A method for modeling air traffic control radars

Abstract

The application provides an air traffic control radar modeling method, comprising the following steps: selecting initial sample points, and obtaining the flyable range of each initial sample point by designing a simulation system for an air traffic control radar; constructing a training sample set; reducing the data dimension by using a principal component dimension reduction method and reconstructing the kernel function of a Kriging model; selecting different correlation functions and regression functions for combination, obtaining different Kriging model modeling schemes; solving the weight of each Kriging model modeling scheme; obtaining the output result of each Kriging model modeling scheme; constructing a weighted average aircraft flight range prediction model based on the output result of each Kriging model modeling scheme and the weight of each Kriging model modeling scheme; and the model can quickly calculate the reasonable flight range of an aircraft according to weather and air resistance information. The application improves the efficiency and accuracy of air traffic control radar modeling.

Description

Technical Field

[0001] This invention belongs to the field of air traffic control technology, specifically relating to an air traffic control radar modeling method. Background Technology

[0002] With the rapid development of my country's air traffic sector, the monitoring of aircraft air traffic conditions places increasingly higher demands on air traffic control technology. To ensure flight safety and the normal operation of air traffic, radar detection systems have been established. These systems can monitor the flight range (distance) of aircraft in real time. Under these conditions, unfortunate events such as aircraft disappearances can be avoided.

[0003] The specific air traffic control system mainly includes three subsystems: radar, aircraft, and weather. Existing technology uses 12 design variables, including flight information, radar signals, weather forecasts, aircraft drag, and flight range, as input parameters for the air traffic control radar design simulation system, thus obtaining simulation results through analog communication technology. However, simulation-based estimation is expensive, time-consuming, and labor-intensive. Parameters such as weather and air drag change rapidly, requiring faster calculation of flight range (distance) to promptly control the aircraft's flight status. Currently, a common solution is to use a substitute model to replace the original model. This substitute model, also known as a meta-model, is a mathematical tool used to simulate the approximate relationship between inputs and outputs. Kriging, a commonly used substitute model, is an accurate interpolation method and a form of generalized linear regression used to formulate an optimal estimator in the sense of minimum mean square error, offering significant advantages in handling nonlinear problems. However, there are still two problems with Kriging modeling for high-dimensional air traffic control radar: First, the most suitable correlation and regression functions cannot be determined in the process of Kriging modeling of black box problems, resulting in the failure to achieve optimal modeling accuracy; Second, due to the inversion of the covariance correlation matrix and the solution of Kriging correlation parameters, the Kriging approximation process for high-dimensional problems is very time-consuming, or even impossible to construct. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the aforementioned background technology by providing an air traffic control radar modeling method. This method employs principal component dimensionality reduction to lower the dimensionality of the air traffic control radar problem and determines the most suitable weighted combination of regression and correlation functions for the air traffic control problem, thereby improving the efficiency and accuracy of air traffic control radar modeling.

[0005] The technical solution adopted in this invention is: an air traffic control radar modeling method, comprising the following steps:

[0006] Initial sample points are selected, and the flight range of aircraft corresponding to each initial sample point is obtained by designing a simulation system for air traffic control radar; the initial sample points are characteristic quantities used to characterize air traffic control conditions.

[0007] A training sample set is constructed based on the initial samples and their corresponding flight ranges of the aircraft.

[0008] Based on the training sample set, the kernel function of the Kriging model is reconstructed using the principal component dimensionality reduction method;

[0009] Different Kriging modeling schemes are obtained by selecting different correlation and regression functions and combining them in pairs;

[0010] The weights of each Kriging modeling scheme are determined based on the likelihood function;

[0011] The output results of each Kriging modeling scheme are obtained based on the input parameters of the test point;

[0012] The predicted flight range of the aircraft at the test point is obtained based on the output results of each Kriging model modeling scheme and the weight calculation of each Kriging model model modeling scheme.

[0013] In the above technical solution, the initial sample points include wavelength, transmitter power, flight loss, noise figure, antenna efficiency, radar range, altitude, latitude separation, range resolution, bandwidth, reliability monitoring, and operating ambient temperature.

[0014] In the above technical solution, the process of reconstructing the kernel function of the Kriging model based on the training sample set using the principal component dimensionality reduction method includes: calculating the covariance matrix of the sample data in the training sample set; finding the eigenvalues ​​of the covariance matrix and the corresponding unit eigenvectors; sorting the eigenvalues ​​in descending order; and selecting the unit eigenvectors corresponding to the top-ranked eigenvalues ​​to calculate the new kernel function.

[0015] In the above technical solution, Gaussian function and Matern function are used as correlation functions.

[0016] The regression functions used in the above technical solutions include constant regression function, linear regression function and quadratic regression function.

[0017] In the above technical solution, the process of selecting the unit eigenvector corresponding to the top-ranked eigenvalues ​​to calculate the new kernel function includes: defining the linear mapping expression:

[0018] F l :B→B

[0019]

[0020] n represents the number of design quantity indicators; n = 12; a new composite variable is obtained by linearly mapping x, and the first h principal components are selected as the new vector space, reducing the dimension of the indicators from n to h;

[0021] The kernel function for each dimension is represented as follows:

[0022]

[0023] By multiplying the tensors of h kernel functions, a new kernel function based on Kriging and principal component dimensionality reduction is finally generated:

[0024]

[0025] Among them, F l () represents the regression function, and B represents the parameter vector space; R represents the unit eigenvector, which is the eigenvector corresponding to the principal component; l () represents the spatial correlation kernel function of the l-th dimension, θ l X is the hyperparameter of the l-th dimension, where x and w are any two different sets of air traffic data obtained through observation, and X = (x... 1 x 2 , ..., x n ) T ; w = (w 1 w 2 , ..., w n ) T ;x i and w i These represent the i-th design quantity index data.

[0026] In the above technical solution, the weight w of each modeling scheme is calculated using the following formula. i :

[0027]

[0028]

[0029] in, The improved exponential form of the likelihood function value for the modeling scheme of the i-th Kriging model; It is the process variance estimate of the i-th candidate Kriging prediction model, |R i | is the determinant of the correlation matrix of the i-th candidate Kriging prediction model; a = 1.

[0030] The beneficial effects of this invention are as follows: This invention employs a dimensionality reduction method to lower the dimensionality of the air traffic control radar problem, reducing the time consumption for optimizing relevant parameters and constructing relevant function matrices during Kriging modeling, thereby improving the efficiency of air traffic control radar modeling. This invention integrates multiple regression and correlation functions using a likelihood function-weighted method, ensuring optimal modeling accuracy under existing experimental conditions. This invention can effectively predict the flight range (distance) of aircraft in the air using the established air traffic control Kriging model, requiring aircraft to fly only within a safe flight range, thus achieving flight control. This prevents aircraft from flying out of the safe range and causing flight accidents, avoids expensive simulation estimations and the "curse of dimensionality" of high-dimensional Kriging modeling, and improves modeling accuracy, thereby ensuring flight safety and the real-time normal operation of air traffic. Unfortunate events such as aircraft disappearances can be avoided. Attached Figure Description

[0031] Figure 1 The prediction accuracy of the test function for different values ​​of the likelihood function parameter a from 1 to 4 in this invention is shown in the figure.

[0032] Figure 2 This is a schematic diagram of the aircraft air traffic control radar system of the present invention;

[0033] Figure 3 This is a schematic diagram of the input parameters for the aircraft flight radar of the present invention;

[0034] Figure 4 This is a graph showing the test results of the modeling time for the air traffic control system according to the present invention;

[0035] Figure 5 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0036] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments to facilitate a clear understanding of the present invention, but these descriptions do not constitute a limitation on the present invention.

[0037] like Figure 5 As shown, this invention provides an air traffic control radar modeling method, comprising the following steps:

[0038] Initial sample points are selected, and the flight range of aircraft corresponding to each initial sample point is obtained by designing a simulation system for air traffic control radar; the initial sample points are characteristic quantities used to characterize air traffic control conditions.

[0039] A training sample set is constructed based on the initial samples and their corresponding flight ranges of the aircraft.

[0040] Based on the training sample set, the kernel function of the Kriging model is reconstructed using the principal component dimensionality reduction method;

[0041] Different Kriging modeling schemes are obtained by selecting different correlation and regression functions and combining them in pairs;

[0042] The weights of each Kriging modeling scheme are determined based on the likelihood function;

[0043] The output results of each Kriging modeling scheme are obtained based on the input parameters of the test point;

[0044] The predicted flight range of the aircraft at the test point is obtained based on the output results of each Kriging model modeling scheme and the weight calculation of each Kriging model model modeling scheme.

[0045] Kriging modeling has been widely used as an alternative model to predict the responses of complex real-world computer models. The air traffic control radar in this invention falls into this category. In the modeling process of this air traffic control radar, this invention selects 20 initial sample points and obtains the flight range of the aircraft at the corresponding sample points through simulation. These are then used as a training set to construct a surrogate model of the air traffic control radar system.

[0046] The selection of training samples significantly impacts the performance of the resulting surrogate model. As the number of training samples increases, modeling accuracy improves, but modeling time also increases. Therefore, the selected training set should not have too many or too few sample points. Kriging not only provides predicted values ​​of the model response but also a measure of prediction uncertainty. This characteristic is very useful for adaptively improving surrogate models.

[0047] The Kriging model can be represented as the sum of a polynomial and a stochastic process, as shown in the equation:

[0048] g(x) = Fβ + z(x)

[0049] Where g(x) is the flight range prediction function to be determined, Fβ is the global estimate of the Kriging model, i.e. the expectation of the Kriging flight range prediction model, and z(x) represents the Gaussian stochastic process that provides local bias.

[0050] Assuming the mean of the stochastic process z(x) is 0, the covariance is defined by the following formula:

[0051]

[0052] Where x and w are any two different sets of air traffic data obtained through observation, x = (X 1 x2 , ..., x n ) T ; w = (w 1 w 2 , ..., w n ) T n represents the number of indicators; E represents the expected value, σ 2 The process variance is between z(w) and z(x). The correlation model has parameter θ, which determines the smoothness of the Kriging model. The choice of correlation function should be influenced by the internal mechanisms of aircraft flight range. For problems like air traffic, where the internal mechanisms are unclear and highly nonlinear, arbitrarily choosing a single correlation function lacks comprehensiveness and robustness, resulting in a low-accuracy aircraft flight range prediction model. Therefore, it is necessary to combine multiple correlation functions using weighted methods.

[0053] Given an initial sample dataset containing 20 air traffic scenarios, a Kriging prediction model is constructed using this dataset as the training set. For a set of air traffic scenario data x containing 12 indicators, the predicted aircraft flight range g(x) follows a normal distribution: g(x) ~ N(μ g (x), σ g (x)). Here, the predicted value μ of the Kriging prediction model at a given air traffic observation data point x can be calculated. g (x) and variance σ g (x) are respectively:

[0054]

[0055]

[0056] The covariance correlation matrix R can be expressed by the following formula:

[0057]

[0058] The parameter θ has a significant impact on the prediction accuracy of the Kriging model. The estimated value of θ is usually obtained by maximizing the likelihood function L(θ).

[0059]

[0060] The unconstrained optimization problem described above can be solved using several numerical optimization methods, such as genetic algorithms, cross-validation, and improved Hooke and Jeeves methods.

[0061]

[0062] Principal component analysis (PCA) dimensionality reduction can transform 12 high-dimensional input design variables—wavelength, transmitter power, flight loss, noise figure, antenna efficiency, radar range, altitude, latitudinal separation, range resolution, bandwidth, reliability monitoring, and ambient temperature—into low-dimensional input parameters for reconstructing new correlation functions. This simplifies the process of establishing these correlation functions, reducing the time spent on parameter optimization and correlation function matrix construction during modeling, ultimately achieving efficient construction of an air traffic control proxy model. After observing the corresponding values ​​of the 12 inputs, the maximum flight range (distance) of the aircraft can be obtained through the substitution model, avoiding the need to obtain the flight range of the aircraft at corresponding sample points through simulation.

[0063] The mathematical theory behind principal component analysis (PC) dimensionality reduction is principal component theory. It utilizes the idea of ​​dimensionality reduction, employing multivariate statistical methods to transform all indicators into multiple composite indicators. These transformed composite indicators are called principal components (PCs). Different linear combinations of the original design variables can constitute different principal components (PCs). Provided that the principal components (PCs) are independent and meet accuracy requirements, the dimensionality-reduced principal components (PCs) offer greater advantages in modeling efficiency compared to the original variables. These features make it particularly suitable for studying high-dimensional and complex problems.

[0064] The study of air traffic control issues involves 12 indicators, represented by x. 1 x 2 , ..., x 12 Therefore, a 12-dimensional random vector x = (x 1 x 2 , ..., x 12 ) T Any sampling point is formed by these 12 indicators. A new composite variable can be obtained by performing a linear transformation on the following equation:

[0065]

[0066] u i1 This represents the unit eigenvector, which is the eigenvector corresponding to the principal component. If h principal components (PCs) are selected, it's equivalent to reducing the number of indicators from n dimensions to h dimensions. Principal component v i The greater the variance, the greater the amount of original data information it carries. This specific embodiment aims for principal components (PCs) to be independent of each other and to have the maximum variance.

[0067] Based on the above analysis, the specific calculation process of the principal component dimensionality reduction method is described as follows:

[0068] Step 1: Calculate the covariance matrix of the sample data for the air traffic control problem. Calculate the covariance matrix of the sample data ∑=σ 2R = (s ij ) 12×12 ;s ij This represents the element in the i-th row and j-th column of the covariance matrix.

[0069] Step 2: Find the eigenvalues ​​λ of ∑ i and the corresponding unit eigenvector u i The eigenvalues ​​λ of the covariance matrix ∑ i Arranged in descending order, i.e., λ1, λ2, ..., λ 12 (λ1≥λ2≥…≥λ 12 The corresponding unit eigenvector u i (i = 1, 2, ..., 12) are the principal components v i The corresponding feature vectors. The feature values ​​corresponding to each input variable are sorted by magnitude and in descending order.

[0070] Step 3: Principal Component (PC) Selection. After completing the Kriging dimensionality reduction modeling of the air traffic control problem, subsequent steps require multiple modeling operations using different regression and correlation functions, followed by weighted summation. The fewer principal components (PCs) selected, the less Kriging modeling overhead is consumed, even to the point of being negligible. Therefore, this invention aims to select the fewest principal components (PCs) while still reflecting most of the original data information. Based on the principal component dimensionality reduction method and training set, this invention ultimately retains the first, second, and third ranked principal components (PCs) to construct the Kriging model. The amount of information reflected can be measured by the contribution rate (CR) of the eigenvalues.

[0071]

[0072] When the first, second and third principal components (PCs) are retained, the cumulative contribution rate (CR) is greater than 80%, so it can be considered that the three selected principal components can reflect the characteristics of all 12 original variables to a certain extent.

[0073] Step 4: Generate a new kernel function for the air traffic control problem. First, a linear mapping expression is defined:

[0074] F l :B→B

[0075]

[0076] Let x represent the unit eigenvector, which is the eigenvector corresponding to the principal component. Projecting an n-dimensional vector space onto an h-dimensional vector space, x originally has n principal components, but after projection, it becomes h principal components. This mapping reduces a 12-dimensional problem to 3-dimensional. Taking the Gaussian correlation function as an example, the kernel function corresponding to each dimension is expressed as:

[0077]

[0078] Among them, R l () represents the spatial correlation kernel function of the l-th dimension, θ l F is the hyperparameter of the l-th dimension. l () represents the regression function, where x and w are any two different sets of air traffic data obtained through observation. Finally, a new kernel function based on Kriging and principal component dimensionality reduction can be generated through the tensor product of the three kernel functions:

[0079]

[0080] For the air traffic control problem (h=3), this invention uses a new Kriging kernel function obtained after dimensionality reduction to replace the original high-dimensional kernel function, so as to improve the modeling efficiency of the Kriging model.

[0081] Air traffic control systems are considered black-box problems. A significant challenge in modeling such black-box problems using Kriging models is the selection of regression and correlation functions. This invention, through principal component analysis, transforms the high-dimensional air traffic control modeling problem into a low-dimensional (3D) problem. This approach offers lower computational cost and faster processing speed, but accuracy is typically only guaranteed by selecting the most suitable regression and correlation functions, and the computational accuracy of the model remains unknown until validated on a test set. Furthermore, the internal mechanisms of aircraft flight range prediction are highly complex, involving highly nonlinear systems, and a single regression or correlation function cannot accurately describe its underlying physical phenomena. To address these issues, this invention introduces a likelihood function-based weighting method. Multiple modeling schemes for the low-dimensional problem are weighted according to their likelihood functions. Since low-dimensional Kriging modeling is computationally inexpensive and fast, this weighting technique can improve modeling accuracy with lower computational cost. This method provides a more effective and efficient solution to the dimensionality-reduced air traffic control system modeling problem.

[0082] Commonly used correlation models include linear, exponential, and Gaussian correlation functions. Among these, the Gaussian correlation function is the most frequently used; however, it has been observed in many numerical applications that Gaussian correlation models are prone to ill-conditioned behavior. Current techniques also use Matern correlation functions or other correlation functions, each with its own advantages and disadvantages. Weighting correlation functions can achieve complementarity among them. The choice of correlation function should be driven by the underlying phenomenon. If the underlying phenomenon is continuously differentiable, the correlation function is likely to exhibit parabolic behavior near the origin, meaning a Gaussian, cubic, or spline function should be chosen. Conversely, if the physical phenomenon exhibits linear behavior near the origin, exponential, linear, or spherical correlation functions usually perform better. Therefore, directly selecting a particular correlation function for modeling an air traffic control problem before clearly understanding the physical processes involved cannot guarantee its reliability and stability.

[0083] Before addressing the air traffic control modeling problem, this invention verified through 12 low-dimensional and high-dimensional functions that Gaussian and Matern correlation functions offer relatively optimal fitting results among various correlation functions. While the Gaussian kernel function provides the best fit in most cases, it falls short of Matern in some situations. Furthermore, an interesting characteristic of the Matern correlation function family is that the sample path of the corresponding Gaussian process is differentiable to the order v-1. For v = 1 / 2, the Matern kernel function coincides with the exponential correlation function; as v→∞, it tends towards the Gaussian correlation function. Many studies consider the Matern correlation function as a transitional state between the exponential and Gaussian correlation functions. Therefore, this invention selects Gaussian and Matern, two universally recognized best-performing correlation functions, for weighted calculation, ensuring both accuracy and coverage of all potential phenomena.

[0084] The exponential correlation function is:

[0085]

[0086] The relevant functions for Matern (Matern Linear) are:

[0087]

[0088] The Gaussian correlation function is:

[0089]

[0090] Depending on the type of regression function used, the Kriging metamodel has received different names: SimpleKriging, Ordinary Kriging, and Universal Kriging. Different types of regression functions are suitable for different practical problems. The most commonly used regression functions are based on multinomials, for example:

[0091] Constant regression function: β0

[0092] Linear regression function:

[0093] Quadratic regression function:

[0094] By combining the two best-performing correlation functions and the three most commonly used regression functions in pairs, six modeling schemes for air traffic control problems can be obtained. However, for black box problems, it is impossible to determine in advance which of the six modeling schemes will achieve the highest accuracy. Therefore, the next step of this invention is to improve the modeling accuracy by weighting the six modeling schemes based on the known information obtained during the Kriging modeling process.

[0095] In statistics, likelihood and probability are two different concepts, but in informal contexts like aircraft flight prediction problems, they are almost synonymous. Probability is the likelihood of an event occurring under specific conditions, while the likelihood function is an inference about the possible environments (parameters) that produce a given outcome, expressed as L(θ|X). It can be understood as the probability corresponding to parameter θ given the outcome X. When the predicted aircraft flight range and the parameters representing air traffic conditions correspond, likelihood and probability are numerically equal.

[0096] P(X|θ)=L(θ|X)

[0097] The two are equal in numerical value, but they have different meanings, although they can describe the same thing from different perspectives.

[0098] The likelihood function in the Kriging modeling problem for air traffic control radar describes the probability of an event occurring under different parameters, given that the flight range (distance) of a portion of the aircraft is known. This problem focuses on maximizing the likelihood function, requiring the identification of the most probable conditions for the known event to produce that outcome. The goal is to infer the probability of unknown events based on these most probable conditions. After maximizing the likelihood function to obtain the parameter θ, the calculated likelihood function value is the maximum likelihood value, which approximates the probability of the unknown event under the most probable conditions. A higher probability indicates a better fit for the chosen modeling scheme; therefore, weighting the modeling scheme using the likelihood function is theoretically feasible.

[0099] The expression for the likelihood function usually involves multiple products, so after logarithmic transformation, the likelihood function becomes:

[0100]

[0101] The formula shows that the likelihood function value is related to the number of sampling points n, the determinant of the correlation matrix |R|, and the process variance. These variables are relevant, and they can all be trained after the Kriging modeling process for air traffic control radar is completed, so they can be considered as known.

[0102] The logarithmic likelihood function ln L(θ) is the most commonly used due to its simple calculation. However, directly weighting air traffic control models based on the logarithmic likelihood function ln L(θ) has been shown to be ineffective in experiments. This is because the logarithmic processing weakens the numerical advantage of the likelihood function value, leading to an unreasonable weight allocation and ultimately resulting in the accuracy of the integrated modeling not meeting the expected requirements. Therefore, when calculating the weights, it is necessary to base them on the likelihood function L(θ) itself, that is, to transform ln L(θ) back to L(θ) through the following processing:

[0103]

[0104] As can be seen from the formula, both variance and the size of the determinant of the correlation matrix have a significant impact on the likelihood function value. However, problems arise when directly calculating the weights using the above formula. Taking the LEVY function as an example, 25 initial sampling points are generated using Latin square sampling to establish 6 Kriging models, as shown in Table 1. After logarithmic processing, the variances of the 6 Kriging models are of similar (or the same) order of magnitude, and the model with smaller variance will be assigned a larger weight. However, the determinant of the correlation matrix itself has a range of [0, 1], and after logarithmic processing, it undergoes a drastic change in order of magnitude, causing the likelihood function values ​​of different Kriging models to lose comparability.

[0105] Table 1. Parameters of the LEVY function

[0106]

[0107] The correlation function value can directly and quantitatively describe the degree to which the target value of a measured air traffic condition data is affected by other observed data: when two sample points are close to each other, the correlation function value is close to 0, otherwise it is close to 1; it is continuous throughout the entire air traffic condition data space. Therefore, this invention directly uses the correlation function value to calculate the weights, eliminating the need for logarithmic processing. However, it is worth noting that the correlation function value ranges from 0 to 1. If the value of 'a' is too large, the correlation function value will have almost no effect on the magnitude of L(θ). Therefore, the value of 'a' should be controlled, i.e., the definition (number of sampling points) in the original likelihood function formula cannot be maintained. To improve the original likelihood function formula, the prediction accuracy of the weighted results of three test functions obtained by taking different values ​​of 'a' from 1 to 4 is as follows: Figure 1 ,Depend on Figure 1 It can be seen that as 'a' increases, the prediction error also increases. Therefore, in this specific embodiment, the value of 'a' is set to 1 when calculating the weight.

[0108] To solve for the weight w of the i-th candidate modeling scheme i The following formula is required:

[0109]

[0110]

[0111] in, The exponential form of the likelihood function value for the i-th Kriging modeling scheme; It is the process variance estimate of the i-th candidate Kriging prediction model, |R i | is the determinant of the correlation matrix of the i-th candidate Kriging prediction model.

[0112] After weighting the modeling schemes for the six air traffic control problems based on the likelihood function, the output of the aircraft flight range (distance) predictor at the unknown new point x becomes:

[0113]

[0114] Among them, y i (x) is the flight range result of the i-th candidate aircraft flight predictor.

[0115] The weighted flight range (distance) result can be closer to the actual output value than most modeling schemes, thus ensuring modeling accuracy.

[0116] Specific air traffic control model diagrams are as follows: Figure 2As shown. The air traffic control radar simulation system designed in this paper incorporates real-time data such as flight information, radar signals, weather forecasts, aircraft drag, and flight mileage as simulation parameters during the simulation process. To make the radar system design parameters easier to modify and determine their values, the model provides a GUI (see...). Figure 3 Radar and weather parameters can be changed via the GUI. During the simulation, the effects of different parameters can be seen on the oscilloscope screen. The oscilloscope screen displays the aircraft's actual range and the change in the radar's estimated aircraft distance over time under certain parameter settings.

[0117] This embodiment uses 12 design variables as the parameter settings for the air traffic control radar design simulation system, thereby obtaining simulation results through analog communication technology. Since the simulation results change over time, the maximum detection range of the radar is used as the simulation result, which is output to the MATLAB workspace. Based on the simulation results and the principal component analysis method, 1, 2, and 3 principal components are retained to construct the Kriging model, and the modeling time for the three cases is recorded. Furthermore, the Kriging model is directly built using the simulation data, and the modeling time is also recorded.

[0118] Figure 4 The modeling time is shown for four different scenarios. In this modeling process, the training set to test set ratio is 2:8, meaning 20 initial sample points are selected, and the corresponding expensive simulation values ​​(i.e., the flight range of the aircraft) are obtained through simulation and used as training samples for modeling. Because from Figure 4 As can be seen, with the increase in the number of sample points, not only does the simulation time increase, but the time required to build models using the Kriging method for principal component reduction air traffic control problems and the Kriging method for direct air traffic control problems also gradually increases, weakening the advantage of this invention in terms of evaluation speed. Therefore, under this trade-off, this invention selects 20 initial sample points as the training set. Finally, the mean absolute error (MAE) is calculated using a test set containing 80 sets of sample points to evaluate the accuracy of the established model.

[0119]

[0120] Where N is the number of sample points in the test set (N = 80), y j These are the model's predicted values. These are expensive simulation values.

[0121] The test errors and their respective weights for each modeling scheme in this specific embodiment are shown in Table 3.

[0122] Table 2 Test errors and their weights for each modeling scheme

[0123]

[0124] The following conclusions can be drawn from the chart:

[0125] from Figure 4 As can be seen, with the increase in the number of sample points, the time required to directly build the Kriging model is significantly greater than the time required to build the Kriging model after selecting 3 principal components.

[0126] As can be seen from Table 3, the average absolute error of the model calculated based on the likelihood function weighting on the test set is 3.1855, which is lower than any of the six selected modeling schemes, indicating that the modeling accuracy of the weighted model is improved.

[0127] In summary, principal component dimensionality reduction can reduce the time required for Kriging modeling, while likelihood function-based weighting can improve the accuracy of Kriging modeling. Combining these two techniques in air traffic control system modeling can improve modeling efficiency while ensuring relatively optimal modeling accuracy.

[0128] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A method for modeling air traffic control radar, characterized in that: Includes the following steps: Initial sample points are selected, and the flight range of the aircraft corresponding to each initial sample point is obtained through an air traffic control radar design simulation system; the initial sample points are characteristic quantities used to characterize air traffic conditions. A training sample set is constructed based on the initial samples and their corresponding flight ranges of the aircraft. Based on the training sample set, the kernel function of the Kriging model is reconstructed using the principal component dimensionality reduction method; Three regression functions and two correlation functions were selected to construct the Kriging model; The selected correlation and regression functions are combined in pairs, and different Kriging modeling schemes are obtained by training the training sample set based on the reconstructed kernel function. The weights of each Kriging modeling scheme are determined based on the likelihood function; The output of each Kriging modeling scheme is obtained based on the input parameters of the test point; the input parameters are consistent with the feature quantities of the initial sample points; the output parameters are the reasonable flight range of the aircraft. The predicted flight range of the aircraft at the test point is obtained based on the output results of each Kriging model modeling scheme and the weight calculation of each Kriging model model modeling scheme. The initial sample points include wavelength, transmitter power, flight loss, noise figure, antenna efficiency, radar range, altitude, latitude separation, range resolution, bandwidth, reliability monitoring, and operating ambient temperature.

2. The method according to claim 1, characterized in that: The process of reconstructing the kernel function of the Kriging model based on the training sample set using principal component dimensionality reduction includes: calculating the covariance matrix of the sample data in the training sample set; finding the eigenvalues ​​and corresponding unit eigenvectors of the covariance matrix; sorting the eigenvalues ​​in descending order; and selecting the unit eigenvectors corresponding to the top-ranked eigenvalues ​​to calculate the new kernel function.

3. The method according to claim 1, characterized in that: The Gaussian function and the Matern function are used as correlation functions.

4. The method according to claim 1, characterized in that: The regression functions used include constant regression, linear regression, and quadratic regression.

5. The method according to claim 2, characterized in that: The process of selecting the unit eigenvectors corresponding to the top-ranked eigenvalues ​​to calculate the new kernel function includes: defining the linear mapping expression: n represents the number of design quantity indicators; n=12; through the... The linear mapping transformation yields a new composite variable; the first choice... Each principal component serves as a new vector space, reducing the dimension of the indicator from... Reduced to ; The kernel function for each dimension is represented as follows: pass The tensor product of the kernel functions ultimately generates a new kernel function based on Kriging and principal component dimensionality reduction: ； in, Represents the regression function. Represents the parameter vector space; This represents the unit eigenvector, which is the eigenvector corresponding to the principal component; Indicates the first Spatial correlation kernel function of dimension It is the first Hyperparameters of dimension It is obtained by observing any two different sets of air traffic data. ; ;x i and w i These represent the i-th design quantity index data.

6. The method according to claim 1, characterized in that: The weights w of each modeling scheme are calculated using the following formula. i : in, For the first The improved exponential form of the likelihood function values ​​of a Kriging modeling scheme; It is the first Process variance estimates for each candidate Kriging prediction model It is the first The determinant of the correlation matrix of the candidate Kriging prediction models; a=1.

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