Sea surface small target detection method based on optimization characteristic mode decomposition

Abstract

The invention belongs to the technical field of radar signal processing, and discloses a sea surface small target detection method based on optimized characteristic mode decomposition, which comprises the following steps: S1, acquiring to-be-detected signal data; s2, decomposing an original signal into a plurality of modal components by using FMD, and selecting an envelope spectrum entropy as a fitness function; s3, performing global optimization on the fitness function in the FMD by using an SOS algorithm; s4, introducing a PSO algorithm to carry out local optimization on key parameters of the FMD; s5, components with low envelope spectrum entropy values and correlation coefficients larger than a threshold value are reserved; s6, extracting an envelope spectrum entropy and frequency band energy ratio feature from the screened modal components, introducing a Gini coefficient as a weighting factor, and constructing a GSEBE joint feature; and S7, inputting the entropy value of the envelope spectrum into a DELM classifier with a controllable false alarm, and realizing target detection based on comparison between a predicted value and a judgment threshold. According to the invention, the capability of distinguishing sea clutters and target echoes is enhanced, and more accurate classification detection is realized.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, specifically relating to a method for detecting small targets on the sea surface based on optimized feature mode decomposition. Background Technology

[0002] In maritime radar detection, sea clutter is a common echo interference caused by sea surface fluctuations. Currently, the key to effectively detecting weak targets on the sea surface in complex sea clutter backgrounds lies in how to separate and extract discriminative structured sparse features from strong interference. In recent years, researchers have proposed various feature extraction methods based on mode decomposition (EMD) to address the non-stationarity of signals. For example, Empirical Mode Decomposition (EEMD) is widely used in echo analysis due to its adaptability, but it suffers from mode aliasing. EEMD alleviates this deficiency to some extent by averaging with multiple noise additions, and some existing techniques have proposed detection frameworks combining spectral entropy and kurtosis features based on EEMD, effectively enhancing target characterization capabilities. To further improve the stability of the decomposed components, CEEMD improves the consistency of the decomposition through a noise cancellation mechanism and has been applied by some existing techniques to extract energy perturbation features from weak signals. In contrast, Variational Mode Decomposition (VMD) has advantages in handling signal spectral suppression and center frequency clustering. Some existing techniques fuse VMD with multi-channel features to improve the model's robustness to high-frequency clutter. Eigenmode decomposition (EMD), a novel method in recent years, can adaptively filter prior features during the decomposition process. Some existing techniques use EMD as a basis to construct combined feature evaluation indices, effectively achieving clutter suppression and signal preservation for significant components in echo signals. Currently, small target detection methods are gradually evolving towards higher accuracy, interpretability, and lower complexity, becoming an important research trend in the field of marine target detection.

[0003] However, sea clutter exhibits a complex spatial distribution and significant non-stationarity over time, making its performance highly uncertain under different detection conditions. This complexity is further exacerbated in high-resolution observation environments. Furthermore, sea clutter possesses typical non-Gaussian multidimensional statistical characteristics, which often mask the effective features of weak targets. In contrast, target echo signals themselves have weak energy and are easily submerged in sea clutter and environmental noise, resulting in extremely low signal-to-noise ratios and severely impacting accurate target detection. Current technologies struggle to update discrimination criteria in real time, and their ability to distinguish between sea clutter and target echoes remains insufficient, requiring further improvement in detection reliability and efficiency. Summary of the Invention

[0004] The purpose of this invention is to provide a method for detecting small targets on the sea surface based on optimized feature mode decomposition, which addresses the technical problem that the existing technology still has insufficient ability to distinguish between sea clutter and target echoes, and that the reliability and efficiency of detection still need to be further improved.

[0005] The sea surface small target detection method based on optimized feature mode decomposition includes the following steps:

[0006] S1: Acquire the signal data to be detected, where the signal samples include two types: sea clutter echoes and echoes containing targets;

[0007] S2: Use FMD to decompose the original signal into several modal components, and select the envelope spectrum entropy as the fitness function;

[0008] S3: Use the SOS algorithm to perform global optimization of the fitness function in FMD;

[0009] S4: Introduce the PSO algorithm to locally optimize the key parameters of FMD;

[0010] S5: Compare the envelope spectral entropy values ​​and correlation coefficients of adjacent modal components, and retain the components with lower envelope spectral entropy values ​​and correlation coefficients greater than the threshold.

[0011] S6: Extract the envelope spectral entropy and frequency band energy ratio features from the screened modal components, introduce the Gini coefficient as a weighting factor, and construct the GSEBE joint features;

[0012] S7: Input the normalized envelope spectrum entropy value into the DELM classifier with controllable false alarm rate, set a target false alarm rate, and adjust it by finding the decision threshold that is closest to the target false alarm rate; compare the predicted value obtained after training the test data with the decision threshold to achieve target detection.

[0013] Preferably, step S2 includes the following steps:

[0014] S21: Input original signal dataset x, number of decomposition modes n, filter length L;

[0015] S22: Use an FIR filter bank initialized with K Hanning windows, each filter corresponding to a different bandwidth and center frequency, and set the iteration to start from i=1;

[0016] S23: Perform filter bank convolution on the input signal x to obtain the k-th mode component.

[0017]

[0018] Where * denotes convolution operation, This represents the k-th filter in the i-th iteration;

[0019] S24: When The autocorrelation spectrum reaches a local maximum after crossing zero. When the estimated period is obtained, Using the original signal x and modal components and estimated period Update the filter coefficients; once one iteration is complete, set i = i + 1.

[0020] S25: Determine if the maximum number of iterations has been reached; if not, return to step S23; otherwise, continue to step S26.

[0021] S26: Calculate the correlation coefficient CC between every two modal components and construct the correlation matrix CC. K×K ; Retain the two modes with the largest CC values ​​and calculate their envelope spectral entropy;

[0022] S27: Retain the mode with the smaller envelope spectral entropy among the two modes, and set K = K-1;

[0023] S28: Determine whether the current number of modes K is greater than the number of decomposed modes n. If it is equal, stop the iteration; otherwise, return to step S23 to continue merging redundant modes until the number of remaining modes is n.

[0024] Preferably, step S26 includes: for each modal component u k Perform a Hilbert transform and obtain the envelope e. k (n):

[0025]

[0026] Where H(·) denotes the Hilbert transform of the signal, u k (n) represents the k-th modal component of the n-th pulse echo;

[0027] Calculating the envelope spectrum E using Fast Fourier Transform k (f):

[0028] E k (f)=|FFT(e k (n))|

[0029] Where FFT(·) represents performing a fast Fourier transform, and f is the frequency;

[0030] For envelope spectrum E k (f) Normalize to obtain the envelope spectral power density P k (f):

[0031]

[0032] Calculate the envelope spectrum entropy:

[0033]

[0034] Among them, H kLet represent the envelope spectral entropy of the k-th IMF, and ε represent a small constant to prevent numerical overflow.

[0035] Preferably, in step S3, the main mechanisms of the SOS algorithm include a mutualistic symbiosis phase, a symbiotic symbiosis phase, and a parasitic phase:

[0036] 1) In the mutualistic stage, two individuals x are randomly selected from the initial population. i and x j By learning from each other and enhancing each other's survival capabilities, the updated position representation is as follows:

[0037] x i，new =x i +rand(0,1)·(x best -M e B1)

[0038] x j，new =x j +rand(0,1)·(x best -M e B2)

[0039] Where rand(0,1) represents a random number uniformly distributed between 0 and 1; M e Represents an individual organism x i and x j The interaction between them, the calculation formula: x best B1 and B2 represent the best individual in the current population; B1 and B2 are the corresponding individuals x. i and x j The benefit factor represents the ability of an individual organism to gain benefits through reciprocal relationships, and is usually taken as 1 or 2.

[0040] 2) In the symbiotic stage, individual organism x i Able to obtain from other biological individuals x j It benefits itself without affecting the other party, and leverages the optimal individual x best To learn:

[0041] x i，new =x i +rand(-1, 1)·(x best -x j )

[0042] Where rand(-1, 1) represents a random number uniformly distributed between -1 and 1;

[0043] 3) During the parasitic stage, randomly select an individual x i As a host, the parasitic organism invades the host and generates a parasite x. v If xv The fitness is better than that of a certain individual x j Then x j Replaced; otherwise, x j It possesses immunity and is preserved, expressed as follows:

[0044] x v =x i

[0045] x v (p)=rand(1,length(p))*(ub(p)-lb(p))+lb(p)

[0046] Where p represents a mutant, length represents the number of mutants p; ub and lb represent the upper and lower bounds of the search, respectively.

[0047] Preferably, step S4 includes the following steps:

[0048] S41: First, initialize a set of particles in the search space, and use the position vector x i This indicates that each particle possesses a velocity vector v. i During the iteration process of the PSO algorithm, each particle records its own historical best position. And the current global optimal position G of the entire population. best ;

[0049] S42: Introducing the Logistic chaotic mapping to optimize the inertia weights, with the number of iterations set to n, the expression for the Logistic chaotic mapping is as follows:

[0050] d n+1 =μd n (1-d n )

[0051] Where d represents a random number generated by the chaotic mapping, and d∈(0,1); μ represents the control parameter of the Logistic mapping. Setting μ puts the system in a chaotic state and updates the velocity and position of the particles.

[0052] The preferred formula for calculating the updated particle velocity and position is as follows:

[0053]

[0054] x i，n+1 =x i，n +v i，n

[0055] Where, x i，n+1 and v i，n+1 Let x represent the position vector and velocity vector of the particle at iteration n+1, respectively.i，n and v i，n Let these represent the particle's position vector and velocity vector after n iterations, respectively. and Let d represent the historical optimal position of the particle and the global optimal position of the corresponding population after n iterations, respectively. n c1 and c2 represent the random numbers generated by the chaotic mapping after n iterations; c1 and c2 represent the cognitive learning factor and the social learning factor, respectively; r1 and r2 represent random numbers uniformly distributed in the interval [0, 1].

[0056] Preferably, step S6 includes the following steps:

[0057] S61: Divide the spectrum into low-frequency bands f L and high frequency band f H Calculate the frequency band energy proportion R of the low-frequency band:

[0058]

[0059] Where X(f) represents the band energy at the corresponding frequency f;

[0060] S62: Calculate the Gini coefficient of the envelope spectral entropy H and the frequency band energy proportion R respectively as weighting factors:

[0061]

[0062] Among them, G H and G R Let p represent the envelope spectral entropy H and the band energy proportion R, respectively. i and r i Let represent the envelope spectral entropy and the frequency band energy percentage of the i-th modal component, respectively, and K represent the total number of modal components;

[0063] S63: Calculate the GSEBE joint features. The GSEBE joint features are composed of a weighted combination of spectral entropy and energy percentage. The calculation formula is: GSEBE = G H ·H+G R ·R.

[0064] Preferably, step S7 includes the following steps:

[0065] S71: The DELM classifier is trained layer by layer in unsupervised learning to extract features; the reconstructed features extracted by each layer of the DELM classifier are used as the input of the next layer, and multiple layers of network are stacked in sequence to gradually mine the deep structural features of the input data.

[0066] S72: After completing multi-layer feature extraction, the DELM classifier completes the supervised learning task through the output layer and outputs weights; the output layer of the DELM classifier still adopts the ELM structure and uses the extracted deep features as input, combined with the sample label T, to solve the final output weights, and then further calculates the predicted value;

[0067] S73: Set a target false alarm rate (FAR) desired Adjustments are made by finding the threshold θ that is closest to the target false alarm rate.

[0068]

[0069] Among them, P fa (λ) represents the false positive rate, which is used to measure the error rate. λ is a preliminary threshold that is automatically generated during the decision-making process. The test set is finally classified based on the calculated optimal threshold θ.

[0070] Preferably, in step S71, the formula for calculating the output weights in the DELM classifier is as follows:

[0071]

[0072] Where C is the regularization coefficient, I is the identity matrix, X represents the input sample matrix, and H represents the hidden layer output matrix;

[0073] In step S72, the formula for calculating the final output weights is:

[0074]

[0075] Among them, H + Let be the generalized inverse matrix of the hidden layer output matrix; the formula for calculating the predicted value is: Where g represents the activation function.

[0076] This invention offers the following advantages: It proposes a method for detecting small targets on the sea surface based on optimized feature mode decomposition (EMD), achieving dual collaborative optimization of key parameters in EMD. First, the SOS algorithm is used for global search to obtain the optimal feature fitness component, ensuring good sparsity and discriminative power of the mode components. Then, the PSO algorithm is introduced to locally fine-tune parameters such as the decomposition step size and scale window, improving the stability and feature completeness of mode extraction. Furthermore, in the feature extraction stage, a Gini weighting mechanism is used to fuse envelope spectral entropy and frequency band energy proportion, enhancing the ability to distinguish between sea clutter and target echoes. Finally, the DELM model is used to accurately classify signal types. Attached Figure Description

[0077] Figure 1This is a flowchart of the sea surface small target detection method based on optimized feature mode decomposition in this invention.

[0078] Figure 2 This is a network structure diagram of the DELM classifier in this invention.

[0079] Figure 3 The FMD time-domain plot generated during the experimental verification of this invention.

[0080] Figure 4 The FMD spectrum generated during the experimental verification of this invention.

[0081] Figure 5 The detection performance graphs at different observation times were generated during the experimental verification of this invention. Detailed Implementation

[0082] The following detailed description of the embodiments, with reference to the accompanying drawings, will further illustrate the specific implementation of the present invention, in order to help those skilled in the art to have a more complete, accurate, and thorough understanding of the inventive concept and technical solutions of the present invention.

[0083] like Figures 1-5 As shown, the present invention provides a method for detecting small targets on the sea surface based on optimized feature mode decomposition, which includes the following steps.

[0084] S1: Acquire the signal data to be detected, where the signal samples include two types: sea clutter echoes and echoes containing the target.

[0085] Before using the data, the signal samples are normalized and standardized, and labeled "0" (sea clutter) and "1" (target echo) according to their category. In step S1, the detection problem is categorized as a binary hypothesis test:

[0086]

[0087] In this context, H0 assumption indicates that the echo signal contains only sea clutter, while H1 assumption indicates that the echo signal contains target echoes. z(n), c(n), and s(n) represent the radar echo, sea clutter, and target echo of the unit to be detected, respectively, and N is the number of pulse echoes. p (n), c p (n) represent the radar echo and sea clutter of the reference element, respectively, and P represents the total number of reference elements.

[0088] S2: The original signal is decomposed into several modal components using FMD (Eigenmode Decomposition), and the envelope spectral entropy is selected as the fitness function.

[0089] Step S2 includes the following steps.

[0090] S21: Input the original signal dataset x, the number of decomposition modes n, and the filter length L.

[0091] S22: Use an FIR filter bank initialized with K Hanning windows, each filter corresponding to a different bandwidth and center frequency, and set the iteration to start from i=1.

[0092] S23: Perform filter bank convolution on the input signal x to obtain the k-th mode component.

[0093]

[0094] Where * denotes convolution operation, This represents the k-th filter in the i-th iteration.

[0095] S24: When The autocorrelation spectrum reaches a local maximum after crossing zero. When the estimated period is obtained, Using the original signal x and modal components and estimated period Update the filter coefficients. Once one iteration is complete, set i = i + 1.

[0096] S25: Determine if the maximum number of iterations has been reached. If not, return to step S23; otherwise, continue to step S26.

[0097] S26: Calculate the correlation coefficient CC between every two modal components and construct the correlation matrix CC. K×K Retain the two modes with the largest CC values ​​and calculate their envelope spectral entropy. For each modal component u... k Perform a Hilbert transform and obtain the envelope e. k (n):

[0098]

[0099] Where H(·) denotes the Hilbert transform of the signal, u k (n) represents the k-th mode component of the n-th pulse echo.

[0100] Calculating the envelope spectrum E using Fast Fourier Transform k (f):

[0101] E k (f)=|FFT(e k (n))|

[0102] Where FFT(·) represents performing a fast Fourier transform, and f is the frequency.

[0103] For envelope spectrum Ek (f) Normalize to obtain the envelope spectral power density P k (f):

[0104]

[0105] Calculate the envelope spectrum entropy:

[0106]

[0107] Among them, H k Let represent the envelope spectral entropy of the k-th IMF, and ε represent a small constant to prevent numerical overflow.

[0108] S27: Retain the mode with the smaller envelope spectral entropy among the two modes, and set K = K-1.

[0109] S28: Determine whether the current number of modes K is greater than the number of decomposed modes n. If it is equal, stop the iteration; otherwise, return to step S23 to continue merging redundant modes until the number of remaining modes is n.

[0110] S3: Use the SOS (Symbiotic Search) algorithm to globally optimize the fitness function in FMD.

[0111] This step uses the fitness function as a biological individual to search for the optimal combination of indicators to measure the sparsity and separability of different modal components, providing an optimization starting point for subsequent modality screening.

[0112] The main mechanisms of the SOS algorithm include the mutualistic phase, the symbiotic phase, and the parasitic phase.

[0113] 1) In the mutualistic stage, different organisms improve their adaptability through mutualism. Two individuals x are randomly selected from the initial population. i and x j By learning from each other and enhancing each other's survival capabilities, the updated position representation is as follows:

[0114] x i，new =x i +rand(0,1)·(x best -M e B1)

[0115] x j，new =x j +rand(0,1)·(x best -M e B2)

[0116] Where rand(0,1) represents a random number uniformly distributed between 0 and 1; M e Represents an individual organism x i and xj The interaction between them, the calculation formula: x best B1 and B2 represent the best individual in the current population; B1 and B2 are the corresponding individuals x. i and x j The benefit factor represents the ability of an individual organism to gain benefits through reciprocal relationships, and is usually taken as 1 or 2.

[0117] 2) In the symbiotic stage, individual organism x i Able to obtain from other biological individuals x j It benefits itself without affecting the other party, and leverages the optimal individual x best To learn:

[0118] x i，new =x i +rand(-1, 1)·(x best -x j )

[0119] Here, rand(-1, 1) represents a random number uniformly distributed between -1 and 1.

[0120] 3) During the parasitic stage, randomly select an individual x i As a host, the parasitic organism invades the host and generates a parasite x. v If x v The fitness is better than that of a certain individual x j Then x j Replaced; otherwise, x j They possess immunity and are preserved. This stage increases the randomness of the population, preventing it from getting trapped in local optima.

[0121] x v =x i

[0122] x v (p)=rand(1,length(p))*(ub(p)-lb(p))+lb(p)

[0123] Where p represents a mutant, length represents the number of mutants p; ub and lb represent the upper and lower bounds of the search, respectively.

[0124] S4: Introduce the PSO (Particle Swarm Optimization) algorithm to perform local optimization of the key parameters of FMD.

[0125] This step, based on the initial fitness structure obtained by the SOS algorithm, introduces the PSO algorithm to locally optimize the key parameters of FMD (key parameters as particles) to improve the discriminativeness and stability of the decomposed modes, and further enhance the fineness and generalization ability of feature representation.

[0126] Step S4 includes the following steps.

[0127] S41: First, initialize a set of particles in the search space, and use the position vector x i This indicates that each particle possesses a velocity vector v. i This is used to adjust the particle's direction and step size within the search space. During the iteration process of the PSO algorithm, each particle records its historical best position. And the current global optimal position G of the entire population. best .

[0128] S42: Introducing the Logistic chaotic mapping to optimize the inertia weights, with the number of iterations set to n, the expression for the Logistic chaotic mapping is as follows:

[0129] d n+1 =μd n (1-d n )

[0130] Where d represents the random number generated by the chaotic mapping, and d∈(0,1); μ represents the control parameter of the Logistic mapping. It is known from experience that when μ∈(3.57,4], the system is in a chaotic state. This optimization algorithm selects μ=4, that is, the system is in a completely chaotic state.

[0131] The formulas for updating the particle's velocity and position are as follows:

[0132]

[0133] x i，n+1 =x i，n +v i，n

[0134] Where, x i，n+1 and v i，n+1 Let x represent the position vector and velocity vector of the particle at iteration n+1, respectively. i，n and v i，n Let these represent the particle's position vector and velocity vector after n iterations, respectively. and Let d represent the historical optimal position of the particle and the global optimal position of the corresponding population after n iterations, respectively. n c1 and c2 represent the random numbers generated by the chaotic mapping after n iterations; c1 and c2 represent the cognitive learning factor and the social learning factor, respectively; r1 and r2 represent random numbers uniformly distributed in the interval [0,1].

[0135] S5: Compare the envelope spectral entropy values ​​and correlation coefficients of adjacent modal components, and retain the components with lower envelope spectral entropy values ​​and correlation coefficients greater than the threshold.

[0136] This step effectively filters out noise modes, improving the stability and effectiveness of signal feature extraction. The threshold for the correlation coefficient can be set to 0.3.

[0137] S6: Extract envelope spectral entropy and frequency band energy proportion features from the screened modal components, introduce the Gini coefficient as a weighting factor, and construct the GSEBE joint feature. This step enhances the sparsity and energy difference of the feature representation.

[0138] Step S6 includes the following steps.

[0139] S61: Divide the spectrum into low-frequency bands f L and high frequency band f H Calculate the frequency band energy proportion R of the low-frequency band:

[0140]

[0141] Where X(f) represents the band energy at the corresponding frequency f.

[0142] S62: Calculate the Gini coefficient of the envelope spectral entropy H and the frequency band energy proportion R respectively as weighting factors:

[0143]

[0144]

[0145] Among them, G H and G R Let p represent the envelope spectral entropy H and the band energy proportion R, respectively. i and r i Let represent the envelope spectral entropy and the frequency band energy percentage of the i-th modal component, respectively, and K represent the total number of modal components.

[0146] S63: Calculate the joint features of GSEBE. The joint features of GSEBE (Gini-indexed Spectral Entropy and Band Energy) are composed of a weighted combination of spectral entropy and energy proportion, and the calculation formula is: GSEBE = G H ·H+G R ·R.

[0147] S7: Input the normalized envelope spectrum entropy value into the DELM classifier with controllable false alarm rate, set a target false alarm rate, and adjust it by finding the decision threshold that is closest to the target false alarm rate; compare the predicted value obtained after training the test data with the decision threshold to achieve target detection.

[0148] Step S7 includes the following steps.

[0149] S71: The DELM classifier undergoes unsupervised learning layer-by-layer training to extract features. During this process, the calculation formula for the output weights in the DELM classifier is as follows:

[0150]

[0151] Where C is the regularization coefficient, I is the identity matrix, X represents the input sample matrix, and H represents the hidden layer output matrix. The reconstructed features extracted from each layer of the DELM classifier serve as the input to the next layer, and multiple layers are stacked sequentially to build a multi-layer network, thereby gradually mining the deep structural features of the input data.

[0152] S72: After completing multi-layer feature extraction, the DELM classifier completes the supervised learning task through the output layer and outputs the weights.

[0153] The output layer of the DELM classifier still uses the ELM structure, and uses the extracted deep features as input, combined with the sample labels T, to solve for the final output weights:

[0154]

[0155] Among them, H + Let be the generalized inverse of the hidden layer output matrix. Further calculation yields the predicted value, using the following formula: Where g represents the activation function.

[0156] S73: Set a target false alarm rate (FAR) desired Adjustments are made by finding the threshold θ that is closest to the target false alarm rate.

[0157]

[0158] Among them, P fa (λ) represents the false positive rate, which is used to measure the error rate. λ is a preliminary threshold that is automatically generated during the decision-making process.

[0159] Based on the calculated optimal threshold θ, the test set is finally classified. This indicates that the target echo is not included, which falls under the H0 hypothesis. If the signal is positive, it is determined to contain the target echo, which falls under the H1 hypothesis. By updating the threshold θ, the false alarm rate of DELM can be effectively controlled, thereby achieving fine control over classification performance.

[0160] To verify the effectiveness of this method, experiments were conducted using two typical datasets from the IPIX small target radar dataset for the sea surface. The first dataset, collected in 1993, contains 10 samples, each covering four polarization channels: HH, HV, VH, and VV. Each channel contains 14 range cells and an echo sequence with approximately 1.3 seconds of observation time. The target is a 1.2-meter diameter metal-encased sphere floating on the sea surface. The overall signal-to-clutter ratio (SCR) ranges from -0.3 dB to 16 dB, with most samples exhibiting low SCR and weak target characteristics, making detection challenging. The second dataset, collected in 1998, has the same structure as the first, but each range cell contains approximately 60 seconds of observation pulses. The target is a small boat on the sea surface, with an SCR range of -1.8 dB to 28 dB. The maximum SCR difference between polarization channels exceeds 10 dB, indicating significant differences in polarization characteristics. The resulting FMD time-domain plot is shown below. Figure 3 As shown, the resulting FMD spectrum is as follows Figure 4 As shown in Figure 5, the detection performance at different observation times after measurement is as follows. The verification results show that the proposed method improves upon the time-frequency three-feature detector by 5.35% under HH polarization and by 35.28% under VV polarization.

[0161] The present invention has been described above by way of example with reference to the accompanying drawings. Obviously, the specific implementation of the present invention is not limited to the above-described manner. Any non-substantial improvements made using the inventive concept and technical solution of the present invention, or the direct application of the inventive concept and technical solution of the present invention to other occasions without modification, are all within the protection scope of the present invention.

Claims

1. A method for detecting small targets on the sea surface based on optimized feature mode decomposition, characterized in that: Includes the following steps: S1: Acquire the signal data to be detected, where the signal samples include two types: sea clutter echoes and echoes containing targets; S2: Use FMD to decompose the original signal into several modal components, and select the envelope spectrum entropy as the fitness function; S3: Use the SOS algorithm to perform global optimization of the fitness function in FMD; S4: Introduce the PSO algorithm to locally optimize the key parameters of FMD; S5: Compare the envelope spectral entropy values ​​and correlation coefficients of adjacent modal components, and retain the components with lower envelope spectral entropy values ​​and correlation coefficients greater than the threshold. S6: Extract envelope spectral entropy and frequency band energy proportion features from the screened modal components, introduce the Gini coefficient as a weighting factor, and construct GSEBE joint features; S7: Input the normalized envelope spectrum entropy value into the DELM classifier with controllable false alarm rate, set a target false alarm rate, and adjust it by finding the decision threshold that is closest to the target false alarm rate; compare the predicted value obtained after training the test data with the decision threshold to achieve target detection.

2. The method for detecting small targets on the sea surface based on optimized feature mode decomposition according to claim 1, characterized in that: Step S2 includes the following steps: S21: Input original signal dataset x, number of decomposition modes n, filter length L; S22: Use an FIR filter bank initialized with K Hanning windows, each filter corresponding to a different bandwidth and center frequency, and set the iteration to start from i=1; S23: Perform filter bank convolution on the input signal x to obtain the k-th mode component. Where * denotes convolution operation, This represents the k-th filter in the i-th iteration; S24: When The autocorrelation spectrum reaches a local maximum after crossing zero. When the estimated period is obtained, Using the original signal x and modal components and estimated period Update the filter coefficients; once one iteration is complete, set i = i + 1. S25: Determine if the maximum number of iterations has been reached; if not, return to step S23; otherwise, continue to step S26. S26: Calculate the correlation coefficient CC between every two modal components and construct the correlation matrix CC. K×K ; Retain the two modes with the largest CC values ​​and calculate their envelope spectral entropy; S27: Retain the mode with the smaller envelope spectral entropy among the two modes, and set K = K-1; S28: Determine whether the current number of modes K is greater than the number of decomposed modes n. If it is equal, stop the iteration; otherwise, return to step S23 to continue merging redundant modes until the number of remaining modes is n.

3. The method for detecting small targets on the sea surface based on optimized feature mode decomposition according to claim 2, characterized in that: Step S26 includes: for each modal component u k Perform a Hilbert transform and obtain the envelope e. k (n): Where H(·) denotes the Hilbert transform of the signal, u k (n) represents the k-th modal component of the n-th pulse echo; Calculating the envelope spectrum E using Fast Fourier Transform k (f): E k (f)=|FFT(e k (n))| Where FFT(·) represents performing a fast Fourier transform, and f is the frequency; For envelope spectrum E k (f) Normalize to obtain the envelope spectral power density P k (f): Calculate the envelope spectrum entropy: Among them, H k Let represent the envelope spectral entropy of the k-th IMF, and ε represent a small constant to prevent numerical overflow.

4. The method for detecting small targets on the sea surface based on optimized feature mode decomposition according to claim 1, characterized in that: In step S3, the main mechanisms of the SOS algorithm include a mutualistic symbiosis phase, a symbiotic symbiosis phase, and a parasitic phase: 1) In the mutualistic stage, two individuals x are randomly selected from the initial population. i and x j By learning from each other and enhancing each other's survival capabilities, the updated position representation is as follows: x i，new =x i +rand(0,1)·(x best -M e B1) x j,new =x j +rand(0,1)·(x best -M e B2) Where rand(0,1) represents a random number uniformly distributed between 0 and 1; M e Represents an individual organism x i and x j The interaction between them, the calculation formula: x best B1 represents the best individual in the current population; B1 and B are the corresponding individuals x. i and x j The benefit factor represents the ability of an individual organism to gain benefits through reciprocal relationships, and is usually taken as 1 or 2. 2) In the symbiotic stage, individual organism x i Able to obtain from other biological individuals x j It benefits itself without affecting the other party, and leverages the optimal individual x best To learn: x i，new =x i +rand(-1,1)·(x best -x j ) Where rand(-1, 1) represents a random number uniformly distributed between -1 and 1; 3) During the parasitic stage, randomly select an individual x i As a host, the parasitic organism invades the host and generates a parasite x. v If x v The fitness is better than that of a certain individual x j Then x j Replaced; otherwise, x j It possesses immunity and is preserved, expressed as follows: x v =x i x v (p)=rand(1,length(p))*(ub(p)-lb(p))+lb(p) Where p represents a mutant, length represents the number of mutants p; ub and lb represent the upper and lower bounds of the search, respectively.

5. The method for detecting small targets on the sea surface based on optimized feature mode decomposition according to claim 1, characterized in that: Step S4 includes the following steps: S41: First, initialize a set of particles in the search space, and use the position vector x i This indicates that each particle possesses a velocity vector v. i During the iteration process of the PSO algorithm, each particle records its own historical best position. And the current global optimal position G of the entire population. best ; S42: Introducing the Logistic chaotic mapping to optimize the inertia weights, with the number of iterations set to n, the expression for the Logistic chaotic mapping is as follows: d n+1 <μd n (1-d n ) Where d represents a random number generated by the chaotic mapping, and d∈(0,1); μ represents the control parameter of the Logistic mapping. Setting μ puts the system in a chaotic state and updates the velocity and position of the particles.

6. The method for detecting small targets on the sea surface based on optimized feature mode decomposition according to claim 5, characterized in that: The formulas for updating the particle's velocity and position are as follows: x i，n+1 =x i，n +v i，n Where, x i，n+1 and v i，n+1 Let x represent the position vector and velocity vector of the particle at iteration n+1, respectively. i，n and v i，n Let these represent the particle's position vector and velocity vector after n iterations, respectively. and Let d represent the historical optimal position of the particle and the global optimal position of the corresponding population after n iterations, respectively. n c1 and c2 represent the random numbers generated by the chaotic mapping after n iterations; c1 and c2 represent the cognitive learning factor and the social learning factor, respectively; r1 and r2 represent random numbers uniformly distributed in the interval [0, 1].

7. The method for detecting small targets on the sea surface based on optimized feature mode decomposition according to claim 1, characterized in that: Step S6 includes the following steps: S61: Divide the spectrum into low-frequency bands f L and high frequency band f H Calculate the frequency band energy proportion R of the low-frequency band: Where X(f) represents the band energy corresponding to frequency f; S62: Calculate the Gini coefficient of the envelope spectral entropy H and the frequency band energy proportion R respectively as weighting factors: Among them, G H and G R Let p represent the envelope spectral entropy H and the band energy proportion R, respectively. i and r i Let represent the envelope spectral entropy and the frequency band energy percentage of the i-th modal component, respectively, and K represent the total number of modal components; S63: Calculate the GSEBE joint features. The GSEBE joint features are composed of a weighted combination of spectral entropy and energy percentage. The calculation formula is: GSEBE = G H ·H+G R ·R.

8. The method for detecting small targets on the sea surface based on optimized feature mode decomposition according to claim 1, characterized in that: Step S7 includes the following steps: S71: The DELM classifier is trained layer by layer in unsupervised learning to extract features; the reconstructed features extracted by each layer of the DELM classifier are used as the input of the next layer, and multiple layers of network are stacked in sequence to gradually mine the deep structural features of the input data. S72: After completing multi-layer feature extraction, the DELM classifier completes the supervised learning task through the output layer and outputs weights; the output layer of the DELM classifier still adopts the ELM structure and uses the extracted deep features as input, combined with the sample label T, to solve the final output weights, and then further calculates the predicted value; S73: Set a target false alarm rate (FAR) desired Adjustments are made by finding the threshold θ that is closest to the target false alarm rate. Among them, P fa (λ) represents the false positive rate, which is used to measure the error rate. λ is a preliminary threshold that is automatically generated during the decision-making process. The test set is finally classified based on the calculated optimal threshold θ.

9. The method for detecting small targets on the sea surface based on optimized feature mode decomposition according to claim 1, characterized in that: In step S71, the formula for calculating the output weights in the DELM classifier is as follows: Where C is the regularization coefficient, I is the identity matrix, X represents the input sample matrix, and H represents the hidden layer output matrix; In step S72, the formula for calculating the final output weights is: Among them, H + Let be the generalized inverse matrix of the hidden layer output matrix; the formula for calculating the predicted value is: Where g represents the activation function.

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