RCS data difference evaluation method based on radar detection probability

Abstract

The invention discloses an RCS data difference evaluation method based on radar detection probability, and belongs to the technical field of radar target characteristic analysis and radar signal processing. Comprising the following steps: firstly, acquiring RCS data of a target in different frequencies, polarization modes, angular domain ranges or test environments, and performing preprocessing such as interpolation, normalization and noise filtering; fitting the RCS data by adopting a plurality of statistical distribution models, obtaining parameters through maximum likelihood estimation, moment estimation or kernel density estimation, and selecting an optimal distribution model by utilizing KS test; target echoes and noise are simulated based on a Monte Carlo method, a detection threshold is calculated in combination with a preset false alarm probability, and radar detection probability Pd curves under different signal-to-noise ratio conditions are obtained; pd curves under different test conditions are extracted, difference indexes such as a root-mean-square error, a mean absolute error and a maximum absolute error are calculated, and quantitative evaluation of consistency between RCS data is achieved; and finally outputting an evaluation result.

Description

Technical Field

[0001] This invention relates to the fields of radar target characteristic analysis and radar signal processing technology, and in particular to a method for evaluating the difference in RCS data based on radar detection probability, which can be used for overall RCS consistency evaluation, stealth performance evaluation, and comparative analysis of radar system detection performance. Background Technology

[0002] Radar Cross Section (RCS) is a crucial physical parameter for measuring the scattering characteristics of a target. Common RCS testing methods include compact field testing, static field testing, flight dynamic testing, and indoor near-field testing. However, due to differences in testing methods, equipment, and environments, even when measuring the same target, different RCS measurement results may be obtained. This measurement difference directly affects the application effectiveness of the data; therefore, it is necessary to evaluate the differences in RCS data under different measurement conditions. Existing methods for evaluating RCS data differences mainly employ the following three categories:

[0003] The first type is the intuitive comparison method, which involves graphically displaying and empirically comparing RCS curves obtained under different conditions. This type of method can intuitively compare the trend of RCS curves, but it is difficult to perform quantitative analysis.

[0004] The second type is the point-to-point comparison method, which compares RCS data under different measurement conditions point by point according to angle or frequency, and calculates indicators such as average error and mean square error. This type of method is sensitive to local errors and cannot reflect the overall scattering statistical characteristics of the target.

[0005] The third category is statistical characteristic comparison methods, which describe RCS differences through statistical measures such as mean and variance. This type of method only reflects some statistical characteristics of RCS and cannot reflect all distribution information of RCS.

[0006] The aforementioned methods all suffer from an inherent flaw: they focus solely on the RCS data itself, neglecting its practical applications. In real-world engineering applications, radar system performance metrics are directly correlated with the probability of detection (Pd). Therefore, comparing only RCS amplitudes or statistics cannot accurately reflect differences in radar detection capabilities. Consequently, there is an urgent need for a method that can quantitatively assess RCS differences from the perspective of radar detection probability, directly linking the assessment results to actual radar system performance and overcoming the technical deficiency of existing methods where "data differences are not correlated with system performance." Summary of the Invention

[0007] To overcome the aforementioned technical deficiencies, this invention proposes a method for evaluating RCS data differences based on radar detection probability, taking an RCS application perspective. This method links RCS data differences to differences in radar detection performance, quantifying RCS data differences from the perspective of Probability of Detection (Pd), achieving engineering-significant RCS consistency comparisons. It is applicable to RCS data evaluation for different targets, frequencies, testing methods, and measurement systems. This invention proposes a method for evaluating radar cross section (RCS) data differences based on radar detection probability, belonging to the field of radar target characteristic analysis and radar signal processing technology. This method uses the Probability of Detection (Pd) as the core evaluation index to quantify the differences in RCS data under different conditions from the perspective of radar detection performance. The method of this invention includes the following steps: First, acquire RCS data of the target at different frequencies, polarization modes, angular domains, or test environments, and perform preprocessing such as interpolation, normalization, and noise filtering; fit the RCS data using various statistical distribution models, including Gamma, Weibull, Lognormal, Gumbel, Rayleigh, and Gaussian mixture models (GMM), and obtain parameters through maximum likelihood estimation, moment estimation, or kernel density estimation; select the optimal distribution model using the Kolmogorov-Smirnov (KS) test; simulate target echo and noise based on the Monte Carlo method, calculate the detection threshold by combining the preset false alarm probability, and obtain the detection probability Pd curve under different signal-to-noise ratio conditions; extract the Pd curves under different test conditions, and calculate the difference indicators such as root mean square error (RMSE), mean absolute error (MAE), and maximum absolute error (MaxAE) to achieve quantitative evaluation of the consistency between RCS data; finally, output the evaluation results, which can be used for RCS consistency verification and radar detection performance comparison analysis under different test sites, measurement systems, or target conditions. The specific technical solution is as follows:

[0008] A method for evaluating the difference in RCS data based on radar detection probability includes the following steps:

[0009] S1: RCS data acquisition and preprocessing. Acquire RCS data of the target under different conditions, such as different frequencies, polarization modes, measurement methods, angular domain ranges, near / far field conditions, and perform normalization preprocessing.

[0010] S2: RCS distribution modeling and parameter estimation. Various statistical distribution models are used to fit the RCS data. These models include, but are not limited to, Gamma, Weibull, Lognormal, Gumbel, Rayleigh, and Gaussian mixture models (GMM). The model parameters are obtained using maximum likelihood estimation, moment estimation, or kernel density estimation methods. The optimal distribution model is selected through the Kolmogorov-Smirnov test.

[0011] S3: Detection probability calculation based on Monte Carlo simulation. Based on the selected statistical model, Monte Carlo random sampling is used to simulate the target echo and noise process. Combined with the preset false alarm probability inverse solution detection threshold, the detection probability Pd under different signal-to-noise ratios or transmission power conditions is calculated.

[0012] S4: Comparison of detection probability curve differences: Extract the Pd curves corresponding to different RCS data and compare the differences of Pd within a certain detection probability range;

[0013] S5: Evaluation output, based on the Pd difference index, forms the final consistency evaluation conclusion, which is used for engineering RCS data difference evaluation or engineering detectability analysis.

[0014] An electronic device includes: one or more processors; and a memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method.

[0015] A computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, cause the processor to implement the method described thereon.

[0016] A computer program product includes a computer program that, when executed by a processor, implements the method.

[0017] Compared with the prior art, the present invention has the following advantages:

[0018] (1) This invention starts from the actual detection performance of radar and introduces the detection probability Pd into the RCS difference evaluation process, so that the evaluation results have stronger engineering significance;

[0019] (2) This invention can fully utilize the RCS distribution characteristics information. The Pd curve is calculated from the RCS distribution and includes multiple statistical characteristics such as mean, variance, skewness, and kurtosis. Compared with the traditional evaluation method that only relies on a single statistical quantity, it can more completely reflect the impact of RCS differences on detection performance.

[0020] (3) This invention is more in line with the focus of radar designers. Due to the complexity of target attitude and scattering structure, RCS has random fluctuations in the angular domain, while engineering design usually focuses on the overall detection performance under the statistical model, rather than a single angle value. The evaluation method based on Pd takes statistical characteristics as its core, which is more in line with the actual system design requirements;

[0021] (4) The present invention adopts the Monte Carlo simulation method, which can be applied to scenarios where the fitting distribution has no analytical solution, thereby improving the scope of computational applicability;

[0022] (5) The method of the present invention has a clear structure and reproducible process. It is applicable to different measurement systems, frequencies and target models. It can evaluate the differences of RCS data from the perspective of radar detection probability. It can be widely used for the overall RCS consistency evaluation and stealth performance comparison. Attached Figure Description

[0023] The accompanying drawings are used to illustrate the technical solutions of this invention and do not constitute a limitation on the scope of protection of this invention. The drawings are described below:

[0024] Figure 1 This is a schematic diagram of the overall process of the RCS data difference assessment method based on radar detection probability proposed in this invention.

[0025] Figure 2 This is a schematic diagram showing the fitting results of RCS data under different distribution models.

[0026] Figure 3 This is a schematic diagram of the detection probability calculation process based on Monte Carlo simulation proposed in this invention;

[0027] Figure 4 This is the target RCS distribution fitting result at different frequencies in an embodiment of the present invention;

[0028] Figure 5 This is a comparison chart of the Pd curves of the target at different frequencies in an embodiment of the present invention. Detailed Implementation

[0029] The embodiments of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0030] This invention proposes a method for evaluating the difference in RCS data based on radar detection probability. The core idea is as follows: first, obtain RCS data under different conditions and perform normalization preprocessing; second, statistically model the RCS data under different conditions; third, calculate the corresponding Pd curve using the Monte Carlo method; and finally, quantitatively evaluate the RCS difference based on the deviation between the Pd curves. This invention uses radar detection probability as the core evaluation factor. Compared with traditional RCS data difference comparison methods, it can evaluate the difference in RCS data from the perspective of detection probability and can also intuitively reflect the impact of different RCS values ​​on radar detection performance. Figure 1 As shown, the specific steps include the following:

[0031] Step S1: RCS Data Acquisition and Preprocessing. Collect RCS data of the target under different test conditions, including but not limited to frequency, polarization, angle range, measurement system, or environment. To ensure data comparability, each set of data needs to be processed uniformly, including uniform step size, amplitude normalization, and outlier removal. If the angular domain sampling intervals are inconsistent, linear or spline interpolation can be used to preprocess the raw data. Mapped to a grid with a uniform angle step For example, linear interpolation is represented as:

[0032] ;

[0033] If a systematic bias exists, mean normalization can be used for correction, as shown in the formula:

[0034] ;

[0035] in, The normalized value. This represents the average of the original data.

[0036] Step S2: RCS Distribution Modeling and Parameter Estimation. For each set of preprocessed RCS data, various statistical distribution models are used for fitting, including but not limited to Gamma distribution, Weibull distribution, log-normal distribution, Gumbel distribution, Rayleigh distribution, and Gaussian mixture model (GMM). The results are as follows: Figure 2 As shown. The following are the formulas for each distribution model:

[0037] Gamma distribution: ;

[0038] in, As variables, For shape parameters, For scale parameters;

[0039] Weibull distribution: ;

[0040] in, For shape parameters, For scale parameters;

[0041] Log-normal distribution: ;

[0042] in, The logarithmic mean is... The standard deviation is the logarithm.

[0043] Gumbel distribution: ;

[0044] Among them, position parameters , For scale parameters;

[0045] Rayleigh distribution: ;

[0046] in, For scale parameters;

[0047] Gaussian mixture model: ;

[0048] in, The mixing coefficient, It is the mean vector. Let represent the density function of the i-th Gaussian component.

[0049] Model parameters are obtained through maximum likelihood estimation (MLE), moment estimation (MOM), or kernel density estimation (KDE) methods, as shown in the following formulas:

[0050] Maximum likelihood estimation works by maximizing the likelihood function, where θ is the distribution parameter:

[0051] ;

[0052] Moment estimation uses sample moments, and the formula is as follows:

[0053] ;

[0054] The kernel density estimation formula is as follows, where K is the kernel function and h is the bandwidth:

[0055] ;

[0056] To ensure the effectiveness of the model, the Kolmogorov-Smirnov (KS) test was used to optimize the fit. The KS test statistic is defined by the following formula, where... Let be the empirical distribution function. For the model's cumulative distribution function:

[0057] ;

[0058] Based on the p-value obtained from the test:

[0059] ;

[0060] A higher p-value indicates a better fit; the model with the highest p-value is selected as the optimal distribution model. When the samples exhibit multimodal characteristics, the GMM or KDE method can be preferentially used to improve the robustness of the fit.

[0061] Step S3: Calculation of detection probability based on Monte Carlo simulation. For example... Figure 3 As shown, noise can generally be modeled as zero-mean Gaussian white noise, given a false alarm probability (usually set to 10). -6 After determining the level, the detection threshold is deduced based on the statistical distribution of the noise, ensuring that the probability of noise exceeding the threshold does not exceed the set false alarm probability. When calculating the detection probability, firstly, based on the optimal statistical distribution model obtained in step S2, a large number of simulated target echo samples are generated using a random number generator based on the probability characteristics of this distribution; simultaneously, a corresponding number of noise samples are generated based on the Gaussian distribution characteristics of the noise. The generation of random samples follows the principle of "sampling within the corresponding numerical range according to the selected probability distribution," that is, the computer uniformly samples in the cumulative probability space of the distribution and then maps it back to the amplitude value, thereby obtaining a simulated signal consistent with the real physical process. For each set signal-to-noise ratio (SNR) or transmit power level, the target echo sample and noise sample are superimposed and then compared with the detection threshold: when the amplitude of the superimposed signal exceeds the detection threshold, it is recorded as "target detected"; otherwise, it is recorded as "not detected." A large number of independent samples are repeated at each SNR point, and the proportion of "target detected" is statistically analyzed; this proportion is the detection probability Pd for the corresponding SNR. By repeating the above process under multiple SNR or transmit power conditions, a complete Pd curve can be obtained. The number of Monte Carlo samples can be set according to accuracy requirements; for example, when the number of samples per SNR point is 10. 4 The detection probability error can be obtained at approximately ±1%. When an analytical solution exists for the selected distribution, the analytical results can be used to verify the simulation results. Under the same SNR conditions, the analytical and simulation results are obtained separately, and the absolute value is calculated by subtracting the simulation value from the analytical value. When the difference is lower than a preset threshold (e.g., 1%) across all SNR ranges, the Monte Carlo results are considered valid and the simulation process is reliable.

[0062] Step S4: Quantification of Probability Curve Differences. Extract the Pd curves generated under different test conditions and calculate their difference indices within a specific SNR range or a specific Pd range (e.g., 0.6~0.9). This invention selects three indices—Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Maximum Absolute Error (MaxAE)—to measure curve differences. RMSE reflects the overall deviation, MAE reflects the average level deviation, and MaxAE reflects the degree of deviation under the most unfavorable conditions. These indices can intuitively reflect the degree of difference in radar detection performance between different RCS data.

[0063] Step S5: Evaluation Output and Result Analysis. Based on the above discrepancy indicators, a final RCS consistency evaluation conclusion is formed. The system can automatically output Pd curves and error statistics tables, providing a reference for radar design or other RCS applications. The evaluation results can be used for data consistency verification between different test sites or different measurement systems, and also for performance change analysis of stealth targets.

[0064] To verify the ability of the method of this invention to evaluate the RCS differences at different frequencies, taking the B-2 target as an example, its overall RCS data at frequencies of 1GHz, 1.3GHz, 3GHz, 5GHz, and 10GHz were selected as input and executed. Figure 1 The method flow is shown.

[0065] First, according to step S2, multiple model fitting is used, and the optimal model is selected through the KS test. Since the distribution is multimodal, the optimal model is GMM, and the results are as follows. Figure 4 As shown.

[0066] Subsequently, following step S3, the Pd curves under different frequency conditions were calculated using Monte Carlo simulation. The results are as follows... Figure 5 As shown, as the frequency decreases, the Pd curve shifts to the right overall. This means that under the same signal-to-noise ratio, the radar's detection probability of the target decreases significantly, which is consistent with its distribution change pattern. Therefore, it is feasible to compare the differences in RCS from the perspective of Pd.

[0067] According to step S4, the Pd curve is further quantitatively compared with RMSE, MAE and MaxAE. The results show that the high and low frequency curves are significantly different. The method of the present invention can use radar detection probability as the core evaluation index to quantitatively evaluate the consistency of RCS data from the perspective of Pd curve differences.

[0068] In summary, this invention establishes a complete evaluation chain from RCS data to Pd curves and then to difference quantification indicators. Using radar detection probability as the core evaluation factor, it maps RCS distributions under different conditions to Pd curves and quantifies the consistency of RCS data based on the differences in Pd curves. Therefore, this method provides a clear and easily reproducible judgment criterion for verifying the consistency between radar design and RCS measurement. The method has a clear implementation process and can be automated through software systems, demonstrating significant engineering application value. Equivalent solutions that adjust model selection, parameter estimation, or simulation procedures without altering the fundamental principles of this invention are all within the scope of protection of this invention.

Claims

1. A method for evaluating the difference in RCS data based on radar detection probability, characterized in that, Includes the following steps: S1, RCS data acquisition and preprocessing: acquire RCS data of the target under different test conditions, including but not limited to frequency, polarization mode, angular domain range, test system or measurement environment, and perform uniform step size interpolation, amplitude normalization and outlier removal on the data to form a comparable sample set; S2, RCS distribution modeling and parameter estimation: The preprocessed RCS data is fitted with various statistical distribution models, including but not limited to Gamma distribution, Weibull distribution, log-normal distribution, Gumbel distribution, Rayleigh distribution and Gaussian mixture model (GMM). The model parameters are obtained by maximum likelihood estimation, moment estimation or kernel density estimation methods, and the optimal fitting model is selected by KS test. S3, Radar detection probability calculation based on Monte Carlo simulation, according to the selected optimal statistical model, generates target echo samples and noise samples through Monte Carlo random sampling, and calculates the Pd curve under different signal-to-noise ratios or transmit power conditions by combining the set false alarm probability inverse solution detection threshold. S4, Quantification of the difference in detection probability curves: Extract the Pd curves generated under different test conditions, calculate the difference in RMSE, MAE and MaxAE within the preset detection probability range, and realize the quantification of the difference in detection probability between different RCS data. S5, Evaluation Output: Output the RCS consistency evaluation result based on the difference index of the Pd curve, and generate the transmit power-detection probability relationship curve by combining the radar equation. This curve is used for RCS consistency verification and radar detection performance comparison analysis under different measurement systems, frequencies, or target conditions.

2. The method according to claim 1, characterized in that, The preprocessing of the RCS data includes: linear or spline interpolation for data with inconsistent sampling intervals, and mean normalization correction for data with systematic shifts.

3. The method according to claim 1, characterized in that, In the parameter estimation process of the various statistical distribution models, when the RCS sample exhibits multimodal characteristics, the Gaussian Mixture Model (GMM) or the Kernel Density Estimation (KDE) method is preferred to improve the robustness of the fit. When the p-values ​​of the KS tests of multiple distributions are all greater than 0.05, the distribution with the highest p-value is selected as the optimal distribution.

4. The method according to claim 1, characterized in that, The number of Monte Carlo simulation samples shall not be less than 10. 5 In the case of a selected distribution model having an analytical solution, the Monte Carlo simulation results are verified using analytical formulas. If the error between the two does not exceed a preset threshold, the simulation results are considered valid.

5. The method according to claim 1, characterized in that, In the quantitative index of the difference in the detection probability curve, the root mean square error is used to characterize the overall deviation, the mean absolute error is used to characterize the average level deviation, and the maximum absolute error is used to characterize the degree of deviation under the most unfavorable conditions.

6. The method according to claim 1, characterized in that, The evaluation output is automated through a computer program, automatically outputting Pd curves, difference indicators, and evaluation reports, thus achieving integrated processing of RCS data difference evaluation and radar detection performance correlation analysis.

7. The method according to claim 1, characterized in that, RCS data under different test conditions include RCS data at frequencies of 1GHz, 1.3GHz, 3GHz, 5GHz and 10GHz.

8. An electronic device, characterized in that, include: One or more processors; A memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, cause the processor to perform the method described in any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the method described in any one of claims 1 to 7.

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