Rcs dynamic estimation method and device based on bayesian optimization

Abstract

The application relates to the technical field of SAR satellite load parameter setting, and provides an RCS dynamic estimation method and device based on Bayesian optimization. The method performs peak value detection on the RCS equivalent values in sample data, divides the sample data into different types of data sets based on the detection results, sets Bayesian dynamic estimation target functions and estimation intervals for the different types of data sets, respectively trains Bayesian dynamic estimation models of the different types of data sets, then obtains to-be-estimated data, determines the data type of the to-be-estimated data based on the RCS equivalent value peak value detection result of the to-be-estimated data, calls the trained Bayesian dynamic estimation model of the corresponding type to determine the RCS estimation value of the to-be-estimated data, solves the problem that manual parameter setting cannot meet self-adaptive accurate estimation in a complex scene, ensures the estimation accuracy and reliability of the RCS in the complex scene, realizes self-adaptive adjustment of the RCS estimation, and significantly improves the estimation precision of the RCS.

Description

A Bayesian-Optimized Dynamic RCS Estimation Method and Apparatus Technical Field

[0001] This application relates to the field of SAR satellite payload parameter setting technology, and in particular to a method and apparatus for dynamic RCS estimation based on Bayesian optimization. Background Technology

[0002] Synthetic Aperture Radar (SAR), as a core sensor in modern remote sensing, has evolved from early single-frequency, single-polarization modes to a new generation of systems with multi-band imaging capabilities including X / C / L / Ku / Ka, full polarization, and sliding spotting. With the deployment of advanced satellites such as TerraSAR-X, Sentinel-1, and Gaofen-3, SAR image resolution has broken through the sub-meter level, and its sensitivity to the Radar Cross-Section (RCS) parameter has increased exponentially. As a physical quantity describing the electromagnetic scattering characteristics of a target, the numerical accuracy of RCS directly affects the radiometric calibration accuracy of the SAR system (errors must be controlled within ±0.5 dB), target detection probability (improving RCS accuracy by 1 dB can increase the detection rate by more than 15%), and the accuracy of ground feature classification (e.g., the tolerance for RCS error in crop identification accuracy is only ±0.3 dB).

[0003] The current mainstream methods for calculating RCS can be divided into three categories:

[0004] (1) High-frequency approximation methods: including physical optics and geometric optics, which are suitable for large targets, but the error can reach 5-8dB in edge diffraction and multiple scattering scenarios;

[0005] (2) Numerical calculation methods: such as the method of moments (MoM), the finite element method (FEM), and the finite-difference time-domain method (FDTD). Although these methods can handle complex targets (such as aircraft cavity structures), their computational complexity is high. Simulation of typical fighter targets in the X-band requires more than One grid cell;

[0006] (3) Hybrid methods: such as physical optics-equivalent current method (PO-ECM), which can balance accuracy and efficiency in the simulation of ultra-large targets such as aircraft carriers, still requires prior knowledge of the target's accurate three-dimensional model.

[0007] High-frequency approximation methods are primarily implemented through experimental measurements. Compact-field tests at the U.S. Air Force Research Laboratory show that even in a standard anechoic chamber environment, the RCS measurement results of a 1:20 scale model can still deviate from the full-size physical object by ±2 dB. Outdoor dynamic measurements are more susceptible to environmental clutter, atmospheric attenuation, and other factors. For example, environmental noise can cause a 10 to 15 dB deterioration in the signal-to-noise ratio, and Ka-band attenuation can reach 0.1 dB / km.

[0008] The numerical calculation method mainly involves querying the two-dimensional matrix numerical distribution of RCS in the database, and then manually adjusting RCS using static estimation strategies such as maximum, minimum or average values.

[0009] A typical database is the Global Backscattering Coefficient Database constructed by the Chinese Academy of Sciences. Although this database contains more than 2 million sets of measured data, covering 12 typical land cover types, it has the following fundamental defects:

[0010] 1) Insufficient sample coverage: Measured data for polar ice sheets (accounting for 8% of the global area) account for only 0.3% of the reservoir capacity, and the data gap rate for the rainy season in tropical rainforests (accounting for 6% of the land area) reaches 75%;

[0011] 2) Model extrapolation error: When extrapolating parameters using the Ulaby microwave scattering model, the root mean square error (RMSE) is as high as 4.7 dB in densely populated or facility-rich areas (IEEE TGRS 2021 data).

[0012] 3) Static modeling defects: The manual gain control (MGC) calculation model uses a fixed parameter lookup table, which cannot adapt to the dynamic changes in the incident angle of SAR satellites (such as the incident angle of Sentinel-1, which varies from 20° to 45°), resulting in nonlinear fluctuations in RCS (fluctuation amplitude can reach ±6dB).

[0013] Meanwhile, the aforementioned databases were primarily constructed using theoretical simulation data, and their accuracy is limited by the following factors:

[0014] 1) Limitations of theoretical models: Existing models (such as the Ulaby scattering model and the Integral Equation Model (IEM) model) have poor applicability to complex terrains (such as cities, forests, and glaciers). For example, in vegetated areas, the root mean square error (RMSE) between theoretical simulations and measured data can reach 3-5 dB (IEEE TGRS 2022 data), leading to increased radiometric calibration errors in SAR imaging.

[0015] 2) Insufficient spatiotemporal resolution: Existing databases typically have a temporal resolution that is updated quarterly or annually (such as the ESAGlobScat database), which cannot reflect short-term changes on the Earth's surface (such as floods, snowmelt, and crop growth). At the same time, the spatial resolution is mostly 1km×1km grid, which is difficult to accurately match the imaging requirements of high-resolution SAR satellites (such as TerraSAR-X's 0.25m resolution);

[0016] 3) Uneven data coverage: There is a severe lack of measured data in regions such as polar regions, tropical rainforests, and deserts, resulting in large extrapolation errors. For example, the RCS simulation data of the Antarctic ice sheet can have an error of ±4dB, affecting the accuracy of polar glacier monitoring.

[0017] Furthermore, existing SAR systems primarily employ two RCS estimation strategies: static estimation and manual intervention. The former cannot adapt to dynamic scenarios. For example, in marine monitoring, dynamic changes in ocean waves can cause RCS fluctuations of ±10 dB, and static estimation strategies cannot be adjusted in real time, resulting in a decrease in the SAR image signal-to-noise ratio (SNR). The latter is costly and inefficient, making it difficult to meet the real-time requirements of emergency observation scenarios such as earthquakes and typhoons.

[0018] Therefore, how to dynamically and efficiently estimate RCS is a technical problem that needs to be solved. Summary of the Invention

[0019] In view of this, embodiments of this application provide a method and apparatus for dynamic RCS estimation based on Bayesian optimization, in order to solve the problems of RCS estimation in the prior art being difficult to adapt to dynamic scenarios and having high estimation costs and low efficiency.

[0020] A first aspect of this application provides a Bayesian optimization-based dynamic RCS estimation method, comprising:

[0021] Obtain N sample data points; where each sample data point includes the measured value of the data and the equivalent value of the radar cross section (RCS).

[0022] Peak detection is performed on the RCS equivalent value of each sample data, and the N sample data are divided into different types of datasets based on the peak detection results; the dataset types include unimodal distribution type, bimodal distribution type, and multimodal distribution type.

[0023] Set the Bayesian dynamic estimation objective function and estimation interval for different types of datasets;

[0024] Bayesian dynamic estimation models are trained for different types of datasets based on a defined objective function and estimation interval.

[0025] Obtain the data to be estimated and its equivalent RCS value. Perform peak detection on the equivalent RCS value of the data to be estimated. Determine the data type of the RCS value to be estimated based on the peak detection result. The data type is one of the dataset types.

[0026] The RCS estimate of the data to be estimated is determined using a trained Bayesian dynamic estimation model corresponding to the data type.

[0027] A second aspect of this application provides a Bayesian optimization-based RCS dynamic estimation device, comprising:

[0028] The acquisition module is configured to acquire N sample data points; each sample data point includes the measured value of the data and the equivalent value of the radar cross section (RCS).

[0029] The classification module is configured to perform peak detection on the RCS equivalent value of each sample data and divide the N sample data into different types of datasets based on the peak detection results; among them, the dataset types include unimodal distribution type, bimodal distribution type, and multimodal distribution type.

[0030] The configuration module can be set to set the Bayesian dynamic estimation objective function and estimation interval for different types of datasets;

[0031] The training module is configured to train Bayesian dynamic estimation models for different types of datasets based on a defined objective function and estimation interval.

[0032] The acquisition module is also configured to acquire the data to be estimated and the RCS equivalent value of the data to be estimated, perform peak detection on the RCS equivalent value of the data to be estimated, and determine the data type of the RCS value to be estimated based on the peak detection result; the data type is one of the dataset types.

[0033] The estimation module is configured to use a trained Bayesian dynamic estimation model corresponding to the data type to determine the estimated RCS value of the data to be estimated.

[0034] A third aspect of this application provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described method.

[0035] A fourth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described method.

[0036] The beneficial effects of this application embodiment compared with the prior art are as follows: This application embodiment performs peak detection on the RCS equivalent value in the sample data, divides the sample data into different types of datasets based on the detection results, sets Bayesian dynamic estimation objective function and estimation interval for each type of dataset, trains Bayesian dynamic estimation models for each type of dataset, then obtains the data to be estimated, determines its data type based on the peak detection result of the RCS equivalent value of the data to be estimated, and calls the trained Bayesian dynamic estimation model of the corresponding type to determine the RCS estimation value of the data to be estimated. This solves the problem that manual parameter settings cannot meet the adaptive and accurate estimation in complex scenarios, ensures the accuracy and reliability of RCS estimation in complex scenarios, realizes adaptive adjustment of RCS estimation, and significantly improves the accuracy of RCS estimation. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 is a flowchart illustrating a Bayesian optimization-based dynamic RCS estimation method provided in an embodiment of this application.

[0039] Figure 2 is an RCS histogram of typical single-peak, double-peak, and multi-peak data provided in the embodiments of this application.

[0040] Figure 3 is a flowchart illustrating the method for setting the Bayesian dynamic estimation objective function and estimation interval for various datasets according to an embodiment of this application.

[0041] Figure 4 is a flowchart illustrating the method for training Bayesian dynamic estimation models for different types of datasets based on a defined objective function and estimation interval, as provided in the embodiments of this application.

[0042] Figure 5 is a flowchart illustrating the method for determining the dynamic equilibrium factor provided in an embodiment of this application.

[0043] Figure 6 is a schematic diagram showing the estimation results of different types of datasets obtained using the method provided in the embodiments of this application.

[0044] Figure 7 is a comparison of model estimation errors before and after removing difference data for unimodal distribution data.

[0045] Figure 8 is a comparison of model estimation errors before and after removing difference data for bimodal distribution data.

[0046] Figure 9 shows a comparison of model estimation errors before and after removing difference data for multi-peak distribution data.

[0047] Figure 10 is a schematic diagram showing the estimation results of different types of datasets obtained using the retrained model.

[0048] Figure 11 is a flowchart illustrating another Bayesian optimization-based RCS dynamic estimation method provided in an embodiment of this application.

[0049] Figure 12 is a schematic diagram of an RCS dynamic estimation device based on Bayesian optimization provided in an embodiment of this application.

[0050] Figure 13 is a schematic diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0051] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0052] The following describes in detail, with reference to the accompanying drawings, a method and apparatus for dynamic estimation of RCS based on Bayesian optimization according to embodiments of this application.

[0053] As mentioned above, existing SAR systems' RCS estimation strategies mainly include static estimation strategies and manual intervention strategies. The former primarily uses fixed strategies (such as maximum, minimum, and average values) to estimate RCS values, which cannot adapt to dynamic scenarios; the latter requires manual setting of RCS parameters, which is time-consuming, costly, and inefficient, making it difficult to meet the real-time requirements of emergency observation scenarios. Furthermore, existing SAR systems' RCS estimation strategies lack differentiated processing based on classification. Different land surface types (such as cities, farmland, and water bodies) exhibit significantly different RCS characteristics, but existing systems have not established classification optimization models. For example, the multiple scattering effect in urban areas causes RCS values ​​to be 6-8 dB higher than theoretical predictions, while existing methods still use a uniform strategy, leading to parameter setting deviations.

[0054] In view of this, this application provides a Bayesian optimization-based dynamic RCS estimation method. This method involves peak detection of the equivalent RCS values ​​in sample data, dividing the sample data into different dataset types based on the detection results, setting a Bayesian dynamic estimation objective function and estimation interval for each dataset type, and training Bayesian dynamic estimation models for each dataset type. Then, the data to be estimated is obtained, and its data type is determined based on the peak detection results of the equivalent RCS values. The corresponding trained Bayesian dynamic estimation model is then called to determine the estimated RCS value for that data. This method solves the problem that manual parameter settings cannot meet the requirements for adaptive and accurate estimation in complex scenarios, ensuring the accuracy and reliability of RCS estimation in complex scenarios, achieving adaptive adjustment of RCS estimation, and significantly improving the accuracy of RCS estimation.

[0055] Figure 1 is a flowchart illustrating a Bayesian optimization-based dynamic RCS estimation method provided in an embodiment of this application. As shown in Figure 1, the method includes the following steps:

[0056] In step S101, N sample data are obtained.

[0057] Each sample data point includes the measured value of this data and the equivalent value of the radar cross section (RCS).

[0058] In step S102, peak detection is performed on the RCS equivalent value of each sample data, and the N sample data are divided into different types of datasets based on the peak detection results.

[0059] The dataset types include unimodal distribution, bimodal distribution, and multimodal distribution.

[0060] In step S103, the Bayesian dynamic estimation objective function and estimation interval are set for different types of datasets.

[0061] In step S104, Bayesian dynamic estimation models for different types of datasets are trained based on the determined objective function and estimation interval.

[0062] In step S105, the data to be estimated and the RCS equivalent value of the data to be estimated are obtained, peak detection is performed on the RCS equivalent value of the data to be estimated, and the data type of the RCS value to be estimated is determined based on the peak detection result.

[0063] The data type is one of the dataset types.

[0064] In step S106, the trained Bayesian dynamic estimation model corresponding to the data type is used to determine the estimated RCS value of the data to be estimated.

[0065] In some embodiments of this application, the method may be executed by a server or by a terminal device with certain processing capabilities.

[0066] In some embodiments of this application, N sample data can be obtained, each sample data including at least the measured value of the data and the equivalent value of the radar cross section (RCS).

[0067] Peak detection can be performed on the RCS equivalent value of each sample data point, and the N sample data points can be divided into different types of datasets based on the peak detection results. In one example, the dataset type can include unimodal distribution, bimodal distribution, and multimodal distribution.

[0068] Among them, the unimodal distribution type can be a dataset type whose RCS equivalent histogram contains only one peak; the bimodal distribution type can be a dataset type whose RCS equivalent histogram contains two peaks with a distance greater than a preset distance threshold; and the multimodal distribution type can be a dataset type whose RCS equivalent histogram contains at least three discrete peaks and whose inter-peak difference coefficient is greater than a preset difference coefficient threshold.

[0069] In some embodiments of this application, a Bayesian dynamic estimation objective function and estimation interval can be set for different types of datasets, and a Bayesian dynamic estimation model for different types of datasets can be trained based on the determined objective function and estimation interval.

[0070] After training each Bayesian dynamic estimation model, the data to be estimated and its equivalent RCS value can be obtained. Peak detection is then performed on the equivalent RCS value, and the data type of the RCS value to be estimated is determined based on the peak detection result. This data type is one of the dataset types. In other words, the peak detection result of the equivalent RCS value can be used to determine whether the data to be estimated is unimodal, bimodal, or multimodal.

[0071] In some embodiments of this application, a trained Bayesian dynamic estimation model corresponding to the data type can be used to determine the estimated RCS value of the data to be estimated.

[0072] According to the technical solution provided in the embodiments of this application, peak detection is performed on the RCS equivalent value in the sample data. Based on the detection results, the sample data is divided into different types of datasets. Bayesian dynamic estimation objective function and estimation interval are set for each type of dataset, and Bayesian dynamic estimation models for each type of dataset are trained. Then, the data to be estimated is obtained, and its data type is determined based on the peak detection result of the RCS equivalent value of the data to be estimated. The trained Bayesian dynamic estimation model of the corresponding type is called to determine the RCS estimation value of the data to be estimated. This solves the problem that manual parameter settings cannot meet the adaptive and accurate estimation in complex scenarios, ensures the accuracy and reliability of RCS estimation in complex scenarios, realizes adaptive adjustment of RCS estimation, and significantly improves the accuracy of RCS estimation.

[0073] In some embodiments of this application, the N sample data may be, for example, microwave frequency band data of global surface features from SAR satellites for 2023–2024, totaling 16,045 data points. This data is based on massive multi-source SAR remote sensing data and is mainly used for calculating the SAR payload satellite payload parameters RCS and MGC. It is one of the most complete SAR scattering characteristic databases currently available, constructed using a spatiotemporal data fusion method. The constructed global surface backscattering characteristic data includes three frequency bands (L, C, and X), four seasons, and 40 incident angles (20° to 60°), with a spatial resolution better than 1 km (0.01°) and a temporal resolution of 90 days. It includes various land cover types (ocean, forest, city, grassland, desert, etc.) and target scenes (ports, specific facilities and buildings, specific facility sites), and features high spatiotemporal resolution, multiple frequency bands, and high precision, which can support precise control of SAR payload parameters.

[0074] A systematic analysis of the histogram distribution characteristics of RCS data from typical imaging tasks in the aforementioned 16,045 data points can be performed, and land cover classification and parameter optimization can be carried out based on multimodal peak characteristics. By performing peak detection on the RCS numerical distribution under multiple incident angle conditions in the L / C / X three-band (i.e., L, C, and X bands), the scattering characteristics of the target scene are divided into three typical distribution patterns:

[0075] 1) A unimodal distribution characterizes scenarios with a simple and stable scattering mechanism. Its histogram exhibits a symmetrical Gaussian shape, with a kurtosis coefficient greater than 3.5 and a standard deviation less than 1.2 dB. This type of distribution mainly occurs in uniformly shaped ground features, such as:

[0076] Calm sea surface (peak value around -35dB);

[0077] Mature farmland (peak values ​​are concentrated in the range of -12dB to -8dB).

[0078] Desert without vegetation cover (peak value approximately -22 dB).

[0079] 2) A bimodal distribution reflects a composite scenario with two dominant scattering mechanisms, characterized by a significant bimodal structure with a spacing of 4-8 dB in the histogram. Typical applications include:

[0080] The area where land and sea meet (-35dB sea surface peak and -5dB land peak);

[0081] Forest-lake mixed zone (-10dB vegetation peak and -25dB water surface peak);

[0082] Desert-oasis transition zone (-22dB sand peak and -15dB vegetation peak).

[0083] 3) Multi-peak distribution corresponds to heterogeneous materials with complex scattering sources. Their histograms exhibit multiple discrete peaks (usually ≥3), with inter-peak difference coefficients exceeding 25%. This distribution pattern has significant target identification value, for example:

[0084] Urban building complex: includes multiple scattering peaks such as roads (-15dB), low-rise buildings (-5dB), and high-rise buildings (+5dB);

[0085] Specific facilities: Buildings exhibit periodic peaks (intervals of 1.5 dB), while some sites show azimuth-related spikes.

[0086] Port area: Three types of scattering sources can be distinguished: water area (-35dB), wharf (-12dB), and container stack (+5dB).

[0087] Figure 2 is an RCS histogram of typical unimodal, bimodal, and multimodal data provided in the embodiments of this application. The horizontal axis represents the RCS value, and the vertical axis represents the number of RCS values, i.e., the number of values ​​in the two-dimensional RCS matrix.

[0088] As shown in Figure 2, the RCS histogram distribution in the topmost pattern includes only one peak, so its corresponding data is a unimodal distribution type; the RCS histogram distribution in the middle pattern includes two peaks with a spacing greater than a preset distance threshold, so its corresponding data is a bimodal distribution type; the RCS histogram distribution in the bottommost pattern includes more than three peaks, and the difference between each peak is greater than a preset difference coefficient threshold, so its corresponding data is a multimodal distribution type.

[0089] Figure 3 is a flowchart illustrating the method for setting the Bayesian dynamic estimation objective function and estimation interval for various datasets according to embodiments of this application. As shown in Figure 3, the method includes the following steps:

[0090] In step S301, for any dataset, the objective function is determined as the inverse of the absolute value of the difference between the RCS equivalent value and the estimated RCS value.

[0091] In step S302, the estimated interval of the single-peak distribution type dataset is determined to be the interval range obtained by adding or subtracting a preset threshold from the peak position of the single peak.

[0092] In step S303, the estimation interval of the bimodal distribution type dataset is determined to be the range consisting of the smaller peak value minus a preset threshold to the larger peak value plus a preset threshold.

[0093] In step S304, the estimation interval of the multi-peak distribution type dataset is determined to be the range consisting of the minimum peak value minus a preset threshold to the maximum peak value plus a preset threshold.

[0094] In some embodiments of this application, setting the Bayesian dynamic estimation objective function and estimation interval for various datasets can be as follows: for any dataset, the objective function is determined to be the inverse of the absolute value of the difference between the RCS equivalent value and the estimated RCS value.

[0095] Furthermore, the estimation interval for a single-peak distribution dataset is determined to be the range obtained by adding or subtracting a preset threshold from the peak position of the single peak; the estimation interval for a bimodal distribution dataset is determined to be the range formed by subtracting a preset threshold from the smaller peak in the bimodal distribution to adding a preset threshold to the larger peak; and the estimation interval for a multimodal distribution dataset is determined to be the range formed by subtracting a preset threshold from the smallest peak in the multimodal distribution to adding a preset threshold to the largest peak.

[0096] In other words, the RCS equivalent value for each imaging task in the corresponding scene is set to Set the RCS value estimated by the model to According to the Bayesian optimization strategy, the goal of Bayesian optimization is to find suitable sample points to maximize the objective function value. Therefore, to minimize the error between the RCS value obtained from model training and the equivalent RCS value in the corresponding scenario, the objective function of the model can be dynamically estimated using Bayesian methods. Set as The objective function aims to make the model estimate... infinitely close In other words, the smaller the RCS estimation error, the better.

[0097] Simultaneously, the estimation range of RCS for each imaging task in different types of datasets can be determined. This step is crucial for the accurate training and parameter optimization of subsequent models. The specific implementation method is as follows:

[0098] Single-peak distribution type data: Because this type of data has concentrated and stable scattering characteristics, its RCS value distribution shows a symmetrical Gaussian shape and a small standard deviation (<1.2dB). Therefore, the smallest interval containing more than a preset proportion (e.g., 95%) of data points can be used as the estimation interval.

[0099] That is, the range between the peak position and a preset threshold can be calculated as the estimation range for unimodal distribution data. The preset threshold can be set according to actual needs, for example, 2dB.

[0100] Some typical examples could be: for the unimodal distribution data in a calm sea scene where the peak value is around -35dB, determine -35±2.4dB (i.e., -37.4dB to -32.6dB) as the estimation interval; for the unimodal distribution data in a mature farmland scene where the peak value is concentrated in the range of -12dB to -8dB, first take the center value of the range of -12dB to -8dB, and then determine the center value ±2dB as the estimation interval; for the unimodal distribution data in a desert area scene where the peak value is approximately -22dB, determine -22±2.4dB (-24.4dB to -19.6dB) as the estimation interval.

[0101] Bimodal data: This type of data has two dominant scattering mechanisms with a peak spacing of about 4-8 dB. The RCS characteristics of the two scattering sources need to be considered simultaneously.

[0102] Therefore, the method for determining the estimation range can be as follows: First, detect two peak positions P1 and P2 respectively; then calculate the distribution range corresponding to each peak: P1 ± preset threshold and P2 ± preset threshold; finally, take the minimum and maximum values ​​of the two interval endpoints as the overall estimation range. That is, take the union of the first interval formed by P1 ± preset threshold and the second interval formed by P2 ± preset threshold as the overall estimation range.

[0103] Some typical examples are as follows: If the preset threshold is set to 3dB, for the bimodal distribution data in the sea-land interface scenario with a peak of -35dB sea surface and -5dB land, the peak interval [-35dB, -5dB] can be expanded to [-38dB, -2dB] to obtain the estimation interval; for the bimodal distribution data in the forest-lake mixed area scenario with a peak of -10dB vegetation and -25dB water surface, the peak interval [-25dB, -10dB] can be expanded to [-28dB, -7dB] to obtain the estimation interval; for the bimodal distribution data in the desert-oasis transition zone scenario with a peak of -22dB sand dune and -15dB vegetation, the peak interval [-22dB, -15dB] can be expanded to [-25dB, -12dB] to obtain the estimation interval.

[0104] Multi-peak distribution data: This type of data has ≥3 discrete peaks, and the inter-peak difference coefficient is greater than a preset difference coefficient threshold (e.g., 25%). Therefore, when determining the estimation range, it is necessary to cover all significant scattering sources. In one example, the difference between the minimum lower bound and the preset threshold of all local intervals and the sum of the maximum upper bound and the preset threshold can be taken as the global estimation range.

[0105] Figure 4 is a flowchart illustrating the method for training Bayesian dynamic estimation models for different types of datasets based on a defined objective function and estimation interval, as provided in this application embodiment. As shown in Figure 4, the method includes the following steps:

[0106] In step S401, for any type of dataset, an initial set of sampling points is uniformly determined within the estimation interval of the dataset.

[0107] In step S402, candidate sampling points are obtained within the estimation interval of the dataset; the candidate sampling points do not belong to the sampling point set.

[0108] In step S403, a Gaussian regression model is constructed, and the RCS estimate of the candidate sampling points is determined based on the initial set of sampling points using the Gaussian regression model.

[0109] In step S404, in response to the determination that the iteration termination condition is not met based on the RCS estimation value, the model parameters of the Gaussian regression model are updated, and the initial sampling point set and candidate sampling points are updated to obtain the updated sampling point set and updated candidate sampling points.

[0110] In step S405, the steps of determining the RCS estimate of the updated candidate sampling points, updating the model parameters of the Gaussian regression model when the iteration termination condition is not met based on the RCS estimate and the number of iterations, and updating the sampling point set and candidate sampling points again are executed iteratively until the iteration termination condition is met, so as to obtain the trained Bayesian dynamic estimation model corresponding to this type of dataset.

[0111] In some embodiments of this application, when training a Bayesian dynamic estimation model for any type of dataset based on a defined objective function and estimation interval, an initial set of sampling points can be uniformly determined within the estimation interval of the dataset first. Then, candidate sampling points are obtained within the estimation interval of the dataset; these candidate sampling points do not belong to the set of sampling points. The candidate sampling points can be randomly determined within the estimation interval.

[0112] Simultaneously, a Gaussian regression model can be constructed, and the RCS estimates of candidate sampling points can be determined based on the initial set of sampling points. If the iteration termination condition is not met based on the RCS estimates, the model parameters of the Gaussian regression model are updated, and the initial set of sampling points and candidate sampling points are also updated, resulting in an updated set of sampling points and updated candidate sampling points.

[0113] The process iteratively executes the steps of determining the RCS estimate of the updated candidate sampling points, updating the model parameters of the Gaussian regression model when the iteration termination condition is not met based on the RCS estimate and the number of iterations, and updating the sampling point set and candidate sampling points again, until the iteration termination condition is met, thus obtaining the trained Bayesian dynamic estimation model corresponding to this type of dataset.

[0114] In some embodiments of this application, the Gaussian regression model can be ;in, For Gaussian regression model, The mean of the current set of sample points. This represents the covariance between each sampling point in the current sampling point set and the candidate sampling points. For the current set of sampling points, This is the current candidate sampling point.

[0115] In some embodiments of this application, the step of updating the current sampling point set may include: in response to determining that the objective function corresponding to the current candidate sampling point is greater than a preset error threshold, determining that the union of the current sampling point set and the current candidate sampling point is the updated sampling point set; and in response to determining that the objective function corresponding to the current candidate sampling point is less than or equal to the preset error threshold, determining that the previous sampling point set is the updated sampling point set.

[0116] The step of updating candidate sampling points may include using an adaptive acquisition function to determine the updated candidate sampling points within the estimation interval.

[0117] Among them, the updated candidate sampling points have the smallest RCS estimation error. The RCS estimation error is the difference between the RCS estimation value and the equivalent RCS value of the updated candidate sampling points. The RCS estimation value of the updated candidate sampling points is determined based on the Gaussian regression model composed of the current model parameters.

[0118] In some embodiments of this application, the adaptive acquisition function is: ;in, For the updated candidate sampling points, For the current set of sampling points, As the current candidate sampling point, The parameter space includes the set of possible values ​​for the current sampling point to be optimized; The function is used to calculate the set of values ​​of the independent variable when the function reaches its minimum value. As a dynamic equilibrium factor;

[0119] ; This is the conditional mean of the current set of sample points. This is the mean of the current set of sampled points; The current set of sampling points and the initial set of sampling points covariance, , For set The measured values ​​in For set The equivalent value of RCS in the data. For set The number of sampling points in the sample; For the kernel matrix, , and All are greater than or equal to 1 and less than or equal to 1. Positive integers;

[0120] ; The conditional covariance between the current set of sampled points and the current candidate sampled point. This is the covariance between each sample point in the current sample point set and the current candidate sample point set; The current set of sampling points and the initial set of sampling points. covariance, It is a two-dimensional matrix, where the first... Line number The elements of the column are the current set of sampling points. The a-th sampling point and the initial sampling point set The Middle The covariance of each sampling point and All are greater than or equal to 1 and less than or equal to 1. Positive integers; For the initial set of sampling points The covariance of the current set of candidate sampling points .

[0121] It plays a crucial role in Gaussian regression, as it uses the known initial set of sampling points. Information is transmitted through the model to the new sample, i.e., the current set of sampling points. In the predictions.

[0122] Figure 5 is a flowchart illustrating the method for determining the dynamic equilibrium factor provided in an embodiment of this application. As shown in Figure 5, the method includes the following steps:

[0123] In step S501, in response to determining that the number of iterations is less than the threshold of the first iteration, the value of the dynamic balance factor is determined to be the first value.

[0124] In step S502, in response to determining that the number of iterations is greater than or equal to the first threshold and less than the second threshold, the value of the dynamic balance factor is determined to be the second value.

[0125] In step S503, in response to determining that the number of iterations is greater than or equal to the second threshold, the value of the dynamic balance factor is determined to be the third value.

[0126] Among them, the first value is greater than the second value, and the second value is greater than the third value.

[0127] In some embodiments of this application, a dynamic equilibrium factor is determined. It is possible; if the number of iterations is determined to be less than the threshold of the first iteration, then it can be determined. The value is the first possible value; if it is determined that the number of iterations is greater than or equal to the first threshold and less than the second threshold, then it can be determined that... The value is the second possible value; if it is determined that the number of iterations is greater than or equal to the threshold of the second iteration, then it can be determined. The value is the third possible value.

[0128] The values ​​of the first, second, and third count thresholds can be determined according to actual needs, and the values ​​of the first, second, and third values ​​can also be determined according to actual needs. The determining principle can be that a dynamic balancing factor is used to automatically adjust the weights of exploration and exploitation based on the current optimization stage.

[0129] For example, exploration can be emphasized in the early stages of training (such as the first 20% of epochs), therefore setting... A larger value is used to expand the sampling range and cover the potential optimal region. In the middle stages of training (e.g., 20%–80% of the epochs), a balance is struck between exploration and exploitation, and the value is appropriately reduced. The value of is used to gradually converge the model to the high potential range. In the later stages of training (such as the last 20% of epochs), the focus is on utilizing , setting Use a smaller value to refine the search for the optimal solution.

[0130] In some embodiments of this application, the iteration termination condition includes at least one of the following: the number of iterations reaches a preset upper limit; the objective function value is greater than or equal to a preset target threshold; the objective function value is determined by the RCS estimate of the candidate sampling point and the equivalent RCS value of the candidate sampling point; in k consecutive iterations, the estimation accuracy improvement rate of the current Gaussian regression model is less than a preset proportion threshold; the prediction variance of the Gaussian regression model is less than a preset variance threshold.

[0131] In some embodiments of this application, the sample data may include historical data and real-time data. That is, in addition to the historical SAR remote sensing data mentioned above, the sample data in the embodiments of this application may also include real-time satellite data. By combining historical data and real-time data, the accuracy of RCS prediction can be improved.

[0132] To verify the technical effectiveness of the technical solution provided in the embodiments of this application, the following experiment was designed: In the initialization settings, the learning rate was set to 0.0002, the decay rate was 0.5, and it was set to decay once every 20 epochs; in the intelligent termination condition settings, the default training time was set to 100 epochs, but the training would terminate early if any of the following conditions were met: Error saturation: the average error change over the last 10 epochs was <0.1% (the optimal solution was reached); Performance convergence: the estimation accuracy improved by <0.5% (the model tended to be stable); Uncertainty threshold: the variance of the Gaussian process regression prediction was <0.01 (the estimation range was fully covered).

[0133] Figure 6 is a schematic diagram illustrating the estimation results of different types of datasets obtained using the method provided in the embodiments of this application. The left side of Figure 6 shows the estimation results for unimodal distribution data, the middle side shows the estimation results for bimodal distribution data, and the right side shows the estimation results for multimodal distribution data. The blue portion represents data with smaller RCS value errors in each dataset, while the red portion represents data with larger RCS value errors in each dataset.

[0134] As shown in Figure 6, since most of the three types of data obtained are theoretical simulation values, there is a certain amount of data error, meaning the quality of the directly obtained three types of data is poor. This poor-quality data will seriously affect the accuracy of RCS estimation. Therefore, values ​​with error values ​​outside the preset range can be set as differences. When the model is retrained, the difference data with large errors will be removed, and the parameters of the trained Bayesian dynamic estimation model will be adjusted.

[0135] Figure 7 shows a comparison of model estimation errors for unimodal distribution data before and after removing interpolated data. Figure 8 shows a comparison of model estimation errors for bimodal distribution data before and after removing interpolated data. Figure 9 shows a comparison of model estimation errors for multimodal distribution data before and after removing interpolated data.

[0136] The Error Scatter Plot in the figure represents an error scatter plot. The horizontal axis, Selected Value, represents the RCS value selected by the model, and the vertical axis represents the true RCS value. The red curve, Fit Line, represents the fitted curve of the scatter distribution, while the green curves, Upper Bound and Lower Bound, represent the boundary lines of the main scatter distribution. As shown in Figures 7 to 9, the distribution of each type of data is more concentrated after removing the difference data.

[0137] The model was retrained using the data of each type after removing the difference data, and the retrained model was used to estimate the data of each type. Figure 10 is a schematic diagram of the estimation results of different types of datasets obtained using the retrained model. The blue part represents data with smaller RCS errors in each dataset, and the red part represents data with larger RCS errors in each dataset. As shown in Figure 10, the proportion of good data with smaller estimation errors in the re-estimation results is significantly increased.

[0138] Table 1 shows the estimation results obtained from estimation experiments on different types of samples provided in the embodiments of this application.

[0139] Table 1. Estimation results obtained from estimation experiments on different types of samples.

[0140]

[0141] As can be seen from Table 1, the average deviation of the estimation results obtained by using the method provided in the embodiments of this application is less than 1 dB, and the deviation is greatly reduced, proving that the technical solution provided in the embodiments of this application can significantly improve the accuracy of RCS estimation.

[0142] Figure 11 is a flowchart illustrating another Bayesian optimization-based dynamic RCS estimation method provided in an embodiment of this application. As shown in Figure 11, the input data types can be determined first, including RCS unimodal distribution data, RCS bimodal distribution data, and RCS multimodal distribution data; then, the objective function of the Bayesian optimization model corresponding to each type of data is set, and the estimation interval of the Bayesian optimization model corresponding to each type of data is determined; next, the sampling points are initialized and evaluated.

[0143] If the iteration termination condition has not been met, then the Gaussian regression model is used to process the initial set of sampling points. The process involves fitting the data and generating the next candidate sampling point based on the adaptive acquisition function. Then, the RCS of the next candidate sampling point is estimated. If the error between the RCS of the next candidate sampling point and its equivalent RCS is less than a preset error threshold, the next candidate sampling point can be added to the current candidate sampling point set. The above steps are then iteratively executed until the iteration termination condition is met.

[0144] Otherwise, if the error between the estimated RCS value of the next candidate sampling point and its equivalent RCS value is greater than or equal to the preset error threshold, the next candidate sampling point can be eliminated, and the above steps can be iteratively executed until the iteration termination condition is met.

[0145] When the iteration termination condition is met, the model parameters can be determined, thus obtaining the trained model.

[0146] The technical solution provided in this application addresses the problem that manual parameter settings cannot meet the requirements for adaptive and accurate estimation in complex scenarios. By using the Bayesian optimization method to adjust the original RCS estimation strategy, the accuracy and reliability of RCS estimation in complex scenarios are ensured. Adaptive adjustment of RCS estimation is achieved, significantly improving the adjustment efficiency and estimation accuracy of RCS, shortening the adjustment cycle to the second level (while traditional methods require several hours), and achieving a target error of ≤ ±0.5dB.

[0147] Meanwhile, since existing technologies do not consider the impact of different climates on the estimation quality of radar cross section, the technical solution provided in this application adjusts the original estimation strategy process, which can efficiently eliminate poor-quality data products during the estimation process, effectively improving the application effect of the data and enhancing the pertinence and accuracy of parameter settings.

[0148] All of the above-mentioned optional technical solutions can be combined in any way to form the optional embodiments of this application, and will not be described in detail here.

[0149] The following are embodiments of the apparatus described in this application, which can be used to execute the embodiments of the method described in this application. For details not disclosed in the apparatus embodiments of this application, please refer to the embodiments of the method described in this application.

[0150] Figure 12 is a schematic diagram of a Bayesian optimization-based RCS dynamic estimation device provided in an embodiment of this application. As shown in Figure 12, the device includes:

[0151] The acquisition module 1201 is configured to acquire N sample data; where each sample data includes the measured value of the data and the equivalent value of the radar cross section (RCS).

[0152] The classification module 1202 is configured to perform peak detection on the RCS equivalent value of each sample data and divide the N sample data into different types of datasets based on the peak detection results; among them, the dataset types include unimodal distribution type, bimodal distribution type and multimodal distribution type.

[0153] Module 1203 is configured to set the Bayesian dynamic estimation objective function and estimation interval for different types of datasets.

[0154] Training module 1204 is configured to train Bayesian dynamic estimation models for different types of datasets based on a defined objective function and estimation interval.

[0155] The acquisition module 1201 is also configured to acquire the data to be estimated and the RCS equivalent value of the data to be estimated, perform peak detection on the RCS equivalent value of the data to be estimated, and determine the data type of the RCS value to be estimated based on the peak detection result; the data type is one of the dataset types.

[0156] The estimation module 1205 is configured to use a trained Bayesian dynamic estimation model corresponding to the data type to determine the estimated RCS value of the data to be estimated.

[0157] According to the technical solution provided in the embodiments of this application, peak detection is performed on the RCS equivalent value in the sample data. Based on the detection results, the sample data is divided into different types of datasets. Bayesian dynamic estimation objective function and estimation interval are set for each type of dataset, and Bayesian dynamic estimation models for each type of dataset are trained. Then, the data to be estimated is obtained, and its data type is determined based on the peak detection result of the RCS equivalent value of the data to be estimated. The trained Bayesian dynamic estimation model of the corresponding type is called to determine the RCS estimation value of the data to be estimated. This solves the problem that manual parameter settings cannot meet the adaptive and accurate estimation in complex scenarios, ensures the accuracy and reliability of RCS estimation in complex scenarios, realizes adaptive adjustment of RCS estimation, and significantly improves the accuracy of RCS estimation.

[0158] In some implementations, a Bayesian dynamic estimation objective function and estimation interval are set for each type of dataset, including: for any dataset, the objective function is determined to be the negative of the absolute value of the difference between the RCS equivalent value and the estimated RCS value; the estimation interval for a unimodal distribution dataset is determined to be the range obtained by adding or subtracting a preset threshold from the peak position of the unimodal distribution; the estimation interval for a bimodal distribution dataset is determined to be the range formed by subtracting a preset threshold from the smaller peak value in the bimodal distribution to adding a preset threshold to the larger peak value; and the estimation interval for a multimodal distribution dataset is determined to be the range formed by subtracting a preset threshold from the smallest peak value in the multimodal distribution to adding a preset threshold to the largest peak value.

[0159] In some implementations, Bayesian dynamic estimation models for different types of datasets are trained based on a defined objective function and estimation interval. This includes: for any type of dataset, uniformly determining an initial set of sampling points within the estimation interval of the dataset; obtaining candidate sampling points within the estimation interval of the dataset; ensuring that candidate sampling points do not belong to the sampling point set; constructing a Gaussian regression model and using the Gaussian regression model to determine the RCS estimates of the candidate sampling points based on the initial set of sampling points; in response to the determination that the iteration termination condition is not met based on the RCS estimates, updating the model parameters of the Gaussian regression model, and updating the initial set of sampling points and candidate sampling points to obtain an updated set of sampling points and updated candidate sampling points; iteratively executing the steps of determining the updated RCS estimates of the candidate sampling points, updating the model parameters of the Gaussian regression model, and updating the sampling point set and candidate sampling points again when the iteration termination condition is not met based on the RCS estimates and the number of iterations, until the iteration termination condition is met, thus obtaining the trained Bayesian dynamic estimation model corresponding to this type of dataset.

[0160] In some implementations, the Gaussian regression model is ;in, For Gaussian regression model, The mean of the current set of sample points. This represents the covariance between each sampling point in the current sampling point set and the candidate sampling points. For the current set of sampling points, This is the current candidate sampling point.

[0161] In some implementations, the step of updating the current sampling point set includes: in response to determining that the objective function corresponding to the current candidate sampling point is greater than or equal to a preset error threshold, determining that the union of the current sampling point set and the current candidate sampling point is the updated sampling point set; and in response to determining that the objective function corresponding to the current candidate sampling point is less than the preset error threshold, determining that the previous sampling point set is the updated sampling point set; the step of updating candidate sampling points includes: using an adaptive acquisition function to determine the updated candidate sampling points in the estimation interval; wherein the updated candidate sampling points have the minimum RCS estimation error, the RCS estimation error is the difference between the RCS estimation value and the RCS equivalent value of the updated candidate sampling points, and the RCS estimation value of the updated candidate sampling points is determined based on a Gaussian regression model composed of the current model parameters.

[0162] In some implementations, the adaptive acquisition function is: ; in, For the updated candidate sampling points, For the current set of sampling points, As the current candidate sampling point, For parameter space, The function is used to calculate the set of values ​​of the independent variable when the function reaches its minimum value. As a dynamic equilibrium factor; ; This is the conditional mean of the current set of sample points. This is the mean of the current set of sampled points; The current set of sampling points and the initial set of sampling points covariance, , For set The measured values ​​in For set The equivalent value of RCS in the data. For set The number of sampling points in the sample; For the kernel matrix, , and All are greater than or equal to 1 and less than or equal to 1. Positive integers; ; The conditional covariance between the current set of sampled points and the current candidate sampled point. This is the covariance between each sample point in the current sample point set and the current candidate sample point set; The current set of sampling points and the initial set of sampling points. covariance, For the initial set of sampling points The covariance of the current set of candidate sampling points.

[0163] In some implementations, the dynamic equilibrium factor The following method is used to determine: in response to determining that the number of iterations is less than the threshold of the first iteration, the following method is used to determine... The value is the first possible value; in response to determining that the number of iterations is greater than or equal to the first threshold and less than the second threshold, determine... The value is the second possible value; in response to determining that the number of iterations is greater than or equal to the second threshold, the value is determined. The value is the third value; where the first value is greater than the second value, and the second value is greater than the third value.

[0164] In some implementations, the iteration termination condition includes at least one of the following: the number of iterations reaches a preset upper limit; the objective function value is greater than or equal to a preset target threshold; the objective function value is determined by the RCS estimate of the candidate sampling point and the equivalent RCS value of the candidate sampling point; in k consecutive iterations, the improvement rate of the estimation accuracy of the current Gaussian regression model is less than a preset proportion threshold; the prediction variance of the Gaussian regression model is less than a preset variance threshold.

[0165] In some implementations, the sample data includes historical data and real-time data.

[0166] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0167] Figure 13 is a schematic diagram of an electronic device provided in an embodiment of this application. As shown in Figure 13, the electronic device 13 of this embodiment includes: a processor 1301, a memory 1302, and a computer program 1303 stored in the memory 1302 and executable on the processor 1301. When the processor 1301 executes the computer program 1303, it implements the steps in the various method embodiments described above. Alternatively, when the processor 1301 executes the computer program 1303, it implements the functions of each module / unit in the various device embodiments described above.

[0168] Electronic device 13 can be a desktop computer, laptop, handheld computer, cloud server, or other electronic device. Electronic device 13 may include, but is not limited to, processor 1301 and memory 1302. Those skilled in the art will understand that FIG13 is merely an example of electronic device 13 and does not constitute a limitation on electronic device 13, and may include more or fewer components than illustrated, or different components.

[0169] The processor 1301 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0170] The memory 1302 can be an internal storage unit of the electronic device 13, such as a hard disk or RAM of the electronic device 13. The memory 1302 can also be an external storage device of the electronic device 13, such as a plug-in hard disk, Smart Media Card (SMC), Secure Digital (SD) card, FlashCard, etc., equipped on the electronic device 13. The memory 1302 can also include both internal and external storage units of the electronic device 13. The memory 1302 is used to store computer programs and other programs and data required by the electronic device.

[0171] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0172] If an integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program may include computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. A computer-readable medium may include: any entity or device capable of carrying computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0173] 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 dynamic RCS estimation method based on Bayesian optimization, characterized in that, include: Obtain N sample data points; each sample data point includes the measured value and the equivalent radar cross section (RCS) value of the data. Peak detection is performed on the equivalent RCS value of each sample data point, and based on the peak detection results, the N sample data points are divided into different dataset types; the dataset types include unimodal distribution, bimodal distribution, and multimodal distribution. A Bayesian dynamic estimation objective function and estimation interval are set for each dataset type. Based on the determined objective function and estimation interval, Bayesian dynamic estimation models for each dataset type are trained. The data to be estimated and its equivalent RCS value are obtained; peak detection is performed on the equivalent RCS value of the data to be estimated; based on the peak detection results, the data type of the RCS value to be estimated is determined; the data type is one of the dataset types. The trained Bayesian dynamic estimation model corresponding to the data type is used to determine the estimated RCS value of the data to be estimated.

2. The method according to claim 1, characterized in that, For each type of dataset, a Bayesian dynamic estimation objective function and estimation interval are set, including: for any dataset, the objective function is determined to be the negative of the absolute value of the difference between the RCS equivalent value and the estimated RCS value; the estimation interval for a unimodal distribution dataset is determined to be the range obtained by adding or subtracting a preset threshold from the peak position of the unimodal distribution; the estimation interval for a bimodal distribution dataset is determined to be the range formed by subtracting a preset threshold from the smaller peak value of the bimodal distribution to adding a preset threshold to the larger peak value; and the estimation interval for a multimodal distribution dataset is determined to be the range formed by subtracting a preset threshold from the smallest peak value of the multimodal distribution to adding a preset threshold to the largest peak value.

3. The method according to claim 1, characterized in that, The method involves training Bayesian dynamic estimation models for different types of datasets based on a defined objective function and estimation interval. The process includes: uniformly determining an initial set of sampling points within the estimation interval of any dataset type; obtaining candidate sampling points within the estimation interval of the dataset; ensuring that the candidate sampling points do not belong to the set of sampling points; constructing a Gaussian regression model and using the Gaussian regression model to determine the RCS estimates of the candidate sampling points based on the initial set of sampling points; updating the model parameters of the Gaussian regression model and updating the initial set of sampling points and the candidate sampling points in response to a determination that the iteration termination condition is not met based on the RCS estimates, thus obtaining an updated set of sampling points and updated candidate sampling points; iteratively executing the steps of determining the updated RCS estimates of the candidate sampling points, updating the model parameters of the Gaussian regression model and updating the set of sampling points and candidate sampling points again when the iteration termination condition is not met based on the RCS estimates and the number of iterations, until the iteration termination condition is met, thus obtaining the trained Bayesian dynamic estimation model corresponding to this type of dataset.

4. The method according to claim 3, characterized in that, The Gaussian regression model is ;in, For the Gaussian regression model, The mean of the current set of sample points. The covariance between each sampling point in the current sampling point set and the candidate sampling point is given. For the current set of sampling points, This is the current candidate sampling point.

5. The method according to claim 3, characterized in that, The step of updating the current sampling point set includes, in response to determining that the objective function corresponding to the current candidate sampling point is greater than a preset error threshold, determining that the union of the current sampling point set and the current candidate sampling point is the updated sampling point set; And in response to determining that the objective function corresponding to the current candidate sampling point is less than or equal to the preset error threshold, the current sampling point set is determined to be the updated sampling point set; The step of updating candidate sampling points includes using an adaptive acquisition function to determine updated candidate sampling points in the estimation interval; wherein, the updated candidate sampling points have the minimum RCS estimation error, the RCS estimation error is the difference between the RCS estimation value and the RCS equivalent value of the updated candidate sampling points, and the RCS estimation value of the updated candidate sampling points is determined based on a Gaussian regression model composed of the current model parameters.

6. The method according to claim 5, characterized in that, The adaptive acquisition function is: ;in, For the updated candidate sampling points, For the current set of sampling points, As the current candidate sampling point, For parameter space, The function is used to calculate the set of values ​​of the independent variable when the function reaches its minimum value. As a dynamic equilibrium factor; ； This is the conditional mean of the current set of sample points. This is the mean of the current set of sampled points; The current set of sampling points and the initial set of sampling points covariance, ， For set The measured values ​​in For set The equivalent value of RCS in the data. For set The number of sampling points in the sample; For the kernel matrix, ， and All are greater than or equal to 1 and less than or equal to 1. Positive integers; ； The conditional covariance between the current set of sampled points and the current candidate sampled point. This is the covariance between each sample point in the current sample point set and the current candidate sample point set; The current set of sampling points and the initial set of sampling points. covariance, For the initial set of sampling points The covariance of the current set of candidate sampling points.

7. The method according to claim 6, characterized in that, The dynamic balance factor The following method is used to determine: in response to determining that the number of iterations is less than the threshold of the first iteration, the following method is used to determine... The value is the first possible value; in response to determining that the number of iterations is greater than or equal to the first threshold and less than the second threshold, determine... The value is the second possible value; in response to determining that the number of iterations is greater than or equal to the second threshold, the value is determined. The value is the third value; where the first value is greater than the second value, and the second value is greater than the third value.

8. The method according to claim 3, characterized in that, The iteration termination condition includes at least one of the following: the number of iterations reaches a preset upper limit; the objective function value is greater than or equal to a preset target threshold; the objective function value is determined by the estimated RCS value of the candidate sampling point and the equivalent RCS value of the candidate sampling point; in k consecutive iterations, the improvement rate of the estimation accuracy of the current Gaussian regression model is less than a preset proportion threshold; the prediction variance of the Gaussian regression model is less than a preset variance threshold.

9. The method according to claim 1, characterized in that, The sample data includes historical data and real-time data.

10. A dynamic RCS estimation device based on Bayesian optimization, characterized in that, include: The acquisition module is configured to acquire N sample data points, each including a measured value and an equivalent radar cross section (RCS). The classification module is configured to perform peak detection on the equivalent RCS value of each sample data point and classify the N sample data points into different dataset types based on the peak detection results. The dataset types include unimodal, bimodal, and multimodal distributions. The setting module is configured to set the Bayesian dynamic estimation objective function and estimation interval for each dataset type. The training module is configured to train Bayesian dynamic estimation models for each dataset type based on the determined objective function and estimation interval. The acquisition module is further configured to acquire the data to be estimated and its equivalent RCS value, perform peak detection on the equivalent RCS value, and determine the data type of the RCS value based on the peak detection results. The data type is one of the dataset types. The estimation module is configured to use the trained Bayesian dynamic estimation model corresponding to the data type to determine the estimated RCS value of the data to be estimated.

11. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 9.

12. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 9.

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