Rcs all-probability size extrapolation method and system based on electromagnetic scattering mechanism

Abstract

The application discloses an RCS full-probability size extrapolation method and system based on an electromagnetic scattering mechanism, and the method is as follows: 1, a backscattering electric field formula under different sizes is derived according to the electromagnetic scattering mechanism, and a target RCS calculation expression of an incident wave vector is obtained according to the definition of a radar cross section (RCS); the target RCS calculation expression is converted into a variant formula used for constructing a covariance function through a coefficient method and an integral mean value theorem; 2, the variant formula is inversely transformed and then is disassembled; 3, a polynomial covariance function is used to represent a polynomial part in the inversely transformed formula, and a spectral mixture covariance function is used to represent a cosine part in the inversely transformed formula; the two kinds of covariance functions are combined into an SPFPE covariance function; 4, the SPFPE covariance function is initialized by using a random number method; 5, hyperparameters of the SPFPE covariance function are optimized with a maximum log-likelihood as an optimization target, and an SPFPE-GPR method is obtained; 6, the target RCS is extrapolated by using the SPFPE-GPR method.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of target radar cross section (RCS) extrapolation, and particularly relates to an RCS full-probability size extrapolation method and system based on an electromagnetic scattering mechanism. BACKGROUND

[0002] Radar cross section (RCS) is an important physical parameter for radar to detect target objects, and reflects the reflection strength of electromagnetic waves by the target objects. With the continuous iterative development of leading technologies such as stealth and counter-stealth, detection and counter-detection, higher requirements are put forward for the accuracy and performance of RCS measurement.

[0003] In the microwave anechoic chamber measurement of radar cross section (RCS), the far-field condition and the quiet zone condition need to be met, resulting in an exponential increase in the construction cost of the test system with the target electric size. In order to reduce the experimental cost, electromagnetic simulation technology (such as the method of moments and the finite element method) is widely used in RCS prediction, but the calculation complexity is restricted by the target electric size, and with the continuous increase of the target size, the memory and calculation time required for simulation increase exponentially. Therefore, in recent years, the technical field has begun to study various RCS extrapolation methods for different sizes. These methods establish mathematical models and algorithms, combine the measured or simulated small-size target data, and extrapolate the RCS of large-size targets, in which the accuracy of the RCS extrapolation based on the Gaussian process is higher. However, the existing Gaussian process RCS extrapolation method has the following problems: the premise of accurate extrapolation is to regard the local fluctuation of RCS as a normal distribution with a noise mean value of 0. If the complex target cannot meet this condition, the parameter optimization will be affected, thereby deviating from the true value and reducing the accuracy of the extrapolation. In addition, the existing RCS extrapolation method cannot perform confidence evaluation, and cannot determine the reliability of the results. The lack of reliability verification significantly increases the risk of engineering decision-making. Based on this, the application provides an RCS full-probability size extrapolation method and system based on an electromagnetic scattering mechanism to extrapolate the RCS of a complex target, so as to solve the above problems in the existing method. SUMMARY

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

[0005] To achieve the above purpose, the technical solution adopted by the application is as follows:

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

[0007] Step one: according to the electromagnetic scattering mechanism, the backscattering electric field formula under different sizes is derived, and then the target RCS calculation expression of the incident wave vector is obtained according to the definition of radar scattering cross section (RCS); then the target RCS calculation expression of the incident wave vector is converted into a variant formula for constructing the covariance function through the undetermined coefficient method and the integral mean value theorem;

[0008] Step two: the RCS variant formula obtained in step one is inverse transformed, and the variant formula is disassembled;

[0009] Step three: according to the properties of Gaussian process, the polynomial part in the RCS inverse transform formula is represented by a polynomial covariance function, and the cosine part in the RCS inverse transform formula is represented by an SM (spectral mixture) covariance function; based on the multiplicative property of Gaussian process, the above two kinds of covariance functions are combined into a spectral-polynomial full probability extrapolation (SPFPE) covariance function, which is used to construct the SPFPE-GPR method of the application;

[0010] Step four: the SPFPE covariance function is initialized by using a random number method;

[0011] Step five: the hyperparameters of the SPFPE covariance function are optimized by taking the maximization of the log marginal likelihood as the optimization objective, so as to obtain the SPFPE-GPR (GPR stands for Gaussian Process Regression) method;

[0012] Step six: the RCS of the target is extrapolated by using the SPFPE-GPR method.

[0013] In order to prove the efficiency of the method, it is compared with the existing RCS size extrapolation method in the specific embodiment, and the results show that the method has obvious superiority.

[0014] Preferably, in step one, the backscattering electric field formula is as follows:

[0015]

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

[0017] On the illuminated surface |H inc |=1 / η, is the unit vector of the incident electric field, let the initial size of the target be 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, get the backscattering electric field formula under different sizes:

[0020]

[0021] The radar cross section RCS is defined as Where, |E in | is 1; thus the target RCS calculation expression about the incident wave vector is obtained:

[0022]

[0023] Where, dBsm is the 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] Where, α, β, γ are unknown numbers, r iο ′ is the point on the i-th illuminated surface S′ i , A i is the area of the i-th illuminated surface S′ i .

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

[0028]

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

[0030] Let the original value of RCS be σ(x), and the value after inverse transformation be Then σ(x) and have the following relationship: Then

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

[0032] In 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) denote the mean function, C h1 (x, x'), C h2 (x, x') and C H (x, x') denote the covariance function related to inputs x and x'.

[0033] GP (GPR, Gaussian Process) is a distribution for modeling functions, which can be regarded as the joint Gaussian distribution of function values on any input point set. The symbol "~" means that the function "obeys" a certain distribution; in the present application, it means that the function obeys a Gaussian process.

[0034] According to the analysis of Gaussian process properties, h(x) ~ GP(m h (x), C h (x, x') where C h (x, x') = α(x T x') 2 + β(x T x') + γ According to the asymptotic expression of C SM (x, x') = ω q cos [2πμ q (x-x') q ] * exp [-2πν 2 (x-x') q ], {ω q , μ q , ν i | q = 1,..., Q} are hyperparameters, and Q is the number of spectral mixing; since then where A i denotes the i-th illumination surface S' ithe area of the circle,

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

[0036] First, the spectral mixture covariance function parameters are initialized; 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 weight [ω1, ω2,.., ω Q ]; let the parameters where R q μ ~ Uniform (0, 1), Δ min = min δ 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 parameters where R q v ~ |N (0, 1) |, Δ max = x N - x1, so as to obtain the variance [v1, v2,.., v Q ];

[0037] Next, the polynomial covariance function parameters are initialized, which are regarded as the modulation factor of ω in spectral mixture; after obtaining the spectral mixture parameters, define Let be randomly divided into three parts, set as corresponding to α(x T x′) 2 , β(x T x′), γ, respectively, then Take x T x′ = mean (X), so where X is the training data size vector.

[0038] Preferably, in step five, the maximum log marginal likelihood function expression is:

[0039]

[0040] where θ is the set of hyperparameters in the SPFPE covariance function, v n represents the noise variance, I is the unit matrix, K represents the SPFPE covariance matrix, y represents a vector composed of all outputs in the training data; The partial derivative of theta is:

[0041]

[0042] where tr(.) denotes the trace of a matrix, and κ = (K + ν n I) -1 y, and finally the covariance matrix K.

[0043] The application further discloses an RCS full-probability size extrapolation system based on an electromagnetic scattering mechanism, which is used for executing the method and comprises the following modules.

[0044] A covariance function variant formula construction module: a backscattering electric field formula under different sizes is derived according to an electromagnetic scattering mechanism, then a target RCS calculation expression of an incident wave vector is obtained according to the definition of a radar cross section (RCS), and then the target RCS calculation expression of the incident wave vector is converted into a variant formula for constructing a covariance function through an undetermined coefficient method and an integral mean value theorem.

[0045] A variant formula inverse transformation module: the obtained variant formula is inversely transformed, and the inversely transformed variant formula is disassembled.

[0046] An SPFPE covariance function synthesis module: according to the properties of a Gaussian process, a polynomial covariance function is used to represent a polynomial part in the inverse transformation formula, and a spectral mixture covariance function is used to represent a cosine part in the inverse transformation formula; based on the multiplicative property of the Gaussian process, the two covariance functions are combined into an SPFPE covariance function.

[0047] An initialization module: a random number method is used to initialize the obtained SPFPE covariance function.

[0048] An optimization module: hyperparameters of the SPFPE covariance function are optimized to maximize a log marginal likelihood, and an SPFPE-GPR method is obtained.

[0049] A target RCS extrapolation module: the obtained SPFPE-GPR method is used to extrapolate the RCS of the target.

[0050] The application has the following beneficial technical effects:

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

[0052] Figure 1 is a method flowchart for extrapolating the RCS of a target according to a preferred embodiment of the application.

[0053] Figure 2 is a schematic diagram of a missile head model used by the RCS extrapolation method of the preferred embodiment of the present application;

[0054] Figure 3 is a schematic diagram of a comparison of RCS data of a missile head target extrapolated by three methods at different sizes, respectively;

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

[0056] The technical solutions of the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0057] As shown in Figure 1 , the RCS full-probability size extrapolation system based on electromagnetic scattering mechanism according to the preferred embodiment of the present application mainly includes six steps:

[0058] First, the backscattering electric field formula at different sizes is derived according to the electromagnetic scattering mechanism, and then the target RCS calculation expression of the incident wave vector is obtained according to the definition of radar cross section (RCS). Then, the target RCS calculation expression of the incident wave vector is converted into a variant formula for constructing the covariance function through the undetermined coefficient method and the integral mean value theorem. The specific process is as follows:

[0059] The backscattering electric field formula based on electromagnetic scattering mechanism is as follows:

[0060]

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

[0062] On the illuminated surface, there are |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, and the following formula is obtained:

[0063]

[0064] Continuing to deduce the backscattering electric field formula of different sizes:

[0065]

[0066] The radar cross section RCS is defined as Where |E in | is 1. Thus, the RCS expression of the target of different sizes about the incident wave vector is obtained:

[0067]

[0068] The dBsm in the electromagnetic scattering cross section is a logarithmic unit, which represents the RCS measured in decibels (dB) and the order of magnitude of the square meter (m 2 ).

[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] Where α, β, γ are unknown numbers, r iο ′ is the point on the i-th irradiation surface S′ i , and A i is the area of the i-th irradiation surface S′ i .

[0072] Second, the inverse transformation of the variant formula obtained in step one is carried out, and then the inverse transformation of the variant formula is disassembled; the specific steps are as follows:

[0073] The inverse transformation of formula (5) is carried out to obtain the inverse transformation form of the RCS variant formula about the incident wave vector target:

[0074]

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

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

[0077] Thirdly, according to the property of Gaussian process, the polynomial part in the inverse transform formula is represented by a polynomial covariance function, and the cosine part in the inverse transform formula is represented by a spectral mixture covariance function; based on the multiplicative property of Gaussian process, the above two kinds of covariance functions are combined into SPFPE covariance function; the specific process is as follows:

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

[0079] In 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′)) is concluded, wherein C H (x, x′) = C h1 (x, x′) * C h2 (x, x′), wherein m h1 (x), m h2 (x) and m H (x) represent mean functions, C h1 (x, x′), C h2 (x, x′) and C H (x, x′) represent covariance functions related to inputs x and x′.

[0080] According to the property analysis of Gaussian process, h(x) ~ GP(m h (x), C h (x, x′)), wherein,

[0081] C h (x, x′) = α(x T x′) 2 + β(x T x′) + γ, and similarly Wherein C SM (x, x′) = ω q cos [2πμ q (x-x′)] × exp [-2πν q (x-x′) 2 ] asymptotic representation, wherein {ω q , μ q , ν qis a hyper-parameter, and Q is the number of spectral mixtures. Since then where A i is the area of the i-th illuminated surface S' i ,

[0082] From the above derivation, the SPFPE covariance function for extrapolating the target RCS is obtained as

[0083] Fourthly, the SPFPE covariance function is initialized.

[0084] In this embodiment, the RCS data of the missile head under different sizes are obtained by using the MOM (Method of Moments) in the Feko software, and the related parameters are θ = 0, f = 1Ghz, scale ∈ (1, 20], the size ratio 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] Firstly, the SM covariance function parameters are initialized. Let the parameters be where q = 1, 2,..., Q, y is the RCS of the training data, and σ y is the standard deviation of the training data RCS, so as to obtain the weight [ω1, ω2,.., ω Q ]; let the parameters be where R q μ ~ Uniform (0, 1) (sampling uniform distribution), Δ min = min δ i , δ i = x i+1 -x i , i = 1,..., N-1, x is the size of the training data, and N is the length of the training data set, so as to obtain the mean [μ1, μ2,.., μ Q ]; let the parameters be where R q v ~ |N (0, 1) | (sampling non-negative normal distribution), Δ max = x N -x1, so as to obtain the variance [v1, v2,.., v Q ]. Thus, the SM covariance function parameter initialization is completed.

[0086] Next, the polynomial covariance function parameters are initialized, which can be regarded as the modulation factor of ω in SM. After obtaining the SM parameters, define Let Randomly divided into three parts, set as Corresponding to alpha (x T x′) 2 Beta (x T x′), gamma three items, then Here x T x′=mean (X), so Where X is the training data size vector. Therefore, the parameter initialization of the polynomial covariance function is completed.

[0087] The fifth step is to maximize the log marginal likelihood function to optimize the hyperparameters of the SPFPE covariance function, so as to obtain the Gaussian process model, and the SPFPE-GPR method is obtained;Specifically as follows:

[0088] The maximum log marginal likelihood function expression is:

[0089]

[0090] Where theta is the set of hyperparameters in the SPFPE covariance function, v n Indicates the noise variance, I is the unit matrix, K represents the SPFPE covariance matrix, y represents the vector composed of all outputs in the training data. The partial derivative of theta is:

[0091]

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

[0093] The sixth step is to use the SPFPE-GPR method constructed by the above steps to extrapolate the RCS of the missile head under different sizes, so as to obtain the result.

[0094] In order to verify the correctness of the method and evaluate the feasibility of the confidence interval, the existing proportional model and NLS-GPR proxy model method are compared respectively.

[0095] In the above steps, according to the electromagnetic scattering mechanism and Gaussian process, the SPFPE covariance function used in the method is obtained, then the initial parameters in the covariance function are obtained by using random number initialization method, and then the parameters are optimized by maximizing the log marginal likelihood function, so as to obtain the RCS extrapolation method with high performance and high accuracy.

[0096] To show the high efficiency of the method of the application, the proportional model, the NLS-GPR proxy model and the SPFPE-GPR method of the application are selected for comparison. RMSE is used as the evaluation basis. The smaller the RMSE is, the better the fitting effect is, and vice versa. The specific comparison results are shown in Figure 3 The proportional model extrapolates by size ratio relationship, and the best result is RMSE = 1.06. This method cannot perform confidence evaluation. The NLS-GPR proxy model obtains the overall trend of data through NLS, and then extrapolates the local fluctuation of RCS by using the SM-GPR method to obtain the extrapolation result. The best result is RMSE = 0.176. This method contains a linear part, and it is difficult to perform confidence evaluation. The best extrapolation result of the SPFPE-GPR method of the application is RMSE = 0.087. According to the above comparison data, the SPFPE-GPR method improves the accuracy by 91.8% compared with the proportional model, and improves the accuracy by 50.6% compared with the NLS-GPR proxy model. Therefore, the method adopted in the application is superior to the other two methods in extrapolating RCS of different sizes, and shows excellent performance and accuracy.

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

[0098] The covariance function variant formula construction module: according to the electromagnetic scattering mechanism, the backscattering electric field formula under different sizes is derived, and then the target RCS calculation expression of the incident wave vector is obtained according to the definition of the radar cross section RCS; and then the target RCS calculation expression of the incident wave vector is converted into a variant formula for constructing the covariance function through the undetermined coefficient method and the integral mean value theorem.

[0099] The variant formula inverse transformation module: the obtained variant formula is inversely transformed, and the inversely transformed variant formula is disassembled;

[0100] The SPFPE covariance function synthesis module: according to the properties of the Gaussian process, the polynomial covariance function is used to represent the polynomial part in the inverse transformation formula, and the spectral mixture covariance function is used to represent the cosine part in the inverse transformation formula; based on the multiplicative property of the Gaussian process, the above two kinds of covariance functions are combined into the SPFPE covariance function;

[0101] The initialization module: the obtained SPFPE covariance function is initialized by using the random number method;

[0102] The optimization module: the hyperparameters of the SPFPE covariance function are optimized to maximize the log marginal likelihood as the optimization target, and the SPFPE-GPR method is obtained;

[0103] Target RCS extrapolation module: extrapolate the RCS of the target using the derived SPFPE-GPR method.

[0104] Other contents of the embodiment can refer to the above method embodiments.

[0105] The above is only a preferred embodiment of the present application, and does not limit the present application in any form. Although the present application has been disclosed as above with a preferred embodiment, it is not intended to limit the present application. Any person skilled in the art can make some changes or modifications to the above disclosed technical content without departing from the scope of the technical solution of the present application, and any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present application are still within the scope of the technical solution of the present application.

Claims

1. A method of RCS all-probability size extrapolation based on electromagnetic scattering mechanism, characterized in that, The method comprises the following steps: Step one: according to the electromagnetic scattering mechanism, a backscattering electric field formula under different sizes is derived, and then a target RCS calculation expression of an incident wave vector is obtained according to the definition of a radar scattering cross section (RCS); and then through the method of undetermined coefficients and the integral mean value theorem, the target RCS calculation expression of the incident wave vector is converted into a variant formula used for constructing a covariance function; Step two: the variant formula obtained in step one is inverse transformed, and then the inverse transformed variant formula is disassembled; Step three: according to the properties of a Gaussian process, a polynomial covariance function is used to represent a polynomial part in the inverse transformed formula, and a spectral mixture covariance function is used to represent a cosine part in the inverse transformed formula; and based on the multiplicative property of the Gaussian process, the two kinds of covariance functions are combined into an SPFPE covariance function; Step four: a random number method is used to initialize the SPFPE covariance function obtained in step three; Step five: hyperparameters of the SPFPE covariance function in step four are optimized with the optimization objective of maximizing a log marginal likelihood, and an SPFPE-GPR method is obtained; Step six: the SPFPE-GPR method obtained in step five is used to extrapolate the RCS of the target; In step one, the backscattering electric field formula is as follows: (1) wherein is the incident wave vector, , is the imaginary unit, is the wave impedance, and represent the observation point and the source point, respectively, denotes the outward unit normal vector of the th illuminated surface, represents the th illuminated surface, is the number of illuminated surfaces, is the intensity of the incident magnetic field at the surface point ; On the irradiation surface there are , , is the unit vector of the incident electric field, let the target initial size be , the actual size , and the magnification factor , the relationship between them is , then the following formula is obtained: （2） Continue to derive, and a backscattering electric field formula under different sizes is obtained: （3） The radar cross section, RCS, is defined as where, is set to 1; thus obtaining the target RCS computation expression in terms of the incident wave vector: （4） wherein is the logarithmic unit; According to the method of undetermined coefficients and the integral mean value theorem, formula (4) is converted into a variant formula: （5） wherein is an unknown, is the point on the th illuminated surface is the area of the th illuminated surface is the area of the th illuminated surface 2. The RCS all-probability size extrapolation method based on electromagnetic scattering mechanism according to claim 1, characterized in that, In step two, formula (5) is inverse transformed, and an inverse transformed form of the variant formula of the target RCS of the incident wave vector is obtained: （6） Let the above formula (6) in , ; Let RCS original value be , the value after inverse transform is , then and there is the following relationship: ; then .

3. The RCS all-probability size extrapolation method based on electromagnetic scattering mechanism according to claim 2, characterized in that, Step three, according to the properties of Gaussian process, the polynomial covariance function represents Part, spectral mixing covariance function represents Part, based on the multiplicative property of Gaussian process, the above two functions are combined into SPFPE covariance function; In Gaussian processes, if , , then there is the conclusion that where where , and denote the mean function, , and denote the covariance function with respect to inputs and . According to the analysis of the Gaussian process properties, we have , where, , is asymptotically represented by , where, is a hyperparameter, is the number of spectral mixtures; since , we have where, .

4. The RCS all-probability size extrapolation method based on electromagnetic scattering mechanism according to claim 3, characterized in that, In step four, the SPFPE covariance function is initialized, and the specific process is as follows: First, initialize the spectral mixture covariance function parameters; let the parameters where, , is the RCS of the training data, is the standard deviation of the training data RCS, thus obtaining the weights ; let the parameters where, , , , is the size of the training data, is the length of the training data set, thus obtaining the mean ; let the parameters where, , , thus obtaining the variance ; The polynomial covariance function parameters are then initialized, considering them as modulation factors in the spectral mixture ; after obtaining the spectral mixture parameters, define , and randomly divide into three parts, set as , respectively corresponding to three items, then , take , so that , wherein is the training data size vector.

5. The RCS all-probability size extrapolation method based on electromagnetic scattering mechanism according to claim 4, characterized in that, In step five, the expression of the log marginal likelihood function to be maximized is as follows: where is a set of hyperparameters in the SPFPE covariance function, denotes the noise variance, is the identity matrix, denotes the SPFPE covariance matrix, y denotes a vector of all outputs in the training data; the partial derivative of is wherein, denotes the trace of a matrix, and finally the SPFPE covariance matrix is derived.

6. A system for RCS all-probability size extrapolation based on electromagnetic scattering mechanisms for performing the method according to any one of claims 1-5, characterized in that, The method comprises the following modules: A covariance function variant formula construction module: according to the electromagnetic scattering mechanism, a backscattering electric field formula under different sizes is derived, and then a target RCS calculation expression of an incident wave vector is obtained according to the definition of a radar scattering cross section (RCS); and then through the method of undetermined coefficients and the integral mean value theorem, the target RCS calculation expression of the incident wave vector is converted into a variant formula used for constructing a covariance function; A variant formula inverse transformation module: the obtained variant formula is inverse transformed, and then the inverse transformed variant formula is disassembled; An SPFPE covariance function synthesis module: according to the properties of a Gaussian process, a polynomial covariance function is used to represent a polynomial part in the inverse transformed formula, and a spectral mixture covariance function is used to represent a cosine part in the inverse transformed formula; and based on the multiplicative property of the Gaussian process, the two kinds of covariance functions are combined into an SPFPE covariance function; An initialization module: a random number method is used to initialize the obtained SPFPE covariance function; An optimization module: hyperparameters of the SPFPE covariance function are optimized with the optimization objective of maximizing a log marginal likelihood, and an SPFPE-GPR method is obtained; A target RCS extrapolation module: the obtained SPFPE-GPR method is used to extrapolate the RCS of the target.

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