Sea surface small target detection method fusing OTFS and depth expansion

Abstract

The invention discloses a sea surface small target detection method fusing OTFS modulation and a depth expansion structure, belongs to the field of radar signal processing, and achieves the purpose of improving feature detection performance. The method comprises the following steps: mapping a signal from a time domain to a delay-Doppler domain by using OTFS modulation, constructing a sparse recovery model, and converting an FISTA iteration process into a trainable network structure by using depth expansion; a GAN model is used to carry out adaptive optimization on parameters of each layer, and a CBAM mechanism is introduced to enhance the response capability of a key area. And a multi-stage loss function design and a false alarm rate control mechanism are utilized, so that the detection precision and the anti-interference performance of the model are improved. An IPIX data set is adopted for verification, the average detection rates under four polarization modes are 88.2%, 91.5%, 90.0% and 83.3% respectively, and it is indicated that the performance of the method is good.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar signal processing, and particularly relates to a sea surface small target detection method fusing OTFS and deep unfolding. BACKGROUND

[0002] Sea clutter is a natural reflection phenomenon commonly encountered in the process of radar detection on the sea, which is derived from the echo signal generated by the wave disturbance on the sea surface. Due to its complex spatial distribution structure and strong instability with time variation, it shows high unpredictability under different sea conditions and detection conditions. In addition, sea clutter has obvious multi-dimensional non-Gaussian statistical characteristics, especially under high resolution conditions. In contrast, target echo signals are often weak and submerged in background noise, with a low signal-to-clutter ratio, which significantly increases the difficulty of detecting weak targets on the sea surface and becomes a long-standing technical challenge in the field of marine radar target detection.

[0003] At present, the key to small target detection under the sea clutter background is to extract discriminative features with distinguishing degrees between the target and the clutter. In order to enhance the expression ability of the target signal, researchers have proposed various feature extraction methods from different angles. Chen et al. designed a multi-scale decomposition strategy based on wavelet packet entropy, which effectively suppressed the high-frequency clutter interference while preserving the time-frequency information. In view of the multi-modal and nonlinear characteristics of sea clutter, Li et al. constructed an energy spectrum feature model based on the improved empirical wavelet transform, which showed high stability in target detection under various sea conditions. Since there is obvious frequency drift characteristic in the sea clutter echo, Zhao et al. proposed a method combining Hilbert spectrum analysis and marginal spectrum extraction to accurately characterize the dynamic spectrum structure. In order to further improve the anti-interference ability in complex background, Wang et al. introduced the graph structure modeling idea, constructed a clutter-target graph and extracted structural consistency features based on graph signal filtering technology, which significantly improved the separability of weak targets. In addition, in view of the strong dependence of traditional model training in the small sample scene, Zheng et al. combined the self-supervised learning mechanism with the modal residual feature fusion strategy to realize the effective enhancement and separation of the target under the condition of no label. At present, the feature extraction method combining time-frequency decomposition, structure modeling and deep expression is gradually becoming a research hotspot in sea clutter small target detection, and based on the above reasons, the application designs a. SUMMARY

[0004] The purpose of the application is to solve the problems in the prior art, and a sea surface small target detection method fusing OTFS and deep unfolding is proposed.

[0005] A sea surface small target detection method fusing OTFS and deep unfolding, comprising the following steps:

[0006] S1: Obtain a to-be-detected signal, wherein the to-be-detected signal includes a sea clutter signal and a target-containing echo signal, and the to-be-detected signal is subjected to normalized preprocessing, and the sea clutter signal and the target-containing echo signal are marked with "0" labels and "1" labels respectively;

[0007] S2: The normalized signal is input into a time-varying channel model for propagation, time-frequency mapping is performed through a matched filter, and a two-dimensional sine Fourier transform SFFT is adopted to obtain a received signal in a delay-Doppler domain:

[0008]

[0009] The signal has a sparse structure characteristic;

[0010] S3: A fast iterative shrinkage threshold algorithm FISTA is adopted for channel sparse reconstruction modeling, momentum acceleration and soft threshold operation are alternately iterated and calculated, and a sparse estimation problem is converted into a minimum optimization model with block sparse constraints;

[0011] S4: The fast iterative shrinkage threshold algorithm FISTA is expanded into a deep neural network with a layer-by-layer structure to construct a Tensor-FISTA-Net, a momentum path is updated for residual error estimation z k [k,l], and a residual projection module is used to correct estimation error r k [k,l];

[0012] S5: A CBAM attention mechanism is introduced in each layer of the network to enhance the response capability of a target region from two dimensions of a channel and space, and then the enhanced features are input into a generator subnetwork of a GAN to extract non-sparse structure information and perform non-linear mapping; meanwhile, a WGAN-GP adversarial training structure is introduced, key parameters in each layer of the network are dynamically generated by the generator, the discriminator measures the distribution difference between the generated structure and the real label, and parameter adaptive optimization training is realized through a feedback mechanism;

[0013] S6: Sparse feature and energy distribution feature are extracted from the final sparse estimation result, wherein the sparse feature is composed of the variance of an autocorrelation function and the l 2,1 norm of the target-containing echo signal, two types of features are extracted in parallel to form a two-dimensional feature vector F combined ;

[0014] S7: F combined is input into a GAN classification discriminator, Lovasz-Softmax Loss is introduced as a main loss function, and a preset threshold parameter θ is combined to judge the output result When , it is determined that the signal contains a target, otherwise, it is determined that the signal does not contain a target; by adjusting θ, the false alarm rate of the model is controlled, and adaptive optimization of the detection performance is realized.

[0015] In the above method, the detection problem is classified as a binary hypothesis test:

[0016]

[0017] wherein H0 hypothesis represents that only sea clutter signal is in the echo signal, H1 hypothesis represents that target echo is contained in the echo signal, z(n), c(n) and s(n) represent radar echo, sea clutter and target echo of the unit to be detected respectively, z p (n), c p (n) represent radar echo and sea clutter of the reference unit respectively.

[0018] In the above method, in step S2, the process of obtaining the sparse signal in the delay-Doppler domain by using two-dimensional symplectic Fourier transform includes the following steps:

[0019] S21: in the channel propagation process, assuming that the time-varying channel has P paths, the channel can be represented as:

[0020]

[0021] wherein h i , τ i and v i represent channel gain, delay and Doppler shift of the i-th path respectively, and l and k represent time delay index and Doppler index respectively;

[0022] S22: after the time domain signal s(t) is transmitted through the channel, the received signal r(t) is obtained:

[0023] r(t) = ∫∫h(τ, v)s(t-τ)e j2πv(t-τ dτdv + n(t)

[0024] wherein n(t) is Gaussian additive noise.

[0025] S23: in the demodulation process at the receiving end, the received signal r(t) is subjected to Wigner-Ville transform and matched filtering by using a shaping filter g rx (t), so as to obtain the time-frequency domain signal Y[n, m]:

[0026] Y[n, m] = ∫r(t)g rx (t-nT)e -j2πmΔf(t-nT) dt

[0027] wherein T represents the duration of each symbol, and TΔf = 1.

[0028] S24: Y[n, m] is converted back to the DD domain by symplectic finite Fourier transform (SFFT):

[0029]

[0030] where N and M represent the number of time symbols and frequency subcarriers in each frame, respectively, and n and m represent the time and frequency indices, respectively.

[0031] In the above method, in step S3, the channel sparse reconstruction modeling is performed using the fast iterative shrinkage thresholding algorithm (FISTA), and the process of alternating iterative calculation of momentum acceleration and soft thresholding operation includes the following steps:

[0032] S31: The channel estimation problem can be converted into the following optimization model:

[0033]

[0034] where s is the observation data, A is the measurement matrix, x is the vector to be recovered, λ is the regularization parameter, and x g represents the gth subvector after partitioning. When the algorithm is initialized, the shrinkage coefficient t1=1 is set, and in the kth iteration, the update is performed according to the following steps:

[0035] S32: First, the auxiliary variable is constructed by the results of the first two iterations:

[0036] z k = x k-1 + α k (x k-1 -x k-2 )

[0037] where α k is the momentum coefficient, and t k is the shrinkage coefficient, and its update method is:

[0038]

[0039] S33: Then, the gradient correction is performed using the current momentum estimate value z k to obtain the intermediate variable:

[0040] r k = z k - μA T (Az k -s)

[0041] where μ is the gradient step size parameter;

[0042] S34: In order to strengthen the block sparse characteristics of the signal, each subvector r k in r g is normalized to obtain a new estimate x gFor each group r g The following update is applied:

[0043]

[0044] Where (·) + represents taking the non-negative part;

[0045] S35: By repeating the momentum superposition, gradient correction and soft threshold update operation, the objective function value is gradually optimized, and the iteration ends after meeting the termination condition.

[0046] In the above method, in step S4, the fast iterative shrinkage thresholding algorithm FISTA is unfolded into a deep neural network with a layer-by-layer structure, and the process of constructing Tensor-FISTA-Net includes the following steps:

[0047] S41: The OTFS receiving end restores the received time-frequency domain signal to the DD domain by SFFT to obtain the complex form of the received symbol The real part and the imaginary part are spliced to form a tensor input:

[0048]

[0049] Where, and represent the real part and the imaginary part of the complex number, represents the real-imaginary part splicing of the complex tensor, that is, is a tensor with a size of KxLx2;

[0050] S42: The FISTA iteration formula is unfolded into each layer of the network, and the momentum mechanism and momentum coefficient a k are introduced to improve the convergence speed, and the historical output is used to construct the momentum estimate value z k [k, l] to update the current layer state. The updated feature map is calculated by residual back-projection:

[0051]

[0052] Where H represents the sparse mapping matrix based on the DD domain in the OTFS system, H H represents its Hermitian conjugate, and mu k represents the learnable step size of the kth layer.

[0053] In the above method, in step S5, the following steps are specifically included:

[0054] S51: The CBAM module is composed of channel attention and spatial attention. In the channel attention mechanism, the input feature map Global average pooling and max pooling are performed respectively to obtain two channel description vectors F avg and F max , which are input into a shared multi-layer perception (MLP) and added together, and then a sigmoid activation function is used to obtain channel attention weights:

[0055] M c (F)=σ(MLP(F avg )+MLP(F max ))

[0056] where σ(·) represents a sigmoid function.

[0057] S52: The obtained weights are applied to the original input feature map to perform channel dimension weighting, and the output is:

[0058] F1=M c (F)⊙F

[0059] where ⊙ represents element-wise multiplication.

[0060] S53: Then, the spatial attention mechanism is entered. First, average pooling and max pooling operations are performed on F1 in the channel dimension to obtain two spatial description maps and After concatenating the two along the channel dimension, a 7x7 convolution operation is performed, and a sigmoid activation function is used to obtain spatial attention weights:

[0061]

[0062] where [·;·] represents channel concatenation operation.

[0063] S54: The CBAM is used to perform attention weighting on the feature map r k [k,l], and the enhanced feature map is obtained:

[0064]

[0065] where β k is the channel and spatial enhancement factor of CBAM.

[0066] S55: The is input into the generator subnetwork G k (·), which extracts local sparse structures and performs nonlinear mapping processing. The output is subjected to sparse contraction by a Soft function to obtain the next layer estimate:

[0067]

[0068] S56: In order to improve the continuity and stability of the generated results, WGAN-GP is used as the training target. The loss function of the discriminator is:

[0069]

[0070] where, denotes the expectation, denotes the reconstructed channel output by the generator, X real denotes the real sparse channel sample, is a random linear interpolation sample, and ∈ ~ U(0,1), λ gp is the gradient penalty weight.

[0071]

[0072] η θ (x) = sign(x) * max(|x|- θ, 0)

[0073] where sign(·) is the sign function, which is used to retain the sign of the element, and θ is the learnable shrinkage threshold.

[0074] S58: The final channel estimation result is output as:

[0075]

[0076] The sparse estimation value is used for subsequent feature extraction tasks.

[0077] In the above method, in step S6, the following steps are specifically included:

[0078] S61: Define the autocorrelation function when the delay is τ as:

[0079]

[0080] S62: Define the variance as:

[0081]

[0082] S63: Let be the matrix composed of , define its l 2,1 norm as:

[0083]

[0084] S64: An adaptive weighted fusion mechanism is introduced, and the generator module in the GAN network automatically learns the fusion weight ε ∈ [0, 1]. The final sparse feature is defined as:

[0085] F sparse = ε * VarR + (1 - ε) · ||D|| 2,1

[0086] S65: Introduce the energy distribution feature as a parallel indicator, first define the total energy:

[0087]

[0088] S66: Calculate the normalized energy probability distribution p of the signal in the DD domain k,l , and further define the energy entropy to represent the dispersion degree of the energy distribution:

[0089]

[0090] S67: Finally, the fused sparsity indicator and energy entropy form a two-dimensional feature vector:

[0091] F combined = [F sparse , H E ].

[0092] In the above method, in step S7, the GAN classification discriminator is constructed, Lovasz-Softmax Loss is introduced as the main loss function, and the process of judging whether there is a target in the echo signal includes the following steps:

[0093] S71: Let the model output prediction probability be p = (p1, p2, …, p N ), and the corresponding true label be y = (y1, y2, …, y N ) ∈ {0, 1} N , then Lovasz-Softmax Loss can be expressed as:

[0094]

[0095] Where Δ i represents the weight term based on the IoU gradient, which is used to emphasize the error contribution of the boundary region.

[0096] S72: By counting the misjudgment in the verification set, set the threshold θ so that the false alarm rate satisfies the following constraint:

[0097]

[0098] Where N0 is the number of sea clutter samples, γ is the maximum acceptable false alarm rate, which is set to 0.05; is the indicator function;

[0099] S73: If , it is determined that it does not contain target echoes, which belongs to the H0 hypothesis, if If yes, it is determined that the target echo is contained, and it belongs to the H1 hypothesis, and by updating the threshold value theta, the false alarm rate of the GAN can be effectively controlled, and the classification performance can be finely controlled.

[0100] The beneficial effects of the present application are: compared with the prior art, the present application uses OTFS modulation to map the signal from the time domain to the DD domain, and uses the idea of deep unfolding to embed the FISTA optimization process into the generative adversarial network framework, and introduces a tensor parameter modeling method to replace the traditional matrix operation. In view of the problems of the existing Tensor-FISTA-Net method, such as unclear target and background response, lack of spatial attention ability and the like in the feature extraction process, the CBAM mechanism is further introduced to adaptively enhance the key feature response from the channel and spatial dimensions. Then, sparse feature and energy distribution features are extracted, and the feature vectors are input into the GAN classifier, and the false alarm rate of the model is controlled by updating the decision threshold in real time. The IPIX data set is used for verification, and the average detection rates under four polarization modes are 88.2%, 91.5%, 90.0% and 83.3% respectively, which shows that the performance of the method is good. BRIEF DESCRIPTION OF DRAWINGS

[0101] Figure 1 is the OTFS-FISTA-Net algorithm flow chart of the OTFS and deep unfolding fusion sea surface small target detection method proposed by the present application.

[0102] Figure 2 is the structural difference diagram of the signal before and after OTFS modulation in the present application.

[0103] Figure 3 is the detection rate curve of the four methods under different false alarm rates.

[0104] Figure 4 is the detection performance of the five detection methods under four polarizations. DETAILED DESCRIPTION

[0105] REFERENCE Figures 1-4 A sea surface small target detection method fusing OTFS and deep unfolding, as shown in Figure 1 , comprising the following steps:

[0106] S1: acquiring a to-be-detected signal, wherein the to-be-detected signal includes a sea clutter signal and a target echo signal containing target echo, and performing normalization preprocessing on the to-be-detected signal, and marking the sea clutter signal and the target echo signal containing target echo with "0" labels and "1" labels respectively;

[0107] S2: inputting the normalized signal into a time-varying channel model for propagation, performing time-frequency mapping through a matched filter, and obtaining a received signal in a delay-Doppler domain (DD domain) by using a two-dimensional sine Fourier transform (SFFT) The signal has a sparse structure characteristic;

[0108] S3: Fast Iterative Shrinkage Thresholding Algorithm (FISTA) is used for channel sparse reconstruction modeling. Momentum acceleration and soft thresholding operation are iteratively calculated alternately to convert the sparse estimation problem into a minimum optimization model with block sparse constraints.

[0109] S4: FISTA is expanded into a deep neural network with layer-by-layer structure to construct Tensor-FISTA-Net. Momentum path is used to update residual error estimation z k [k,l] and residual projection module is used to correct the estimation error r k [k,l];

[0110] S5: CBAM attention mechanism is introduced in each layer of the network to enhance the response ability of the target area from the channel and spatial dimensions. Then the enhanced features are input into the generator subnetwork of GAN to extract non-sparse structure information and perform nonlinear mapping. WGAN-GP adversarial training structure is introduced to dynamically generate key parameters in each layer of the network by the generator, and the discriminator measures the distribution difference between the generated structure and the real label, and realizes adaptive optimization training through the feedback mechanism.

[0111] S6: Sparse feature and energy distribution feature are extracted from the final sparse estimation result. The sparse feature is composed of the variance of the autocorrelation function and the l 2,1 norm weighted. Two types of features are extracted in parallel to form a two-dimensional feature vector F combined ;

[0112] S7: F combined is input into the GAN classification discriminator, Lovasz-Softmax Loss is introduced as the main loss function, and the output result is judged by combining the preset threshold parameter θ. When , it is determined that the target signal is contained, otherwise it is determined that the target signal is not contained; by adjusting θ, the false alarm rate of the model is controlled, and the adaptive optimization of the detection performance is realized.

[0113] In step S1, the detection problem is classified as a binary hypothesis test:

[0114]

[0115] Where H0 hypothesis represents that only sea clutter signal is contained in the echo signal, and H1 hypothesis represents that target echo is contained in the echo signal. z(n), c(n) and s(n) represent radar echo, sea clutter and target echo of the detection unit, respectively. p (n) and c p (n) represent radar echo and sea clutter of the reference unit, respectively.

[0116] In step S2, the process of obtaining the sparse signal in the delay-Doppler domain by using two-dimensional symplectic Fourier transform includes the following steps:

[0117] S21: In the process of channel propagation, assuming that the time-varying channel has P paths, the channel can be expressed as:

[0118]

[0119] where h i , τ i and v i represent the channel gain, delay and Doppler shift of the i-th path respectively, and l and k represent the delay index and Doppler index respectively.

[0120] S22: After the time-domain signal s(t) is transmitted through the channel, the received signal r(t) is obtained:

[0121] r(t) = ∫∫ h(τ, v) s(t - τ) e j2πv (t - τ) dτ dv + n(t)

[0122] where n(t) is Gaussian additive noise.

[0123] S23: In the demodulation process at the receiving end, the received signal r(t) is subjected to Wigner-Ville transform and matched filtering using a shaping filter g rx (t), so as to obtain the time-frequency domain signal Y[n, m]:

[0124]

[0125] where T represents the duration of each symbol, and TΔf = 1.

[0126] S24: Convert Y[n, m] back to the DD domain by symplectic finite Fourier transform (SFFT):

[0127]

[0128] where N and M represent the number of time symbols and frequency subcarriers contained in each frame respectively, and n and m represent the time and frequency indices respectively.

[0129] In step S3, the channel sparse reconstruction is modeled by using the fast iterative shrinkage thresholding algorithm (FISTA), and the process of iterative calculation by alternation of momentum acceleration and soft thresholding operation includes the following steps:

[0130] S31: The channel estimation problem can be converted into the following optimization model:

[0131]

[0132] Among them, s is the observation data, A is the measurement matrix, x is the vector to be restored, λ is the regularization parameter, and x g represents the gth subvector after the partition. When the algorithm is initialized, the shrinkage coefficient t1 is set to 1. In the kth iteration, the update is performed according to the following steps.

[0133] S32: First, construct auxiliary variables using the results of the first two iterations:

[0134] z k =x k-1 +α k (x k-1 -x k-2 )

[0135] Among them, α k is the momentum coefficient, and t k is the shrinkage coefficient, which is updated as follows:

[0136]

[0137] S33: Next, use the current momentum estimate z k Perform gradient correction to obtain intermediate variables:

[0138] r k =z k -μA T (Az k -s)

[0139] Among them, μ is the gradient step size parameter.

[0140] S34: In order to enhance the block sparseness of the signal, r k Each subvector r in g Normalize them separately to get the new estimate x g For each group r g , apply the following updates:

[0141]

[0142] in,(·) + Indicates taking the non-negative part.

[0143] S35: By repeating the above momentum superposition, gradient correction and soft threshold update operations, the objective function value is gradually optimized. The iteration ends when the termination condition is met.

[0144] In step S4, FISTA is expanded into a layer-by-layer deep neural network. The process of constructing Tensor-FISTA-Net includes the following steps:

[0145] S41: The OTFS receiving end restores the received time-frequency domain signal to the DD domain through SFFT to obtain a complex form of received symbol The real part and the imaginary part are spliced to form a tensor input:

[0146]

[0147] wherein, and represent the real part and the imaginary part of the complex number respectively, represents the real-imaginary part splicing of the complex tensor, that is, is a tensor with a size of KxLx2.

[0148] S42: The FISTA iterative formula is expanded to each layer of the network, and a momentum mechanism and a momentum coefficient a are introduced k to improve the convergence speed. The momentum estimate value z is constructed using the historical output k [k, l] to update the current layer state. The updated feature map is calculated through residual back projection:

[0149]

[0150] wherein, H represents a sparse mapping matrix based on the DD domain in the OTFS system, H H represents its Hermitian conjugate, μ k represents the learnable step size of the kth layer.

[0151] In step S5, the CBAM attention mechanism is introduced, and the enhanced features are input into the generator subnetwork of the GAN. At the same time, the WGAN-GP adversarial training structure is introduced, and the process of parameter adaptive optimization training is realized through the feedback mechanism, which includes the following steps:

[0152] S51: The CBAM module is composed of channel attention and spatial attention. In the channel attention mechanism, the input feature map is respectively subjected to global average pooling and maximum pooling to obtain two channel description vectors F avg and F max . After being subjected to shared multi-layer perception (MLP) and addition, the channel attention weight is obtained by using the Sigmoid activation function:

[0153] M c (F)=σ(MLP(F avg )+MLP(F max ))

[0154] wherein, σ(·) represents the Sigmoid function.

[0155] S52: The obtained weight is applied to the original input feature map to perform channel dimension weighting, and the output is:

[0156] F1 = M c (F) ￡ F

[0157] where ￡ denotes element-wise multiplication.

[0158] S53: Then enter the spatial attention mechanism. First, average pooling and max pooling operations are performed on F1 in the channel dimension to obtain two spatial description maps and After concatenating them along the channel dimension, a 7x7 convolution operation is performed, and the spatial attention weight is obtained through the Sigmoid activation function:

[0159]

[0160] where [·; ·] denotes the channel concatenation operation.

[0161] S54: Use CBAM to perform attention weighting on the feature map r k [k, l], to obtain the enhanced feature map:

[0162]

[0163] where β k is the channel and spatial enhancement factor of CBAM.

[0164] S55: Input into the generator subnetwork G k (·), extract local sparse structures and perform nonlinear mapping processing. The output is subjected to sparse contraction through the Soft function to obtain the next layer estimate:

[0165]

[0166] S56: To improve the continuity and distribution stability of the generated results, WGAN-GP is used as the training target. The loss function of the discriminator is:

[0167]

[0168] where denotes the expectation, denotes the reconstructed channel output by the generator, X real denotes the real sparse channel sample, is a random linear interpolation sample, and ∈ ~ U(0, 1), λ gp is the gradient penalty weight.

[0169] S57: After k layers of deep unfolding, the output sparse estimate xk It will be used for discriminant classification analysis of subsequent modules. In order to enhance the sparsity control of the final output, the network introduces a soft threshold function η at the end θ (·) Perform soft threshold shrinkage:

[0170]

[0171] η θ (x) = sign(x) max(|x|-θ,0)

[0172] Here, sign(·) is a sign function used to preserve the element sign, and θ is a learnable shrinkage threshold.

[0173] S58: The final channel estimation result is output as:

[0174]

[0175] This sparse estimate is used for subsequent feature extraction tasks.

[0176] In step S6, the final sparse estimation result Extract sparse features (by the variance of the autocorrelation function and l 2,1 norm weighted composition) and energy distribution characteristics, and constitute a two-dimensional feature vector F combined The process includes the following steps:

[0177] S61: The autocorrelation function when the delay is τ is defined as:

[0178]

[0179] S62: Define variance as:

[0180]

[0181] S63: Set for The matrix formed by defining its l 2,1 The norm is:

[0182]

[0183] S64: Introduce an adaptive weighted fusion mechanism, where the generator module in the GAN network automatically learns the fusion weight ε∈[0,1]. The final sparsity feature is defined as:

[0184] F sparse =ε·Var R +(1-ε)·||D|| 2,1

[0185] S65: Introduce the energy distribution feature as a parallel indicator, first define the total energy:

[0186]

[0187] S66: Calculate the normalized energy probability distribution p of the signal in the DD domain k,l , and then define the energy entropy to represent the dispersion degree of the energy distribution:

[0188]

[0189] S67: Finally, the fused sparsity indicator and energy entropy form a two-dimensional feature vector:

[0190] F combined =[F sparse ,H E ]

[0191] In step S7, the GAN classification discriminator is constructed, and Lovasz-Softmax Loss is introduced as the main loss function. The process of judging whether there is a target in the echo signal includes the following steps:

[0192] S71: Let the model output prediction probability be p=(p1,p2,…,p N ), and the corresponding true label be y=(y1,y2,…,y N )∈{0,1} N , then Lovasz-Softmax Loss can be expressed as:

[0193]

[0194] Where Δ i represents the weight term based on the IoU gradient, which emphasizes the error contribution of the boundary region.

[0195] S72: By counting the misjudgment in the verification set, set the threshold θ so that the false alarm rate satisfies the following constraint:

[0196]

[0197] Where N0 is the number of sea clutter samples; γ is the maximum acceptable false alarm rate, set to 0.05; is the indicator function.

[0198] S73: If , it is determined that it does not contain target echoes, belonging to the H0 hypothesis. If , it is determined that it contains target echoes, belonging to the H1 hypothesis. By updating the threshold θ, the false alarm rate of GAN can be effectively controlled, thereby realizing fine control of the classification performance.

[0199] The data used in this paper is from the IPIX radar target database collected in 1993 on the east coast of Canada. The radar works in x-band, the working frequency is 9.39GHz, and the resolution is 30m. The target to be detected is a small ball wrapped with metal wire, about 1m in diameter. The data contains 4 polarization modes, HH, HV, VH, and VV, each of which is composed of 14 range cells, and each range cell contains 217 (131.072s) pulses.

[0200] It is obvious that the present application can be implemented by other embodiments without departing from the spirit or essential characteristics thereof. The above-described embodiments are only illustrative and not restrictive, and all modifications within the scope of the present application or equivalent to the scope of the present application are intended to be included in the present application.

Claims

1. A method for detecting small targets on the sea surface by integrating OTFS and deep expansion, characterized in that: The following steps are involved: S1: Acquire the signal to be detected, which includes the sea clutter signal and the target echo signal, and perform normalization preprocessing on the signal to be detected, marking the sea clutter signal and the target echo signal with a "0" label and a "1" label respectively; S2: The normalized signal is input into the time-varying channel model for propagation, time-frequency mapping is performed through a matched filter, and the two-dimensional sigmoid Fourier transform (SFFT) is used to obtain the received signal in the delay-Doppler domain: The signal has a sparse structure characteristic; S3: The fast iterative shrinkage threshold algorithm FISTA is used for channel sparse reconstruction modeling. Through alternating iterative calculations using momentum acceleration and soft thresholding operations, the sparse estimation problem is transformed into a minimization optimization model with block sparsity constraints. S4: Expand the fast iterative shrinkage threshold algorithm FISTA into a layer-by-layer deep neural network, construct Tensor-FISTA-Net, and update the residual estimate z through the momentum path k [k,l], and use the residual projection module to correct the estimation error r k [k,l]; S5: The CBAM attention mechanism is introduced in each network layer to enhance the responsiveness of the target region in both channel and spatial dimensions. The enhanced features are then fed into the GAN generator subnetwork to extract non-sparse structural information and perform nonlinear mapping. Furthermore, the WGAN-GP adversarial training structure is introduced. The generator dynamically generates key parameters in each network layer, while the discriminator measures the distribution difference between the generated structure and the true label. A feedback mechanism is used to achieve adaptive parameter optimization training. S6: Extract the sparsity feature and energy distribution feature from the final sparse estimation result, where the sparsity feature is determined by the variance of the autocorrelation function and l 2,1 Norm weighted composition, the two types of features are extracted in parallel to form a two-dimensional feature vector F combined ; S7: F combined Input GAN classification discriminator, introduce Lovasz-Softmax Loss as the main loss function, and combine the preset threshold parameter θ to judge the output result when When , it is determined to contain target signals, otherwise it is determined to be without target. By adjusting θ to control the false alarm rate of the model, adaptive optimization of detection performance is achieved.

2. The method for detecting small targets on the sea surface by integrating OTFS and deep expansion according to claim 1 is characterized in that: In step S1, the detection problem is formulated as a binary hypothesis test: Wherein, H0 hypothesis indicates that the echo signal contains only sea clutter signal, H1 hypothesis indicates that the echo signal contains target echo, z(n), c(n), s(n) represent the radar echo, sea clutter and target echo of the unit to be detected respectively, z p (n), c p (n) represent the radar echo and sea clutter of the reference cell, respectively.

3. The method for detecting small sea targets by integrating OTFS and deep expansion according to claim 1 is characterized in that: In step S2, the process of obtaining a sparse signal in the delay-Doppler domain using a two-dimensional sigmoid Fourier transform includes the following steps: S21: During channel propagation, assuming that the time-varying channel has P paths, the channel can be expressed as: Among them, h i , τ i and v i denote the channel gain, delay and Doppler shift of the i-th path respectively, and l and k represent the delay index and Doppler index, respectively; S22: The time domain signal s(t) is transmitted through the channel to obtain the received signal r(t): r(t)=∫∫h(τ,v)s(t-τ)e j2πv(t-τ) dτdv+n(t) Where n(t) is Gaussian additive noise; S23: During demodulation at the receiving end, a shaping filter g is used. rx (t) Perform Wigner transform and matched filtering on the received signal r(t) to obtain the time-frequency domain signal Y[n,m]: Y[n,m]=∫r(t)g rx (t-nT)e -j2πmΔf(t-nT) dt Where T represents the duration of each symbol, and TΔf=1; S24: Convert Y[n,m] back to the DD domain via the symplectic finite Fourier transform (SFFT): Wherein, N and M represent the number of time symbols and frequency subcarriers contained in each frame, respectively, and n and m represent the time and frequency indexes, respectively.

4. The method for detecting small targets on the sea surface by integrating OTFS and deep expansion according to claim 1, characterized in that: In step S3, the fast iterative shrinkage threshold algorithm FISTA is used to perform channel sparse reconstruction modeling. The process of alternating iterative calculation through momentum acceleration and soft threshold operation includes the following steps: S31: The channel estimation problem can be transformed into the following optimization model: Among them, s is the observation data, A is the measurement matrix, x is the vector to be restored, λ is the regularization parameter, and x g It represents the g-th sub-vector after division. When the algorithm is initialized, the shrinkage coefficient t1 is set to 1. In the k-th iteration, it is updated according to the following steps: S32: First, construct auxiliary variables using the results of the first two iterations: z k =x k-1 +α k (x k-1 -x k-2 ) Among them, α k is the momentum coefficient, and t k is the shrinkage coefficient, which is updated as follows: S33: Next, use the current momentum estimate z k Perform gradient correction to obtain intermediate variables: r k =z k -μA T (Az k -s) Among them, μ is the gradient step parameter; S34: In order to enhance the block sparseness of the signal, r k Each subvector r in g Normalize them separately to get the new estimate x g , for each group r g , apply the following updates: in,(·) + Indicates taking the non-negative part; S35: By repeating the above momentum superposition, gradient correction and soft threshold update operations, the objective function value is gradually optimized, and the iteration ends after the termination condition is met.

5. The method for detecting small sea targets by integrating OTFS and deep expansion according to claim 1, characterized in that: In step S4, the fast iterative shrinkage threshold algorithm FISTA is expanded into a deep neural network with a layer-by-layer structure. The process of constructing Tensor-FISTA-Net includes the following steps: S41: The OTFS receiver restores the received time-frequency domain signal to the DD domain through SFFT to obtain the complex received symbol Concatenate its real and imaginary parts to form the tensor input: in, and represent the real and imaginary parts of a complex number, respectively. represents the concatenation of the real and imaginary parts of the complex tensor, that is, is a tensor of size K×L×2; S42: Expand the FISTA iterative formula to each layer of the network, introduce the momentum mechanism and momentum coefficient α k Improve the convergence speed and use historical output to construct momentum estimate z k [k,l], to update the current layer state, and update the feature map by residual back projection calculation: Among them, H represents the sparse mapping matrix based on DD domain in OTFS system, H H represents its Hermitian conjugation, μ k represents the learnable step size of the k-th layer.

6. The method for detecting small targets on the sea surface by integrating OTFS and deep expansion according to claim 2, characterized in that: In step S5, the following steps are specifically included: S51: The CBAM module consists of two parts: channel attention and spatial attention. In the channel attention mechanism, the input feature map is first Perform global average pooling and maximum pooling respectively to obtain two channel description vectors F avg With F max After the two are added together through a shared multi-layer perceptron MLP, the channel attention weight is obtained using the Sigmoid activation function: M c (F)=σ(MLP(F avg )+MLP(F max )) Where σ(·) represents the Sigmoid function; S52: Apply the obtained weights to the original input feature map to perform channel dimension weighting, and the output is: F1=M c (F)⊙F Among them, ⊙ represents element-by-element multiplication; S53: Then enter the spatial attention mechanism, first perform average pooling and maximum pooling operations on F1 in the channel dimension, and obtain two spatial description maps and After concatenating the two along the channel dimension, they are input into a 7×7 convolution operation and activated by the Sigmoid function to obtain the spatial attention weight: Among them, [·;·] represents the channel splicing operation; S54: Using CBAM to feature map r k [k, l] performs attention weighting to obtain the enhanced feature map: Among them, β k is the channel space enhancement factor of CBAM; S55: Input generator subnetwork G k In (·), the local sparse structure is extracted and nonlinear mapping is performed. The output is sparsely shrunk by the Soft function to obtain the next layer estimate: S56: To improve the continuity and distribution stability of the generated results, WGAN-GP is used as the training target, and the loss function of its discriminator is: in, Expressing hope, represents the reconstructed channel output by the generator, X real represents the real sparse channel sample, is a random linear interpolation sample, and ∈~U(0,1), λ gp is the gradient penalty weight; S57: After k layers of depth expansion, the output sparse estimate x k It will be used for discriminant classification analysis of subsequent modules. In order to enhance the sparsity control of the final output, the network introduces a soft threshold function η at the end θ (·) Perform soft threshold shrinkage: or θ (x)=sign(x)·max(|x|-θ,0) Where sign(·) is a sign function used to preserve the element sign, and θ is a learnable shrinkage threshold; S58: The final channel estimation result is output as: This sparse estimate is used for subsequent feature extraction tasks.

7. The method for detecting small sea targets by integrating OTFS and deep expansion according to claim 2, characterized in that: In step S6, the following steps are specifically included: S61: The autocorrelation function when the delay is τ is defined as: S62: Define variance as: S63: Set for The matrix formed by defining its l 2,1 The norm is: S64: Introducing an adaptive weighted fusion mechanism, the generator module in the GAN network automatically learns the fusion weight ε∈[0,1], and the final sparsity feature is defined as: F sparse =e·Var R +(1-e)·||D|| 2,1 S65: Introducing energy distribution characteristics as a parallel indicator, first define total energy: S66: Calculate the normalized energy probability distribution p of the signal in the DD domain k,l , and then define energy entropy to characterize the discrete degree of energy distribution: S67: Finally, the fused sparsity index and energy entropy are combined to form a two-dimensional feature vector: F combined =[F sparse ,H E ]。 8. The method for detecting small targets on the sea surface by integrating OTFS and deep expansion according to claim 2, characterized in that: In step S7, a GAN classification discriminator is constructed, and Lovasz-Softmax Loss is introduced as the main loss function. The process of determining whether there is a target in the echo signal includes the following steps: S71: Let the model output prediction probability be p=(p1,p2,…,p N ), the corresponding true label is y=(y1,y2,…,y N )∈{0,1} N , then Lovasz-Softmax Loss can be expressed as: Among them, Δ i Represents the weight term based on IoU gradient, which is used to emphasize the error contribution of the boundary area; S72: By counting the number of misjudgments in the validation set, a threshold θ is set so that the false alarm rate satisfies the following constraint: Where N0 is the number of sea clutter samples, γ is the maximum acceptable false alarm rate, which is set to 0.05; is the indicator function; S73: If It is determined that the target echo is not included, which belongs to the H0 hypothesis. If It is determined to contain the target echo, which belongs to the H1 hypothesis. By updating the threshold θ, the false alarm rate of GAN can be effectively controlled, and fine control of the classification performance can be achieved.

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