A sea clutter suppression method based on complex number and adaptive dynamic weighting

Abstract

This application provides a sea clutter suppression method based on complex numbers and adaptive dynamic weighting, relating to the field of marine radar signal processing technology. The method includes performing a short-time Fourier transform on the raw radar echo data to generate a spectrum; standardizing preprocessing to obtain preprocessed in-phase and quadrature component signals; performing frequency domain pre-separation to obtain low-frequency sea clutter component signals; performing phase compensation and outputting the IMF corresponding to the low-frequency sea clutter components through improved complex EMD decomposition; performing multi-criteria adaptive selection to obtain the filtered IMF; calculating the high-frequency residual of the original signal; and performing dynamic weighted reconstruction and energy calibration based on the high-frequency residual and the filtered IMF to output the target signal after clutter suppression. This application improves the method's ability to capture signal phase information and suppresses mode aliasing by extending the time-domain EMD to the complex domain; and introduces an adaptive dynamic weighting mechanism to adjust the weight allocation in real time during the decomposition process, thereby improving sea clutter suppression performance.

Description

Technical Field

[0001] This application relates to the field of marine radar signal processing technology, and more specifically, to a sea clutter suppression method based on complex numbers and adaptive dynamic weighting. Background Technology

[0002] The unique rough and undulating characteristics of the sea surface cause it to interact with radar electromagnetic waves, generating strong backscattered echoes—sea clutter. This phenomenon has always been a challenge in radar target detection. After matched filtering and Doppler processing, sea clutter exhibits a symmetrically distributed ridge structure in the range-Doppler spectrum, with the ridge amplitude of each range cell showing a non-uniform distribution. This complex characteristic not only severely weakens the radar's ability to detect weak targets but is further exacerbated by the unique Doppler distribution characteristics near zero frequency of skywave radar (where sea clutter dominates), leading to a significant decrease in detection performance. Existing research shows that sea clutter is affected by multiple environmental factors such as wind speed, ocean currents, and swells, and exhibits strong non-stationary characteristics. Coupled with the diversity of radar parameter selection, sea clutter suppression has become a long-standing bottleneck problem hindering the field's development. This problem is particularly prominent when the target's RCS (Radar Cross Section) is close to or smaller than that of sea clutter, directly restricting the target detection capability of sea-based radar under complex weather conditions.

[0003] Traditional sea clutter suppression methods include: (1) Time-domain cancellation method: such as Lv, Zhou. Study on Sea Clutter Suppression Methods based on a Realistic Radar Dataset[J].Remote Sensing, 2019, 11(23):2721.DOI:10.3390 / rs11232721.; The core logic of the time-domain cancellation method relies on the parameter estimation of the simplified clutter model. The model simplifies sea clutter into a few discrete sinusoidal harmonic components. The key parameters (amplitude, angular frequency, initial phase) of the clutter harmonics are extracted by analyzing the radar echo spectrum through FFT. Based on the estimated parameters, the clutter time-domain signal is reconstructed, and then the reconstructed clutter is subtracted from the original echo to obtain the residual signal. The cancellation is completed iteratively. The premise of this logic is that the actual characteristics of the clutter must be completely matched with the preset discrete harmonic model, otherwise the parameter estimation will be biased.

[0004] (2) Wavelet Transform Method: Chinese Invention Patent CN105717494A discloses a method for designing sea clutter suppression curves for marine radar based on wavelet transform. It uses discrete wavelet transform to decompose radar echo data within the measurement range, then sets the high-frequency coefficients to zero, and uses the upper-level approximation to estimate the background sea clutter power level. Then, based on the range parameters and sea clutter suppression intensity parameters, the corresponding adjustable sea clutter suppression curve is calculated. Finally, the estimated actual sea clutter background power level curve is superimposed with the adjustable sea clutter suppression curve to obtain the overall sea clutter suppression curve. This method achieves high adaptability while sacrificing detail recognition and directly controls the sea clutter suppression intensity. However, it cannot automatically adjust the intensity based on sea state. In high sea states, clutter energy broadens, and a fixed scale cannot cover all clutter frequency bands, resulting in clutter residue. In low sea states, clutter energy is concentrated, and a fixed scale easily misclassifies the high-frequency components of the target as clutter, causing target suppression. It is highly dependent on manual control.

[0005] (3) EMD decomposition (Empirical Mode Decomposition) algorithm: Chinese invention patent CN118276021A discloses a radar target detection method based on WPE-EEMD and improved multifractal spectrum feature parameters. The method includes processing sea clutter and targets through ensemble empirical mode decomposition (EEMD) to obtain intrinsic mode function components; calculating the weighted permutation entropy of each order of intrinsic mode components for target and sea clutter components; and removing abnormal components according to the threshold of the weighted permutation entropy. The EMD algorithm achieves intrinsic decomposition of sea clutter by adaptively filtering intrinsic mode functions (IMFs), showing unique advantages in handling nonlinear and non-stationary characteristics. However, its inherent mode mixing and boundary effect defects restrict the practical application effect. This scheme (CN118276021A) directly decomposes the original signal containing sea clutter and targets. The cross-linking of different scale components in the signal further aggravates mode mixing. A similar approach is proposed in Chinese invention patent CN119959903A, which describes a method for detecting sea surface targets based on time-frequency feature enhancement and false alarm rate control. The core technical path of this approach is as follows: CEEMDAN decomposition - signal reconstruction - STFT time-frequency mapping - CNN false alarm rate control. This approach suffers from the same problem as the previous one. Although it reduces noise residue in EMD through adaptive noise allocation, it still directly decomposes the original signal. The frequency band components of clutter and the frequency band components of the target overlap. Given that mode aliasing already exists in CEEMDAN decomposition, CNN cannot distinguish the aliased frequency components and can only classify based on existing time-frequency features. It cannot solve the feature distortion caused by mode aliasing at its root. Summary of the Invention

[0006] To address the aforementioned problems, this application employs a sea clutter suppression method based on complex numbers and adaptive dynamic weighting, comprising: Perform a short-time Fourier transform on the raw radar echo data to generate a spectrum. The raw radar echo data is standardized and preprocessed to obtain preprocessed in-phase and quadrature component signals. Low-frequency sea clutter component signals are obtained by frequency domain pre-separation based on the spectrum diagram and the preprocessed in-phase and quadrature component signals. After phase compensation based on the low-frequency sea clutter component signal, the IMF corresponding to the low-frequency sea clutter component is output through improved complex EMD decomposition. Multi-criteria adaptive selection is performed on the IMFs corresponding to low-frequency sea clutter components to obtain the filtered IMFs; The high-frequency residual of the original signal is calculated based on the low-frequency sea clutter component signal. Dynamic weighted reconstruction and energy calibration are performed based on the high-frequency residual of the original signal and the filtered IMF, and the target signal after clutter suppression is output.

[0007] Optionally, the standardization preprocessing includes performing mean-removal and variance-normalization processes on the in-phase component I and quadrature component Q of the original radar echo data according to the following formula, respectively, to obtain the in-phase component after mean-removal and variance-normalization. and orthogonal components : ; In the formula, and Let I and Q represent the mean values ​​of the in-phase component and quadrature component, respectively, of the original radar echo data. and These represent the standard deviations of the in-phase component I and the quadrature component Q of the original radar echo data, respectively. Then, the quadrature phase error is calculated based on the following formula. : ; In the formula, This represents the expectation operator, used to perform operations on... The results are averaged based on the orthogonal phase error. In-phase components after mean and variance normalization and orthogonal components Phase rotation is performed to obtain the preprocessed in-phase component signal. and orthogonal component signals ,include: ; .

[0008] Optionally, frequency domain pre-separation includes: The energy spectrum is calculated based on the spectrogram, and a threshold truncation is performed on the energy spectrum to determine the left boundary frequency f. left and right boundary frequency f right Based on the left boundary frequency f, the following formula is used. left and right boundary frequency f right Calculate the cutoff frequency : ; A frequency mask is constructed based on the cutoff frequency using the following formula: ; Perform Fourier transforms on the preprocessed in-phase and quadrature component signals to obtain the frequency domain signal. Use a frequency mask to separate the frequency domain signal to obtain the clutter frequency domain signal. Convert the clutter frequency domain signal back to the time domain to obtain the low-frequency sea clutter component signal. Based on the following formula: ; In the formula, This represents the preprocessed complex radar signal. Indicates that through Fourier transform This converts the time-domain signal of the complex radar signal into a frequency-domain signal. Indicates the use of separating S + and S - The corresponding clutter band mask, where S + yes The corresponding positive frequency side clutter, S - yes The corresponding negative frequency side clutter, This indicates that an inverse Fourier transform is performed on the filtered frequency domain signal.

[0009] Optionally, phase compensation includes calculating the phase difference based on the following formula. : ; In the formula, arg() represents the argument operator, used to take the phase angle of a complex number. This represents the expectation operator, used to perform operations on... The element-wise results are averaged. express and Multiply at each time point, express The conjugate of the complex number is used to calculate and The phase difference between them; Then based on the phase difference pair Performing a phase rotation yields the phase and... Consistent new components : .

[0010] Optionally, the improved complex EMD decomposition includes: treating the low-frequency sea clutter component signal as the real part of a complex signal, constructing the imaginary part through Hilbert transform to obtain the complete complex signal, performing EMD decomposition on the complete complex signal, optimizing the envelope fitting using cubic spline interpolation, stopping when the IMF energy difference between two adjacent decompositions is <0.25, and decomposing up to 15 layers, outputting the IMF corresponding to the low-frequency sea clutter component.

[0011] Optionally, the IMF multi-criteria adaptive selection includes performing target-dominant screening and forced retention screening on the IMFs corresponding to low-frequency sea clutter components to obtain target-dominant IMFs and forced retention IMFs, and merging the target-dominant IMFs and forced retention IMFs to obtain the final retained IMF.

[0012] Optionally, the target-driven screening includes screening IMFs corresponding to low-frequency sea clutter components using spectral flatness, autocorrelation time, and kurtosis as thresholds to obtain IMFs that meet any of the thresholds; Forced retention screening includes retaining the last three orders of the IMF corresponding to low-frequency sea clutter components.

[0013] Optionally, dynamic weighted reconstruction includes applying weights to the final retained IMFs in ascending order based on the following formula to obtain weighted IMFs, and then performing a high-frequency residual operation on the weighted IMFs to obtain the weighted reconstructed intermediate signal. : ; In the formula, Indicates the index of the IMF. This indicates the values ​​retained after filtering, corresponding to S. + The decomposed set of IMF indexes. S represents + The dynamic weights of the IMF should be retained accordingly. express Correspondingly retaining the IMF's dynamic weights, and having ; S represents + After complex EMD decomposition, the k-th IMF is selected and retained. Indicates the items retained after filtering, corresponding to The decomposed set of IMF indexes. express After complex EMD decomposition, the k-th IMF is selected and retained. This represents the high-frequency residual of the original signal.

[0014] Optionally, the high-frequency residual of the original signal The calculation is based on the following formula: ; In the formula, This represents the original input signal.

[0015] Optionally, energy calibration includes energy normalization of the intermediate signal based on the following formula to obtain the clutter-suppressed target signal. : ; In the formula, This represents the intermediate signal after weighted reconstruction. Represents the original input signal. and They represent signals respectively. and The square of the L2 norm is equivalent to the energy of the signal. This represents the numerical stability coefficient.

[0016] The beneficial effects of the sea clutter suppression method based on complex numbers and adaptive dynamic weighting provided in this application are as follows: (1) The method provided in this application proposes an improved strategy of complex-adaptive weighting based on empirical mode decomposition. By extending the time domain EMD to the complex domain, the method's ability to capture signal phase information is significantly improved, and the mode mixing phenomenon is effectively suppressed. At the same time, a dynamic weighted reconstruction mechanism is introduced to adjust the weight allocation of different IMF components in real time during the decomposition process, thereby improving the sea clutter suppression performance.

[0017] (2) The method provided in this application enhances the ability to capture signal phase information and suppresses mode aliasing by extending Empirical Mode Decomposition (EMD) in the complex domain. Secondly, a dynamic weighted reconstruction mechanism is designed to adjust the weight allocation of Intrinsic Mode Functions (IMFs) in real time, optimizing the contribution of high-frequency target components. Experiments were conducted based on measured data from the IPIX radar to compare the performance of the method provided in this application, the root cycle cancellation method, and the wavelet weighted reconstruction method under high and low sea states (significant wave height 1 m to 1.4 m). The results show that the method provided in this application achieves an average clutter suppression amplitude of approximately 8.07 dB under high and low sea states, while the average target signal suppression amplitude is approximately 1.14 dB, significantly better than traditional methods (wavelet clutter suppression is 2.27-4.88 dB, and the root cycle method is less than 1.5 dB). Furthermore, the method provided in this application effectively preserves the target spectral characteristics through frequency domain pre-separation and dynamic weighting strategies, significantly improving the signal-to-noise ratio. This application provides an efficient solution for radar target detection under strong sea clutter backgrounds. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0019] Figure 1 It is a time-frequency diagram of a single distance gate; Figure 2 This is the sea clutter spectrum at 30 seconds. Figure 3 It is a time-frequency diagram with virtual targets added under high sea states; Figure 4 It is a time-frequency graph that incorporates virtual targets under low sea states; Figure 5 This is a spectrum under high sea state conditions after processing by the sea clutter suppression method based on complex numbers and adaptive dynamic weighting provided in the embodiments of this application; Figure 6 This is a spectrum of the sea clutter suppression method based on complex numbers and adaptive dynamic weighting provided in this application embodiment, after processing at 30 seconds under high sea state. Figure 7 This is a spectrum of the sea clutter suppression method based on complex numbers and adaptive dynamic weighting provided in this application embodiment, after processing at 50 seconds under high sea state conditions; Figure 8 This is a spectrum diagram under low sea state conditions after processing by the sea clutter suppression method based on complex numbers and adaptive dynamic weighting provided in the embodiments of this application; Figure 9 This is a spectrum of sea clutter suppression under low sea state for 30 seconds after processing by the complex number and adaptive dynamic weighting sea clutter suppression method provided in the embodiments of this application; Figure 10 This is a spectrum of sea clutter suppression at low sea state for 50 seconds after processing by the complex number and adaptive dynamic weighting sea clutter suppression method provided in this application embodiment; Figure 11 This is a histogram showing the difference in average suppression between the main clutter component and the target signal under high / low sea states using the root periodic cancellation suppression method. Figure 12 This is a histogram showing the difference in average suppression between the principal components of clutter and the target signal under high / low sea states using a wavelet transform-based weighted reconstruction method. Figure 13 This is a histogram showing the difference in average suppression between the main clutter component and the target signal under high / low sea states using the complex number and adaptive dynamic weighting-based sea clutter suppression method provided in this application embodiment. Detailed Implementation

[0020] To make the technical problems, technical solutions, and beneficial effects to be solved by this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the scope of this application.

[0021] The sea clutter data used in this application is from the IPIX radar (Ice Multiparameter Imaging X-Band Radar) data collected by Dartmouth at McMaster University in Canada in 1993. The main radar parameters are shown in Table 1.

[0022] Table 1 Main Radar Parameters

[0023] Data from the 8th range gate in the 280th experiment was selected, with a significant wave height of 1.4 meters and sea state 3. Therefore, this experimental result can be considered as high-sea-state sea clutter data. The polarization method in this embodiment is VV polarization. A short-time Fourier transform (FFT) was performed on the data using a Hamming window with a width of 4096 data points, a window shift distance of 1024 data points, and 1024 FFT points. This yields the time-frequency image of a single range gate and the sea clutter spectrum at 30 seconds, as shown below. Figure 1 and Figure 2 As shown.

[0024] It can be seen that sea clutter has a strong clutter component and an increase in fundamental noise near zero frequency.

[0025] Clutter under different sea states was studied. Data from the 7th range gate of the 26th data acquisition experiment was used for low sea state data, and data from the 8th range gate of the 280th experiment was used for high sea state data. The significant wave height for low sea state data was 1 meter, and the sea state was 2. An LFM (Linear Frequency Modulated Signal) signal with a frequency range linearly varying between -50Hz and 50Hz was added to the data at 45-55s and 95-105s. Some of this signal was masked by clutter components. The time-frequency images for high and low sea states are shown below. Figure 3 and Figure 4 As shown, under high sea states, the low-frequency sea clutter component near zero frequency is more broadened and stronger, making it easier for target signals to be hidden in the clutter spectrum and reducing the likelihood of the target being detected by radar.

[0026] Therefore, this application proposes a complex and adaptive dynamic weighting-based sea clutter suppression method (CEADW-EMD), which achieves efficient suppression of sea clutter and preservation of weak target features by integrating complex signal processing, adaptive dynamic weighting and empirical mode decomposition techniques.

[0027] The sea clutter suppression method based on complex numbers and adaptive dynamic weighting provided in this application includes: Perform a short-time Fourier transform on the raw radar echo data to generate a spectrogram.

[0028] The raw radar echo data is standardized and preprocessed to obtain preprocessed in-phase and quadrature component signals.

[0029] Standardization preprocessing includes performing mean-removal and variance-normalization on the in-phase component I and quadrature component Q of the original radar echo data according to the following formula, respectively, to obtain the in-phase component after mean-removal and variance-normalization. and orthogonal components : ; In the formula, and Let I and Q represent the mean values ​​of the in-phase component and quadrature component, respectively, of the original radar echo data. and These represent the standard deviations of the in-phase component I and the quadrature component Q of the original radar echo data, respectively. Then, the quadrature phase error is calculated based on the following formula. : ; In the formula, This represents the expectation operator, used to perform operations on... The results are averaged based on the orthogonal phase error. In-phase components after mean and variance normalization and orthogonal components Phase rotation is performed to obtain the preprocessed in-phase component signal. and orthogonal component signals ,include: ; .

[0030] The raw IQ data is standardized and preprocessed to eliminate the problems of DC bias and phase imbalance introduced by hardware devices.

[0031] Low-frequency sea clutter component signals are obtained by frequency domain pre-separation based on the spectrum diagram and the preprocessed in-phase and quadrature component signals.

[0032] Frequency domain pre-separation includes: The energy spectrum is calculated based on the spectrogram, and a threshold truncation is performed on the energy spectrum to determine the left boundary frequency f. left and right boundary frequency f right Based on the left boundary frequency f, the following formula is used. left and right boundary frequency f right Calculate the cutoff frequency : ; A frequency mask is constructed based on the cutoff frequency using the following formula: ; Perform Fourier transforms on the preprocessed in-phase and quadrature component signals to obtain the frequency domain signal. Use a frequency mask to separate the frequency domain signal to obtain the clutter frequency domain signal. Convert the clutter frequency domain signal back to the time domain to obtain the low-frequency sea clutter component signal. Based on the following formula: ; In the formula, This represents the preprocessed complex radar signal. Indicates that through Fourier transform This converts the time-domain signal of the complex radar signal into a frequency-domain signal. Indicates the use of separating S + and S - The corresponding clutter band mask, where S + yes The corresponding positive frequency side clutter, S - yes The corresponding negative frequency side clutter, This indicates that an inverse Fourier transform is performed on the filtered frequency domain signal.

[0033] After phase compensation based on the low-frequency sea clutter component signal, the IMF corresponding to the low-frequency sea clutter component is output through improved complex EMD decomposition.

[0034] Phase compensation includes calculating the phase difference based on the following formula. : ; In the formula, arg() represents the argument operator, used to take the phase angle of a complex number. This represents the expectation operator, used to perform operations on... The element-wise results are averaged. express and Multiply at each time point, express The conjugate of the complex number is used to calculate and The phase difference between them; Then based on the phase difference pair Performing a phase rotation yields the phase and... Consistent new components : ; The improved complex EMD decomposition includes: treating the low-frequency sea clutter component signal as the real part of a complex signal, constructing the imaginary part through Hilbert transform to obtain the complete complex signal, performing EMD decomposition on the complete complex signal, using cubic spline interpolation to optimize the envelope fitting, stopping when the IMF energy difference between two adjacent decompositions is <0.25, and decomposing up to 15 layers, outputting the IMF corresponding to the low-frequency sea clutter component.

[0035] Multi-criteria adaptive selection is performed on the IMF corresponding to the low-frequency sea clutter component to obtain the filtered IMF.

[0036] The IMF multi-criteria adaptive selection involves performing target-dominant screening and mandatory retention screening on the IMFs corresponding to low-frequency sea clutter components to obtain target-dominant IMFs and mandatory retention IMFs, and merging the target-dominant IMFs and mandatory retention IMFs to obtain the final retained IMF.

[0037] The target-driven screening involves using spectral flatness, autocorrelation time, and kurtosis as thresholds to screen IMFs corresponding to low-frequency sea clutter components, obtaining IMFs that satisfy any of the thresholds; Forced retention screening includes retaining the last three orders of the IMF corresponding to low-frequency sea clutter components.

[0038] This process involves the separation of... and Improved complex EMD decomposition was performed separately. During the decomposition process, cubic spline interpolation was used to optimize the instantaneous frequency resolution, and the relative tolerance of the decomposition termination criterion was set to 0.25 to balance modal aliasing suppression and computational efficiency. The maximum number of IMFs was limited to 15 layers.

[0039] A multi-criteria adaptive selection mechanism is proposed for the intrinsic mode functions (IMFs) obtained from the decomposition: Calculate the spectral flatness of each IMF In the formula, This represents the spectral flatness of the k-th intrinsic mode function (IMF). Represents the power value of the power spectrum corresponding to the k-th IMF at each frequency point; autocorrelation time and kurtosis , retain satisfaction , or The IMF is determined, and the last three IMFs are forcibly retained to prevent over-suppression of the target component.

[0040] The high-frequency residual of the original signal is calculated based on the low-frequency sea clutter component signal. Dynamic weighted reconstruction and energy calibration are performed based on the high-frequency residual of the original signal and the filtered IMF, and the target signal after clutter suppression is output.

[0041] Dynamic weighted reconstruction involves applying weights to the final retained IMFs in ascending order based on the following formula to obtain weighted IMFs, and then performing a high-frequency residual operation on the weighted IMFs to obtain the weighted reconstructed intermediate signal. : ; In the formula, Indicates the index of the IMF. This indicates the values ​​retained after filtering, corresponding to S. + The decomposed set of IMF indexes. S represents + The dynamic weights of the IMF should be retained accordingly. express Correspondingly retaining the IMF's dynamic weights, and having ; S represents + After complex EMD decomposition, the k-th IMF is selected and retained. Indicates the items retained after filtering, corresponding to The decomposed set of IMF indexes. express After complex EMD decomposition, the k-th IMF is selected and retained. Represents the high-frequency residual of the original signal; High-frequency residuals of the original signal The calculation is based on the following formula: ; In the formula, This represents the original input signal.

[0042] α k β k The range of values ​​is limited to The weight is a reasonable range determined based on the stability of actual signal reconstruction and engineering application experience, without compromising complex EMD decomposition and linear reconstruction. When the weight is less than 1.0, it weakens the already determined effective IMF components, which is not conducive to preserving the target features; when the weight is too large, it easily amplifies the local oscillations of the IMF, causing reconstruction distortion or clutter reinjection. Therefore, a weight of 1.0 is adopted. The weak gain range is used to achieve a moderate enhancement of higher-order effective components. For high-frequency residuals s... HFThe IMFs mainly contain high-frequency noise not represented by the IMFs and a small amount of transient structural information. Direct equal-weighted merging can easily introduce clutter interference. Therefore, a suppressive merging weight of 0.6 is used during reconstruction to reduce high-frequency clutter energy while retaining necessary structural information. This value is derived from multi-scenario experimental verification and can balance signal continuity and clutter suppression effects. After IMF screening, the retained IMFs are sorted from low to high order according to their decomposition order, and weights are assigned progressively increasing values. The weight range is limited to 1.0 to 1.3, where 1.0 is the starting point for weighting, and the lowest-order retained IMFs are not enhanced. 1.3 is the ending point for weighting, and the highest-order retained IMFs are enhanced to the maximum extent. The weights of IMFs of intermediate orders are obtained by increasing proportionally within this range according to their order. The specific step size is automatically determined by the actual number of retained IMFs, so it is not necessary to pre-fix the step size.

[0043] Energy calibration involves normalizing the energy of the intermediate signal based on the following formula to obtain the target signal after clutter suppression. : ; In the formula, This represents the intermediate signal after weighted reconstruction. Represents the original input signal. and They represent signals respectively. and The square of the L2 norm is equivalent to the energy of the signal. This represents the numerical stability coefficient.

[0044] To maintain phase consistency, phase difference is compensated through cross-correlation calculations, and energy normalization is used to ensure that the output signal energy is equivalent to the input energy. Here, ε balances numerical stability and signal fidelity to ensure that the CEADW-EMD method can operate under different noise environments.

[0045] The method described in this application was used to suppress these two sets of data, and the suppression effect was observed. We obtained the time-frequency images of each window signal after suppression and extracted the spectrum diagrams at different times before and after suppression, specifically at 30s (without virtual targets, for comparison) and 50s (including virtual targets). Using this method, the average clutter suppression amplitude and the average target suppression amplitude at times containing virtual targets were calculated from the spectrum comparison diagrams before and after suppression under high and low sea states, respectively. Figures 5-10 As shown.

[0046] It can be seen that the CEADW-EMD method not only has a good suppression effect on the low-frequency sea clutter intensity component, but also has a good signal preservation ability.

[0047] Finally, this method is compared with the root cycle cancellation suppression algorithm and the wavelet transform weighted reconstruction algorithm. To ensure universality, we use a stratified sampling method to statistically analyze data under different sea state conditions. High sea state samples are derived from all 28 sets of range-gate data collected during the 18th and 19th sea trials, with significant wave heights exceeding 2 meters. In contrast, low sea state data are taken from equal-quantity range-gate data from the 25th and 26th trials, corresponding to significant wave heights of approximately 1 meter. Based on experimental observations, the spectral analysis conditions are set as follows: the spectral amplitude of the clutter principal component is greater than or equal to 15 dB (before suppression). Histograms are generated by calculating the average suppression difference between the clutter principal component and the target signal using the three different methods, and the results are as follows. Figures 11-13 As shown.

[0048] As shown in the figure, when the spectral broadening of the sea clutter echo signal is strong, the root cyclic cancellation method cannot effectively suppress the clutter. Wavelet weighted reconstruction achieves better suppression under high sea state conditions, but it cannot correctly preserve the added virtual targets, thus still failing to improve the signal-to-noise ratio. The method proposed in this application achieves the best results. The virtual signal is well preserved, with an average suppression amplitude of approximately 1 dB. Furthermore, in low sea state data statistics, the suppression amplitude of the strong component spectrum of sea clutter is approximately 6 dB, effectively improving the signal-to-noise ratio.

[0049] Regarding the suppression of sea clutter, all three methods have a certain degree of suppression effect, with the CEADW-EMD method showing the best performance.

[0050] Regarding target echo preservation, only the CEADW-EMD method can preserve the target well, with the suppression of the target echo consistently below 1.5dB. Wavelet weighted reconstruction and root cyclic cancellation neither preserve the target signal well. Among them, the root cyclic cancellation algorithm performs the worst, with a suppression of the target exceeding 6dB.

[0051] like Figure 11 As shown, the suppression effect of the root cycle cancellation method is less than 1.5 dB. It can also be observed that the root cycle cancellation method cannot retain the two virtual targets added to the spectrum, with an average suppression range of over 6.5 dB for the targets.

[0052] like Figure 12 As shown, wavelet-weighted reconstruction performs only moderately well in suppressing sea clutter components and preserving the signal. The average clutter suppression amplitude is 2.27–4.88 dB, and the average signal suppression amplitude is 4.92–5.16 dB. Since the suppression effect on the target is greater than the suppression effect on clutter, the signal-to-noise ratio cannot be improved.

[0053] like Figure 13As shown, the CEADW-EMD method can not only significantly suppress sea clutter components but also preserve signal components well. The average suppression effect on sea clutter can reach more than 7dB, while the average suppression effect on targets does not exceed 1.5dB. Therefore, this method can effectively improve the signal-to-noise ratio.

[0054] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A sea clutter suppression method based on complex numbers and adaptive dynamic weighting, characterized in that, include: Perform a short-time Fourier transform on the raw radar echo data to generate a spectrum. The raw radar echo data is standardized and preprocessed to obtain preprocessed in-phase and quadrature component signals. Low-frequency sea clutter component signals are obtained by frequency domain pre-separation based on the spectrum diagram and the preprocessed in-phase and quadrature component signals. After phase compensation based on the low-frequency sea clutter component signal, the IMF corresponding to the low-frequency sea clutter component is output through improved complex EMD decomposition. Multi-criteria adaptive selection is performed on the IMFs corresponding to low-frequency sea clutter components to obtain the filtered IMFs; The high-frequency residual of the original signal is calculated based on the low-frequency sea clutter component signal. Dynamic weighted reconstruction and energy calibration are performed based on the high-frequency residual of the original signal and the filtered IMF, and the target signal after clutter suppression is output.

2. The sea clutter suppression method based on complex numbers and adaptive dynamic weighting according to claim 1, characterized in that: The standardization preprocessing includes performing mean-removal and variance-normalization processes on the in-phase component I and quadrature component Q of the original radar echo data according to the following formula, respectively, to obtain the in-phase component after mean-removal and variance-normalization. and orthogonal components : ； In the formula, and Let I and Q represent the mean values ​​of the in-phase component and quadrature component, respectively, of the original radar echo data. and These represent the standard deviations of the in-phase component I and the quadrature component Q of the original radar echo data, respectively. Then, the quadrature phase error is calculated based on the following formula. : ； In the formula, This represents the expectation operator, used to perform operations on... The results are averaged based on the orthogonal phase error. In-phase components after mean and variance normalization and orthogonal components Phase rotation is performed to obtain the preprocessed in-phase component signal. and orthogonal component signals ,include: ； 。 3. The sea clutter suppression method based on complex numbers and adaptive dynamic weighting according to claim 2, characterized in that: The frequency domain pre-separation includes: The energy spectrum is calculated based on the spectrogram, and a threshold truncation is performed on the energy spectrum to determine the left boundary frequency f. left and right boundary frequency f right Based on the left boundary frequency f, the following formula is used. left and right boundary frequency f right Calculate the cutoff frequency : ； A frequency mask is constructed based on the cutoff frequency using the following formula: ； Perform Fourier transforms on the preprocessed in-phase and quadrature component signals to obtain the frequency domain signal. Use the frequency mask to separate the frequency domain signal to obtain the clutter frequency domain signal. Convert the clutter frequency domain signal back to the time domain to obtain the low-frequency sea clutter component signal. Based on the following formula: ； In the formula, This represents the preprocessed complex radar signal. Indicates that through Fourier transform This converts the time-domain signal of the complex radar signal into a frequency-domain signal. Indicates the use of separating S + and S - The corresponding clutter band mask, where S + yes The corresponding positive frequency side clutter, S - yes The corresponding negative frequency side clutter, This indicates that an inverse Fourier transform is performed on the filtered frequency domain signal.

4. The complex sum and adaptive dynamic weighting sea clutter suppression method according to claim 1, characterized in that: The phase compensation includes calculating the phase difference based on the following formula. : ； In the formula, arg() represents the argument operator, used to take the phase angle of a complex number. This represents the expectation operator, used to perform operations on... The element-wise results are averaged. express and Multiply at each time point, express The conjugate of the complex number is used to calculate and The phase difference between them; Then based on the phase difference pair Performing a phase rotation yields the phase and... Consistent new components : 。 5. The complex sum and adaptive dynamic weighting sea clutter suppression method according to claim 4, characterized in that: The improved complex EMD decomposition includes: treating the low-frequency sea clutter component signal as the real part of a complex signal, constructing the imaginary part through Hilbert transform to obtain the complete complex signal, performing EMD decomposition on the complete complex signal, optimizing the envelope fitting using cubic spline interpolation, stopping when the IMF energy difference between two adjacent decompositions is <0.25, and decomposing up to 15 layers, outputting the IMF corresponding to the low-frequency sea clutter component.

6. The complex sum and adaptive dynamic weighting sea clutter suppression method according to claim 1, characterized in that: The IMF multi-criteria adaptive selection includes performing target-dominant screening and forced retention screening on the IMFs corresponding to low-frequency sea clutter components to obtain target-dominant IMFs and forced retention IMFs, and merging the target-dominant IMFs and forced retention IMFs to obtain the final retained IMF.

7. The complex sum and adaptive dynamic weighting sea clutter suppression method according to claim 6, characterized in that: The target-driven screening includes screening IMFs corresponding to low-frequency sea clutter components using spectral flatness, autocorrelation time, and kurtosis as thresholds to obtain IMFs that meet any of the thresholds; The forced retention screening includes retaining the last three orders of the IMF corresponding to the low-frequency sea clutter component.

8. The complex sum and adaptive dynamic weighting sea clutter suppression method according to claim 6, characterized in that: The dynamic weighted reconstruction includes applying weights to the final retained IMFs in ascending order based on the following formula to obtain a weighted IMF, and then performing a high-frequency residual operation on the weighted IMFs to obtain the weighted reconstructed intermediate signal. : ； In the formula, Indicates the index of the IMF. This indicates the values ​​retained after filtering, corresponding to S. + The decomposed set of IMF indexes. S represents + The dynamic weights of the IMF should be retained accordingly. express Correspondingly retaining the IMF's dynamic weights, and having ; S represents + After complex EMD decomposition, the k-th IMF is selected and retained. This indicates the items retained after filtering, corresponding to... The decomposed set of IMF indexes. express After complex EMD decomposition, the k-th IMF is selected and retained. This represents the high-frequency residual of the original signal.

9. The complex sum and adaptive dynamic weighting sea clutter suppression method according to claim 8, characterized in that: The high-frequency residual of the original signal The calculation is based on the following formula: ； In the formula, This represents the original input signal.

10. The complex sum and adaptive dynamic weighting sea clutter suppression method according to claim 1, characterized in that: The energy calibration includes energy normalization of the intermediate signal based on the following formula to obtain the target signal after clutter suppression. : ； In the formula, This represents the intermediate signal after weighted reconstruction. Represents the original input signal. and They represent signals respectively. and The square of the L2 norm is equivalent to the energy of the signal. This represents the numerical stability coefficient.

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