanced Fourier Filtering Mamba). Detailed information on the experimental results is shown in Table 1, which presents the comparison of MSE, MAE, and R² under 1-step, 4-step, and 16-step prediction.

[0050] Table 1: Comparison of MSE, MAE, and R² under 1-step, 4-step, and 16-step predictions STF-Mamba (This invention) <![CDATA[MSEMAER 2 ]]> <![CDATA[2.47×10 -4 1.19×10 -2 0.9711]]> <![CDATA[1.19×10 -3 2.34×10 -2 0.8605]]> <![CDATA[3.56×10 -3 4.06×10 -2 0.5840]]> LSTM <![CDATA[MSEMAER 2 ]]> <![CDATA[7.14×10 -4 1.98×10 -2 0.9165]]> <![CDATA[1.86×10 -3 3.13×10 -2 0.7826]]> <![CDATA[4.49×10 -3 4.66×10 -2 0.4748]]> GF-RNN <![CDATA[MSEMAER 2 ]]> <![CDATA[4.36×10 -4 1.60×10 -2 0.9490]]> <![CDATA[1.48×10 -3 2.68×10 -2 0.8270]]> <![CDATA[4.10×10 -3 4.47×10 -2 0.5201]]> Transformer <![CDATA[MSEMAER 2 ]]> <![CDATA[3.35×10 -4 1.37×10 -2 0.9609]]> <![CDATA[1.44×10 -3 2.60×10 -2 0.8311]]> <![CDATA[3.75×10 -3 4.17×10 -2 0.5619]]> The method of this invention exhibits optimal performance across all evaluation metrics and prediction step sizes. In single-step prediction tasks, the method achieves an MSE of 2.47 × 10⁻⁶. -4 It is significantly better than Transformer (3.35×10).-4 ), GF-RNN (4.36×10) -4 ) and LSTM (7.14×10 -4 ), which reduces MSE by 65.4% compared to LSTM; R 2 The MSE reached 0.9711. With increasing prediction step size, the performance degradation of the method in this invention is significantly slower than that of the comparative model. In the 4-step prediction, the MSE of this invention is only 1.19 × 10⁻⁶. -3 R 2 The MSE remained at 0.8605; in the 16-step prediction, the MSE of this invention was 3.56 × 10⁻⁶. -3 R 2 The value is 0.5840, still the highest among all methods. These results fully demonstrate that the adaptive Fourier and Mamba sea clutter prediction methods of this invention have higher accuracy, robustness, and stability in multi-step prediction tasks.

[0051] In summary, this invention demonstrates excellent performance in experimental verification using measured sea clutter data, providing an efficient and reliable technical solution for sea clutter prediction.

[0052] Example 2: See Figure 2 As another embodiment of the present invention, an adaptive Fourier and Mamba sea clutter prediction system is also proposed, comprising: The spatiotemporal augmentation input preprocessing module is used for input preprocessing of spatiotemporal augmentation: acquiring raw sea clutter radar echo data and converting it into amplitude data; based on the amplitude data, through spatial correlation calculation, selecting the center range gate to be predicted and the temporal amplitude sequences of the adjacent range gates before and after the center range gate to construct a multi-channel input tensor; the input tensor is normalized and linearly mapped to obtain projection features. Based on the projection features Construct a joint coding mechanism to generate initial features ; An adaptive Fourier filter module is used for adaptive Fourier filtering: the initial features Adaptive frequency band separation is achieved by performing a Fourier transform in the frequency domain and introducing learnable frequency band parameters. The separated frequency bands are then subjected to frequency-point feature transformation and enhancement using a learnable multilayer perceptron. The enhanced features are then reconstructed in the time domain by calculating the mixed spectrum and performing an inverse Fourier transform to obtain the time-domain features. ; Dual-path Mamba module for dual-path Mamba time series modeling: the time-domain features Activate to obtain shared context Shared context Entering two parallel paths, Mamba processing is performed to output local detail features respectively. Long-term trend characteristics The local detail features With the aforementioned long-term trend characteristics The output features are obtained by cross-modulation and enhancement fusion through a cross-gating fusion mechanism. ; Output module, used to output predicted values: the output features The final feature tensor is obtained after stacking adaptive Fourier filtering and dual-path Mamba temporal modeling. The feature tensor Global contextual representations are extracted from the normalized sequence, and a multilayer perceptron is used as the prediction head to map the converged contextual representations into predicted sea clutter amplitude values ​​for the next k time steps.

[0053] Example 3: In yet another embodiment of the present invention, a computer-readable storage medium is provided, storing a computer program that, when executed by a processor, is used to implement the adaptive Fourier and Mamba sea clutter prediction method as described in Example 1 above.

[0054] The program product of this application for implementing the above method may employ a portable compact disk read-only memory and include program code, and may run on a terminal device, such as a personal computer. However, the program product of this application is not limited thereto. In this application, the readable storage medium may be any tangible medium containing or storing a program that may be used by or in conjunction with an instruction execution system, apparatus, or device.

[0055] It should be noted that a computer-readable storage medium may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium may also be any readable medium other than a readable storage medium, capable of transmitting, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0056] The above are merely preferred embodiments of this application and are not intended to limit this application in any way. Although this application has disclosed preferred embodiments as described above, it is not intended to limit this application. Any person skilled in the art can make some modifications or alterations to the above-mentioned technical content to create equivalent embodiments without departing from the scope of the technical solution of this application. The implementation schemes in the above embodiments can also be further combined or replaced. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of this application without departing from the content of the technical solution of this application shall still fall within the scope of this application.

Claims

1. An adaptive Fourier and Mamba sea clutter prediction method, characterized in that, Includes the following steps: S1. Input preprocessing for spatiotemporal augmentation: Raw sea clutter radar echo data is acquired and converted into amplitude data. Based on this amplitude data, spatial correlation calculation is performed to select the center range gate to be predicted and the temporal amplitude sequences of the adjacent range gates before and after the center range gate. A multi-channel input tensor is constructed, and the input tensor is normalized and linearly mapped to obtain the projection features. Based on the projection features Construct a joint coding mechanism to generate initial features ; S2, Adaptive Fourier Filtering: The initial features Adaptive frequency band separation is achieved by performing a Fourier transform in the frequency domain and introducing learnable frequency band parameters. The separated frequency bands are then subjected to frequency-point feature transformation and enhancement using a learnable multilayer perceptron. The enhanced features are then reconstructed in the time domain by calculating the mixed spectrum and performing an inverse Fourier transform to obtain the time-domain features. ; S3, Dual-path Mamba time series modeling: The time-domain features Activate to obtain shared context Shared context The process involves two parallel paths, each processed using Mamba blocks to output local detail features. Long-term trend characteristics The local detail features With the aforementioned long-term trend characteristics The output features are obtained by cross-modulation and enhancement fusion through a cross-gating fusion mechanism. ; S4. Output predicted value: The output features The final feature tensor is obtained after stacking adaptive Fourier filtering and dual-path Mamba temporal modeling. The feature tensor Global context representations are extracted from the normalized sequence, and a multilayer perceptron is used as the prediction head to map the converged global context representations into predicted sea clutter amplitude values ​​for the next k time steps.

2. The method according to claim 1, characterized in that, Based on the amplitude data, through spatial correlation calculation, the temporal amplitude sequences of the center distance gate to be predicted and the adjacent distance gates before and after the center distance gate are selected to construct a multi-channel input tensor, including: S1.1: Based on the amplitude data, calculate the mean-free space autocorrelation function for a single radar pulse echo; S1.2: Averaging the mean-free spatial autocorrelation function across all impulse dimensions yields a curve characterizing the overall spatial correlation; the distance lag index corresponding to the first time the average spatial autocorrelation function value falls below a preset threshold is then calculated. The spatial decorrelation point is determined; the temporal amplitude sequence of the center distance gate to be predicted and the temporal amplitude sequences of the adjacent distance gates before and after the center distance gate are selected through the spatial decorrelation point to construct a multi-channel input tensor; The input tensor is normalized and linearly mapped to obtain the projection features. Based on projection features Construct a joint coding mechanism to generate initial features ,include: S1.3: Perform global minimum-maximum normalization on the input tensor to obtain the normalized tensor S; S1.4: The normalized tensor S is linearly projected through a fully connected layer to obtain the projection features. ; S1.5: Based on projection features Add learnable time codes to each time step of the time-series amplitude sequence. Spatial codes are generated based on the relative spatial positions of multiple input distance gates. and encode the space Replication expansion is performed along the length dimension of the temporal amplitude sequence, using a learnable scaling factor. Encoding the space The contribution is adaptively adjusted and combined with time coding. and projection features Add them together to generate the initial features. .

3. The method according to claim 1, characterized in that, The initial features Adaptive frequency band separation is achieved by performing frequency domain transform using Fourier transform and introducing learnable frequency band parameters, including: S2.1: The initial feature Performing a Fast Fourier Transform independently along the time dimension yields the spectrum. That is, frequency domain representation; S2.2: Frequency points based on Fourier transform Calculate the normalized frequency vector ; S2.3: Introduce two learnable frequency band parameters With frequency band parameters Based on normalized frequency vector Generate low-frequency and high-frequency masks, represented as: ； ； in, For low-frequency masking, For high-frequency mask, For the Sigmoid function, Select the smoothness of the boundary for the temperature coefficient control frequency; S2.4: The low-frequency mask and the high-frequency mask respectively affect the spectrum. Adaptive frequency band separation is performed to obtain the separated low-frequency spectrum and the separated high-frequency spectrum.

4. The method according to claim 1, characterized in that, The separated frequency bands are the separated low-frequency spectrum and the separated high-frequency spectrum. The separated frequency bands are subjected to frequency-point feature transformation and enhancement through a learnable multilayer perceptron. The enhanced features are then reconstructed in the time domain by calculating the mixed spectrum and performing inverse Fourier transform to obtain the time-domain features. ,include: S2.5: Apply a learnable frequency-point filter to both the separated low-frequency spectrum and the separated high-frequency spectrum, wherein the filter applies a filter to each frequency point. Linear transformation and nonlinear activation are performed on the channel vectors to obtain enhanced features, namely enhanced low-frequency spectral features and enhanced high-frequency spectral features; S2.6: The original spectrum and the enhanced features are fused using residuals to obtain a mixed spectrum; S2.7: Perform inverse Fourier transform on the mixed spectrum to obtain the enhanced and denoised time-domain features. .

5. The method according to claim 1, characterized in that, The shared context The process involves two parallel paths, each processed using Mamba blocks to output local detail features. Long-term trend characteristics ,include: Shared Context The system enters two parallel paths: one is a local path, which uses a small convolutional kernel to extract local contextual features, and the other is a global path, which uses a large convolutional kernel to extract global contextual features under a large receptive field. Subsequently, the two paths are modeled temporally using their respective Mamba blocks. The Mamba block for the local path, based on its internal discretized state-space model and selective scanning mechanism, performs state recursion and feature updates along the time dimension on the local context features extracted from the local path, outputting local detail features. The Mamba block of the global path, based on its internal discretized state-space model and selective scanning mechanism, performs state recursion and feature updates along the time dimension on the global context features extracted from the global path, outputting long-term trend features. .

6. The method according to claim 5, characterized in that, The Mamba block for local paths, based on an internal discretized state-space model and a selective scanning mechanism, performs state recursion and feature updates along the time dimension on the local context features extracted from the local path, outputting local detail features. The Mamba block of the global path, based on its internal discretized state-space model and selective scanning mechanism, performs state recursion and feature updates along the time dimension on the global context features extracted from the global path, outputting long-term trend features. ,include: For any time step The Mamba blocks for local and global paths dynamically generate relevant parameters of the state-space model based on the input features at the current time step, including the discretized state transition matrix. Discretized input projection matrix Output projection matrix and skip connection matrix ; Based on the above state space model parameters, the Mamba block recursively calculates the hidden state of the current time step and outputs the output features of the current time step through the hidden state of the current time step. The Mamba block of the local path sequentially performs the above state recursion and feature output on the features of each time step in the local path, and arranges the output features of all time steps in chronological order to form local detail features. The Mamba block of the global path sequentially performs the above state recursion and feature output on the features of each time step in the global path, and arranges the output features of all time steps in chronological order to form long-term trend features. .

7. The method according to claim 1, characterized in that, Local detail features Long-term trend characteristics The output features are obtained through cross-modulation and enhancement fusion using a cross-gating fusion mechanism. ,include: Local detail features Long-term trend characteristics Nonlinear transformation and regularization are performed respectively to generate the first gated signal and the second gated signal for modulation; The first gating signal and the second gating signal are respectively related to long-term trend characteristics. Local details and the shared context Cross modulation is achieved through a triple Hadamard product; The output features after cross-modulation are summed, and the channel dimension is adjusted through a linear projection layer to obtain the aggregated features of multi-scale sea clutter. The aggregated features, after undergoing random deep regularization, are combined with the initial input temporal features. Residual connections yield output features .

8. The method according to claim 1, characterized in that, Feature tensor Global context representations are extracted from the normalized sequence, and a multilayer perceptron is used as the prediction head to map the converged global context representations to predicted sea clutter amplitudes for the next k time steps, including: S4.1: Feature Tensor Global context representations are extracted using layer normalization, and a multilayer perceptron is used as the prediction head. The converged global context representations are projected onto a higher-dimensional hidden space, and nonlinearity is introduced through the GELU activation function to obtain hidden features. ; S4.2: During the training phase, the activated hidden features... By applying the Dropout operation, the output of some neurons is randomly set to zero to obtain regularized hidden features. S4.3: Projecting the regularized hidden features into the output space yields the predicted sea clutter amplitude values ​​for the next k time steps, expressed as: ； in, This represents the predicted sea clutter amplitude at k time steps. This represents the bias term of the second-layer perceptron. This represents the weight matrix of the second-layer perceptron.

9. An adaptive Fourier and Mamba sea clutter prediction system, characterized in that, The prediction system includes: The spatiotemporal augmentation input preprocessing module is used for input preprocessing of spatiotemporal augmentation: acquiring raw sea clutter radar echo data and converting it into amplitude data; based on the amplitude data, through spatial correlation calculation, selecting the center range gate to be predicted and the temporal amplitude sequences of the adjacent range gates before and after the center range gate to construct a multi-channel input tensor; the input tensor is normalized and linearly mapped to obtain projection features. Based on the projection features Construct a joint coding mechanism to generate initial features ; An adaptive Fourier filter module is used for adaptive Fourier filtering: the initial features Adaptive frequency band separation is achieved by performing a Fourier transform in the frequency domain and introducing learnable frequency band parameters. The separated frequency bands are then subjected to frequency-point feature transformation and enhancement using a learnable multilayer perceptron. The enhanced features are then reconstructed in the time domain by calculating the mixed spectrum and performing an inverse Fourier transform to obtain the time-domain features. ; Dual-path Mamba module for dual-path Mamba time series modeling: the time-domain features Activate to obtain shared context Shared context The process involves two parallel paths, each processed using Mamba blocks to output local detail features. Long-term trend characteristics The local detail features With the aforementioned long-term trend characteristics The output features are obtained by cross-modulation and enhancement fusion through a cross-gating fusion mechanism. ; Output module, used to output predicted values: the output features The final feature tensor is obtained after stacking adaptive Fourier filtering and dual-path Mamba temporal modeling. The feature tensor Global context representations are extracted from the normalized sequence, and a multilayer perceptron is used as the prediction head to map the converged global context representations into predicted sea clutter amplitude values ​​for the next k time steps.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it is used to implement the steps of the adaptive Fourier and Mamba sea clutter prediction method according to any one of claims 1-8.

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