High-resolution spaceborne SAR imaging processing method for ship target under complex sea conditions

Abstract

A high-resolution spaceborne SAR imaging processing method for a ship target under complex sea conditions, which method relates to the technical field of radar imaging processing. In the method, by means of a dynamic adjustment strategy from a fine-tuning index, a cumulative energy ratio threshold value can be flexibly adjusted on the basis of real-time signal conditions; a phase compensation function is introduced as a basis function and a time window parameter is added, so as to better adapt to the instability of echoes from strong scattering points under complex sea conditions, thereby further improving the robustness of an algorithm; parameter estimation, residual updating and component extraction are performed in a frequency domain, thereby reducing search dimensions and increasing the operation speed; and a parameterized time-frequency distribution construction method is proposed, thereby effectively reducing the impact of cross terms and sidelobes. Upon verification, after processing is performed by using the method, the image quality of a ship under complex movement conditions is significantly improved.

Description

High-resolution spaceborne SAR ship target imaging processing method under complex sea conditions

[0001] This application claims priority to Chinese Patent Application No. 202510162066.9, filed with the Chinese Patent Office on February 14, 2025, entitled "High-Resolution Spaceborne SAR Ship Target Imaging Processing Method under Complex Sea Conditions", and the entire contents of the aforementioned patent application are incorporated herein by reference. Technical Field

[0002] This invention relates to the field of imaging processing technology, specifically to a high-resolution spaceborne SAR ship target imaging processing method under complex sea conditions. Background Technology

[0003] When ship targets are large or in high-resolution spaceborne SAR imaging, especially under complex sea conditions, the target's motion becomes extremely complex. The Doppler frequency of the original echo signal is time-varying, and the Doppler phase at different scattering points of the target changes significantly with azimuth and time. Existing autofocusing methods cannot achieve good imaging results. From the perspective of echo signals, this kind of motion introduces a high-order Doppler phase into the spaceborne SAR radar echo, which can be represented as a polynomial phase signal (PPS). In the case of high resolution and large targets, a spaceborne SAR echo pulse often contains echo components with several scattering centers. In this case, the echo signal is called a multicomponent polynomial phase signal (mc-PPS).

[0004] Meanwhile, the Adaptive Joint Time-Frequency (AJTF) method, as an improved maximum likelihood method, focuses on finding optimal parameters in the solution space. This is essentially a multidimensional optimization problem with different extremal solutions. However, in the time-frequency decomposition of multi-component polynomial phase signals, the extremal solutions are not necessarily the true solutions corresponding to PPS signal components of different intensities, making it easy to get trapped in local maxima. From an algorithm efficiency perspective, the contradiction between parameter search speed and global convergence needs to be resolved, which further complicates the decomposition optimization problem. This non-convex optimization problem requires a large amount of computation, limiting the algorithm's practical application. Therefore, it is necessary to apply optimization algorithms to the AJTF decomposition process to accelerate the processing speed.

[0005] In the prior art, publication number CN106772373A, entitled "A SAR Imaging Method for Arbitrary Ground Moving Targets," the main solution is to address the problem of defocusing of moving targets caused by range migration in existing technologies, including:

[0006] 1) Construct a front-side looking radar echo signal model;

[0007] 2) After performing range pulse compression on the target echo signal, transform it to the range frequency domain;

[0008] 3) Construct a reference function from the distance-frequency domain expression of the pulse compression signal;

[0009] 4) Multiply the complex conjugate of the reference function by the range-frequency domain expression of the slow target pulse compression signal, and then perform a Fourier transform on the result in the azimuth direction to obtain the range and azimuth two-dimensional frequency domains;

[0010] 5) Perform an inverse Fourier transform in the range direction on the two-dimensional frequency domain to obtain the amplitude spectrum of the target signal;

[0011] It achieves good imaging results without the need for target parameter estimation, using only Fast Fourier Transform without interpolation, and can be used for tracking and identifying any unknown moving target.

[0012] In the prior art, publication number CN115236626A, entitled "Multi-channel Radar Sea Clutter Suppression Method and System Based on Time-Frequency Analysis," discloses a multi-channel radar sea clutter suppression method and system based on time-frequency analysis, comprising:

[0013] Step S1: Calculate the coherence time of sea clutter using sea state series;

[0014] Step S2: Transform the sea clutter data to the time-frequency domain using a coherent time window;

[0015] Step S3: Suppress sea clutter using a subspace projection method based on a time-domain sliding window in the time-frequency domain;

[0016] Step S4: Restore the suppressed clutter data to the post-Doppler domain, and then perform the second stage of suppression;

[0017] It can effectively compensate for sea clutter in multi-channel radar, and fully considers the time-decoherence characteristics of sea clutter, thus enabling more robust suppression of sea clutter in the space-time-frequency domain.

[0018] Therefore, accurate estimation of the MC-PPS signal is crucial for achieving imaging of complex moving targets in spaceborne SAR.

[0019] Limitations: How to design an optimization algorithm that can further improve the search speed and global optimum search capability in time-frequency decomposition, accelerate the processing speed, and propose a parameterized time-frequency distribution construction method to reduce the influence of cross terms and sidelobes;

[0020] How to adapt to signal environments of varying complexity; whether in high-noise or low-noise environments, the system can adjust the predetermined threshold of the cumulative energy ratio according to the current conditions, thereby optimizing the signal processing effect;

[0021] To address the trade-off between computational complexity and global convergence in the AJTF algorithm, and to utilize the Particle Swarm Optimization (PSO) algorithm for co-evolutionary evolutionary optimization, we need to design methods for particle swarm combination and information sharing to estimate and extract multiple PPS signal components in parallel, thereby further improving the search speed and global optimum search capability in time-frequency decomposition. This is a direction that needs improvement.

[0022] The information disclosed in the background section above is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0023] The purpose of this invention is to provide a high-resolution spaceborne SAR ship target imaging processing method under complex sea conditions, so as to solve the problems mentioned in the background art.

[0024] To achieve the above objectives, the present invention provides the following technical solution:

[0025] A high-resolution spaceborne SAR ship target imaging processing method under complex sea conditions is proposed. Based on the AJTF algorithm, an adaptive joint time-frequency imaging processing method is obtained, which is referred to as FDE-AJTF. The specific steps include:

[0026] Step S1: Acquire SAR echo signal data of moving ship targets under complex sea conditions, and define it as an mc-PPS signal for output. Define the PPS signal component of a single strong scattering point as... ;

[0027] Step S2: Construct the phase compensation basis function of the echo signal The PPS signal components are conjugate, and the length and overlap of the time window parameters are adjusted to match the time-frequency characteristics of the echo signal from a high-sea-state ship target.

[0028] Step S3: Use phase compensation basis functions The polynomial phase error is corrected to determine the polynomial phase error of the SAR echo signal in SAR imaging, and the conjugate inner product of the adjusted time window parameter, the SAR echo signal, and the phase compensation basis function is used as the objective function.

[0029] The SAR echo signal is multiplied by the phase compensation basis function to obtain the compensation signal. For compensation signals The result is then transformed into the spectral domain using Fourier transform to obtain the compensated spectrum in the image. ;

[0030] Step S4: Based on the signal corrected in step S3, define the objective function for adaptive joint time-frequency processing as follows:

[0031] ,

[0032] This indicates the parameter that needs to be estimated, which, after imaging processing, is determined based on the maximum value of the spectrum. The location of occurrence determines the peak frequency point. Thus, the parameters are obtained. Then complete the search for all other parameters. Indicated in the spectrum In the middle, the frequency point corresponding to the maximum value , Indicates the PPS signal component With phase compensation basis function Perform a Fourier transform on the product of the two; The first parameter estimated is the frequency point. ;

[0033] Will The energy of the main lobe region at the peak of the signal spectrum is taken as the component intensity of the signal, while The energy in the region outside the main lobe of the function is used as the residual signal;

[0034] By processing the signal using the optimal estimation algorithm, the estimated values ​​of the PPS signal at each order are obtained. The estimated values ​​are defined as follows: The calculation formula is as follows:

[0035] ;

[0036] in, for The intensity component of the maximum value of the spectrum, This represents the optimal estimation results for each order component of the PPS signal. Let denote the order of the polynomial, and The change over time t is represented by t raised to the power of n, where j represents the imaginary unit;

[0037] Step S5: Based on the objective function result optimized in step S4, extract the PPS signal components of each scattering point and calculate the signal residual. Then, perform the same processing on the signal residual, iteratively extract new PPS signal components of scattering points and estimate phase parameters until the residual reaches a predetermined threshold set based on previous data analysis or prior knowledge.

[0038] In each iteration, statistical features of signal-to-noise ratio, scattering point density, and signal change rate are extracted, and after constructing the corresponding dataset, the average difference change rate of these features is calculated.

[0039] The average difference change rate corresponding to the signal-to-noise ratio, scattering point density, and signal change rate is obtained, analyzed, and processed to construct a threshold fine-tuning index. The fine-tuning index is used to provide a dynamic adjustment strategy for a predetermined threshold.

[0040] The residual signal is further processed in the frequency domain. It is then inversely transformed to the time domain and multiplied by the conjugate of the phase compensation function to obtain the time-domain residual signal. ;

[0041] Set the PPS signal to correspond to each order component The threshold value is When the PPS signal component When the value falls below the threshold, the subsequent PPS signal components will be lower than the effective components, and the iterative search will stop.

[0042] Step S6: Optimize the results of step S5 using the co-evolutionary PSO algorithm;

[0043] Step S7: Simulate and verify the FDE-AJTF algorithm and the co-evolutionary PSO algorithm with actual data. Use a complex moving ship target model and real high-resolution spaceborne SAR data to evaluate the imaging quality under different complex sea conditions.

[0044] Compared with the prior art, the beneficial effects of the present invention are: by using a dynamic adjustment strategy of fine-tuning the index, the system can flexibly adjust the cumulative energy ratio threshold according to real-time signal conditions; it can ensure the robustness and processing accuracy of the system under different signal conditions; by using the phase compensation function as the basis function and adding the time window parameter, it is more in line with the actual situation of unstable strong scattering point echoes under high sea states, thus improving the robustness of the algorithm.

[0045] The parameter estimation, residual update, and component extraction steps are performed in the frequency domain, reducing the search dimension and improving the computation speed. Based on this, a parameterized time-frequency distribution construction method is proposed to reduce the influence of cross terms and sidelobes. Finally, simulation and real data verification show that after processing with the FDE-AJTF algorithm, the image quality of ships under complex motion conditions is significantly improved, ship boundaries and structures are clearly displayed, and the geometric, scattering, and structural characteristics of ships can be obtained normally, effectively restoring the application capability of spaceborne SAR images in marine applications.

[0046] It can estimate and extract multiple PPS signal components in parallel, further improving the search speed and global optimal search capability in time-frequency decomposition; the processing results of ship scattering point target model and real high-resolution spaceborne SAR data show that the image quality of complex moving ships is significantly improved. Attached Figure Description

[0047] Figure 1 is a schematic diagram of the overall method flow of the present invention;

[0048] Figure 2 is a flowchart of the PSO optimization algorithm of the present invention;

[0049] Figure 3 is a flowchart of the co-evolutionary PSO algorithm of the present invention;

[0050] Figure 4 shows the original results of the satellite-borne SAR imaging of complex moving ships according to the present invention;

[0051] Figure 5 shows the results of applying the co-evolutionary PSO algorithm to the real data of this invention;

[0052] Figure 6 shows the simulated moving point target imaging processing results of the present invention;

[0053] Figure 7 shows the results of the FDE-AJTF compensation processing of the present invention using the co-evolutionary PSO algorithm. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0055] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly. Example

[0056] Please refer to Figures 1 to 7. The present invention provides a technical solution:

[0057] A high-resolution spaceborne SAR ship target imaging processing method under complex sea conditions, the specific steps of which include:

[0058] An improved version of the classic AJTF method, the Adaptive Joint Time-Frequency (FDE-AJTF) imaging processing method, is derived. This method, referred to as FDE-AJTF, includes the following:

[0059] Step S1: Acquire SAR echo signal data of moving ship targets under complex sea conditions, and define it as an mc-PPS signal for output. Define the PPS signal component of a single strong scattering point as... ;

[0060] Step S2: Construct the phase compensation basis function of the echo signal The PPS signal components are conjugate, and the length and overlap of the time window parameters are adjusted to match the time-frequency characteristics of the echo signal from a high-sea-state ship target.

[0061] Step S3: Use phase compensation basis functions The polynomial phase error is corrected to determine the polynomial phase error of the SAR echo signal in SAR imaging, and the conjugate inner product of the adjusted time window parameter, the SAR echo signal, and the phase compensation basis function is used as the objective function.

[0062] The SAR echo signal is multiplied by the phase compensation basis function to obtain the compensation signal. For compensation signals The result is then transformed into the spectral domain using Fourier transform to obtain the compensated spectrum in the image. ;

[0063] Step S4: Based on the signal corrected in step S3, define the objective function for adaptive joint time-frequency processing as follows:

[0064] ,

[0065] This indicates the parameter that needs to be estimated, which, after imaging processing, is determined based on the maximum value of the spectrum. The location of occurrence determines the peak frequency point. Thus, the parameters are obtained. Then complete the search for all other parameters, where N is the total number of parameters;

[0066] Spectrum In the middle, the frequency point corresponding to the maximum value , Indicates the PPS signal component With phase compensation basis function Perform a Fourier transform on the product of the two; The first parameter estimated is the frequency point. ;

[0067] p represents the index label of the PPT signal, c represents the index label after compensation; FT represents the Fourier transform.

[0068] Will The energy of the main lobe region of the mid-signal spectrum peak is taken as the component intensity of the signal, while The energy in the region outside the main lobe of the function is used as the residual signal;

[0069] By processing the signal using the optimal estimation algorithm, the estimated values ​​of the PPS signal at each order are obtained. The estimated values ​​are defined as follows: The calculation formula is as follows:

[0070]

[0071] in, for The intensity component of the maximum value of the spectrum, This represents the optimal estimation results for each order component of the PPS signal. Let denote the order of the polynomial, and The change over time t is represented by t raised to the power of n, where j represents the imaginary unit;

[0072] Step S5: Based on the objective function result optimized in step S4, extract the PPS signal components of each scattering point and calculate the signal residual. Then, perform the same processing on the signal residual, iteratively extract the new PPS signal components of the scattering point and estimate the phase parameters until the residual reaches the predetermined threshold set according to previous data analysis or prior knowledge.

[0073] In each iteration, statistical features of signal-to-noise ratio, scattering point density, and signal change rate are extracted, and after constructing the corresponding dataset, the average difference change rate of these features is calculated.

[0074] The residual signal is further processed in the frequency domain. It is then inversely transformed to the time domain and multiplied by the conjugate of the phase compensation function to obtain the time-domain residual signal. ;

[0075] Setting PPS signal components The threshold value is When the PPS signal component When the value falls below the threshold, the subsequent PPS signal components will be lower than the effective components, and the iterative search will stop.

[0076] Step S6: Optimize the output of step S5 using the co-evolutionary PSO algorithm, specifically including:

[0077] a) Using the PPS signal components as the initial particle swarm input, the particle size set is defined as {1, 2, ..., ...} },and ∈{1,2,…, } indicates in The first of the particles One particle;

[0078] b) Set the initial fitness function and calculate the fitness of the m′-th particle in the subgroup P;

[0079] The particle position is defined as the position of the particle's parameter set in the multidimensional solution space. The parameters include the start time, end time, and second-order or higher polynomial coefficients of the PPS signal component.

[0080] c) Divide the input signal into three groups. It is the optimal group. It is the second-best group. It is a random group, with the initial number of iterations set to... ;

[0081] FDE-AJTF time-frequency decomposition compensates by searching for second-order and higher phase parameters. The maximum value of the phase-compensated signal spectrum is used as the fitness evaluation function for extraction. The position of this peak is essentially the position of the azimuth scattering center point corresponding to the component signal. Therefore, the scattering center point position is taken as the optimal group particle neighborhood, and this is used to distinguish between the optimal group and the suboptimal group.

[0082] d) Update the positions of the particle swarm by randomly dividing the random group into two subgroups; that is... And each of them is combined with the optimal group and the second-best group to form two new mixed groups; among them, This represents a random group in the g-th iteration. These correspond to two subgroups; this can improve the overall randomness of the population, while also enabling information exchange between the three subgroups.

[0083] e) Update fitness and the local best particle position for each group;

[0084] f) Based on the optimal fitness of the optimal and suboptimal subgroups, perform optimal population replacement. If the maximum local optimal fitness of individuals in the suboptimal subgroup is greater than the maximum value of the optimal population, then the two subgroups exchange roles.

[0085] h) Determine whether the algorithm meets the stopping conditions, including the maximum number of iterations and the convergence of the global fitness result. Convergence is represented by the fitness ratio of the residual signals of the suboptimal solutions before and after extraction. If the maximum number of iterations and fitness ratio conditions are met, then execute step i); otherwise, execute step e).

[0086] i) Output the globally optimal parameters of the best and second-best groups to complete the algorithm estimation;

[0087] Step S7: Simulate and verify the FDE-AJTF algorithm and the co-evolutionary PSO algorithm with actual data. Use a complex moving ship target model and real high-resolution spaceborne SAR data to evaluate the imaging quality under different complex sea conditions.

[0088] To further explain, the acquisition of SAR echo signal data of moving ship targets under complex sea states involves adjusting the time window length and overlap to match the time-frequency characteristics of high-sea-state echo signals. The adjusted time window parameters are then used as the conjugate inner product of the SAR echo signal and the basis functions as the objective function. Specifically, this includes:

[0089] Data Acquisition:

[0090] This embodiment uses a spaceborne synthetic aperture radar (SAR) system to detect moving ship targets, especially under complex sea conditions, such as high waves and strong winds, to acquire their echo signal data. Because complex sea conditions result in signals containing various noises and unstable scattering characteristics, data preprocessing is necessary.

[0091] Initial time window settings:

[0092] Based on sea conditions and target characteristics, an initial time window length and overlap are first set. The time window length defines the time period for signal analysis, while the overlap determines the proportion of overlapping areas between adjacent time windows. The initial time window length is usually estimated based on the signal's frequency range, and the overlap is initially set at 50%, meaning that 50% of the areas in adjacent windows overlap.

[0093] Adaptive time window adjustment:

[0094] Short-Time Fourier Transform (STFT) is applied to the acquired SAR echo signal to obtain its time-frequency distribution map. By analyzing the signal characteristics on the time-frequency map, especially the changes in instantaneous bandwidth and center frequency, if drastic signal changes are found within a certain time window, it means that the scattered point echo in the signal has greater instability under high sea states. In this case, the time window length and overlap are dynamically adjusted to adapt to these signal characteristics. For example, if the bandwidth of the signal fluctuates greatly within a certain time window, the time window length will be automatically increased to capture more stable signal characteristics, while the overlap will be reduced to avoid unnecessary computational redundancy. Through multiple adjustments, the time window parameters are gradually optimized, eventually reaching a state that best matches the signal characteristics.

[0095] Objective function construction and optimization:

[0096] After each time window adjustment, the degree of matching between the adjusted time window parameters and the SAR echo signal is calculated. This degree of matching is evaluated by constructing an objective function, which is the degree of conjugate interaction between the time window parameters, the signal, and the preset basis functions. During the optimization process, the value of the objective function is continuously maximized, and the optimal time window length and overlap are finally selected to achieve the best signal processing effect.

[0097] Data output and preparation:

[0098] Finally, the optimized time window parameters are applied to SAR echo signal processing, and basis function matching is performed. The processed signal is then output for subsequent phase error correction and frequency domain processing steps. This step ensures that the time-frequency characteristics of the signal are adapted to the dynamic environment under complex sea conditions, providing a more accurate and clear signal basis.

[0099] To further explain, after receiving the SAR echo signal, the PPS signal components of each scattering point are extracted, and the signal residual is calculated. Then, the same processing is performed on the signal residual, iteratively extracting the PPS signal components of new scattering points and estimating the phase parameters, until the residual reaches a predetermined threshold set based on previous data analysis or prior knowledge. Specifically, this includes:

[0100] A deterministic method based on the cumulative energy ratio is chosen to set a predetermined threshold for the residual, and the energy of the current PPS signal component is calculated in each iteration. and accumulated energy Define the cumulative energy ratio The calculation formula is:

[0101]

[0102] in, This represents the energy of the PPS signal component extracted in the k-th iteration step. This represents the energy of the PPS signal component extracted in the i-th iteration; The total energy of the target signal is defined as the sum of the energies of all extracted PPS signal components;

[0103] Set a predetermined threshold That is, when When the iteration stops, the energy ratio of the residual signal does not exceed 1% of the target signal, ensuring that the residual mainly contains noise and invalid components. The specific steps are as follows:

[0104] After receiving the SAR echo signal s(t), the initial PPS signal components of each scattering point are first obtained through preliminary processing. ;

[0105] calculate energy Simultaneously calculate the initial residual signal. energy ;

[0106] In the k-th iteration, extract the k-th PPS signal component. Calculate its energy And update the cumulative energy ratio ;

[0107] Update residual signal And calculate its energy. ;

[0108] when or When the energy level drops below 1% of the total signal energy, the iteration stops; at this point, only weak noise and invalid components remain in the residual signal.

[0109] To further explain, statistical features of the signal-to-noise ratio, scattering point density, and signal rate of change are extracted during each iteration. After constructing the corresponding dataset, the average rate of change of the difference of these features is calculated, specifically including:

[0110] The signal-to-noise ratio, scattering point density, and signal rate of change are labeled as SNR, SD, and SVR, respectively.

[0111] Let the set of iteration counts be {1,2,…,i,…,k}, where k is the total number of iterations and i represents the index of the i-th iteration;

[0112] In the i-th iteration, the signal noise is calculated as follows:

[0113]

[0114] in, It is the signal energy at the i-th iteration; It is the noise energy at the i-th iteration;

[0115] The change in SNR difference between adjacent iterations is calculated as follows:

[0116]

[0117] Calculate all Average of the difference changes:

[0118]

[0119] in, It is the average value of the change in the signal-to-noise ratio difference. It is the change in SNR difference between adjacent iterations;

[0120] In the i-th iteration, the scattering point density is calculated as follows:

[0121]

[0122] in, is the number of scattering points in the i-th iteration, and As is the fixed area covered by the signal;

[0123] The change in SD difference between adjacent iterations is calculated as follows:

[0124]

[0125] Calculate all Average of the difference changes:

[0126]

[0127] in, It is the average value of the change in the density difference at the scattering points. It is the change in the difference in scattering point density between adjacent iterations;

[0128] In the i-th iteration, the rate of change of the signal is calculated as follows:

[0129]

[0130] in, This refers to the change in signal characteristics during the i-th iteration; It is a fixed time interval;

[0131] The change in SVR difference between adjacent iteration steps is calculated as follows:

[0132]

[0133] Then, calculate all Average of the difference changes:

[0134]

[0135] in, It is the average value of the change in the rate of change of the signal. It is the change in the difference in the rate of change of the signal between adjacent iterations.

[0136] To further explain, the average difference rate of change corresponding to the signal-to-noise ratio, scattering point density, and signal change rate is obtained, analyzed, and processed to construct a threshold fine-tuning index. This fine-tuning index provides a dynamic adjustment strategy for a predetermined threshold, specifically including:

[0137] Define the fine-tuning index as The calculation formula is as follows:

[0138]

[0139] in, The judgment value is dynamically adjusted, where e is the base of the natural logarithm. To prevent division by zero constants, in this embodiment, , The specific values ​​were determined by the expert panel based on experimental data. Here are the time series normalization coefficients, and f(t) is the amplitude of the PPS signal component at time t. Total observation time The variance of the signal amplitude;

[0140] Based on previous data analysis or prior knowledge, determine sequentially , and The benchmark values ​​are respectively , and ;

[0141] like , and If any two values ​​in the table differ from the corresponding benchmark value by more than 10%, then... The following calibrations were performed; the phase difference of 10% can be adjusted based on experimental verification and expert group analysis using the expert group system, and is not limited to this 10% value.

[0142]

[0143] in, ; This is the fine-tuning index after calibration. Based on experimental data determined by the expert panel;

[0144] Limiting the fine-tuning index The effective range of is [0.5, 1.5]. Within this range, [0.5, 1) indicates that the signal processing allows for a larger noise component and is suitable for complex signal processing environments; [1, 1.5] indicates that the signal processing requires stricter noise suppression and is suitable for high-quality signal processing scenarios.

[0145] 1.1) Signal processing in complex environments:

[0146] In complex sea conditions, signal processing systems need to cope with severe fluctuations in the ocean surface, multipath effects, wind and wave interference, and other electromagnetic noise sources, such as the influence of communication signals from other ships. In this environment, a certain degree of noise is permissible, and the processing methods focus more on ensuring target detection and preliminary imaging rather than the highest precision imaging quality.

[0147] Quantification standard: Signal-to-noise ratio (SNR) in the range of 10-20dB, a lower SNR is allowed, and the processing method is more tolerant of noise;

[0148] The resolution requirement is relatively low, at the 5-10 meter level, with the focus on detecting the target rather than fine imaging.

[0149] Image quality: Images may contain noise and blur, but are sufficient to identify large targets and obtain their approximate location.

[0150] 1.2) High-quality signal processing scenario:

[0151] In relatively calm or standard sea conditions, signal processing systems strive for high-resolution and high-precision imaging with strict noise suppression; such scenarios require high signal quality to clearly distinguish the details of ship targets, making them suitable for applications that require precise target identification and classification.

[0152] Quantitative standard: Signal-to-noise ratio (SNR) above 20-30dB is required to ensure accurate target imaging;

[0153] High resolution is required, with a resolution below 1 meter (sub-meter level) to ensure clear imaging and identification of target details;

[0154] Image quality is excellent; the image is clear with no obvious noise and can accurately distinguish and identify different types of targets.

[0155] when When the value is in the range [0.5, 1), the signal processing allows for more noise components; this represents the predetermined threshold. The cumulative energy ratio can be reduced to between 95% and 99% for use in complex signal processing environments;

[0156] The adjusted cumulative energy ratio threshold is And it is calculated using the following formula:

[0157]

[0158] Example: When hour, In this case, a cumulative energy ratio of 79.2% is required, allowing for a larger proportion of residual noise, making it suitable for complex signal processing environments.

[0159] If during signal processing, Then the cumulative energy ratio At this point, signal processing will tolerate more noise, making it suitable for scenarios with low signal quality or high noise levels.

[0160] when When the value is in the range [1, 1.5], the signal processing requires stricter noise suppression; at this time, the predetermined threshold... The cumulative energy ratio can be increased to between 100% and 149% to ensure higher signal quality, making it suitable for high-quality signal processing scenarios;

[0161] Adjusted cumulative energy ratio threshold Calculated using the following formula:

[0162]

[0163] Example: When hour, In this case, noise must be strictly suppressed.

[0164] If during signal processing, Then the cumulative energy ratio At this point, the signal processing will strictly suppress noise to ensure extremely low signal residuals, making it suitable for high-quality signal processing scenarios.

[0165] By fine-tuning the index With its dynamic adjustment strategy, the system can flexibly adjust the cumulative energy ratio threshold based on real-time signal conditions. It can ensure the robustness and processing accuracy of the system under different signal conditions.

[0166] The experimental data analysis for the above content is as follows:

[0167] This embodiment aims to verify a method based on fine-tuning index. The advantages of dynamic threshold adjustment methods in complex signal processing are demonstrated through experiments. These experiments involve measuring and calculating the signal-to-noise ratio (SNR), scattering point density (SD), and signal rate of change (SVR) under different signal environments to dynamically adjust a predetermined threshold. To optimize signal processing performance;

[0168] Signal acquisition: Three signal sources with different complexities were selected: “Signal source A, signal source D” (low noise environment), “Signal source B, signal source E” (medium noise environment), “Signal source C, signal source F” (high noise environment); the frequency range of each signal source was between 1-10kHz, and the sampling rate was 100kHz;

[0169] Initial parameter settings: Set the reference signal-to-noise ratio Scattering point density Signal change rate ;

[0170] The application of the fine-tuning exponent formula follows the formula below:

[0171]

[0172] Calculate the fine-tuning index ;in , variance of signal amplitude Calculated from actual signal data;

[0173] Signal processing: Using a pre-defined signal processing algorithm, signal energy is extracted for each iteration, and the PPS signal component energy is calculated for each iteration. and total energy Subsequently, the cumulative energy ratio was calculated. ,when When the iteration stops, record the energy of the residual signal;

[0174] Dynamic adjustment: based on the measurements obtained during each iteration. , and The average rate of change of the difference, applied with a fine-tuning index. For the predetermined threshold To make dynamic adjustments, the specific steps are as follows:

[0175] when , and When any two values ​​differ from the reference value by more than 10%, calculate the fine-tuning index after calibration. The cumulative energy ratio threshold is adjusted using a calibrated fine-tuning exponent. ;

[0176] The corresponding calculations are performed for processing different signal sources. The value is recorded, and the cumulative energy ratio to the threshold after each processing is recorded. ;

[0177] Data Recording and Analysis: For each experiment, the average difference rate of change of signal-to-noise ratio (SNR), scattering point density (SD), and signal rate of change (SVR), as well as the final result, were recorded. Value; comparative analysis of experimental results from different signal sources verifies the fine-tuning index. Improvement in signal processing performance;

[0178] The experimental data recording table is shown in Table 1 below:

[0179] Table 1 Verification of the fine-tuning index Improvement in signal processing performance:

[0180]

[0181] Data Analysis:

[0182] For signal sources A and D, the signal-to-noise ratio is higher due to lower noise levels. The difference from the benchmark value is less than 10%, resulting in a fine-tuning index. A lower value indicates that the accumulated energy is lower than the threshold. It can be adjusted to a range below 100% to adapt to more complex environmental requirements;

[0183] For signal sources C and F, the noise is high, and the signal-to-noise ratio is... The difference from the benchmark value exceeds 10%, leading to a fine-tuning of the index. Increase to 1 or higher; at this point, the cumulative energy ratio is higher than the threshold. Adjust to above 100% to achieve strict noise suppression and ensure high-quality signal processing results;

[0184] In the formula for calculating the fine-tuning index Based on signal-to-noise ratio Scattering point density and signal change rate The multiple nonlinear functions comprehensively consider multiple characteristic parameters of the signal, ensuring the rationality and accuracy of the dynamic adjustment strategy;

[0185] In the table, for signal sources C and F, Relatively high (3.5 and 3.4 dB respectively). and It is also correspondingly higher, leading to Reaching 1.15 and 1.12, further calibration was performed. The values ​​are 1.18 and 1.14; this directly affects the cumulative energy ratio threshold. The increases reached 116.82% and 113.86% respectively; this indicates that the present invention, through the dynamic adjustment of the fine-tuning index, can automatically improve the stringency of signal processing in the face of high noise environments, ensuring high-quality signal output.

[0186] In comparison, signal sources A and D Lower (2.8 and 2.9 dB respectively), corresponding to and It is also lower, ultimately leading to The percentages were 94.06% and 96.11%, respectively. This dynamic adjustment strategy shows that in low-noise environments, the system can reduce the cumulative energy ratio threshold, allowing more noise components to exist, thus adapting to complex signal environments.

[0187] In the dynamic adjustment strategy of this invention, the various parameters in the formula... , and There are close numerical relationships between them; for example:

[0188] The increase will directly improve the fine-tuning index. ,because Multiply The value of amplifies the exponent part of the formula; when When the increase is 10%, assuming other conditions remain unchanged, The changes will lead to The increase ranges from 5% to 15%, depending on the overall noise level of the signal;

[0189] The increase in the fine-tuning index The impact is also significant; due to The existence of functions, Each percentage point increase will double the change in the exponential part, further amplifying the effect. and The increase;

[0190] As part of the denominator, its reduction will increase Therefore, a decrease in the rate of change of the signal indicates enhanced signal stability, which increases tolerance to noise and thus reduces... This gives the system a stronger noise suppression capability in high-stability signal processing;

[0191] For example, in signal source C, dB , At that time, the calculated =1.15, and after calibration The value is 1.18; this change directly affects the cumulative energy ratio threshold. It rose to 116.82%, which is 17.82% higher than the standard 99%; this shows that the system can strictly control the signal quality and ensure the reliability of the output signal by increasing the threshold in a high-noise environment.

[0192] Analysis of the tables and formulas shows that this invention demonstrates significant innovation and advantages in the following aspects:

[0193] Dynamic adaptability: through the , and Real-time monitoring and calculation, fine-tuning the index The dynamic adjustment enables the system to adapt to signal environments of varying complexity; whether in high-noise or low-noise environments, the system can adjust the cumulative energy ratio threshold according to the current conditions. This optimizes signal processing performance.

[0194] Precise control: Compared with traditional fixed threshold processing methods, this invention achieves precise control of signal processing thresholds through the calculation and calibration of fine-tuning exponents; the data in the table shows that this method performs well in dealing with different signal environments and can find the best balance between noise control and signal fidelity.

[0195] Enhanced robustness: By comparing the processing results of different signal sources, the present invention demonstrates higher robustness; whether in an environment with drastic signal changes or in a stable signal, the system can ensure the quality of the final processing result by adjusting the fine-tuning index.

[0196] To further explain, The calculation formula is as follows:

[0197]

[0198] In the formula, This represents the intensity value of the SAR echo signal from the ship. Represents the standard rectangular window function. It is the width of the time window; It is the phase constant term; It is time The first-order linear term represents the actual location of the scattering center in the SAR image; It is time The nth-order linear term is related to the complex motion of the target. It is the motion error phase that affects motion compensation and imaging focusing, and needs to be decomposed and compensated. The polynomial order is represented by j, which represents the imaginary unit, indicating that the signal has a phase in complex form.

[0199] Phase compensation basis function The calculation formula is:

[0200]

[0201] in, Indicates a time window. and Set the center and width of the window; setting the time window can accurately fit the time of the real components, choose a cosine window or a rectangular window as needed;

[0202] Because the synthetic aperture time of high-resolution spaceborne SAR is relatively long, and the strong reflection center of the hull changes with the rotation of the imaging angle and position, there will be occlusion or certain fluctuations in the intensity value; it is not completely consistent with the entire synthetic aperture time in time, which will bring uncertain errors to the subsequent parameter estimation and component extraction.

[0203] The calculation formula is as follows:

[0204]

[0205] in, It is a complex constant representing the amplitude and initial phase of the signal; It describes the phase component that changes over time;

[0206] The calculation formula is as follows:

[0207]

[0208] in, Indicates Fourier transform; The result of SAR secondary imaging is the frequency domain of the compensated signal; The maximum value appears at the peak position, using Function representation, i.e. The location of the peak value indicates the spatial location of the reflection point.

[0209] Will The energy of the main lobe region of the mid-signal spectrum peak is taken as the component intensity of the signal, while The energy in the region outside the main lobe of the function is taken as the residual signal, specifically including:

[0210] Its frequency domain characteristics are defined as follows:

[0211]

[0212] in, Indicates the peak frequency point The minimum value of the left and right neighbor ranges is 0. By expanding the neighborhood range, the robustness of the algorithm is improved.

[0213] The main lobe region refers to the region surrounding the peak frequency of the spectrum. A symmetrical interval ,in Indicates the width of the interval;

[0214] The value is set to 0 in the main lobe region, indicating that the PPS signal components in this frequency range are "masked" or "removed".

[0215] Outside the main lobe region, i.e., "others". Maintaining the original spectrum Consistent;

[0216] The calculation formula is as follows:

[0217]

[0218] in, Indicates the inverse Fourier transform; Based on the estimation results The conjugate of the phase compensation function; other components can be gradually extracted from the residual function, and finally all PPS signal components are obtained. The linear sum of all PPS signal components is the mc-PPS signal; at the same time, in order to improve efficiency during the extraction process, a threshold value is set to detect the validity of the PPS signal components. According to the FDE-AJTF time-frequency decomposition objective function analysis, the PPS signal components are extracted one by one according to the signal strength.

[0219] The calculation formula is as follows;

[0220]

[0221] Where M represents the number of PPS signal components in the echo, and m∈{1,2,…,M} represents the m-th PPS signal component. This represents the optimal estimate of each PPS signal component, while The residual is the result after extracting M PPS signal components.

[0222] To further explain, considering the fact that the suboptimal solution extracted by the algorithm during the time-frequency decomposition of the MC-PPS signal is also the true solution, the following co-evolutionary PSO algorithm is designed. The components of the MC-PPS signal are independent of each other, so the extraction of one PPS signal component does not affect other components. The co-evolutionary PSO algorithm sets different permissions for each subgroup and adds a random group. Co-evolution means that superior individuals discovered during the search migrate between different subgroups as shared information to guide the evolutionary progress, thus significantly improving the global convergence efficiency of the algorithm. The co-evolutionary PSO algorithm combines the ability of PSO to explore search spaces with different priorities. The population is divided into an optimal group, a suboptimal group, and a random group. Each subgroup represents a subspace in the solution space, and also represents a subspace of the problem. Solution: The optimal group includes particles with the globally optimal position, and the suboptimal group is artificially prohibited from using the neighborhood of the optimal group for iteration, thus enhancing the global optimality of the optimal group; the suboptimal group only restricts the search region in the suboptimal solution, but retains the probability of subpopulation improvement through particle position updates; if, after a certain iteration, the particles in the suboptimal group have the best fitness among all individuals globally, then the suboptimal group can be promoted to the optimal group, which means that the problem of premature stagnation of particles is solved; the random group does not have an optimal particle and updates together with other groups, improving the randomness of the entire population and the information exchange between groups; when the optimal group obtains a local optimal solution, the suboptimal group retains the ability to search for another optimal solution outside the region, so this method can extract multiple components simultaneously, effectively improving the global convergence speed;

[0223] The PPS signal component is used as the input initial particle swarm, including: the PPS signal component is the azimuth position of the scattering center extracted from the residual function, and other components are extracted step by step from the residual function to finally obtain the PPS signal components of all particles.

[0224] The fitness calculation formula is as follows:

[0225]

[0226] in, It is a Fourier transform. It is the residual signal to be processed. It is the phase compensation function, and the particle Related to parameters, It is the fitness function, used to evaluate the performance of each particle in the solution space;

[0227] Definition of the first The formula for calculating the parameter set of each particle is as follows;

[0228]

[0229] in, Indicates the first The parameter set of a particle is a particle in the particle swarm optimization algorithm. These are the higher-order component parameters of the mc-PPS signal. and These are the start and end times of the time window, respectively. Due to the complex motion of the ship and the occlusion effect under high-resolution conditions, the signal at the reflection point will change, and some signals will appear or disappear during the synthetic aperture time. It is the total number of particles, which mainly depends on the SAR image resolution and the size of the target; Let be the polynomial order of the phase of the input signal;

[0230] Update the fitness and the local best particle position for each group, specifically including: finding the globally optimal and second-best particle fitness within their respective ranges based on the fitness function, and updating the parameters and scattering center position of the optimal particle; simultaneously, restricting the second-best group to search and update near the scattering center region; in the... Updating in progress, the first... The local and global optimal fitness values ​​of each particle are calculated as follows:

[0231]

[0232] in, This represents the local optimal fitness value of the m′-th particle in the g-th generation. This indicates that the particle has evolved from the first iteration to... Record all positional parameters for the next iteration. This represents the globally optimal fitness value in the g-th generation.

[0233] The positions of the m′-th particle in the current local and global optimal solutions are defined as follows:

[0234]

[0235] in, It is the position of the local optimum of the current particle in the g-th iteration; It is the location of the global optimal solution in the g-th iteration;

[0236] The survival of the fittest is determined based on the local fitness of the new randomized mixed group. If the maximum fitness value of a particle in a randomized subgroup is greater than the minimum fitness value of a particle in the optimal group, then the two particles in the new randomized mixed group are swapped to eliminate the inferior. The same process is also applied to the other mixed group of the randomized group.

[0237] The expression for exchanging roles between two subgroups is as follows:

[0238]

[0239] in, It is the maximum value of the local optimal fitness of individuals in the suboptimal subgroup. It is the maximum local optimal fitness of an individual in the optimal population, denoted by [symbol]. Indicates the exchange of individuals into groups; and These are the particle numbers with the highest local optimal fitness in the optimal group and the second-best group, respectively.

[0240]

[0241] Iteration from The three subgroups updated from the previous steps, including the individuals and groups, are then... As the first The three subgroups corresponding to the generation;

[0242] Determine if the algorithm meets the stopping conditions, including the maximum number of iterations and the convergence of the global fitness result, specifically including:

[0243] The maximum number of iterations is set to 300, and the fitness ratio is set to 0.99. Since the Co-evolutionary PSO algorithm can output multiple component solutions simultaneously, if only one valid component remains in the signal, the second component parameter is invalid and requires validity assessment. According to the parameter extraction process, if the suboptimal solution contains the true component parameters, it is independent of the optimal solution, and the extraction of each component is not affected by the extraction of the other. The fitness ratio, used as the convergence criterion, is defined as follows:

[0244]

[0245] in, This represents the fitness of the suboptimal solution during the iteration process. It is the fitness of the suboptimal solution and the residual signal after the optimal component is extracted. The fitness of the suboptimal solution is the ratio of the fitness after the optimal component is extracted to the fitness before. The threshold for judgment, This indicates that the statement is valid. This indicates invalidity; in this embodiment, the value is 0.99. According to the characteristics of the MC-PPS signal, when the suboptimal solution is not the true solution, its fitness will be affected by the extraction of the optimal component, so the ratio is low. When the suboptimal solution is the true solution, the change in fitness is small. Therefore, by judging the parameters of the suboptimal solution, invalid components can be eliminated more accurately.

[0246] To further explain, in summary, to address the image problems encountered by sub-meter-level spaceborne SAR under high sea state conditions, the phase compensation function is used as the basis function, and a time window parameter is added, which better reflects the actual situation of unstable echoes from strong scattering points under high sea states, thus improving the robustness of the algorithm. The parameter estimation, residual update, and component extraction steps are performed in the frequency domain, reducing the search dimension and improving the computation speed. Based on this, a parameterized time-frequency distribution construction method is proposed to reduce the influence of cross terms and sidelobes. Finally, simulation and real data verification show that after processing with the FDE-AJTF algorithm, the image quality of ships under complex motion conditions can be significantly improved, and the ship boundaries and structures can be clearly displayed. The geometric, scattering, and structural characteristics of the ship can be obtained normally, effectively restoring the application capability of spaceborne SAR images in the ocean.

[0247] To address the trade-off between computational complexity and global convergence in the FDE-AJTF algorithm, a co-evolutionary particle swarm optimization (PSO) algorithm is proposed and applied to high-resolution spaceborne SAR compensation processing. To address the contradiction of non-convex optimal computation in the multidimensional solution space of the FDE-AJTF algorithm, this application proposes a co-evolutionary PSO algorithm based on comparisons with genetic algorithms and PSO algorithms. It designs a particle swarm combination partitioning and information sharing method, enabling parallel estimation and extraction of multiple PPS signal components, further improving the search speed and global optimal search capability in time-frequency decomposition. Processing results using ship scattering point target models and real high-resolution spaceborne SAR data show that the image quality of complex moving ships is significantly improved, and the overall processing speed is increased by more than 40%. Imaging results verify the efficiency and robustness of the co-evolutionary PSO algorithm.

[0248] To verify the processing capability of the Co-evolutionary Particle Swarm Optimization (CSO) algorithm for high-resolution spaceborne SAR ship target data, a spaceborne SAR spatial geometric imaging simulation model was established. Signal simulation was performed at nine points on the edge of the ship's hull, with the positions of each point being [00, 1000, –1000, 5050, 500, 50–50, –5050, –500, –50–50], in meters. The simulated ocean background was a complex sea state of level 5. The CSO algorithm was evaluated from three aspects: point target simulation visualization effect, point target quality, and processing speed. Specific imaging parameters and location information are shown in the table below.

[0249] Table 2 Main Simulation Parameters

[0250]

[0251] To evaluate the algorithm's performance on real-world data processing, experiments were conducted using actual spaceborne SAR data. This data was imaged using a sliding spotting mode with a spatial resolution of 0.5 meters, and the data product format was SLC. Figure 4 below shows a spaceborne SAR image of a ship in complex motion. It can be observed that in the original imaging results, due to the complex movement of the sea surface and the three-dimensional motion caused by waves, the ship exhibits severe defocusing. The ship target image shows significant divergence in the azimuth direction, making it impossible to distinguish the ship's structure and shape characteristics. Even with manual target interpretation or deep learning-based algorithms, this imaging result will fail to obtain the ship's typical parameters, rendering it completely incapable of classification and identification for marine surveillance applications.

[0252] After processing with the FDE-AJTF method optimized by co-evolutionary PSO, the scattering center information of each phase component of the ship can be accurately extracted. The image retains the basic outline of the ship as well as geometric information such as length and width. At the same time, the dense area of ​​scattering centers also reflects the scattering structure characteristics of the ship. It can be clearly seen from the image that there is a facility structure in the middle of the hull. Furthermore, under the same HP820 workstation hardware configuration, the co-evolutionary PSO algorithm reduces the time consumption by 42% compared with the standard PSO algorithm. The imaging results verify the efficiency and robustness of the co-evolutionary PSO algorithm.

[0253] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0254] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0255] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0256] [Amended according to Rule 26, 14.01.2026] The above description is only a specific embodiment of this application, but the protection scope of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the protection scope of this application.

[0257] [Revised according to Rule 26, January 14, 2026]

Claims

1. [Corrected according to Rule 26 14.01.2026] A high-resolution space-borne SAR ship target imaging processing method under complex sea conditions, which is improved on the basis of the AJTF algorithm to obtain an adaptive joint time-frequency imaging processing method, hereinafter referred to as FDE-AJTF, characterized in that, The specific steps include: Step S1: Obtain the SAR echo signal data of the moving ship target in complex sea state, and define it as the output of the form of mc-PPS signal, and define the PPS signal component of a single strong scattering point as ； Step S2: Constructing phase compensation basis functions of echo signals The PPS signal components are conjugate, and the length and overlap of the time window parameters are adjusted to match the time-frequency characteristics of the echo signal from a high-sea-state ship target. Step S3: Using phase compensated basis functions The polynomial phase error is corrected, the polynomial phase error of a SAR echo signal in SAR imaging is determined, and the adjusted time window parameter is combined with the SAR echo signal and a phase compensation base function The conjugate inner product is used as the objective function; SAR echo signals are combined with phase compensated basis functions The multiplication is performed to obtain the compensation signal to the compensation signal The result of the Fourier transform into the spectral domain gives the compensated spectrum in the image ； Step S4: Based on the signal corrected in step S3, define the objective function for adaptive joint time-frequency processing as follows: ； This indicates the parameter that needs to be estimated, which, after imaging processing, is determined based on the maximum value of the spectrum. The location of occurrence determines the peak frequency point. Thus, the parameters are obtained. Then complete the search for all other parameters. Spectrum In the middle, the frequency point corresponding to the maximum value ， Indicates the PPS signal component With phase compensation basis function Perform a Fourier transform on the product of the two; The first parameter estimated is the frequency point. ； Will The energy of the main lobe region at the peak of the mid-signal spectrum is taken as the component intensity of the signal, while The energy in the region outside the main lobe of the function is used as the residual signal; By processing the signal using the optimal estimation algorithm, the estimated values ​​of the PPS signal at each order are obtained. The estimated values ​​are defined as follows: The calculation formula is as follows: ； in, for The intensity component of the maximum value of the spectrum, This represents the optimal estimation results for each order component of the PPS signal. Let denote the order of the polynomial, and The change over time t is represented by t raised to the power of n, where j represents the imaginary unit; Step S5: Based on the objective function result optimized in step S4, extract the PPS signal components of each scattering point and calculate the signal residual. Then, perform the same processing on the signal residual, iteratively extract the new PPS signal components of the scattering point and estimate the phase parameters until the residual reaches the predetermined threshold set according to previous data analysis or prior knowledge. In each iteration, statistical features of signal-to-noise ratio, scattering point density, and signal change rate are extracted, and after constructing the corresponding dataset, the average difference change rate of these features is calculated. The average difference change rate corresponding to the signal-to-noise ratio, scattering point density, and signal change rate is obtained, analyzed, and processed to construct a threshold fine-tuning index. The fine-tuning index is used to provide a dynamic adjustment strategy for a predetermined threshold. The residual signal is further processed in the frequency domain. It is then inversely transformed to the time domain and multiplied by the conjugate of the phase compensation function to obtain the time-domain residual signal. ； Setting PPS signal components The threshold value is When the PPS signal component When the value falls below the threshold, the subsequent PPS signal components will be lower than the effective components, and the iterative search will stop. Step S6: Optimize the output of step S5 using the co-evolutionary PSO algorithm; Step S7: Simulate and verify the FDE-AJTF algorithm and the co-evolutionary PSO algorithm with actual data. Use a complex moving ship target model and real high-resolution spaceborne SAR data to evaluate the imaging quality under different complex sea conditions.

2. The high-resolution spaceborne SAR ship target imaging processing method under complex sea conditions according to claim 1, characterized in that: Extract the PPS signal components from each scattering point and calculate the signal residual. Then, perform the same processing on the signal residual, iteratively extracting new PPS signal components from scattering points and estimating phase parameters until the residual reaches a predetermined threshold set based on previous data analysis or prior knowledge. Specifically, this includes: A deterministic method based on the cumulative energy ratio is chosen to set a predetermined threshold for the residual, and the energy of the current PPS signal component is calculated in each iteration. and accumulated energy Define the cumulative energy ratio The calculation formula is: ； in, This represents the energy of the PPS signal component extracted in the k-th iteration step. This represents the energy of the PPS signal component extracted in the i-th iteration; The total energy of the target signal is represented by the sum of the energies of all extracted PPS signal components. Set a predetermined threshold That is, when When the iteration stops, the energy ratio of the residual signal does not exceed 1% of the target signal, to ensure that the residual mainly contains noise and invalid components.

3. The high-resolution spaceborne SAR ship target imaging processing method under complex sea conditions according to claim 2, characterized in that: In each iteration, statistical features of the signal-to-noise ratio, scattering point density, and signal change rate are extracted. After constructing the corresponding dataset, the average rate of change of these features is calculated, specifically including: The signal-to-noise ratio, scattering point density, and signal rate of change are labeled as SNR, SD, and SVR, respectively. Let the set of iteration counts be {1,2,…,i,…,k}, where k is the total number of iterations and i represents the index of the i-th iteration; In the i-th iteration, the signal noise is calculated as follows: ； in, It is the signal energy at the i-th iteration; It is the noise energy at the i-th iteration; The change in SNR difference between adjacent iterations is calculated as follows: ； Calculate all Average of the difference changes: ； in, It is the average value of the change in the signal-to-noise ratio difference. It is the change in SNR difference between adjacent iterations; In the i-th iteration, the scattering point density is calculated as follows: ； in, is the number of scattering points in the i-th iteration, and As is the fixed area covered by the signal; The change in SD difference between adjacent iterations is calculated as follows: ； Calculate all Average of the difference changes: ； in, It is the average value of the change in the density difference at the scattering points. It is the change in the difference in scattering point density between adjacent iterations; In the i-th iteration, the rate of change of the signal is calculated as follows: ； in, This refers to the change in signal characteristics during the i-th iteration; It is a fixed time interval; The change in SVR difference between adjacent iteration steps is calculated as follows: ； Calculate all Average of the difference changes: ； in, It is the average value of the change in the rate of change of the signal. It is the change in the difference in the rate of change of the signal between adjacent iterations.

4. The high-resolution spaceborne SAR ship target imaging processing method under complex sea conditions according to claim 3, characterized in that: The average difference rate of change corresponding to the signal-to-noise ratio, scattering point density, and signal change rate is obtained, analyzed, and processed to construct a threshold fine-tuning index. This fine-tuning index provides a dynamic adjustment strategy for a predetermined threshold, specifically including: Define the fine-tuning index as The calculation formula is as follows: ； in, The judgment value is dynamically adjusted, where e is the base of the natural logarithm. To prevent division by zero constants, Here are the time series normalization coefficients, and f(t) is the amplitude of the PPS signal component at time t. Total observation time The variance of the signal amplitude; Based on previous data analysis or prior knowledge, determine sequentially 、 and The benchmark values ​​are respectively 、 and ； like 、 and If any two values ​​in the table differ from the corresponding benchmark value by more than 10%, then... Perform the following calibrations; ； in, ； To define the fine-tuning index after calibration, the fine-tuning index is limited. The effective range of is [0.5, 1.5]. Within this range, [0.5, 1) indicates that the signal processing allows for a larger noise component and is suitable for complex signal processing environments; [1, 1.5] indicates that the signal processing requires stricter noise suppression and is suitable for high-quality signal processing scenarios. when When the value is in the range [0.5, 1), the signal processing allows for a standard amount of noise component to be used in complex signal processing environments. The adjusted cumulative energy ratio threshold is... And it is calculated using the following formula: ； when When the value is in the range [1, 1.5], the signal processing requires stricter noise suppression. For high-quality signal processing scenarios, the adjusted cumulative energy is higher than the threshold. pass Formula calculation.

5. The high-resolution spaceborne SAR ship target imaging processing method under complex sea conditions according to claim 4, characterized in that: Will The energy of the main lobe region at the peak of the mid-signal spectrum is taken as the component intensity of the signal, while The energy in the region outside the main lobe of the function is taken as the residual signal, specifically including: The frequency domain characteristics are defined as follows: ； in, Indicates the peak frequency point The minimum value of the left and right neighbor ranges is 0. ， It is the width of the time window; The main lobe region refers to the region surrounding the peak frequency of the spectrum. A symmetrical interval ,in This indicates the width of the interval; The value is set to 0 in the main lobe region, indicating that the PPS signal components in this frequency range are "masked" or "removed". "Others" indicates the location outside the main lobe region. Maintaining the original spectrum Consistent.

Images