Air combat target maneuver multi-modal trajectory prediction method and system based on space-time joint attention mechanism

Abstract

The application provides a method and system for air combat target maneuver multi-modal trajectory prediction based on a space-time joint attention mechanism, wherein the method comprises: air combat scene modeling; translation invariance and rotation invariance modeling; stationarity modeling; space-time correlation modeling; multi-modal decoding; and feasibility checking. The method of the application realizes synchronous capture of time mutation and space game through a double-branch attention mechanism; generates multiple possible trajectories for targets in a heterogeneous complex high-dynamic environment through multi-modal prediction, considers uncertainty and variability in trajectory prediction; and introduces an aerodynamic penalty term in the loss function, so as to ensure that the trajectory conforms to the limit of the aircraft body, eliminate physical distortion, and further improve the accuracy and reliability of trajectory prediction.

Description

Technical Field

[0001] This invention belongs to the field of data processing and relates to air combat simulation technology, specifically to a method and system for predicting the multimodal trajectory of air combat target maneuvers based on a spatiotemporal joint attention mechanism. Background Technology

[0002] In air combat, airborne sensors, command platforms, and data link systems form a real-time information network that continuously transmits multi-dimensional state information such as the target's three-dimensional coordinates, velocity vectors, and attitude angles. Accurately predicting the enemy target's maneuver trajectory is a core prerequisite for gaining tactical advantage, directly impacting interception path planning and weapon positioning decisions. Current technologies primarily employ four types of modeling methods for trajectory prediction: kinematic deduction based on physical models, pattern matching based on machine learning, policy simulation based on reinforcement learning, and end-to-end mapping based on deep learning. These methods exhibit significant differences in architectural design and practical effectiveness, and also possess corresponding limitations.

[0003] Physical model-based prediction systems typically consist of a Newtonian kinematics equation derivator, a radar measurement preprocessing module, and a trajectory extrapolation display. Their core relies on pre-defined target dynamic parameters and utilizes a Kalman filter array in an interactive multi-model algorithm to achieve probabilistic weighting under multiple motion assumptions. However, when faced with highly nonlinear maneuvers, such methods suffer from increased errors between predicted and actual trajectories because the model set cannot cover the actual maneuver patterns, and computational delay increases exponentially with the number of models.

[0004] Machine learning-based prediction systems employ a cascaded architecture of feature engineering and classification / regression. First, a situation description vector containing handcrafted features such as relative distance and azimuth rate of change is constructed using expert experience. Then, a combination of support vector machines and decision trees is used to identify predefined maneuver pattern categories. Finally, a Gaussian process regression unit is invoked to generate a single predicted trajectory. However, when facing complex maneuvering strategies of fighter jets, this approach suffers a sharp drop in recognition rate due to insufficient feature representation dimensions. Furthermore, the trajectory generation module lacks multimodal output capabilities, failing to characterize the uncertainty of the target's tactical intentions.

[0005] The reinforcement learning-based prediction system constructs an environment simulator containing a confrontation situation between red and blue teams. It uses deep value networks or proximal policy optimization algorithms to drive the agent to explore the optimal maneuver strategy. Its reward function library integrates evaluation indicators such as energy maneuver advantage and weapon launch conditions. Although it can generate trajectory sequences that conform to the logic of air combat games in the simulation environment, such systems require repeated interactive training to converge.

[0006] Deep learning-based prediction methods currently demonstrate the greatest application potential. Their typical architecture employs a bidirectional recurrent neural network as a temporal encoder, mapping historical trajectory sequences into latent space feature vectors, and then decoding them through fully connected layers to generate deterministic trajectory coordinates. These methods automatically extract spatiotemporal features through end-to-end training, and can integrate environmental constraints (such as terrain elevation data) with adversarial situation information (such as relative azimuth angles between friendly and enemy forces). However, existing systems suffer from three fundamental flaws: First, the network structure processes temporal and spatial features in stages (e.g., temporal encoding followed by spatial encoding), severing the spatiotemporal coupling characteristics of maneuvering actions; second, the mean squared error loss function forces the network to output an average trajectory, failing to characterize the multimodal maneuvering strategies that the target may adopt in tactical games; and third, the generated trajectory may violate fundamental aerodynamic laws, such as instantaneous overload exceeding the limits of the aircraft structure or sudden discontinuities in the velocity vector. Such physical distortions will pose serious decision-making risks during actual deployment. The aforementioned bottlenecks are further exacerbated in complex electromagnetic interference environments. When the signal-to-noise ratio falls below the threshold, the prediction confidence of existing methods based on Long Short-Term Memory (LSTM) networks drops sharply, exposing significant hidden dangers in the battlefield robustness of existing technical systems. Summary of the Invention

[0007] To address the problems existing in the prior art, this invention provides a method and system for predicting the multimodal trajectory of air combat targets based on a spatiotemporal joint attention mechanism. The scheme constructs an encoding and decoding neural network with an embedded spatiotemporal attention module, and uses the network's powerful self-learning capability to predict the trajectory of future air combat targets.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows:

[0009] This invention provides a method for predicting the multimodal trajectory of air combat targets based on a spatiotemporal joint attention mechanism, comprising the following steps:

[0010] Step 1, Air Combat Scenario Modeling: Extract historical trajectory information for each agent based on multi-agent trajectory data;

[0011] Step 2, translation invariance and rotation invariance modeling: Based on the trajectory data obtained in Step 1, a local spatiotemporal coordinate system is established for each scene element to obtain the relative spatiotemporal information of the agent, which can reconstruct the absolute position of an element from another element;

[0012] Step 3, stationarity modeling: Based on the local coordinate system trajectory data obtained in Step 2, perform instance normalization, calculate the position and velocity normalization parameters based on the motion state of all targets in the current scene, and normalize the position and velocity features to obtain stationary trajectory data;

[0013] Step 4: Spatiotemporal correlation modeling: Based on the stationary trajectory data obtained in Step 3, the spatiotemporal context of the scene is fused using a spatiotemporal co-encoder, and the spatiotemporal co-encoder is adaptively output to generate a spatiotemporal co-encoder scene code.

[0014] Step 5: Multimodal decoding: Based on the scene encoding output in Step 4, output multiple future trajectories for each target agent using the hybrid density decoder, and predict the optimal trajectory.

[0015] Furthermore, it also includes the following steps:

[0016] Step 6: Feasibility Verification: Perform physical feasibility verification based on the optimal trajectory predicted in Step 5, thereby achieving trajectory prediction.

[0017] Furthermore, step 1 specifically includes:

[0018] Given all agents' historical observations o over the previous H time steps, extract the historical trajectory sequence of the past H time steps using a sliding window, and construct the input tensor X, defined as follows:

[0019]

[0020] Where: o includes target input source information;

[0021] The set of K possible future trajectories with T time steps for all agents is represented as:

[0022]

[0023] Where: Y k This represents the set of states predicted by the agent at time steps 1 to T.

[0024] Furthermore, step 1 also includes the following steps:

[0025] Using the center of the tactical scenario as the origin, the airborne sensor data is uniformly converted to the North-East coordinate system.

[0026] Furthermore, step 2 includes the following sub-steps:

[0027] Step 2.1: For a given absolute spatiotemporal position (p) i ,v i ,t i The element and another element with an absolute spacetime position (p) j ,v j ,t j The elements of the descriptor are summarized using a three-dimensional descriptor, which includes the relative attitude angle α. i→j Relative azimuth angle β i→j and relative position p i→j =pi -p j Where p is position, v is velocity, and t is timestamp;

[0028] Relative attitude angle α i→j Represented as:

[0029]

[0030] Relative azimuth angle β i→j Represented as:

[0031]

[0032] Therefore, relative spatiotemporal information r i→j Represented as:

[0033] r i→j =[sin(α) i→j ),cos(α i→j ),sin(β i→j ),cos(β i→j ),||p i→j ||];

[0034] Step 2.2: Combine the geometric and semantic attributes of the agent to generate a relative position embedding e using a multilayer perceptron (MLP). i→j .

[0035] Furthermore, step 3 specifically includes the following sub-steps:

[0036] Step 3.1: Based on the motion states of all targets in the current scene, perform the following calculations:

[0037]

[0038]

[0039] Where μ and σ are the mean and variance of a specific variable;

[0040] Step 3.2: Based on the scene mean and variance normalized position and velocity characteristics, the calculation formula is as follows:

[0041]

[0042] in: This represents the normalized feature variables.

[0043] Furthermore, step 4 specifically includes the following sub-steps:

[0044] Step 4.1: Temporal-spatial fusion branch: First, use an LSTM network as the encoder for historical trajectory data, with each agent outputting its own temporal features; then, treat each agent as a token, encode it, and add spatial location encoding, then use a two-layer self-attention encoder as the agent-agent interaction encoder, where the query, key, and value are embedded in the historical trajectory of the encoded entity, and finally output spatial interaction information;

[0045] Step 4.2: Spatial-temporal fusion branch: First, treat each agent as a token, encode it and add spatial location encoding, then use a two-layer self-attention encoder as an agent-agent interaction encoder, where the query, key and value are embedded in the current position of the encoded entity, and finally output spatial interaction information; then use an LSTM network as an encoder for historical trajectory data, and each agent outputs its own spatiotemporal features.

[0046] Step 4.3: The features output from the temporal-spatial fusion branch and the spatial-temporal fusion branch are concatenated and then used to generate gating weights through a multilayer perceptron (MLP). The weighted fusion outputs a spatiotemporal joint scene code. The calculation formula is as follows:

[0047]

[0048]

[0049] Where: Sigmoid(·) represents the normalized nonlinear transformation unit. Spatial interaction information output by the time-space fusion branch. Spatiotemporal features output by the space-time fusion branch.

[0050] Furthermore, step 5 specifically includes the following sub-steps:

[0051] Step 5.1: Extend the spatiotemporal encoded features to a multidimensional latent space using a multilayer perceptron to generate multimodal latent variables that cover the diversity of tactical intentions.

[0052] Step 5.2: The hybrid density network decodes and outputs multimodal multi-entity multi-step prediction location parameters, multimodal multi-entity multi-step prediction variance parameters, and multimodal multi-entity modal probabilities based on the multimodal representation, where the variance parameter represents the trajectory uncertainty;

[0053] For each mode k, the decoder outputs Gaussian distribution parameters and mode probability π. k The calculation formula is as follows:

[0054] μ k ,σ k =MLP(ek )

[0055] π k =Softmax(MLP(e k ))

[0056] Where: Softmax(·) represents the normalized nonlinear transformation unit, μ k σ is the mean. k For variance;

[0057] Step 5.3: Calculate the matching error between the candidate trajectory and the true trajectory, and select the pattern with the smallest error as the optimal prediction.

[0058] Furthermore, step 6 specifically includes the following steps:

[0059] Step 6.1: Introduce penalty terms L for the rate of change of heading angle |Δψ| and overload η into the training loss. phy The calculation formula is as follows:

[0060] L phy =λ1∑max(Δψ|-ψ max ,0)+λ2∑max(η-η max ,0)

[0061] Where: λ1, λ2 represent the weights of the penalty term, and ψ max η represents the maximum tolerance limit for the rate of change of heading angle. max Indicates the maximum tolerance limit for overload;

[0062] Step 6.2: Determine the threshold values ​​for overload, speed, and rate of change of heading angle of the predicted trajectory;

[0063] Step 6.3: Perform local interpolation correction on predicted trajectories that violate physical rules to ensure compliance with body dynamics constraints.

[0064] The present invention also provides a computer system, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the air combat target maneuvering multimodal trajectory prediction method based on spatiotemporal joint attention mechanism provided by the present invention.

[0065] The beneficial effects of this invention are as follows:

[0066] The multimodal trajectory prediction method for air combat target maneuvers provided by this invention combines a spatiotemporal joint attention mechanism. It achieves simultaneous capture of temporal abrupt changes and spatial game theory through a dual-branch attention mechanism. It uses multimodal prediction to generate multiple possible trajectories for targets in heterogeneous, complex, and highly dynamic environments, taking into account the uncertainty and variability in trajectory prediction. An aerodynamic penalty term is introduced into the loss function to ensure that the trajectory conforms to the limits of the fighter jet and eliminates physical distortion, thereby further improving the accuracy and reliability of trajectory prediction and providing more effective support for decision-making in air combat. Attached Figure Description

[0067] Figure 1 This is a schematic diagram of the implementation architecture of the air combat target maneuvering multimodal trajectory prediction method based on spatiotemporal joint attention mechanism provided by the present invention.

[0068] Figure 2 This is a flowchart illustrating the steps of the method for predicting the multimodal trajectory of an air combat target based on a spatiotemporal joint attention mechanism provided by the present invention. Detailed Implementation

[0069] The technical solutions provided by the present invention will be described in detail below with reference to specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention.

[0070] like Figure 1 , Figure 2 As shown, the multimodal trajectory prediction method for air combat target maneuvers based on a spatiotemporal joint attention mechanism provided by this invention includes the following steps:

[0071] S1: Air combat scenario modeling: Based on the given multi-agent trajectory data, extract the historical trajectory information of each agent; specifically including the following steps:

[0072] S1.1: This invention assumes that the air combat scenario can be described as a continuous-space-discrete-space system, involving the self (denoted as A0) and N other intelligent agents (denoted as A1 to A2). N Given all agents' historical observations o over the previous H time steps, a sliding window is used to extract the historical trajectory sequence over the past H time steps, constructing the input tensor X, defined as follows:

[0073]

[0074] Among them, o includes measurement equipment such as airborne sensors, command platforms, and data links that transmit a large amount of target input source information, including observation data such as position p, velocity v, and timestamp t.

[0075] This invention represents the set of K possible future T time-step trajectories of all agents as follows:

[0076]

[0077] Where: Y k This represents the set of states predicted by the agent at time steps 1 to T.

[0078] S1.2: Using the center of the tactical scenario as the origin, the airborne sensor data is uniformly converted to the North-Eastern (NED) coordinate system to eliminate global motion interference.

[0079] For each agent, this invention constructs its local scene context by aggregating potential interaction scene contexts within a specified range, in order to help the model understand the agent's positional changes over time.

[0080] S2: Translation and Rotation Invariance Modeling: To achieve generalization and robustness in air combat trajectory prediction, a local spatiotemporal coordinate system is established for each scene element based on the trajectory data obtained in S1. This eliminates global motion interference and ensures that the model remains invariant to the overall translation and rotation of the scene. Specifically, this includes the following steps:

[0081] S2.1: For a given absolute spatiotemporal position (p) i ,v i ,t i The element and another element with an absolute spacetime position (p) j ,v j ,t j The elements of the descriptor use a three-dimensional descriptor to summarize the relative relationships of the agents, and its components include the relative attitude angle α. i→j Relative azimuth angle β i→j and relative position p i→j =p i -p j To improve numerical stability and avoid gradient explosion caused by abrupt changes in direction, angles are represented using sine and cosine values.

[0082] The relative attitude angle α of the present invention i→j Represented as:

[0083]

[0084] The relative azimuth angle β of the present invention i→j Represented as:

[0085]

[0086] Therefore, relative spatiotemporal information r i→j Represented as:

[0087] r i→j =[sin(α) i→j ),cos(α i→j),sin(β i→j ),cos(β i→j ),||p i→j ||]

[0088] Because the absolute position of an element can be easily reconstructed from another element using a descriptor, all spatiotemporal position information of scene element pairs is preserved;

[0089] S2.2: Combine the geometric attributes of the agent with its semantic attributes (such as category and friend / foe identification), and generate a relative position embedding e using a multi-layer perceptron (MLP). i→j The calculation formula is as follows:

[0090]

[0091] Where: h i ,h j This represents the attribute feature vectors of agents i and j. This indicates vector concatenation.

[0092] S3: Stationarity Modeling: To eliminate differences in the motion scales of different targets, instance normalization is performed based on the local coordinate system trajectory data obtained in S2 to improve the model's convergence speed and generalization ability; specifically, it includes the following steps:

[0093] S3.1: Stationarity refers to the statistical properties of a time series remaining constant over time. However, due to the complex dynamics of entity trajectories in air combat scenarios and the random errors of sensors, non-stationarity is widespread in trajectory spatiotemporal sequence data, posing a severe challenge to accurate prediction. Considering that time series data is usually collected over a long period, these non-stationary sequences inevitably cause the distribution of the prediction model to change over time. Due to covariate shift or conditional shift, this shift leads to performance degradation during testing. To address this issue, this invention uses an instance normalization method on the time series input X;

[0094] S3.2: Calculate the normalized position and velocity parameters based on the motion states of all agents in the current scene. The calculation formula is as follows:

[0095]

[0096] Where μ and σ are the mean and variance of a specific variable.

[0097] S3.3: Based on the scene mean and variance normalized position and velocity characteristics, the calculation formula is as follows:

[0098]

[0099] in: This represents the normalized feature variables.

[0100] S4: Spatiotemporal correlation modeling: To capture the spatiotemporal coupling characteristics of target maneuvering behavior and the game logic between friend and foe, scene spatiotemporal context fusion is performed based on the stationary trajectory data obtained in S3 and a spatiotemporal joint encoder; specifically, the following steps are included:

[0101] S4.1: This invention uses dual-branch parallel modeling and dynamic gating fusion, and by separating temporal and spatial priorities, it overcomes the problem of insufficient modeling of complex game scenarios by traditional methods.

[0102] S4.2: Temporal-spatial fusion branch: First, an LSTM network is used as the encoder for historical trajectory data, and each agent outputs its own temporal features. The calculation formula is as follows:

[0103]

[0104] Where: LSTM(·) represents performing time-series fusion computation on the data.

[0105] Then, each agent is treated as a token, encoded, and spatial location encoded. A two-layer self-attention encoder is used as the agent-agent interaction encoder, where the query, key, and value are embedded with the historical trajectory of the encoded entity. Finally, the spatial interaction information is output. The calculation formula is as follows:

[0106]

[0107] Among them: SelfAttention(·) performs self-attention calculation on the token, and LayerNorm(·) performs layer normalization calculation.

[0108] S4.3: Spatial-Temporal Fusion Branch: First, treat each agent as a token, encode it, and then add spatial location encoding. Use a two-layer self-attention encoder as the agent-agent interaction encoder, where the query, key, and value are embedded with the current location of the encoded entity. Finally, output the spatial interaction information. The calculation formula is as follows:

[0109]

[0110]

[0111] Wherein: EnityEmbed(·) maps each entity to a high-dimensional vector by adding its positional encoding through a trainable linear projector.

[0112] Then, an LSTM network is used as the encoder for historical trajectory data, with each agent outputting its own spatiotemporal features. The calculation formula is as follows:

[0113]

[0114] S4.4: After concatenating the features from the two branches, a multilayer perceptron is used to generate gating weights, which are then weighted and fused to output a spatiotemporal joint scene code. The calculation formula is as follows:

[0115]

[0116] Where: Sigmoid(·) represents the normalized nonlinear transformation unit.

[0117] This invention establishes an interaction model centered on each agent in a future timeline. Each agent's interaction graph is independently constructed based on its characteristics and surrounding environment, allowing for a more accurate capture of its unique behavioral patterns and interaction needs.

[0118] S5: Multimodal Decoding: To generate a physically plausible set of multiple trajectories that covers tactical possibilities, based on the scene encoding output from S4, a hybrid density decoder outputs multiple future trajectories for each target agent; specifically including the following steps:

[0119] S5.1: Due to the complexity and diversity of possible trajectory intentions, the actual trajectory of a target in a combat scenario is often uncertain. To address the uncertainty and variability in trajectory prediction, the multimodal mapping module extends spatiotemporal encoded features to a multidimensional latent space through a multilayer perceptron, generating multimodal latent variables that cover the diversity of tactical intentions.

[0120] S5.2: The hybrid density network decodes and outputs multimodal multi-entity multi-step prediction location parameters, multimodal multi-entity multi-step prediction variance parameters, and multimodal multi-entity modal probabilities based on multimodal representations, where the variance parameter represents trajectory uncertainty;

[0121] For each mode k, the decoder outputs Gaussian distribution parameters (mean μ). k σ k ) and modal probability π k The calculation formula is as follows:

[0122] μ k ,σ k =MLP(e k )

[0123] π k =Softmax(MLP(e k ))

[0124] Where: Softmax(·) represents the normalized nonlinear transformation unit.

[0125] S5.3: By calculating the matching error between the candidate trajectory and the true trajectory, the pattern with the smallest error is selected as the optimal prediction.

[0126] S6: Feasibility Verification: To ensure that the generated trajectory conforms to aerodynamic and structural constraints, a physical feasibility verification is performed based on the optimal trajectory predicted in S5, thereby achieving trajectory prediction; specifically, it includes the following steps:

[0127] S6.1: Introduce penalty terms L for the rate of change of heading angle |Δψ| and overload η into the training loss. phy The calculation formula is as follows:

[0128] L phy =λ1∑max(|Δψ|-ψ max ,0)+λ2∑max(η-η max ,0)

[0129] Where: λ1, λ2 represent the weights of the penalty term, and ψ max η represents the maximum tolerance limit for the rate of change of heading angle. max This indicates the maximum tolerance limit for overload.

[0130] S6.2: Threshold determination is performed on the overload, speed and heading angle change rate of the predicted trajectory. Trajectories exceeding the preset threshold are treated as trajectory segments that violate physical rules and are processed in subsequent S6.3.

[0131] S6.3: Perform local interpolation corrections on trajectory segments that violate physical rules to ensure compliance with the constraints of body dynamics.

[0132] The present invention also provides a computer system, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the air combat target maneuvering multimodal trajectory prediction method based on spatiotemporal joint attention mechanism provided by the present invention.

[0133] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A method for predicting the multimodal trajectory of maneuvering air combat targets based on a spatiotemporal joint attention mechanism, characterized in that, Includes the following steps: Step 1, Air Combat Scenario Modeling: Extract historical trajectory information for each agent based on multi-agent trajectory data; Step 2, translation invariance and rotation invariance modeling: Based on the trajectory data obtained in Step 1, a local spatiotemporal coordinate system is established for each scene element to obtain the relative spatiotemporal information of the agent, which can reconstruct the absolute position of an element from another element; Step 3, stationarity modeling: Based on the local coordinate system trajectory data obtained in Step 2, instance normalization is performed. Based on the motion state of all agents in the current scene, the position and velocity normalization parameters are calculated respectively, and the position and velocity features are normalized to obtain stationary trajectory data. Step 4: Spatiotemporal correlation modeling: Based on the stationary trajectory data obtained in Step 3, the spatiotemporal context of the scene is fused using a spatiotemporal co-encoder, and the spatiotemporal joint scene code is adaptively output; specifically, this includes the following sub-steps: Step 4.1: Temporal-spatial fusion branch: First, use an LSTM network as the encoder for historical trajectory data, and each agent outputs its own temporal features; Then, each agent is treated as a token, encoded, and spatial location encoding is added. A two-layer self-attention encoder is used as the agent-agent interaction encoder, where the query, key, and value are embedded in the historical trajectory of the encoded entity. Finally, the spatial interaction information is output. Step 4.2: Spatial-temporal fusion branch: First, treat each agent as a token, encode it and add spatial location encoding, then use a two-layer self-attention encoder as an agent-agent interaction encoder, where the query, key and value are embedded in the current position of the encoded entity, and finally output spatial interaction information; then use an LSTM network as an encoder for historical trajectory data, and each agent outputs its own spatiotemporal features. Step 4.3: The features output from the temporal-spatial fusion branch and the spatial-temporal fusion branch are concatenated and then gating weights are generated using a multilayer perceptron (MLP). The weighted fusion outputs a spatiotemporal joint scene code. The calculation formula is as follows: in: Represents the normalized nonlinear transformation unit, Spatial interaction information output by the time-space fusion branch. The spatiotemporal features output by the space-time fusion branch; Step 5: Multimodal Decoding: Based on the scene encoding output in Step 4, output multiple future trajectories for each agent using a hybrid density decoder, and predict the optimal trajectory; specifically including the following sub-steps: Step 5.1: Extend the spatiotemporal encoded features to a multidimensional latent space using a multilayer perceptron to generate multimodal latent variables that cover the diversity of tactical intentions. ; Step 5.2: The hybrid density network decodes and outputs multimodal multi-entity multi-step prediction location parameters, multimodal multi-entity multi-step prediction variance parameters, and multimodal multi-entity modal probabilities based on the multimodal representation, where the variance parameter represents the trajectory uncertainty; For each mode The decoder outputs Gaussian distribution parameters and modal probabilities. The calculation formula is as follows: in: Represents the normalized nonlinear transformation unit, The mean, For variance; Step 5.3: Calculate the matching error between the candidate trajectory and the true trajectory, and select the pattern with the smallest error as the optimal prediction.

2. The method for predicting multimodal trajectories of air combat targets based on a spatiotemporal joint attention mechanism according to claim 1, characterized in that... It also includes the following steps: Step 6: Feasibility Verification: Perform physical feasibility verification based on the optimal trajectory predicted in Step 5, thereby achieving trajectory prediction.

3. The method for predicting multimodal trajectories of air combat targets based on a spatiotemporal joint attention mechanism according to claim 1, characterized in that, Step 1 specifically includes: Given all agents in the previous Historical observation over a time step Extract the past using a sliding window Construct the input tensor from the historical trajectory sequence of time steps. The definition is as follows: in: Including information about the input sources of the intelligent agent; All intelligent agents A possible future The set of trajectories with time steps is represented as follows: in: This indicates that the agent is at time step arrive The set of predicted states.

4. The method for predicting multimodal trajectories of air combat targets based on a spatiotemporal joint attention mechanism according to claim 1, characterized in that, Step 1 further includes the following steps: Using the center of the air combat scenario as the origin, the airborne sensor data is uniformly converted to the North-East coordinate system.

5. The method for predicting multimodal trajectories of air combat targets based on a spatiotemporal joint attention mechanism according to claim 1, characterized in that, Step 2 includes the following sub-steps: Step 2.1: For a given location with absolute spacetime position The element and another element with an absolute spacetime position The elements are summarized using a three-dimensional descriptor to represent the relative relationships of the agents. The components of the three-dimensional descriptor include relative attitude angles. Relative azimuth and relative position ,in, For location, For speed, For timestamps; Relative attitude angle Represented as: relative azimuth Represented as: Therefore, relative spatiotemporal information Represented as: ； Step 2.2: Combine the geometric and semantic attributes of the agent to generate relative position embeddings using a multilayer perceptron (MLP). .

6. The method for predicting multimodal trajectories of air combat targets based on a spatiotemporal joint attention mechanism according to claim 1, characterized in that, Step 3 specifically includes the following sub-steps: Step 3.1: Based on the motion states of all agents in the current scene, perform the following calculations respectively: in: and These are the mean and variance of a specific variable; Step 3.2: Based on the scene mean and variance normalized position and velocity characteristics, the calculation formula is as follows: in: This represents the normalized feature variables.

7. The method for predicting multimodal trajectories of air combat targets based on a spatiotemporal joint attention mechanism according to claim 2, characterized in that, Step 6 specifically includes the following steps: Step 6.1: Introduce the rate of change of heading angle into the training loss. Overload Penalty items The calculation formula is as follows: in: , Indicates the weight of the penalty item. This indicates the maximum tolerable limit for the rate of change of heading angle. Indicates the maximum tolerance limit for overload; Step 6.2: Determine the threshold values ​​for overload, speed, and rate of change of heading angle of the predicted trajectory; Step 6.3: Perform local interpolation correction on predicted trajectories that violate physical rules to ensure compliance with body dynamics constraints.

8. A computer system comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method for predicting the maneuvering multimodal trajectory of an air combat target based on a spatiotemporal joint attention mechanism as described in any one of claims 1-7.

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