An air-to-air missile interception probability sensitivity analysis method based on a proxy model

Abstract

The application discloses a kind of air-to-air missile interception probability sensitivity analysis method based on agent model.Interception probability has important significance in missile composite guidance, determines the miss distance and hit probability of missile terminal guidance phase, to effectively improve the interception performance of missile during midcourse guidance and terminal guidance shift, it needs to carry out sensitivity analysis on each error that influences missile interception probability, through sensitivity analysis, the influence size of each error is quantified.However, the timeliness of traditional interception probability calculation method is poor, to solve this problem, the application establishes the support vector machine agent model of particle swarm optimization, to obtain the interception probability calculation model with higher timeliness and accuracy.Based on the agent model, the sensitivity coefficients of 18 kinds of errors are calculated by Sobol index method.The results show that radar angle measurement error and optical radar angle measurement error have the greatest influence on air-to-air missile interception probability.The method shortens the calculation time while ensuring the accuracy, and provides a basis for further sensitivity analysis.

Description

Technical Field

[0001] This invention belongs to the field of navigation technology, specifically relating to a sensitivity analysis method for the probability of air-to-air missile interception based on a proxy model. Background Technology

[0002] With the continuous development of modern military, the performance of airborne radar and air-to-air missiles has been continuously improved, and the radius of combat has been gradually increased. The development direction of air combat today has changed from close-range dogfighting to "detecting the enemy first, firing the enemy first, hitting the enemy first, and disengaging from the enemy first". The main combat style of air combat has become the use of beyond-visual-range air-to-air missiles for beyond-visual-range air combat.

[0003] In missions such as beyond-visual-range (BVR) target engagement, air-to-air missiles employing a single guidance system are no longer sufficient to meet the required performance. Therefore, it is essential to introduce a composite guidance mechanism to increase missile range. Only by reliably intercepting the target during the mid-course and terminal guidance transition can a missile successfully enter the terminal guidance phase for active radar-guided flight. Therefore, it is necessary to analyze various mid-course guidance errors of BVR air-to-air missiles, simulate the probability of interception, and calculate the sensitivity coefficients of various errors, providing a theoretical basis for enhancing the missile's target acquisition performance in the future.

[0004] The probability of interception can be calculated by performing numerous simulations of an established model using the Monte Carlo method and then calculating the probability of interception through statistical analysis. However, this method is computationally inefficient and extremely time-consuming, making it unsuitable for sensitive analysis. Another method for calculating the probability of interception involves establishing a probability of interception estimation model to obtain the probability of interception of the target in a single calculation. This method has a smaller computational load, but this estimation model still requires ballistic simulation calculations and cannot achieve real-time calculation of the probability of interception, thus failing to support sensitivity analysis. Furthermore, existing probability of interception calculation models do not consider errors in optical and radar systems and data link systems, making them unsuitable for calculating the probability of interception in current air combat scenarios. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention provides a sensitivity analysis method for air-to-air missile interception probability based on a surrogate model. Interception probability is crucial in missile composite guidance, determining the miss distance and hit probability during the terminal guidance phase. To effectively improve interception performance during the mid-to-terminal guidance handover period, sensitivity analysis of various errors affecting the missile interception probability is necessary to quantify the magnitude of each error's impact. However, traditional methods for calculating interception probability suffer from poor timeliness. To address this issue, this invention establishes a particle swarm optimization support vector machine surrogate model to obtain a more timely and accurate interception probability calculation model. Based on this surrogate model, this invention calculates the sensitivity coefficients of 18 errors using the Sobol exponent method. Results show that radar angle measurement errors and photo-radar angle measurement errors have the greatest impact on the air-to-air missile interception probability. This invention's method shortens computation time while maintaining accuracy, providing a foundation for further sensitivity analysis.

[0006] The technical solution adopted by this invention to solve its technical problem includes the following steps:

[0007] Step 1: Construct a typical scenario for a closed-loop attack carried out by an aircraft;

[0008] Step 2: Determine the distribution of each error source in the mid-range guidance system and begin closed-loop attack simulation;

[0009] Step 3: Calculate the interception probability using the constructed interception probability calculation model and generate a dataset;

[0010] Step 4: Construct training and testing sets, train the PSO-SVR model, and verify its predictive performance;

[0011] Step 5: Use the trained prediction model to predict the interception probability and calculate the sensitivity coefficient using the Sobol exponent method.

[0012] Furthermore, the typical scenarios of closed-loop attack by the carrier aircraft in step 1 include: the initial position and speed of the carrier aircraft and the target, the missile launch distance, the magnitude and duration of missile thrust, the missile guidance method, and the target maneuvering method.

[0013] Furthermore, the various error sources in step 2 include: inertial navigation horizontal error, inertial navigation vertical error, inertial navigation heading angle error, inertial navigation attitude angle error, inertial navigation angular velocity error, inertial navigation horizontal velocity error, inertial navigation vertical velocity error, inertial navigation acceleration error, atmospheric pressure altitude error, optical-radar ranging error, optical-radar angle measurement error, radar ranging error, radar angle measurement error, radar velocity measurement error, ground data link ranging error, ground data link angle measurement error, ground data link velocity measurement error, and delay error.

[0014] Furthermore, step 3 specifically includes:

[0015] The target indication error is considered as a region near the target. The distance between the target and the center point of the seeker's field of view is treated as a random variable following a Gaussian distribution, with a mean of m and a root mean square of σ. Based on the characteristics of the Gaussian distribution, the target is distributed within a sphere with a radius of 3σ centered at the dispersion center. In this case, the seeker's field of view is a cone with the missile's instantaneous position as its vertex and the seeker antenna's half-beam width as its cone angle. When the target is within this cone, it is considered intercepted. m and σ are updated using statistical inference, and the interception probability is calculated using the following formula:

[0016] P0 = (2F(U1) - 1)(F(U2) - F(U3))

[0017] In the formula: d represents the range of the missile seeker's field of view projected onto the target plane, which is related to the target signal energy of the missile seeker receiver. When no target echo is received at all, d = 0.

[0018] Furthermore, step 4 specifically includes:

[0019] The intercept probability is predicted using machine learning support vector regression (SVR) and optimized using particle swarm optimization (PSO) to improve the prediction performance of SVR.

[0020] The particle swarm optimization algorithm treats all feasible solutions to the problem as a group of random particles in a multidimensional space, forming an optimization swarm. Each particle has its own position and velocity. Assuming there are n particles forming a swarm in the multidimensional space, the velocity and position of particle i are represented by V. i =(v i1 ,...,v in ), X i =(x i1 ,...,x in Let P i For the historical best value of the i-th particle, P g The optimal value is found for the swarm. The particles are iteratively updated multiple times, continuously updating the positions of the particles and the swarm's optimal value. The optimal solution is found by searching among these competing particles. The formula for each particle's iterative optimization of its velocity and position is as follows:

[0021] V i (t+1) =w v V i (t) +c1r1(P i (t) -X i (t) )+c2r2(P g(t) -X i (t) )

[0022] X i (t+1) =X i (t) +w p V i (t)

[0023] In the formula, V i (t) X i (t) Let r1 and r2 be the velocity and position of the i-th particle at iteration t, respectively; r1 and r2 are random parameters; c1 and c2 are learning factors; w v w p These are the velocity inertia weighting coefficient and the distance inertia weighting coefficient, respectively.

[0024] The support vector regression (SVR) is optimized using the particle swarm optimization algorithm. 80% of the dataset generated in step 3 is randomly selected as the training set, and the remaining 20% ​​is used as the test set.

[0025] SVR selects a Gaussian kernel function, specifically:

[0026] k(x i ,x)=exp(-||x i -x|| 2 / η 2 )

[0027] In the formula, η is the parameter of the Gaussian kernel function.

[0028] Furthermore, c1 = 1.5, c2 = 1.7; w v =0.8, w p =1; the particle swarm size is 40, and the number of iterations is 200.

[0029] Furthermore, in step 5, the sensitivity coefficient is calculated using the Sobol index method, which measures the relative importance of the input variables by distributing the total variance of the model output to each input variable and considering the interaction between the input variables.

[0030] Assume that the interception probability and error binding are described by the following functional relationship:

[0031] Y = g(x) x∈K n

[0032] g(x) can be decomposed into a set of functions with increasing dimension:

[0033]

[0034] The constant term g0 is the average value of the function. Where dx represents dx1,...,dx n

[0035]

[0036]

[0037] in Indicates division by x i The integral of all variables except those, Indicates division by x i and x j Integral of all parameters except those;

[0038] The total variance of the output is:

[0039]

[0040] Meanwhile, the total variance is decomposed into the following form:

[0041]

[0042] The variance in this formula is expressed as:

[0043]

[0044]

[0045] Where 1≤i1<... s ≤ns=1,...,n;

[0046] The Sobol index is defined as follows:

[0047]

[0048] The Sobol index method simultaneously calculates the first-order sensitivity coefficient of the input variable and the total effect coefficient; the first-order sensitivity coefficient is used only to quantify the contribution of a single input variable to the output variance, i.e. The total effect coefficient is used to quantify the total contribution of a given input parameter and its interactions to the variance. It includes both the contribution of the variable acting alone to the output variance and the contribution of the variable to the output variance due to its interaction with other variables in the system structure. Among them, S ～i It is the sum of the Sobol exponents without the parameter i.

[0049] The beneficial effects of this invention are as follows:

[0050] ​This invention takes into account errors in optical and radar systems, data link systems, and latency errors under real combat environments. The method described in this invention shortens computation time while maintaining accuracy, providing a foundation for further sensitivity analysis. Attached Figure Description

[0051] Figure 1 This is a flowchart of the method of the present invention;

[0052] Figure 2 This is a flowchart illustrating the process of estimating the target location distribution according to the present invention.

[0053] Figure 3 This is a schematic diagram of a missile intercepting a target according to an embodiment of the present invention;

[0054] Figure 4 This is a schematic diagram illustrating the missile interception probability calculation in an embodiment of the present invention;

[0055] Figure 5 This is a flowchart of the PSO-optimized SVR provided in an embodiment of the present invention;

[0056] Figure 6 This is a schematic diagram of the PSO-SVR prediction performance provided in an embodiment of the present invention. Detailed Implementation

[0057] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0058] This invention provides a support vector regression prediction model based on particle swarm optimization. This algorithm incorporates machine learning for training the prediction model. Furthermore, to improve the stability and accuracy of the prediction model, a metaheuristic algorithm is introduced to optimize the parameters of support vector regression, thereby enhancing the model's predictive ability. This invention replaces the original computational model with a PSO-SVR model and uses the Sobol exponent method to calculate the global sensitivity of each error.

[0059] To achieve the above objectives, the present invention adopts the following technical solution:

[0060] Step 1: Construct a typical scenario for a closed-loop attack carried out by an aircraft;

[0061] Step 2: Determine the distribution of each error source in the mid-range guidance system and begin closed-loop attack simulation;

[0062] Step 3: Calculate the interception probability using the constructed interception probability calculation model and generate a dataset;

[0063] Step 4: Construct training and testing sets, train the PSO-SVR model, and verify its predictive performance;

[0064] Step 5: Use the trained prediction model to predict the interception probability and calculate the sensitivity coefficient using the Sobol exponent method.

[0065] Furthermore, the typical scenario of closed-loop attack by the carrier aircraft in step 1 should include: the initial position and speed of the carrier aircraft and the target, the missile launch distance, the magnitude and duration of missile thrust, the missile guidance method, and the target maneuvering method.

[0066] Furthermore, the guidance error sources in step 2 include: inertial navigation horizontal error, inertial navigation vertical error, inertial navigation heading angle error, inertial navigation attitude angle error, inertial navigation angular velocity error, inertial navigation horizontal velocity error, inertial navigation vertical velocity error, inertial navigation acceleration error, atmospheric pressure altitude error, optical-radar ranging error, optical-radar angle measurement error, radar ranging error, radar angle measurement error, radar velocity measurement error, ground data link ranging error, ground data link angle measurement error, ground data link velocity measurement error, and delay error.

[0067] The attack scenario considered in this invention involves a data link where a ground information station transmits target information to the carrier aircraft. After receiving the target information transmitted from the ground, the carrier aircraft fuses it with target information detected by its airborne radar and optical radar systems, and then sends the fused target information to the missile. During mid-course guidance, the target data received by the missile experiences a delay; therefore, the missile extrapolates the target position using uniform linear motion to improve accuracy.

[0068] Furthermore, the interception probability calculation model in step 3 is a least squares method-based model for estimating the target location dispersion and interception probability. Specifically:

[0069] The target indication error is considered as a region near the target, and the distance of the target relative to the center point of the seeker's field of view is considered as a random variable following a Gaussian distribution, with a mean of m and a root mean square of σ. According to the characteristics of the Gaussian distribution, the target should be distributed within a sphere with a radius of 3σ centered at the dispersion center. In this case, the seeker's field of view can be considered as a cone with the missile's instantaneous position as its vertex and the seeker antenna's half-beamwidth as its cone angle. Only when the target is located within this cone can it be considered intercepted. Statistical inference is used to update m and σ. The formula for calculating the interception probability is as follows:

[0070] P0 = (2F(U1) - 1)(F(U2) - F(U3))

[0071] In the formula: d represents the range of the missile seeker's field of view projected onto the target plane, which is related to the target signal energy of the missile seeker's receiver. When no target echo is received at all, d = 0.

[0072] Furthermore, in step 4, machine learning support vector regression (SVR) is used to predict the intercept probability, and particle swarm optimization (PSO) is used to improve the prediction performance of SVR.

[0073] Particle swarm optimization (PSO) is a global optimization algorithm proposed by simulating the foraging process of bird flocks. It continuously searches for the optimal solution by utilizing the cooperation and communication between individuals.

[0074] The particle swarm optimization algorithm treats all feasible solutions to the problem as a group of random particles in a multidimensional space, forming an optimization swarm. Each particle has its own position and velocity. Assuming there are n particles forming a swarm in the multidimensional space, the velocity and position of particle i are represented by V. i =(v i1 ,...,v in ), X i =(x i1 ,...,x in Let P i For the historical best value of the i-th particle, P g The optimal value is found for the swarm. The particles are iteratively updated multiple times, continuously updating the positions of the particles and the swarm's optimal value. The optimal solution is found by searching among these competing particles. The formula for each particle's iterative optimization of its velocity and position is as follows:

[0075] V i (t+1) =w v V i (t) +c1r1(P i (t) -X i (t) )+c2r2(P g (t) -X i (t) )

[0076] X i (t+1) =X i (t) +w p V i (t)

[0077] In the above formula, V i (t) X i (t)Let r1 and r2 be the velocity and position of the i-th particle at iteration t, respectively; r1 and r2 are random parameters; c1 and c2 are learning factors; w v w p These are the velocity inertia weighting coefficient and the distance inertia weighting coefficient, respectively.

[0078] In the PSO algorithm, the choice of inertia weights is particularly important. Larger inertia weights help with global particle search, while smaller inertia weights help with local search.

[0079] In this invention, c1 = 1.5, c2 = 1.7; w v =0.8, w p =1; the particle swarm size is 40, and the number of iterations is 200.

[0080] SVR utilizes a kernel function to project the original data into a high-dimensional feature space and fits the data points to a suitable hyperplane, minimizing the error distance between the data points and the hyperplane, thereby achieving prediction of the original data points. However, the choice of two parameters in SVR significantly impacts its prediction performance. Therefore, this invention optimizes it using PSO, automatically selecting the optimal parameter values ​​during training. In step 3, 80% of the generated dataset is randomly selected as the training set, and the remaining 20% ​​is used as the test set.

[0081] SVR selects a Gaussian kernel function, specifically:

[0082] k(x i ,x)=exp(-||x i -x|| 2 / η 2 )

[0083] In the formula, η is the parameter of the Gaussian kernel function.

[0084] Furthermore, in step 5, the sensitivity coefficient is calculated using the Sobol index method, which measures the relative importance of the input variables by distributing the total variance of the model output to each input variable and considering the interaction between the input variables.

[0085] Assume that the interception probability and error binding can be described by the following functional relationship:

[0086] Y = g(x) x∈K n

[0087] g(x) can be decomposed into a set of functions with increasing dimension:

[0088]

[0089] The constant term g0 is the average value of the function. Where dx represents dx1,...,dxn .

[0090]

[0091]

[0092] in Indicates division by x i The integral of all other variables is similar. Indicates division by x i and x j The integral of all parameters except those.

[0093] The total variance of the output is:

[0094]

[0095] Meanwhile, the total variance can be decomposed into the following form:

[0096]

[0097] The variance in this formula can be expressed as:

[0098]

[0099]

[0100] Where 1≤i1<... s ≤ns=1,...,n.

[0101] The Sobol index is defined as follows:

[0102]

[0103] The Sobol index method simultaneously calculates the first-order sensitivity coefficient of the input variable and the total effect coefficient. The first-order sensitivity coefficient is used only to quantify the contribution of a single input variable to the output variance when it acts alone. The total effect index is used to quantify the total contribution of a given input parameter and its interactions to the variance. It includes both the contribution of the variable acting alone to the output variance and the contribution of the variable due to its interaction with other variables in the system structure. Among them, S ～i It is the sum of the Sobol exponents without the parameter i.

[0104] Because the first-order sensitivity coefficient and the total effect coefficient do not have special requirements on the type and form of the function, they are widely applicable.

[0105] Example:

[0106] ​An air-to-air missile is a missile launched from an aircraft to attack aerial targets. To achieve beyond-visual-range (BVR) attacks, an air-to-air missile must employ a composite guidance mechanism. During the mid-course guidance phase, the aircraft periodically transmits target motion parameters to the missile via data link; in terminal guidance, the missile uses its onboard radar to detect the target, eliminating the need for target data from the aircraft.

[0107] like Figure 1 This invention discloses a PSO-SVR-based air-to-air missile intercept probability prediction model and performs sensitivity analysis using this model, including the following steps:

[0108] Step 1: Construct a typical scenario for a closed-loop attack on a carrier aircraft.

[0109] The constructed closed-loop attack scenario should initialize the following information: the initial position and velocity of the carrier aircraft and the target, the missile launch distance, the missile thrust magnitude and duration, the missile guidance method, and the target maneuvering method.

[0110] Step 2: Determine the distribution of each error source in the mid-range guidance system and begin closed-loop attack simulation.

[0111] The guidance errors of this invention include: inertial navigation horizontal error, inertial navigation vertical error, inertial navigation heading angle error, inertial navigation attitude angle error, inertial navigation angular velocity error, inertial navigation horizontal velocity error, inertial navigation vertical velocity error, inertial navigation acceleration error, atmospheric pressure altitude error, optical-radar ranging error, optical-radar angle measurement error, radar ranging error, radar angle measurement error, radar velocity measurement error, ground data link ranging error, ground data link angle measurement error, ground data link velocity measurement error, and delay error.

[0112] Assuming that all errors follow a Gaussian distribution with a mean of 0, the standard deviations of each error are randomly initially bound during the simulation. The bound ranges of the standard deviations of each error are shown in Table 1 below:

[0113] Table 1

[0114] Inertial navigation horizontal error (m) [5-100] Inertial navigation vertical error (m) [5-100] Inertial navigation heading angle error (deg) [0.02-0.15] Inertial navigation attitude angle error (deg) [0.01-0.1] Inertial navigation angular velocity error (deg / s) [0.01-0.1] Inertial navigation horizontal velocity error (m / s) [0.2-2] Inertial navigation vertical velocity error (m / s) [0.2-2] <![CDATA[INS acceleration error (m / s 2 )]]> [0.1-1] Atmospheric pressure altitude error (m) [5-50] Lightning ranging error (m) [10-50] Lightning angle measurement error (mrad) [1.5-2] Radar ranging error (m) [50-150] Radar angle measurement error (mrad) [2-4] Radar velocity measurement error (m / s) [2-10] Ground data link ranging error (m) [10-50] Ground data link angular measurement error (mrad) [1-3] Ground data link velocity measurement error (m / s) [2-5] Delay error (ms) [5-15]

[0115] Step 3: Calculate the interception probability using the constructed interception probability calculation model and generate a dataset.

[0116] This invention employs a target location dispersion estimation interception probability calculation model based on the least squares method to calculate the initial interception probability. The target dispersion estimation flowchart is as follows: Figure 2 As shown.

[0117] like Figure 3 As shown, when the missile seeker is activated, the missile is considered to have successfully acquired the target if the target is in the shadowed area. Therefore, the acquisition probability can be obtained by integrating the shadowed area. To simplify the integration, the missile's field of view projection is replaced with a square of the same area for integration, as shown below. Figure 4 As shown. Based on the least squares method estimation model for target location dispersion and interception probability calculation, the calculated interception probability is:

[0118] P0 = (2F(U1) - 1)(F(U2) - F(U3))

[0119] In the formula: d represents the range of the missile seeker's field of view projected onto the target plane, which is related to the target signal energy of the missile seeker receiver. When no target echo is received, d = 0; m and σ are the estimated target position mean and root mean square error, respectively.

[0120] Step 4: Construct training and testing sets, train the PSO-SVR model, and verify its predictive performance.

[0121] like Figure 5 As shown, the PSO-SVR model mainly consists of two parts: training and prediction. The model uses the magnitude of each error as the independent variable and the intercept probability as the dependent variable. During the training phase, the parameters of the SVR model are optimized using the training set data. The purpose of the prediction phase is to predict the intercept probability using the trained SVR model and compare the prediction results with the test set.

[0122] For the test set and training set, the PSO-SVR model performs as follows: Figure 6 As shown. RMSE, MAE, and R are used. 2 Using MAPE as an evaluation index, the model prediction results are analyzed in Table 2 below:

[0123] Table 2

[0124] training set 0.027852 0.022917 0.9617 3.3542 test set 0.040405 0.027818 0.9256 4.1406

[0125] The evaluation metrics show that the PSO-SVR model has high prediction accuracy and can be used as a surrogate model for the sensitivity analysis in step 5.

[0126] Step 5: Using the pre-trained prediction model, calculate the sensitivity coefficient using the Sobol exponent method.

[0127] When using the Sobol exponent method for sensitivity analysis, if the specific form of the analysis function is known, it can be directly calculated analytically. However, the reception probability solved in this invention does not have a specific functional form; therefore, the Monte Carlo method is required for calculation during sensitivity analysis. To address the problems of uneven sampling, large sample sizes, and high time consumption associated with traditional random sampling, this invention employs the high-quality Sobol sampling method to improve fitting accuracy.

[0128] Using the PSO-SVR model as a surrogate model, global sensitivity analysis was performed through SOBO sampling. The calculation results of each error sensitivity coefficient are shown in Table 3 below.

[0129] Table 3

[0130] First-order sensitivity coefficient 0.018 0.015 0.001 0.0486 0.003 0.005 0.0044 0.004 0.014 Total effect coefficient 0.026 0.024 0.004 0.056 0.008 0.01 0.005 0.008 0.022 error R10 R11 R12 R13 R14 R15 R16 R17 R18 First-order sensitivity coefficient 0.054 0.188 0.077 0.17 0.015 0.081 0.14 0.033 0.011 Total effect coefficient 0.06 0.192 0.09 0.172 0.018 0.1 0.15 0.04 0.015

[0131] Where: R1 is the inertial navigation horizontal error; R2 is the inertial navigation vertical error; R3 is the inertial navigation heading angle error; R4 is the inertial navigation attitude angle error; R5 is the inertial navigation angular velocity error; R6 is the inertial navigation horizontal velocity error; R7 is the inertial navigation vertical velocity error; R8 is the inertial navigation acceleration error; R9 is the atmospheric pressure altitude error; R10 is the optical-radar ranging error; R11 is the optical-radar angle measurement error; R12 is the radar ranging error; R13 is the radar angle measurement error; R14 is the radar velocity measurement error; R15 is the ground data link ranging error; R16 is the ground data link angle measurement error; R17 is the ground data link velocity measurement error; and R18 is the delay error.

Claims

1. A sensitivity analysis method for air-to-air missile interception probability based on a surrogate model, characterized in that, The steps include the following: Step 1: Construct a typical scenario for a closed-loop attack carried out by an aircraft; Step 2: Determine the distribution of each error source in the mid-range guidance system and begin closed-loop attack simulation; Step 3: Calculate the interception probability using the constructed interception probability calculation model and generate a dataset; Step 3 specifically involves: Treating the target indication error as a region near the target, and considering the distance of the target relative to the center point of the seeker's field of view as a random variable following a Gaussian distribution, let its mean be... m The mean squared error is Based on the characteristics of the Gaussian distribution, the target is distributed in a circle centered at the scattering center. Within a sphere with radius [radius value], the seeker's field of view is a cone with the missile's instantaneous position as its apex and the seeker antenna's half-beam width as its cone angle; when the target is located within this cone, it is considered intercepted; updates are made using statistical inference. m and The formula for calculating the interception probability is as follows: In the formula: ; ; ; ; d The range of the missile seeker's field of view projected onto the target plane is related to the target signal energy of the missile seeker's receiver. When no target echo is received at all... ; Step 4: Construct training and testing sets, train the PSO-SVR model, and verify its predictive performance; Step 5: Use the trained prediction model to predict the interception probability and calculate the sensitivity coefficient using the Sobol exponent method.

2. The method for sensitivity analysis of air-to-air missile interception probability based on a surrogate model according to claim 1, characterized in that, The typical scenarios for closed-loop attack by the carrier aircraft in step 1 include: the initial position and speed of the carrier aircraft and the target, the missile launch distance, the magnitude and duration of missile thrust, the missile guidance method, and the target maneuvering method.

3. The method for sensitivity analysis of air-to-air missile interception probability based on a surrogate model according to claim 2, characterized in that, The various error sources in step 2 include: inertial navigation horizontal error, inertial navigation vertical error, inertial navigation heading angle error, inertial navigation attitude angle error, inertial navigation angular velocity error, inertial navigation horizontal velocity error, inertial navigation vertical velocity error, inertial navigation acceleration error, atmospheric pressure altitude error, optical-radar ranging error, optical-radar angle measurement error, radar ranging error, radar angle measurement error, radar velocity measurement error, ground data link ranging error, ground data link angle measurement error, ground data link velocity measurement error, and delay error.

4. The method for sensitivity analysis of air-to-air missile interception probability based on a surrogate model according to claim 3, characterized in that, Step 4 specifically involves: The intercept probability is predicted using machine learning support vector regression (SVR) and optimized using particle swarm optimization (PSO) to improve the prediction performance of SVR. The particle swarm optimization algorithm treats all feasible solutions to the problem as a group of random particles in a multidimensional space, forming an optimization swarm; each particle has its own position and velocity; assuming there are... Individual particles constitute a group; particles The velocity and position are respectively expressed as , ;set up For the first The historical best value for each particle, The optimal value is found for the swarm. The particles are iteratively updated multiple times, continuously updating the positions of the particles and the swarm's optimal value. The optimal solution is found by searching among these competing particles. The formula for each particle's iterative optimization of its velocity and position is as follows: In the formula, , The first Individual particles Velocity and position at the next iteration; , The parameter is random. , For learning factors; These are the velocity inertia weighting coefficient and the distance inertia weighting coefficient, respectively. The support vector regression (SVR) is optimized using the particle swarm optimization algorithm. 80% of the dataset generated in step 3 is randomly selected as the training set, and the remaining 20% ​​is used as the test set. SVR selects a Gaussian kernel function, specifically: In the formula, These are the parameters of the Gaussian kernel function.

5. The method for sensitivity analysis of air-to-air missile interception probability based on a surrogate model according to claim 4, characterized in that, The , ; The particle swarm size is 40, and the number of iterations is 200.

6. The method for sensitivity analysis of air-to-air missile interception probability based on a surrogate model according to claim 5, characterized in that, In step 5, the sensitivity coefficient is calculated using the Sobol index method, which measures the relative importance of the input variables by distributing the total variance of the model output to each input variable and considering the interaction between the input variables. Assume that the interception probability and error binding are described by the following functional relationship: Decompose into a set of functions with increasing dimension: constant term It is the average value of the function. ,in express in Indicates except The integral of all variables except those, Indicates except and Integral of all parameters except those; The total variance of the output is: Meanwhile, the total variance is decomposed into the following form: The variance in this formula is expressed as: in ; The Sobol index is defined as follows: The Sobol index method simultaneously calculates the first-order sensitivity coefficient of the input variable and the total effect coefficient. The first-order sensitivity coefficient is used only to quantify the contribution of a single input variable to the output variance, i.e. ; The total effect coefficient is used to quantify the total contribution of a given input parameter and its interactions to the variance. It includes both the contribution of the variable acting alone to the output variance and the contribution of the variable to the output variance due to its interaction with other variables in the system structure. ,in, It does not contain parameters i The sum of the Sobol exponents.

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