An interception point and interception time prediction method for penetration decision

Abstract

The application is a kind of interception point and interception time prediction method for penetration decision. It includes: establishing a three-dimensional attack and defense combat mathematical model; constructing a concentric double-layer spherical shell detectable threat area; constructing a geometric hierarchical training sample set; generating the initial position and direction of the approaching aircraft, constructing the training subset through hierarchical sampling of the generated initial data, configuring the corresponding weight for the sample, forming the initial conditions of the three-dimensional attack and defense combat simulation, under each group of initial combat state, calling the three-dimensional attack and defense combat mathematical model for numerical calculation to obtain the corresponding real interception point and interception time; training the joint regression prediction model according to the generated simulation data. The application can reduce the dependence of the prediction model on the fixed global coordinate system, avoid the problems of large sample size and uneven sample distribution caused by unconstrained space prediction, improve the prediction stability and online calling efficiency under different deployment positions, and help the maneuverable aircraft to make avoidance decisions in advance before interception.

Description

Technical Field

[0001] This invention belongs to the technical fields of aircraft information support, offensive and defensive combat situation prediction, machine learning modeling and penetration decision support, and specifically relates to a method for predicting interception points and interception time for penetration decision-making. Background Technology

[0002] In modern air defense and anti-missile systems, the detection, tracking, and hit accuracy of incoming interceptor missiles are constantly improving, posing a serious threat to the penetration of attack missiles. If the attack missile can acquire the spatial status of the interceptor missile in a timely manner after it enters the effective threat range, and predict the future rendezvous position and time of the two, it can provide important information for triggering evasive maneuvers, selecting maneuver directions, and replanning its trajectory online. Among these, the predetermined interception point can clearly identify the spatial location where the attack missile is vulnerable to interception, which can be used to delineate danger zones, determine the direction of the threat, and assist in selecting evasive maneuver strategies; the predetermined interception time can reflect the remaining time margin available for maneuver evasion, providing a reference for maneuver triggering timing, overload distribution, and online replanning. Therefore, the prediction of the interception point and interception time is a core issue in the front-end information support link of penetration decision-making.

[0003] However, existing data-driven interception prediction methods still have the following shortcomings when applied to penetration decision-making:

[0004] (1) Insufficient spatial generalization ability: Some data-driven prediction methods directly use the absolute positions of attack missiles and interceptor missiles in the global coordinate system as model inputs. The model can easily learn the coordinate distribution characteristics of the training samples in a fixed airspace. When the combat airspace moves as a whole, the deployment position of the attack missiles changes, or the prediction scenario exceeds the original training airspace, the distribution of input data is prone to shift, resulting in a decrease in prediction accuracy and making it difficult to meet the online penetration prediction requirements under different deployment positions.

[0005] (2) Lack of effective constraints on the prediction space: If the relative spatial range of the interceptor missile may be limited, the problem of predicting the interception point and interception time will face an approximately unbounded three-dimensional space. In this case, in order to cover a sufficient number of incoming directions, range layers and intersection states, a large number of simulation samples need to be generated, which can easily lead to an excessively large sample size, increased training costs and increased difficulty in model learning, which is not conducive to building a usable prediction model.

[0006] (3) Uneven distribution of three-dimensional samples: When generating samples in a three-dimensional sphere or shell region, the sample coverage of different distance layers, azimuth angles and elevation angles is often uneven. If ordinary latitude and longitude grid sampling or simple random sampling is used directly, it is easy to have problems such as excessively dense samples in some areas and insufficient samples in others, which makes the model not learn sufficiently in undersampled areas, and thus produces large local prediction errors and extreme errors.

[0007] (4) Insufficient joint prediction capability of interception point and interception time: Some existing data-driven prediction methods usually focus on single target prediction, such as only predicting the location of the interception point or only predicting the remaining interception time, failing to fully utilize the inherent relationship between the spatial location of the interception point and the interception time. For attack missile penetration missions, both the interception point and the interception time jointly determine the effectiveness of danger zone construction, avoidance triggering, and online replanning. If the two are modeled separately, it is easy to underutilize the coupling relationship between spatial threat information and time margin information, affecting the integrity of penetration decision information.

[0008] Therefore, there is an urgent need for a method to predict interception points and interception times for penetration decision-making. Under the condition that the information support platform detects incoming interceptor missiles, it should be able to limit the prediction space through physical constraints, improve the spatial generalization ability by utilizing relative states, and improve the prediction stability through reasonable data generation and training strategies. This would provide reliable spatial threat information and time margin information for the early avoidance and online replanning of attack missiles. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of existing interception point and interception time prediction methods, such as fixed global coordinate dependence, excessively large sample size due to unconstrained prediction space, uneven distribution of three-dimensional samples, and insufficient joint prediction capability of interception point and interception time. This invention provides an interception point and interception time prediction method for penetration decision-making. This method achieves the prediction of interception point and interception time through centralized relative state modeling of maneuvering aircraft, concentric double-layered spherical shell detectable threat domain constraints, geometric hierarchical sampling, and a joint regression prediction model.

[0010] The technical solution for achieving the objective of this invention is: a method for predicting interception points and interception times for penetration decision-making, characterized by comprising the following steps:

[0011] Step (1): Establish a three-dimensional offensive and defensive combat mathematical model: Define the position vector, velocity vector and motion constraints of the maneuvering aircraft, the incoming approaching aircraft and the target point in three-dimensional space, establish a three-dimensional kinematic model of the maneuvering aircraft and the incoming approaching aircraft, set the guidance laws of the maneuvering aircraft flying towards the target point and the incoming approaching aircraft flying towards the maneuvering aircraft respectively, and form a three-dimensional offensive and defensive combat mathematical model to describe the relative motion relationship between the two sides;

[0012] Step (2): Construct a concentric double-layered spherical shell detectable threat domain: Define the spatial region within the effective prediction range of the approaching aircraft by the inner boundary radius and the outer boundary radius, so that the prediction task is transformed from an approximately unbounded space into a finite domain prediction problem with detection conditions and penetration decision significance;

[0013] Step (3): Construct a geometrically layered training sample set: Generate the initial position and direction of the approaching aircraft by Fibonacci spherical sampling in the concentric double-layered spherical shell prediction constraint domain according to different radius layers, and construct a training subset by layered sampling of the generated initial data and configure corresponding weights for the samples. Then, combine the training subset of the approaching aircraft with the speed, yaw angle and pitch angle state variables of the maneuvering aircraft to form the initial conditions of the three-dimensional attack and defense combat simulation. In each initial combat state, call the three-dimensional attack and defense combat mathematical model established in step (1) to perform numerical calculation to obtain the corresponding real interception point and interception time, which will be used as the data label for subsequent joint regression prediction model training and verification.

[0014] Step (4): Train a joint regression prediction model based on the generated simulation data: take the relative state features as input, and the relative displacement of the interception point and the interception time as output, train a prediction model that includes a shared feature extraction backbone and multiple regression heads, and use the trained prediction model to predict the interception point and interception time.

[0015] Compared with the prior art, the significant advantages of this invention are:

[0016] (1) Strong spatial generalization ability: This invention adopts the centralized relative state input of the maneuvering aircraft, which reduces the model's dependence on the fixed global coordinate system and specific training airspace, and makes the model pay more attention to the relative geometric relationship between the attacker and defender.

[0017] (2) The prediction space has physical constraints: By constructing a concentric double-layer spherical shell detectable threat domain, this invention limits the prediction of interception points and interception time to a limited space that meets the sensor detection conditions and the significance of penetration decision-making, thus avoiding the problem of uncontrollable sample size caused by unbounded space prediction.

[0018] (3) More balanced sample coverage: Through Fibonacci spherical sampling, geometric hierarchical sampling and weight correction mechanism, this invention can improve the sample distribution balance under different distance layers and incoming directions, alleviate the problem of insufficient learning in undersampled regions, and further reduce the sample size.

[0019] (4) Fast online prediction speed: The joint regression prediction model after training can directly output the predicted interception point and the predicted interception time from the current relative state. It is suitable for repeated calls under continuous observation and update conditions, providing information support for danger zone judgment and trigger avoidance. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of a three-dimensional attack and defense combat simulation of the present invention.

[0021] Figure 2 This is a schematic diagram of the detectable threat domain of the concentric double-layered spherical shell of the present invention.

[0022] Figure 3 This is a schematic diagram of the online prediction and re-prediction process of the present invention.

[0023] Figure 4 This is a three-dimensional error distribution diagram of the present invention. Detailed Implementation

[0024] The present invention will now be described in further detail with reference to the accompanying drawings.

[0025] To achieve the above objectives, the technical solution adopted by the present invention is as follows: a method for predicting interception points and interception times for penetration decision-making, comprising the following steps:

[0026] Step (1-1): Define the three-dimensional combat objects

[0027] Three types of combat targets are defined: maneuvering aircraft, incoming approaching aircraft, and target points. Maneuvering aircraft are those performing penetration missions, incoming approaching aircraft are those intercepting maneuvering aircraft, and target points are the predetermined locations to be struck or reached by maneuvering aircraft. The position vectors of maneuvering aircraft, incoming approaching aircraft, and target points in a three-dimensional inertial coordinate system are defined, as well as the velocity vectors, velocity magnitudes, yaw angles, pitch angles, and maximum maneuvering acceleration state variables of maneuvering aircraft and incoming approaching aircraft.

[0028] Steps (1-2): Establish a three-dimensional kinematic model, guidance laws, and motion constraints.

[0029] Establish kinematic models of the maneuvering aircraft and the approaching aircraft in three-dimensional space, and describe the changes in position, velocity direction, and velocity magnitude of the maneuvering aircraft and the approaching aircraft over time, respectively. Their expressions are as follows:

[0030] Approaching aircraft m against maneuvering aircraft t

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] Maneuvering aircraft t against ground target g

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] in, and These represent the speeds of the approaching aircraft and the maneuvering aircraft, respectively. and These represent the pitch angles of the approaching aircraft and the maneuvering aircraft, respectively. and These represent the yaw angles of the approaching aircraft and the maneuvering aircraft, respectively. and These represent the normal acceleration commands in the pitch direction for the approaching aircraft and the maneuvering aircraft, respectively. and These represent the normal acceleration commands in the yaw direction for the approaching aircraft and the maneuvering aircraft, respectively. , , These represent the first-order time derivatives of the coordinates of the positions corresponding to the approximate positions of the aircraft; , , These represent the first-order time derivatives of the position coordinates of the attack missile; This indicates the rate of change of velocity of approaching aircraft and attack missiles.

[0045] The guidance laws for the maneuvering vehicle flying towards the target point and the guidance laws for the approaching vehicle flying towards the maneuvering vehicle are defined: Guidance commands are calculated based on the spatial geometric relationships between the maneuvering vehicle, the approaching vehicle, and the target point, and the velocity directions of the maneuvering vehicle and the approaching vehicle are updated in conjunction with the maximum maneuvering acceleration constraint. The expressions are as follows:

[0046]

[0047]

[0048]

[0049]

[0050] in, This represents the relative position vector between the approaching aircraft and the maneuvering aircraft. This represents the relative velocity vector between the approaching aircraft and the maneuvering aircraft. This represents the line-of-sight angular velocity vector; Indicates the closing velocity; Indicates the proportional guidance coefficient; This indicates the desired acceleration command generated by proportional guidance. This indicates the normal acceleration command that the approaching aircraft will actually receive. This represents the unit vector indicating the velocity direction of the approaching aircraft. Represents a three-dimensional identity matrix; The Euclidean norm of a vector; This indicates transpose.

[0051] Step (2) is as follows:

[0052] Step (2-1): Determine the center of the sphere in the prediction constraint domain

[0053] A three-dimensional spherical shell region is established with the current location of the maneuvering aircraft as the center to limit the effective prediction range of the approaching aircraft.

[0054] Step (2-2): Determine the inner boundary of the prediction constraint domain

[0055] inner boundary radius Determine the inner boundary of the prediction constraint domain for the concentric double-layered spherical shell. The radius of the inner boundary... This is used to characterize the minimum safe distance required for a maneuvering aircraft to perform an effective evasive maneuver; when the distance between the approaching aircraft and the maneuvering aircraft is less than the inner boundary radius, the maneuvering aircraft has insufficient time and space margin to perform an evasive maneuver.

[0056] Step (2-3): Determine the outer boundary of the prediction constraint domain

[0057] Outer boundary radius Determine the outer boundary of the prediction constraint domain for the concentric double-layered spherical shell. The radius of the outer boundary... Used to characterize the maximum effective distance that has predictive and penetration decision significance under the detection conditions of the information support platform; when the distance between the approaching aircraft and the maneuvering aircraft is greater than the outer boundary radius, the direct effect of the prediction result on the current evasion decision is reduced, and unconstrained prediction will lead to an increase in sample size.

[0058] Steps (2-4): Formulating a finite field prediction problem

[0059] The inner boundary radius and outer boundary radius By jointly defining the spatial region within the effective prediction range of the approaching aircraft, the task of predicting the interception point and interception time is transformed from an approximately unbounded spatial prediction problem into a finite domain prediction problem with information support for detection conditions and penetration decision-making significance.

[0060] Step (3) is as follows:

[0061] Step (3-1): Divide the spherical shell into radial layers

[0062] Within the concentric double-layered spherical shell prediction constraint domain, based on the inner boundary radius... and outer boundary radius By setting multiple radius layers, a set of radii can be obtained:

[0063]

[0064] in, Indicates the first One radius layer, Indicates the number of radius layers.

[0065] Step (3-2): Generate the initial spatial position of the approaching aircraft.

[0066] Spherical orientation points are generated at each radius layer using the Fibonacci spherical sampling method. Based on these spherical orientation points and the corresponding radius layer, the initial position of the approaching aircraft relative to the maneuvering aircraft is determined, thus obtaining an initial spatial distribution sample of the approaching aircraft covering different distance layers and different directions of attack. The orientation points at one layer are numbered... The sampling expression for the i-th point is generated sequentially:

[0067]

[0068]

[0069]

[0070]

[0071] in For axial coordinates, For plane radius, It is the azimuth angle. To find the golden angle, calculate the direction vector of the i-th sampling point as follows:

[0072]

[0073] From the position of our maneuvering aircraft in the inertial coordinate system, we can calculate the initial position coordinates of the approaching aircraft, as well as the yaw and pitch angles pointing towards the maneuvering aircraft.

[0074] Step (3-3): Construct a balanced training subset and configure sample weights

[0075] For any given radius layer, divide the spherical shell containing it into multiple smaller units according to the binning rules for azimuth and elevation angles. For any given smaller unit, count the original number of samples within that unit, and then randomly select 20 samples from that unit to obtain the number of subset samples corresponding to that unit.

[0076]

[0077] Then calculate the ratio of the parent set to the subset set. Define the weights of the training samples, where This represents the total number of samples in this layer.

[0078] Step (3-4): Establishing initial conditions for three-dimensional attack and defense combat simulation

[0079] Based on the initial position of the approaching aircraft, the range and interval of values ​​for the maneuvering aircraft's speed, yaw angle, pitch angle, and the approaching aircraft's speed are set. The expression is:

[0080]

[0081]

[0082]

[0083]

[0084] in, Indicates the speed of a maneuvering aircraft; and These represent the minimum and maximum values ​​of the speed of the maneuvering aircraft, respectively. Indicates the speed sampling interval of the maneuvering aircraft; This indicates the speed of the approaching aircraft. and These represent the minimum and maximum values ​​of the speed of the approaching aircraft, respectively. This indicates the sampling interval for the speed of the approaching aircraft; Indicates the yaw angle of a maneuvering aircraft; and These represent the minimum and maximum values ​​of the yaw angle of the maneuvering aircraft, respectively. Indicates the yaw angle sampling interval of the maneuvering aircraft; Indicates the pitch angle of a maneuvering aircraft; and These represent the minimum and maximum values ​​of the pitch angle of the maneuvering aircraft, respectively. This indicates the pitch angle sampling interval of the maneuvering aircraft.

[0085] The speed, yaw angle, pitch angle, and speed of the approaching aircraft obtained from the discrete values ​​are combined with the initial position of the approaching aircraft generated in step (3-3) to form multiple sets of initial conditions for three-dimensional attack and defense combat simulation. Each set of initial conditions for three-dimensional attack and defense combat simulation includes the initial position of the maneuvering aircraft, the initial velocity vector of the maneuvering aircraft, the initial position of the approaching aircraft, and the initial velocity vector of the approaching aircraft.

[0086] Steps (3-5): Generate actual interception points and actual interception time tags.

[0087] In each initial engagement state, a three-dimensional attack and defense engagement simulation model is invoked to numerically simulate the motion process of the maneuvering aircraft and the approaching aircraft until the preset rendezvous criteria are met. The spatial position corresponding to the rendezvous moment is recorded as the actual interception point, and the time from the initial moment of the simulation to the rendezvous moment is recorded as the actual interception time. The actual interception point and the actual interception time are used as data labels for the subsequent training and verification of the joint regression prediction model.

[0088] Steps (3-6): Organize the training samples for the joint regression prediction model

[0089] The initial conditions and corresponding simulation outputs of each group of three-dimensional attack and defense combat simulations are organized to construct the input-output sample pairs of the joint regression prediction model. For the initial combat state of group (i), the relative position vector of the incoming approaching aircraft relative to the maneuvering aircraft is calculated based on the initial position of the maneuvering aircraft and the initial position of the approaching aircraft:

[0090]

[0091] The relative position vector, the speed of the maneuvering aircraft and the approaching aircraft, the yaw angle and pitch angle of the maneuvering aircraft and the approaching aircraft, the relative displacement of the actual interception point and the actual interception time obtained by the three-dimensional attack and defense combat simulation model in step (3-4), and the corresponding sample weights are associated and stored to form a dataset for training and validation of the joint regression prediction model.

[0092] Step (4) is as follows:

[0093] Step (4-1): Determine the input and output of the joint regression prediction model.

[0094] The relative state feature vector, velocity, and angle information obtained in steps (3-6) are used as inputs to the joint regression prediction model, and the relative displacement of the interception point and the interception time are used as outputs of the joint regression prediction model.

[0095] Step (4-2): To reduce the impact of differences in the dimensions and numerical ranges of different physical quantities on model training, the input features and output labels are normalized, and the expression is as follows:

[0096] enter:

[0097] Output:

[0098] in Represents the original input features; Indicates the original output label; The standard deviation of each column of the input feature on the training set; The input feature is the mean of each column in the training set; To output the standard deviation of each column of the feature on the training set; This is to output the mean of each column of the feature on the training set.

[0099] Step (4-3): Construct the ResNet-MLP shared feature extraction backbone

[0100] The ResNet residual structure preserves the low-level physical information in the input, and learns higher-level feature representations through hierarchical mapping of multiple residual blocks. The specific expression is as follows:

[0101]

[0102]

[0103]

[0104]

[0105] in, Indicates the first One residual block; Indicates the first Input features of each residual block; and They represent the first Features of the first and second fully connected layers in a residual block; and They represent the first The weight matrix of the two fully connected layers in each residual block; and These represent the bias vectors of the corresponding fully connected layers; and These represent the intermediate features after nonlinear transformation and regularization, respectively. Presentation layer normalization operation; Represents the activation function of the Gaussian error linear unit; This indicates a random deactivation operation.

[0106] To implement residual connections, the shortcut branch mapping expression is defined as follows:

[0107]

[0108] in, Indicates the first Shortcut branch mapping results for each residual block; Indicates the first Input features of each residual block; and They represent the first Layer and first The feature dimension of the layer; Indicates the first Linear projection weight matrix of shortcut branches in each residual block; The bias vector represents the shortcut branch. Finally, the first... The output of the layer residual block is represented as:

[0109]

[0110] Step (4-4): Constructing the multi-output MLP regression head

[0111] Based on the shared features, the network employs a multi-head regression structure to jointly predict four continuous targets. Its specific expression is:

[0112]

[0113]

[0114] in, Indicates the first The hidden layer of the regression head outputs features; Indicates the first Prediction results for each output variable; and They represent the first The weight matrices of the hidden and output layers in the regression head; and These represent the bias vectors of the corresponding layers; This represents the feature vector output from the shared feature extraction backbone; finally, the outputs of the four regression heads are concatenated to obtain a four-dimensional prediction vector.

[0115]

[0116] in, This represents the four-dimensional prediction vector output by the joint regression prediction model; , , These represent the components of the predicted relative displacement of the interception point in the x, y, and z directions, respectively. This indicates the predicted interception time.

[0117] Step (4-5): Construct the joint regression loss function

[0118] MLP learns the relationship between input data and target output, adjusts the weights and biases between neurons in each layer to approximate complex functions, and achieves effective prediction of the target variable. Its expression is:

[0119]

[0120] in, Indicates the first The weighted joint regression loss corresponding to each sample; Indicates the total number of training samples; Indicates the first The weight coefficients corresponding to each sample; Indicates the first The sample at the th Model predictions on each output dimension; Indicates the first The sample at the th The true label values ​​in each output dimension; Indicates the dimension index of the output variable; This represents the output dimension index in the loss calculation. The chain rule is then used to calculate the gradient of the loss with respect to each parameter, and the parameters are updated using an optimization algorithm. Its expression is:

[0121]

[0122] in, This represents the joint regression loss function; Represents the set of network parameters; This represents the gradient of the loss function with respect to the network parameters; This represents the gradient of the loss function with respect to the model output; This represents the gradient of the model output with respect to the network parameters.

[0123] Steps (4-6): Training the joint regression prediction model

[0124] Based on input features, output labels, and a weighted joint regression loss function, the ResNet-MLP joint regression prediction model is trained, updating the network parameters in the shared feature extraction backbone and multiple MLP regression heads. When the training loss meets a preset convergence condition or reaches a preset number of training epochs, the trained joint regression prediction model is saved. This model is used to output the predicted relative displacement of the interception point and the predicted interception time based on the current relative state between the maneuvering aircraft and the approaching aircraft.

[0125] Example

[0126] To verify the feasibility and predictive effectiveness of the proposed interception point and interception time prediction method for penetration decision-making, a three-dimensional attack-defense combat simulation embodiment was constructed. In this embodiment, the maneuvering aircraft, the approaching aircraft, and the target point are all located in a three-dimensional inertial coordinate system, and the initial position of the maneuvering aircraft is set... The target point location is set to The speed of the maneuvering aircraft is set... to Within range and with Set the value interval and the speed of the approaching aircraft. Both the maneuvering aircraft and the approaching aircraft are updated according to a three-dimensional kinematic model, and the simulation time step is set to... .

[0127] During the simulation sample generation process, a concentric double-layered spherical shell prediction constraint domain is first constructed with the current position of the maneuvering aircraft as the center. The inner boundary radius of this prediction constraint domain is taken as... The outer boundary radius is taken as Spherical orientation points are generated at each radius layer using the Fibonacci spherical sampling method. The golden ratio is used. The corresponding golden angle is Based on the mother sample Divide the sample into discrete units .in , , respectively , and Equal width angle division, unit setting The number of parent samples is Twenty samples are randomly selected from each unit, and corresponding weights are calculated for each sample in each unit. The yaw angle of the maneuvering aircraft is set at... to Within range and with Set the value interval, and set the pitch angle to... to Within range and with By setting value intervals, the initial position of the approaching aircraft is combined with the state variables of the maneuvering aircraft's speed, yaw angle, pitch angle, and the speed of the approaching aircraft to form the initial conditions for simulation. The interception time and interception point are calculated using a three-dimensional attack-defense combat simulation model, thereby obtaining data labels for subsequent training and validation of the joint regression prediction model.

[0128] In this embodiment, the shared feature extraction backbone in the ResNet-MLP network structure adopts a five-layer progressive dimensionality reduction residual network structure, with the network size as follows: 9→256→128→64→32→16.

[0129] Each residual module consists of two fully connected layers, employing Layer Normalization, GELU activation, and Dropout for feature transformation. After a shared feature extraction backbone, a 16-dimensional high-level feature vector is obtained, which is then input into four independent regression heads. Each regression head uses a 16→32→1 multilayer perceptron structure. The four regression heads are used to predict:

[0130] (1) Predict the X-direction component of the relative displacement of the interception point;

[0131] (2) Predict the Y-direction component of the relative displacement of the interception point;

[0132] (3) Predict the Z-direction component of the relative displacement of the interception point;

[0133] (4) Predict the interception time.

[0134] During training, weighted mean squared error was used as the loss function, where the sample weights were derived from the weight coefficients obtained during the geometric stratified training subset construction phase. The AdamW optimization algorithm was used for parameter updates during model training, with an initial learning rate of 0.001, a batch size of 1024, and 300 training epochs. A joint regression prediction model was obtained after training.

[0135] Comparative experiments with other algorithms show that, under the same combat scenario conditions, the ResNet-MLP joint regression model used in this embodiment can effectively learn the nonlinear mapping relationship between interception points and interception time, significantly improving online prediction efficiency while maintaining prediction accuracy, and possessing good spatial generalization ability and robustness. Furthermore, in a specific test result, the ResNet-MLP joint regression model trained using a geometrically hierarchical training subset exhibits a three-dimensional Euclidean error of approximately [missing value]. The mean absolute error of the interception time is approximately This result demonstrates that the present invention can achieve joint prediction of interception points and interception times within a finite prediction constraint domain.

[0136] Example 2

[0137] In this embodiment, the kinematic models, guidance laws, velocity ranges, and prediction constraint domain parameters of the maneuvering aircraft and the approaching aircraft remain unchanged; only the absolute deployment positions of the maneuvering aircraft and the target point in three-dimensional space are changed. The new engagement scenario is not included in model training but is used only as an independent test scenario to verify the model's generalization ability.

[0138] Specifically, during the test, the maneuvering aircraft and the target point were translated as a whole to multiple different spatial regions, and the corresponding three-dimensional attack and defense combat simulation data were regenerated. The relative state features in the test scenario were input into the ResNet-MLP joint regression prediction model trained in Example 1, which output the predicted interception point and the predicted interception time, and compared with the actual interception results obtained from numerical simulation.

[0139] Experimental results show that, under various deployment locations, the model's prediction error remains within a small range, the predicted interception point is highly consistent with the actual interception point, and the predicted interception time accurately reflects the future encounter moment. Compared with the training scenario, the prediction accuracy in each test scenario did not show a significant decrease, indicating that the model does not depend on a specific absolute coordinate region.

[0140] This invention limits the effective prediction space by using a concentric double-layer spherical shell prediction constraint domain, improves the uniformity of sample space coverage through Fibonacci spherical sampling and geometric stratified sampling, reduces the model's dependence on a fixed global coordinate system through relative state input, and achieves synchronous prediction of interception point and interception time through a ResNet-MLP joint regression model. This method can provide future spatial threat information and remaining time margin information for hazard zone assessment, avoidance triggering, and online replanning of maneuvering aircraft, and has good engineering application value.

Claims

1. A method for predicting interception points and interception time for penetration decision-making, characterized in that, Includes the following steps: Step (1): Establish a three-dimensional offensive and defensive combat mathematical model: Define the position vector, velocity vector and motion constraints of the maneuvering aircraft, the incoming approaching aircraft and the target point in three-dimensional space, establish a three-dimensional kinematic model of the maneuvering aircraft and the incoming approaching aircraft, set the guidance laws of the maneuvering aircraft flying towards the target point and the incoming approaching aircraft flying towards the maneuvering aircraft respectively, and form a three-dimensional offensive and defensive combat mathematical model to describe the relative motion relationship between the two sides; Step (2): Construct a concentric double-layered spherical shell detectable threat domain: Define the spatial region within the effective prediction range of the approaching aircraft by the inner boundary radius and the outer boundary radius, so that the prediction task is transformed from an approximately unbounded space into a finite domain prediction problem with detection conditions and penetration decision significance; Step (3): Construct a geometrically layered training sample set: Generate the initial position and direction of the approaching aircraft by Fibonacci spherical sampling in the concentric double-layered spherical shell prediction constraint domain according to different radius layers, and construct a training subset by layered sampling of the generated initial data and configure corresponding weights for the samples. Then, combine the training subset of the approaching aircraft with the speed, yaw angle and pitch angle state variables of the maneuvering aircraft to form the initial conditions of the three-dimensional attack and defense combat simulation. In each initial combat state, call the three-dimensional attack and defense combat mathematical model established in step (1) to perform numerical calculation to obtain the corresponding real interception point and interception time, which will be used as the data label for subsequent joint regression prediction model training and verification. Step (4): Train a joint regression prediction model based on the generated simulation data: take the relative state features as input, and the relative displacement of the interception point and the interception time as output, train a prediction model that includes a shared feature extraction backbone and multiple regression heads, and use the trained prediction model to predict the interception point and interception time.

2. The method according to claim 1, characterized in that, Step (1) is as follows: Step (1-1): Define the three-dimensional combat objects The three types of combat targets are defined as maneuvering aircraft, incoming approaching aircraft, and target points. Maneuvering aircraft are aircraft that perform penetration missions, incoming approaching aircraft are aircraft that intercept maneuvering aircraft, and target points are the locations that maneuvering aircraft are intended to strike or reach. Define the position vectors of the maneuvering aircraft, the approaching aircraft, and the target point in the three-dimensional inertial coordinate system, as well as the velocity vectors, velocity magnitudes, yaw angles, pitch angles, and maximum maneuvering acceleration state variables of the maneuvering aircraft and the approaching aircraft. Steps (1-2): Establish a three-dimensional kinematic model, guidance laws, and motion constraints. Establish kinematic models of the maneuvering aircraft and the approaching aircraft in three-dimensional space, and describe the changes in position, velocity direction, and velocity magnitude of the maneuvering aircraft and the approaching aircraft over time, respectively. Their expressions are as follows: Approaching aircraft m to maneuvering aircraft t: ， ， ， ， ， ， maneuvering aircraft t versus ground target g: ， ， ， ， ， ， in, and These represent the speeds of the approaching aircraft and the maneuvering aircraft, respectively. and These represent the pitch angles of the approaching aircraft and the maneuvering aircraft, respectively. and These represent the yaw angles of the approaching aircraft and the maneuvering aircraft, respectively. and These represent the normal acceleration commands in the pitch direction for the approaching aircraft and the maneuvering aircraft, respectively. and These represent the normal acceleration commands in the yaw direction for the approaching aircraft and the maneuvering aircraft, respectively. , , These represent the first-order time derivatives of the coordinates of the positions corresponding to the approximate positions of the aircraft; , , These represent the first-order time derivatives of the position coordinates of the attack missile; This indicates the rate of change of velocity for approaching aircraft and attack missiles; The guidance laws for the maneuvering vehicle flying towards the target point and the guidance laws for the approaching vehicle flying towards the maneuvering vehicle are defined: Guidance commands are calculated based on the spatial geometric relationships between the maneuvering vehicle, the approaching vehicle, and the target point, and the velocity directions of the maneuvering vehicle and the approaching vehicle are updated in conjunction with the maximum maneuvering acceleration constraint. The expressions are as follows: ， ， ， ， in, This represents the relative position vector between the approaching aircraft and the maneuvering aircraft. This represents the relative velocity vector between the approaching aircraft and the maneuvering aircraft. This represents the line-of-sight angular velocity vector; Indicates the closing velocity; Indicates the proportional guidance coefficient; This indicates the desired acceleration command generated by proportional guidance. This indicates the normal acceleration command that the approaching aircraft will actually receive. This represents the unit vector indicating the velocity direction of the approaching aircraft. Represents a three-dimensional identity matrix; The Euclidean norm of a vector; This indicates transpose.

3. The method according to claim 2, characterized in that, Step (2) is as follows: Step (2-1): Determine the center of the sphere in the prediction constraint domain A three-dimensional spherical shell region is established with the current location of the maneuvering aircraft as the center to limit the effective prediction range of the approaching aircraft; Step (2-2): Determine the inner boundary of the prediction constraint domain inner boundary radius Determine the inner boundary of the prediction constraint domain for the concentric double-layered spherical shell, and the inner boundary radius. This is used to characterize the minimum safe distance required for a maneuvering aircraft to perform an effective evasive maneuver; when the distance between the approaching aircraft and the maneuvering aircraft is less than the inner boundary radius, the maneuvering aircraft has insufficient time and space margin to perform an evasive maneuver. Step (2-3): Determine the outer boundary of the prediction constraint domain Outer boundary radius Determine the outer boundary of the predictive constraint domain for the concentric double-layered spherical shell; outer boundary radius. Used to characterize the maximum effective range that has predictive and penetration decision-making significance under the detection conditions of the information support platform; When the distance between the approaching aircraft and the maneuvering aircraft is greater than the outer boundary radius, the direct impact of the prediction results on the current avoidance decision is reduced, and unconstrained prediction will lead to an increase in sample size. Steps (2-4): Formulating a finite field prediction problem From the inner boundary radius and outer boundary radius By jointly defining the spatial region within the effective prediction range of the approaching aircraft, the task of predicting the interception point and interception time is transformed from an approximately unbounded spatial prediction problem into a finite domain prediction problem with information support for detection conditions and penetration decision-making significance.

4. The method according to claim 3, characterized in that, Step (3) is as follows: Step (3-1): Divide the spherical shell into radial layers Within the concentric double-layered spherical shell prediction constraint domain, based on the inner boundary radius... and outer boundary radius By setting multiple radius layers, a set of radii can be obtained: ， in, Indicates the first One radius layer, Indicates the number of radius layers; Step (3-2): Generate the initial spatial position of the approaching aircraft. Spherical orientation points are generated at each radius layer using the Fibonacci spherical sampling method. The initial position of the approaching aircraft relative to the maneuvering aircraft is determined based on these spherical orientation points and the corresponding radius layer, thus obtaining initial spatial distribution samples of approaching aircraft covering different distance layers and different directions of attack. Orientation points at one layer are numbered... The sampling expression for the i-th point is generated sequentially: ， ， ， ， in For axial coordinates, For plane radius, It is the azimuth angle. To find the golden angle, the direction vector of the i-th sampling point is calculated as follows: ， From the position of our maneuvering aircraft in the inertial coordinate system, we can calculate the initial position coordinates of the approaching aircraft, as well as the yaw and pitch angles pointing towards the maneuvering aircraft. Step (3-3): Construct a balanced training subset and configure sample weights For any given radius layer, divide the spherical shell containing it into multiple smaller units according to the binning rules for azimuth and elevation angles. For any given smaller unit, count the original number of samples within that unit, and then randomly select 20 samples from that unit to obtain the number of subset samples corresponding to that unit. ， Then calculate the ratio of the parent set to the subset set. Define the weights of the training samples, where This represents the total number of samples in this layer. Step (3-4): Establishing initial conditions for three-dimensional attack and defense combat simulation Based on the initial position of the approaching aircraft, the range and interval of values ​​for the maneuvering aircraft's speed, yaw angle, pitch angle, and speed are set; the expression is: ， ， ， ， in, Indicates the speed of a maneuvering aircraft; and These represent the minimum and maximum values ​​of the speed of the maneuvering aircraft, respectively. Indicates the speed sampling interval of the maneuvering aircraft; This indicates the speed of the approaching aircraft. and These represent the minimum and maximum values ​​of the speed of the approaching aircraft, respectively. This indicates the sampling interval for the speed of the approaching aircraft; Indicates the yaw angle of a maneuvering aircraft; and These represent the minimum and maximum values ​​of the yaw angle of the maneuvering aircraft, respectively. Indicates the yaw angle sampling interval of the maneuvering aircraft; Indicates the pitch angle of a maneuvering aircraft; and These represent the minimum and maximum values ​​of the pitch angle of the maneuvering aircraft, respectively. Indicates the pitch angle sampling interval of a maneuvering aircraft; The speed, yaw angle, pitch angle of the maneuvering aircraft, and speed of the approaching aircraft obtained by discrete values ​​are combined with the initial position of the approaching aircraft generated in step (3-3) to form multiple sets of initial conditions for three-dimensional attack and defense combat simulation. Each set of initial conditions for three-dimensional attack and defense combat simulation includes the initial position of the maneuvering aircraft, the initial velocity vector of the maneuvering aircraft, the initial position of the approaching aircraft, and the initial velocity vector of the approaching aircraft. Steps (3-5): Generate actual interception points and actual interception time tags. In each initial engagement state, a three-dimensional attack and defense engagement simulation model is invoked to numerically simulate the motion process of the maneuvering aircraft and the approaching aircraft until the preset rendezvous criteria are met. The spatial position corresponding to the rendezvous moment is recorded as the actual interception point, and the time from the initial simulation moment to the rendezvous moment is recorded as the actual interception time. The actual interception point and the actual interception time are used as data labels for subsequent joint regression prediction model training and verification. Steps (3-6): Organize the training samples for the joint regression prediction model The initial conditions and corresponding simulation outputs of each group of three-dimensional attack and defense combat simulations are organized to construct the input-output sample pairs of the joint regression prediction model; for the initial combat state of group (i), the relative position vector of the incoming approaching aircraft relative to the maneuvering aircraft is calculated based on the initial position of the maneuvering aircraft and the initial position of the approaching aircraft: ， The relative position vector, the speed of the maneuvering aircraft and the approaching aircraft, the yaw angle and pitch angle of the maneuvering aircraft and the approaching aircraft, the relative displacement of the actual interception point and the actual interception time obtained by the three-dimensional attack and defense combat simulation model in step (3-4), and the corresponding sample weights are associated and stored to form a dataset for training and validation of the joint regression prediction model.

5. The method according to claim 4, characterized in that, Step (4) is as follows: Step (4-1): Determine the input and output of the joint regression prediction model. The relative state feature vector, velocity, and angle information obtained in steps (3-6) are used as inputs to the joint regression prediction model, and the relative displacement of the interception point and the interception time are used as outputs of the joint regression prediction model. Step (4-2): To reduce the impact of differences in the dimensions and numerical ranges of different physical quantities on model training, the input features and output labels are normalized. The expression is: enter: , Output: , in Represents the original input features; Indicates the original output label; The standard deviation of each column of the input feature on the training set; The input feature is the mean of each column in the training set; To output the standard deviation of each column of the feature on the training set; To output the mean of each column of the feature on the training set; Step (4-3): Construct the ResNet-MLP shared feature extraction backbone The ResNet residual structure preserves the low-level physical information in the input, and learns higher-level feature representations through hierarchical mapping of multiple residual blocks. The specific expression is as follows: ， ， ， ， in, Indicates the first One residual block; Indicates the first Input features of each residual block; and They represent the first Features of the first and second fully connected layers in a residual block; and They represent the first The weight matrix of the two fully connected layers in each residual block; and These represent the bias vectors of the corresponding fully connected layers; and These represent the intermediate features after nonlinear transformation and regularization, respectively. Presentation layer normalization operation; Represents the activation function of the Gaussian error linear unit; Indicates a random deactivation operation; Define the shortcut branch mapping expression as follows: ， in, Indicates the first Shortcut branch mapping results for each residual block; Indicates the first Input features of each residual block; and They represent the first Layer and first The feature dimension of the layer; Indicates the first Linear projection weight matrix of shortcut branches in each residual block; The bias vector represents the shortcut branch. Finally, the first... The output of the layer residual block is represented as: ， Step (4-4): Constructing the multi-output MLP regression head Based on the shared features, the network uses a multi-head regression structure to jointly predict four continuous targets; the specific expression is: ， ， in, Indicates the first The hidden layer of the regression head outputs features; Indicates the first Prediction results for each output variable; and They represent the first The weight matrices of the hidden and output layers in the regression head; and These represent the bias vectors of the corresponding layers; This represents the feature vector output from the shared feature extraction backbone; finally, the outputs of the four regression heads are concatenated to obtain a four-dimensional prediction vector. ， in, This represents the four-dimensional prediction vector output by the joint regression prediction model; , , These represent the components of the predicted relative displacement of the interception point in the x, y, and z directions, respectively. Indicates the predicted interception time; Step (4-5): Construct the joint regression loss function MLP learns the relationship between input data and target output, adjusts the weights and biases between neurons in each layer to approximate complex functions, and achieves effective prediction of the target variable. The expression is: ， in, Indicates the first The weighted joint regression loss corresponding to each sample; Indicates the total number of training samples; Indicates the first The weight coefficients corresponding to each sample; Indicates the first The sample at the th Model predictions on each output dimension; Indicates the first The sample at the th The true label values ​​in each output dimension; Indicates the dimension index of the output variable; This represents the output dimension index in the loss calculation. The chain rule is then used to calculate the gradient of the loss with respect to each parameter, and the parameters are updated using an optimization algorithm. The expression is: ， in, This represents the joint regression loss function; Represents the set of network parameters; This represents the gradient of the loss function with respect to the network parameters; This represents the gradient of the loss function with respect to the model output; This represents the gradient of the model output with respect to the network parameters; Steps (4-6): Training the joint regression prediction model Based on the input features, output labels, and weighted joint regression loss function, the ResNet-MLP joint regression prediction model is trained, and the network parameters in the shared feature extraction backbone and multiple MLP regression heads are updated. When the training loss meets the preset convergence condition or reaches the preset number of training rounds, the trained joint regression prediction model is saved. The model is used to output the relative displacement of the predicted interception point and the predicted interception time based on the current relative state between the maneuvering aircraft and the approaching aircraft.

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