RCS total probability size extrapolation method and system based on electromagnetic scattering mechanism

Abstract

The invention discloses an RCS total probability size extrapolation method and system based on an electromagnetic scattering mechanism, and the method comprises the following steps: 1, deducing backscattering electric field formulas under different sizes according to the electromagnetic scattering mechanism, and obtaining a target RCS calculation expression of an incident wave vector according to the definition of a radar cross section RCS; converting the target RCS calculation expression into a variant formula for constructing a covariance function through an undetermined coefficient method and an integral median theorem; 2, carrying out inverse transformation on the variant formula, and then carrying out disassembly; 3, representing a polynomial part in the inverse transformation formula by adopting a polynomial covariance function, and representing a cosine part in the inverse transformation formula by adopting a spectrum mixed covariance function; the two covariance functions are combined into an SPFPE covariance function; 4, initializing an SPFPE covariance function by using a random number method; 5, optimizing a hyper-parameter of an SPFPE covariance function by taking maximization of logarithmic edge likelihood as an optimization target to obtain an SPFPE-GPR method; and 6, carrying out extrapolation on the target RCS by using an SPFPE-GPR method.

Description

Technical Field

[0001] The present invention belongs to the technical field of target radar cross section (RCS) extrapolation, and in particular relates to a method and system for extrapolating the full probability size of an RCS based on an electromagnetic scattering mechanism. Background Art

[0002] Radar cross section (RCS) is a key physical parameter used by radars to detect target objects, reflecting the strength of electromagnetic wave reflection from the target. With the continuous advancement of cutting-edge technologies such as stealth and counter-stealth, detection and counter-detection, higher requirements are being placed on the accuracy and performance of RCS measurements.

[0003] In microwave anechoic chamber measurements of radar cross section (RCS), far-field and quiet zone conditions must be met, resulting in test system construction costs that increase exponentially with the target's electrical size. To reduce experimental costs, electromagnetic simulation techniques (such as the method of moments and the finite element method) are widely used for RCS prediction. However, their computational complexity is constrained by the target's electrical size. As target size increases, the memory usage and computation time required for simulation increase exponentially. To address this issue, researchers have recently begun to investigate various RCS extrapolation methods for different target sizes. These methods establish mathematical models and algorithms, combining measured or simulated data from small targets to infer the RCS of large targets. Gaussian process-based RCS extrapolation offers the highest accuracy. However, existing Gaussian process RCS extrapolation methods suffer from the following drawbacks: accurate extrapolation relies on treating local RCS fluctuations as normal distributions with zero mean noise. Failure to meet this condition for complex targets can affect parameter optimization, causing the results to deviate from the true value and reducing the accuracy of the extrapolation. Furthermore, existing RCS extrapolation methods cannot perform confidence assessments, making it impossible to determine the reliability of the results. This lack of reliability verification significantly increases the risk of engineering decisions. To address this issue, the present invention proposes a full-probability RCS size extrapolation method and system based on electromagnetic scattering mechanisms to extrapolate the RCS of complex targets, addressing the aforementioned issues with existing methods. Summary of the Invention

[0004] The present invention provides an RCS full-probability size extrapolation method and system based on the electromagnetic scattering mechanism, which solves the technical problems in the prior art such as low accuracy of RCS size extrapolation results and inability to assess confidence.

[0005] To achieve the above object, the technical solutions adopted by the present invention are as follows:

[0006] The RCS full probability size extrapolation method based on the electromagnetic scattering mechanism includes the following steps:

[0007] Step 1: Based on the electromagnetic scattering mechanism, the backscattered electric field formula for different sizes is derived. Then, based on the definition of radar cross section (RCS), the target RCS calculation expression for the incident wave vector is obtained. Then, using the method of undetermined coefficients and the integral mean value theorem, the target RCS calculation expression for the incident wave vector is converted into a variant formula for constructing the covariance function.

[0008] Step 2: Perform an inverse transformation on the RCS variant formula obtained in step 1, and then decompose the variant formula;

[0009] Step 3: Based on the properties of Gaussian processes, a polynomial covariance function is used to characterize the polynomial part of the inverse RCS transform formula, and an SM (spectral mixing) covariance function is used to characterize the cosine part of the inverse RCS transform formula. Based on the multiplicative property of Gaussian processes, the above two covariance functions are combined into a spectral-polynomial full probability extrapolation (SPFPE) covariance function to construct the SPFPE-GPR method of the present invention.

[0010] Step 4: Initialize the SPFPE covariance function using the random number method;

[0011] Step 5: Optimize the hyperparameters of the SPFPE covariance function by maximizing the log-marginal likelihood, thereby obtaining the SPFPE-GPR (Gaussian Process Regression) method.

[0012] Step 6: Use the SPFPE-GPR method to extrapolate the RCS of the target.

[0013] In order to prove the high efficiency of the present method, it was compared with the existing RCS size extrapolation method in a specific implementation manner. The results showed that the method of the present invention has significant superiority.

[0014] Preferably, in step 1, the backscattered electric field formula is as follows:

[0015]

[0016] Where k is the incoming wave vector, j is the imaginary unit, η is the wave impedance, r and r′ represent the observation point and source point respectively, represents the external unit normal vector of the i-th illuminated surface, S′ i represents the i-th irradiated surface, N is the number of irradiated surfaces, H inc is the intensity of the incident magnetic field at the surface point r′;

[0017] On the irradiated surface |H inc |=1 / η, is the unit vector of the incident electric field, and the initial size of the target is p. The relationship between the actual size x and the magnification factor a is x = pa, then the following formula is obtained:

[0018]

[0019] Continue to deduce and get the backscattered electric field formula under different sizes:

[0020]

[0021] Radar cross section RCS is defined as Among them, |E in | is set to 1; thus the target RCS calculation expression for the incident wave vector is obtained:

[0022]

[0023] Among them, dBsm is a logarithmic unit;

[0024] According to the method of undetermined coefficients and the integral mean value theorem, formula (4) is converted into a variant formula:

[0025]

[0026] Among them, α, β, γ are unknowns, r iο ′ is the i-th irradiation surface S′ i Point A i is the i-th irradiated surface S′ i area.

[0027] Preferably, in step 2, formula (5) is inversely transformed to obtain the inverse transformation form of the target RCS variant formula for the incident wave vector:

[0028]

[0029] Let h(x) in the above formula (6) = |αx 2 +βx+γ|,

[0030] Assume that the original RCS value is σ(x), and the value after inverse transformation is Then σ(x) and The following relationship exists: Then there is

[0031] Preferably, in step three, according to the properties of the Gaussian process, the polynomial covariance function characterizes the h(x) part, and the spectral mixture covariance function characterizes In the first part, based on the multiplicative property of Gaussian process, the above two functions are combined into SPFPE covariance function;

[0032] In a Gaussian process, if H(x)=h1(x)h2(x), h1(x)~GP(m h1 (x),C h1 (x,x′)), h2(x)~GP(m h2 (x),C h2 (x,x′)), then H(x)~GP(m H (x),C H (x,x′)), where C H (x,x′)=C h1 (x,x′)*C h2 (x,x′), where m h1 (x), m h2 (x) and m H (x) represents the mean function, C h1 (x,x′),C h2 (x,x′) and C H (x, x′) represents the covariance function of input x and x′;

[0033] A Gaussian process (GP) is a distribution that models functions and can be viewed as a joint Gaussian distribution of function values over any set of input points. The symbol "~" indicates that a function "obeys" a certain distribution; in this context, it means that the function obeys a Gaussian process.

[0034] According to the analysis of Gaussian process properties, we can get h(x)~GP(m h (x),C h (x,x′))、 Among them, C h (x,x′)=α(x T x′) 2 +β(x T x′)+γ, By C SM (x,x′)=ω q cos[2πμ q (xx′)]×exp[-2πν q (xx′) 2 ] asymptotically, {ω q ,μ q ,ν q |q=1,...,Q} is a hyperparameter, Q is the number of spectral mixtures; Then there is Among them, A i Represented as the i-th irradiation surface S′ iThe area,

[0035] Preferably, in step 4, the SPFPE covariance function is initialized as follows:

[0036] First, initialize the spectral mixing covariance function parameters; let the parameters Where q = 1, 2, ..., Q, y is the RCS of the training data, σ y is the standard deviation of the training data RCS, so as to obtain the weights [ω1,ω2,..,ω Q ]; Let the parameter Among them, R q μ ~Uniform(0,1),Δ min =minδ i , δ i =x i+1 -x i ,i=1,...,N-1,x is the size of the training data, N is the length of the training data set, so as to obtain the mean [μ1,μ2,..,μ Q ]; Let the parameter Among them, R q v ~|N(0,1)|,Δ max =x N -x1, thus obtaining the variance [v1,v2,..,v Q ];

[0037] Next, initialize the polynomial covariance function parameters and regard them as the modulation factor of ω in the spectral mixing; after obtaining the spectral mixing parameters, define Will Randomly divided into three parts, set Corresponding to α(x T x′) 2 ,β(x T x′),γ, then we have Take x T x′=mean(X), so Where X is the training data size vector.

[0038] Preferably, in step 5, the expression for maximizing the log-marginal likelihood function is:

[0039]

[0040] Among them, θ is the set of hyperparameters in the SPFPE covariance function, v n represents the noise variance, I is the identity matrix, K represents the SPFPE covariance matrix, and y represents the vector composed of all outputs in the training data; The partial derivative with respect to θ is:

[0041]

[0042] Where tr(.) represents the trace of the matrix, κ=(K+ν n I) -1 y, and finally the covariance matrix K is obtained.

[0043] The present invention also discloses an RCS full probability size extrapolation system based on electromagnetic scattering mechanism, which is used to execute the above method and includes the following modules:

[0044] Covariance function variant formula construction module: Based on the electromagnetic scattering mechanism, the backscattered electric field formula at different sizes is derived. Then, based on the definition of radar cross section (RCS), the target RCS calculation expression for the incident wave vector is obtained. Then, through the method of undetermined coefficients and the integral mean value theorem, the target RCS calculation expression for the incident wave vector is converted into a variant formula for constructing the covariance function.

[0045] Variant formula inverse transformation module: performs inverse transformation on the obtained variant formula, and then decomposes the variant formula after inverse transformation;

[0046] SPFPE covariance function synthesis module: Based on the properties of Gaussian processes, a polynomial covariance function is used to characterize the polynomial part of the inverse transform formula, and a spectral mixture covariance function is used to characterize the cosine part of the inverse transform formula. Based on the multiplicative property of Gaussian processes, the above two covariance functions are combined to form the SPFPE covariance function.

[0047] Initialization module: Use the random number method to initialize the obtained SPFPE covariance function;

[0048] Optimization module: Optimize the hyperparameters of the SPFPE covariance function by maximizing the log-marginal likelihood, and obtain the SPFPE-GPR method;

[0049] Target RCS extrapolation module: Use the obtained SPFPE-GPR method to extrapolate the RCS of the target.

[0050] The beneficial technical effects brought by the present invention are:

[0051] Compared with the methods used in the prior art, the SPFPE-GPR method adopted in the present invention significantly improves the extrapolation performance and accuracy under the same complex model. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 is a flow chart of a method for extrapolating a target RCS according to a preferred embodiment of the present invention;

[0053] Figure 2 Schematic diagram of a missile warhead model used in the RCS extrapolation method according to a preferred embodiment of the present invention;

[0054] Figure 3 This is a comparison diagram of the RCS data of missile warhead targets of different sizes using three methods.

[0055] Figure 4 This is a block diagram of an RCS full-probability size extrapolation system based on electromagnetic scattering mechanism in a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0056] The following will clearly and completely describe the technical solutions of the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0057] like Figure 1 As shown, this embodiment is an RCS full probability size extrapolation system based on the electromagnetic scattering mechanism, which is mainly divided into 6 steps:

[0058] The first step is to derive the backscattered electric field formula for different sizes based on the electromagnetic scattering mechanism. Then, based on the definition of radar cross section (RCS), the target RCS calculation expression for the incident wave vector is obtained. Then, using the method of undetermined coefficients and the integral mean value theorem, the target RCS calculation expression for the incident wave vector is converted into a variant formula for constructing the covariance function. The details are as follows:

[0059] Based on the electromagnetic scattering mechanism, the backscattered electric field formula is obtained:

[0060]

[0061] Where k is the incoming wave vector, j is the imaginary unit, η is the wave impedance, r and r′ represent the observation point and source point respectively, represents the external unit normal vector of the i-th illuminated surface, S′ i represents the i-th irradiated surface, N is the number of irradiated surfaces, H inc is the intensity of the incident magnetic field at the surface point r′.

[0062] On the irradiated surface |H inc |=1 / η, is the unit vector of the incident electric field. Assuming that the initial size of the target is p, the relationship between the actual size x and the magnification factor a is x = pa, then the following formula is obtained:

[0063]

[0064] Continuing to deduce, we can get the backscattered electric field formula under different sizes:

[0065]

[0066] Radar cross section RCS is defined as Among them, |E in | is set to 1. Thus, the RCS expression for the incident wave vector at different target sizes is obtained:

[0067]

[0068] The dBsm in the electromagnetic scattering cross section is a logarithmic unit that represents the RCS measured in decibels (dB) in square meters (m 2 ) is the logarithm of .

[0069] According to the method of undetermined coefficients and the integral mean value theorem, formula (4) can be converted into a variant formula:

[0070]

[0071] Among them, α, β, γ are unknowns, r iο ′ is the i-th irradiation surface S′ i Point A i is the i-th irradiated surface S′ i area.

[0072] The second step is to perform an inverse transformation on the variant formula obtained in step 1, and then decompose the variant formula after the inverse transformation; the details are as follows:

[0073] By inversely transforming formula (5), we can obtain the inverse transformation form of the target RCS variant formula for the incident wave vector:

[0074]

[0075] Let h(x)=|αx in the above formula (6) 2 +βx+γ|,

[0076] Assuming that the original RCS value is σ(x), the value after inverse transformation is Then σ(x) and The following relationship exists: Then there is

[0077] In the third step, according to the properties of the Gaussian process, the polynomial covariance function is used to represent the polynomial part of the inverse transform formula, and the spectral mixture covariance function is used to represent the cosine part of the inverse transform formula. Based on the multiplicative property of the Gaussian process, the above two covariance functions are combined into the SPFPE covariance function; the details are as follows:

[0078] According to the properties of Gaussian process, the polynomial covariance function represents the h(x) part, and the SM covariance function represents The above two kernel functions are combined into the SPFPE covariance function.

[0079] In a Gaussian process, if H(x)=h1(x)h2(x), h1(x)~GP(m h1 (x),C h1 (x,x′)), h2(x)~GP(m h2 (x),C h2 (x,x′)), then H(x)~GP(m H (x),C H (x,x′)), where C H (x,x′)=C h1 (x,x′)*C h2 (x,x′), where m h1 (x), m h2 (x) and m H (x) represents the mean function, C h1 (x,x′),C h2 (x,x′) and C H (x,x′) represents the covariance function of input x and x′.

[0080] According to the analysis of Gaussian process properties, we know that h(x)~GP(m h (x),C h (x,x′)), where

[0081] C h (x,x′)=α(x T x′) 2 +β(x T x′)+γ, similarly in Can be C SM (x,x′)=ω q cos[2πμ q (xx′)]×exp[-2πν q (xx′) 2 ] asymptotically, where {ω q ,μ q ,ν q|q=1,...,Q} is a hyperparameter, Q is the number of spectral mixtures. Then there is Among them, A i Represented as the i-th irradiation surface S′ i The area,

[0082] Through the above derivation, the SPFPE covariance function used to extrapolate the target RCS is obtained:

[0083] The fourth step is to initialize the SPFPE covariance function;

[0084] In this embodiment, the MOM (Method of Moments) in Feko software is used to obtain the RCS data of missile heads at different sizes. The relevant parameters are θ=0, f=1GHz, scale∈(1,20], the scale step is 0.1, and a total of 190 data sampling points are obtained, of which the training set is 100 groups of data and the test set is 90 groups of data. The specific initialization method is as follows:

[0085] First, initialize the SM covariance function parameters. Let the parameters Where q = 1, 2, ..., Q, y is the RCS of the training data, σ y is the standard deviation of the training data RCS, so as to obtain the weights [ω1,ω2,..,ω Q ]; Let the parameter Among them, R q μ ~Uniform(0,1) (sampling uniform distribution), Δ min =minδ i , δ i =x i+1 -x i ,i=1,...,N-1,x is the size of the training data, N is the length of the training data set, so as to obtain the mean [μ1,μ2,..,μ Q ]; Let the parameter Among them, R q v ~|N(0,1)|(sampled non-negative normal distribution), Δ max =x N -x1, thus obtaining the variance [v1,v2,..,v Q ]. At this point, the SM covariance function parameters are initialized.

[0086] Next, initialize the polynomial covariance function parameters, which can be regarded as the modulation factor of ω in SM. After obtaining the SM parameters, define Will Randomly divided into three parts, set Corresponding to α(x T x′) 2 ,β(x T x′),γ, then we have Here we take x T x′=mean(X), so Where X is the training data size vector. Therefore, the parameters of the polynomial covariance function are initialized.

[0087] The fifth step is to optimize the hyperparameters of the SPFPE covariance function by maximizing the log-marginal likelihood function, thereby obtaining a Gaussian process model and obtaining the SPFPE-GPR method; the details are as follows:

[0088] The expression for maximizing the log-marginal likelihood function is:

[0089]

[0090] Among them, θ is the set of hyperparameters in the SPFPE covariance function, v n represents the noise variance, I is the identity matrix, K represents the SPFPE covariance matrix, and y represents the vector composed of all outputs in the training data. The partial derivative with respect to θ is:

[0091]

[0092] Where tr(.) represents the trace of the matrix, κ=(K+ν n I) -1 y, the final covariance matrix K will be calculated.

[0093] In the sixth step, the SPFPE-GPR method constructed in the above steps is used to extrapolate the RCS of missile warheads of different sizes to obtain the results.

[0094] In order to verify the correctness of the method of the present invention and the feasibility of evaluating the confidence interval, comparisons were made with the existing proportional model and NLS-GPR proxy model methods.

[0095] In the above steps, based on the electromagnetic scattering mechanism and Gaussian process, the SPFPE covariance function used in the method of the present invention is obtained. Then, the random number initialization method is used to obtain the initial parameters in the covariance function. The parameters are then optimized by maximizing the logarithmic marginal likelihood function, thereby obtaining an RCS extrapolation method with high performance and high accuracy.

[0096] In order to demonstrate the efficiency of the method of the present invention, the proportional model, NLS-GPR proxy model and the SPFPE-GPR method of the present invention were selected for comparison. RMSE was used as the evaluation basis. The smaller the RMSE, the better the fitting effect, and vice versa. The specific comparison results are shown in Figure 2. Figure 3 As shown, the proportional model is extrapolated through the size ratio relationship, and the best result is RMSE = 1.06. This method cannot be used for confidence assessment. The NLS-GPR proxy model obtains the overall trend of the data through NLS, and then uses the SM-GPR method to extrapolate the local fluctuations of RCS to obtain the extrapolated result. The best result is RMSE = 0.176. This method contains a linear part and is difficult to perform confidence assessment. The best extrapolation result using the SPFPE-GPR method of the present invention is RMSE = 0.087. According to the above comparison data, the SPFPE-GPR method has an accuracy improvement of 91.8% compared to the proportional model and an accuracy improvement of 50.6% compared to the NLS-GPR proxy model. Therefore, the method adopted by the present invention is superior to the other two methods in extrapolating RCS of different sizes, showing excellent performance and accuracy.

[0097] like Figure 4 As shown, this embodiment discloses an RCS full-probability size extrapolation system based on electromagnetic scattering mechanism, which is used to execute the above method and includes the following modules:

[0098] Covariance function variant formula construction module: Based on the electromagnetic scattering mechanism, the backscattered electric field formula at different sizes is derived. Then, based on the definition of radar cross section (RCS), the target RCS calculation expression for the incident wave vector is obtained. Then, through the method of undetermined coefficients and the integral mean value theorem, the target RCS calculation expression for the incident wave vector is converted into a variant formula for constructing the covariance function.

[0099] Variant formula inverse transformation module: performs inverse transformation on the obtained variant formula, and then decomposes the variant formula after inverse transformation;

[0100] SPFPE covariance function synthesis module: Based on the properties of Gaussian processes, a polynomial covariance function is used to characterize the polynomial part of the inverse transform formula, and a spectral mixture covariance function is used to characterize the cosine part of the inverse transform formula. Based on the multiplicative property of Gaussian processes, the above two covariance functions are combined to form the SPFPE covariance function.

[0101] Initialization module: Use the random number method to initialize the obtained SPFPE covariance function;

[0102] Optimization module: Optimize the hyperparameters of the SPFPE covariance function by maximizing the log-marginal likelihood, and obtain the SPFPE-GPR method;

[0103] Target RCS extrapolation module: Use the obtained SPFPE-GPR method to extrapolate the RCS of the target.

[0104] For other contents of this embodiment, please refer to the above method embodiment.

[0105] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with this profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. The RCS full probability size extrapolation method based on electromagnetic scattering mechanism is characterized by: The following steps are involved: Step 1: Based on the electromagnetic scattering mechanism, the backscattered electric field formula for different sizes is derived. Then, based on the definition of radar cross section (RCS), the target RCS calculation expression for the incident wave vector is obtained. Then, using the method of undetermined coefficients and the integral mean value theorem, the target RCS calculation expression for the incident wave vector is converted into a variant formula for constructing the covariance function. Step 2: Perform an inverse transformation on the variant formula obtained in step 1, and then decompose the inverse transformed variant formula; Step 3: Based on the properties of the Gaussian process, the polynomial covariance function is used to characterize the polynomial part of the inverse transform formula, and the spectral mixture covariance function is used to characterize the cosine part of the inverse transform formula; based on the multiplicative property of the Gaussian process, the above two covariance functions are combined into the SPFPE covariance function; Step 4: Use the random number method to initialize the SPFPE covariance function obtained in step 3; Step 5: Optimize the hyperparameters of the SPFPE covariance function in step 4 by maximizing the log-marginal likelihood, and obtain the SPFPE-GPR method; Step 6: Use the SPFPE-GPR method obtained in step 5 to extrapolate the RCS of the target.

2. The RCS full probability size extrapolation method based on the electromagnetic scattering mechanism as claimed in claim 1 is characterized in that: In step 1, the backscattered electric field formula is as follows: Where k is the incoming wave vector, j is the imaginary unit, η is the wave impedance, r and r' represent the observation point and source point respectively, represents the external unit normal vector of the i-th illuminated surface, S i ' represents the i-th irradiated surface, N is the number of irradiated surfaces, H inc is the intensity of the incident magnetic field at the surface point r'; On the irradiated surface |H inc |=1 / η, is the unit vector of the incident electric field, and the initial size of the target is p. The relationship between the actual size x and the magnification factor a is x = pa, then the following formula is obtained: Continue to deduce and get the backscattered electric field formula under different sizes: Radar cross section RCS is defined as Among them, |E in | is set to 1; thus the target RCS calculation expression for the incident wave vector is obtained: Among them, dBsm is a logarithmic unit; According to the method of undetermined coefficients and the integral mean value theorem, formula (4) is converted into a variant formula: Among them, α, β, γ are unknowns, r iο ' is the i-th irradiation surface S i 'Point A i is the i-th irradiation surface S i 'area.

3. The RCS full probability size extrapolation method based on the electromagnetic scattering mechanism as claimed in claim 2 is characterized by: In step 2, the inverse transformation of formula (5) is performed to obtain the inverse transformation form of the target RCS variant formula for the incident wave vector: Let h(x) in the above formula (6) = |αx 2 +βx+γ|, Assume that the original RCS value is σ(x), and the value after inverse transformation is Then σ(x) and The following relationship exists: Then there is 4. The RCS full probability size extrapolation method based on the electromagnetic scattering mechanism as claimed in claim 3 is characterized by: Step 3: According to the properties of Gaussian process, the polynomial covariance function characterizes the h(x) part, and the spectral mixture covariance function characterizes In the first part, based on the multiplicative property of Gaussian process, the above two functions are combined into SPFPE covariance function; In a Gaussian process, if H(x)=h1(x)h2(x), h1(x)~GP(m h1 (x),C h1 (x,x')), h2(x)~GP(m h2 (x),C h2 (x,x')), then H(x)~GP(m H (x),C H (x,x')), where C H (x,x')=C h1 (x,x')*C h2 (x,x'), where m h1 (x), m h2 (x) and m H (x) represents the mean function, C h1 (x,x'),C h2 (x,x') and C H (x,x') represents the covariance function of input x and x'; According to the properties of Gaussian process, we can get h(x)~GP(m h (x),C h (x,x'))、 Among them, C h (x,x')=α(x T x') 2 +β(x T x')+γ, By C SM (x,x′)=ω q cos[2πμ q (xx′)]×exp[-2πν q (xx′) 2 ] asymptotically, {ω q ,μ q ,ν q |q=1,...,Q} is a hyperparameter, Q is the number of spectral mixtures; Then there is in, 5. The RCS full probability size extrapolation method based on the electromagnetic scattering mechanism as claimed in claim 4 is characterized in that: In step 4, the SPFPE covariance function is initialized as follows: First, initialize the spectral mixing covariance function parameters; let the parameters Where q = 1, 2, ..., Q, y is the RCS of the training data, σ y is the standard deviation of the training data RCS, so as to obtain the weights [ω1,ω2,..,ω Q ]; Let the parameter Among them, R q μ ~Uniform(0,1),Δ min =minδ i , δ i =x i+1 -x i ,i=1,...,N-1,x is the size of the training data, N is the length of the training data set, so as to obtain the mean [μ1,μ2,..,μ Q ]; Let the parameter Among them, R q v ~|N(0,1)|,Δ max =x N -x1, thus obtaining the variance [v1,v2,..,v Q ]; Then initialize the polynomial covariance function parameters and regard them as the modulation factor of ω in the spectral mixing; after obtaining the spectral mixing parameters, define Will Randomly divided into three parts, Corresponding to α(x T x') 2 ,β(x T x'), γ, then we have Take x T x'=mean(X), so Where X is the training data size vector.

6. The RCS full probability size extrapolation method based on the electromagnetic scattering mechanism as claimed in claim 5 is characterized by: In step 5, the expression for maximizing the log-marginal likelihood function is: Among them, θ is the set of hyperparameters in the SPFPE covariance function, v n represents the noise variance, I is the identity matrix, K represents the SPFPE covariance matrix, and y represents the vector composed of all outputs in the training data; The partial derivative with respect to θ is: Where tr(.) represents the trace of the matrix, κ=(K+ν n I) -1 y, and finally the covariance matrix K is obtained.

7. An RCS full-probability size extrapolation system based on electromagnetic scattering mechanism, used to execute the method according to any one of claims 1 to 6, characterized in that: Includes the following modules: Covariance function variant formula construction module: Based on the electromagnetic scattering mechanism, the backscattered electric field formula at different sizes is derived. Then, based on the definition of radar cross section (RCS), the target RCS calculation expression for the incident wave vector is obtained. Then, through the method of undetermined coefficients and the integral mean value theorem, the target RCS calculation expression for the incident wave vector is converted into a variant formula for constructing the covariance function. Variant formula inverse transformation module: performs inverse transformation on the obtained variant formula, and then decomposes the variant formula after inverse transformation; SPFPE covariance function synthesis module: Based on the properties of Gaussian processes, a polynomial covariance function is used to characterize the polynomial part of the inverse transform formula, and a spectral mixture covariance function is used to characterize the cosine part of the inverse transform formula. Based on the multiplicative property of Gaussian processes, the above two covariance functions are combined to form the SPFPE covariance function. Initialization module: Use the random number method to initialize the obtained SPFPE covariance function; Optimization module: Optimize the hyperparameters of the SPFPE covariance function by maximizing the log-marginal likelihood, and obtain the SPFPE-GPR method; Target RCS extrapolation module: Use the obtained SPFPE-GPR method to extrapolate the RCS of the target.

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