An aircraft trajectory prediction method and system based on spatial gridding and heuristic search

Abstract

The embodiment relates to the technical field of aerospace safety, and provides a kind of aircraft trajectory prediction method and system based on space gridding and heuristic search.The adaptive grid resolution adjustment is carried out to high-speed aircraft trajectory prediction, and the possible high-probability trajectory is calculated quickly according to the aircraft type, the problems that computing resource coordination is not flexible, aircraft type perception is not sensitive and the calculation binding physical constraint is lower in the current high-speed aircraft trajectory prediction are solved.

Description

Technical Field

[0001] This application relates to the field of aerospace safety technology, and more specifically, to a method and system for predicting aircraft trajectories based on spatial gridding and heuristic search. Background Technology

[0002] Trajectory prediction of near-space high-speed vehicles is a key protective step in countering enemy aerospace attacks. The dynamism, accuracy, and real-time nature of trajectory prediction are crucial for air defense and missile defense systems to continuously maintain aerospace security. With the increasing maneuverability of modern military targets, particularly the emergence of new threats such as hypersonic vehicles and stealthy cruise high-speed vehicles, modern aerospace warfare rules are trending towards rapid response, precision strikes, and flexible penetration, posing a severe challenge to existing air defense and missile defense systems and traditional reconnaissance and early warning technologies.

[0003] In the current environment of rapid development of near-space high-speed vehicles, air defense and missile defense systems face increasingly severe security challenges. Existing vehicle trajectory prediction methods discretize the state space using a fixed-resolution grid and combine it with kinematic models (such as uniform velocity and cooperative turning models) for trajectory prediction. While these methods are generally applicable, they lack specificity, making it difficult to effectively handle prediction biases caused by differences in target type. Traditional vehicle trajectory prediction and evaluation mechanisms have the following limitations:

[0004] (1) Fixed resolution mesh, lacking dynamic adjustment mechanism. Most existing mesh generation methods use a fixed mesh resolution, which cannot be dynamically adjusted according to the target state. This leads to difficulties in coordinating computational resources and low utilization efficiency. For example, unnecessary fine meshes are used when the target is flying at low speed and in a stable state, wasting computational resources. Overly coarse meshes are used when the target is maneuvering at high speed, resulting in the loss of key detail information.

[0005] (2) The cost function is simple and does not deeply bind physical constraints. The trajectory evaluation function (cost function) used in existing prediction methods is usually too simplified, focusing on the geometric or kinematic level. It lacks modeling of the physical feasibility of the aircraft and environmental constraints, such as the impact of the aerodynamic characteristics of the target and environmental avoidance requirements on maneuverability. This may lead to the algorithm searching for a trajectory that is mathematically "optimal" but physically impossible to achieve, resulting in a decrease in prediction accuracy under complex conditions.

[0006] (3) The ability to perceive differences in target types is weak, and the prediction model lacks personalized adaptive adjustment. Existing systems usually treat different aircraft as homogeneous targets and use the same set of model parameters for prediction. They cannot transform multi-source detection information such as radar and electro-optical signals into key prior knowledge such as target maneuvering pattern library. This results in a weak ability to accurately identify and classify target types and an inability to dynamically predict the internal parameters of the model. Ultimately, the motion model is not sensitive to the special behavior of aircraft and the prediction bias is large.

[0007] To address the aforementioned issues, existing technologies urgently need improvement. Summary of the Invention

[0008] The purpose of this application is to provide a method and system for predicting aircraft trajectories based on spatial gridding and heuristic search. This trajectory prediction method is adaptive to target type, balances accuracy and efficiency, and is deeply bound to physical constraints to meet the needs of modern defense systems. By deeply integrating dynamic grid partitioning and improved heuristic search algorithms, the accuracy and flexibility of flight trajectory prediction are enhanced, providing a reference for improving aerospace security defense.

[0009] Firstly, this application provides a method for predicting aircraft trajectories based on spatial gridding and heuristic search, the technical solution of which is as follows:

[0010] The continuous six-dimensional state space information of the aircraft is discretized into grid points of different resolutions at each grid level, and the prior probability distribution of each grid point is determined; the six-dimensional state space information includes three-dimensional spatial position information and three-dimensional velocity components.

[0011] The current state parameters of the aircraft are obtained, and the optimal grid level is dynamically selected from multiple grid levels based on the state parameters. The state vector of the aircraft is then mapped to the optimal grid level. The state parameters include the magnitude of velocity and the magnitude of acceleration. The state vector includes position and velocity.

[0012] Based on the type of the aircraft, a maneuvering mode is determined from a pre-built maneuvering mode library, and a candidate trajectory is generated based on a preset kinematic integral model.

[0013] The state transition cost of the candidate trajectory is calculated based on the state transition cost function; and the time cost from the current state to the target region is estimated based on the heuristic function.

[0014] The sum of the state transition cost and the time cost is used as the total cost. Based on the candidate trajectory, a heuristic search is performed on the discretized grid space to find the optimal trajectory for the aircraft to reach the target area.

[0015] Furthermore, the continuous six-dimensional state space information of the aircraft is discretized into grid points of different resolutions at each grid level. Previously, the method also included:

[0016] Construct L mesh levels with different resolutions; where the resolution Δl of the l-th mesh level satisfies the geometric series relationship: Δl = Δ0·ρ (l-1)； Δ0 is the base resolution, and ρ is the scaling factor.

[0017] The continuous six-dimensional state space information of the spacecraft is discretized into grid points of different resolutions at each grid level, including:

[0018] Based on the preset three-dimensional spatial boundary and the resolution Δl of each grid level, the three-dimensional spatial position information is uniformly divided into several cubic grid units. The center point or vertex of each cubic grid unit represents a discrete position state, thereby forming a discrete position grid that includes the position state.

[0019] Based on the preset velocity range and the resolution Δl of each grid level, the three-dimensional velocity components are discretized to form a velocity discrete grid that includes the velocity state.

[0020] The position discrete grid and the velocity discrete grid are combined by Cartesian product to form a complete discrete state point, with each point representing a specific combination of position and velocity.

[0021] Furthermore, the prior probability distribution of each grid point is determined, including:

[0022]

[0023] Where r is the position vector of the current grid point; summation iterates through all known or preset target regions of interest n; w n The priority weight for this target region is determined by the importance of the task; f n (z) is the altitude preference function, reflecting the target's activity altitude layer in the region; α is the range attenuation coefficient; r is the distance from the current grid point to the target region. n The distance. P lijk Z represents the prior probability of the ijk-th grid point; ijk The height of grid point ijk is given; N is the number of all grid points; i,j,k are the three-dimensional coordinates of the grid points.

[0024] Furthermore, dynamically selecting the optimal grid level from multiple grid levels based on the state parameters includes:

[0025] Based on the aforementioned state parameters, the optimal grid level index l is dynamically calculated using an online-learned decision function. optimalThe decision function is:

[0026] l optimal = floor( L * (λ * (||a|| / a max ) + (1-λ) * (||v|| / v scale ) ) )

[0027] Where L is the total number of grid layers; a max This is the reference value for maximum acceleration; v scale λ is the speed reference threshold; λ is the maneuver intensity weighting factor, 0≤λ≤1, used to adjust the relative importance of acceleration and speed in decision-making.

[0028] Furthermore, the pre-built maneuver pattern library includes multiple maneuver patterns; each maneuver pattern is associated with a trigger probability; the trigger probability is determined by a base probability and an adjustment amount based on the aircraft type.

[0029] Furthermore, based on the type of the aircraft, a maneuvering mode is determined from a pre-built maneuvering mode library, and candidate trajectories are generated based on a preset kinematic integral model, including:

[0030] Based on the current aircraft type, multiple candidate maneuver commands are generated from the corresponding maneuver mode library according to the action commands of each maneuver mode and their associated trigger probabilities, through a weighted random selection method.

[0031] For each candidate maneuver command, a constraint acceleration is determined; the constraint acceleration is a function of aerodynamic constraints, control capability constraints, and fuel consumption constraints.

[0032] Based on the constrained acceleration, a preset kinematic integral model is used to recursively calculate the current state and generate the predicted state for the next time step.

[0033] The process of iteratively executing the maneuver extension, physical constraint correction, and constraint state recursion generates a continuous sequence of state points over a future period starting from the current state, and generates multiple candidate trajectories.

[0034] Furthermore, the state transition cost is composed of a weighted sum of physical feasibility cost, speed cost, altitude cost, and probability cost;

[0035] The heuristic time cost from the current state to the target region includes:

[0036] h(s) = (κ type / v avg ) · d scaled (s, G)

[0037] h(s) is the heuristic time cost from the current state to the target region; κ type The adjustment factor corresponding to the current type of aircraft; v avg d represents the average speed of the current type of aircraft in the current environment. scaled (s, G) represents the scaled distance from state s to the target region G.

[0038] Furthermore, a heuristic search is performed on the discretized grid space based on the candidate trajectories to find the optimal trajectory for the aircraft to reach the target area, including:

[0039] Starting from the search origin, multiple candidate trajectory segments are generated in each iteration; the sum of the state transition cost and heuristic time cost of each segment is calculated as the total cost of that segment;

[0040] Select the candidate trajectory segment with the minimum total cost for path expansion to obtain a new state node; repeat the above iterative process until the target area is reached; backtrack all selected candidate trajectory segments and connect them to form the optimal trajectory.

[0041] Secondly, this application also proposes an aircraft trajectory prediction system based on spatial gridding and heuristic search, including:

[0042] The module is used to discretize the continuous six-dimensional state space information of the aircraft into grid points of different resolutions at each grid level, and determine the prior probability distribution of each grid point; the six-dimensional state space information includes three-dimensional spatial position information and three-dimensional velocity components.

[0043] The selection and mapping module is used to obtain the current state parameters of the aircraft, dynamically select the optimal grid level from multiple grid levels based on the state parameters, and map the state vector of the aircraft to the optimal grid level; the state parameters include velocity magnitude and acceleration magnitude; the state vector includes position and velocity;

[0044] The generation module is used to determine the maneuvering mode from a pre-built maneuvering mode library according to the type of the current aircraft, and generate candidate trajectories based on a preset kinematic integral model;

[0045] The cost calculation module is used to calculate the state transition cost of the candidate trajectory based on the state transition cost function; and to estimate the time cost from the current state to the target region based on a heuristic function.

[0046] The search module is used to perform a heuristic search in a discretized grid space based on the sum of the state transition cost and the time cost as the total cost, in order to find the optimal trajectory for the aircraft to reach the target area.

[0047] Thirdly, this application also proposes an electronic device comprising: one or more processors, and a memory for storing one or more computer programs; characterized in that the computer programs are configured to be executed by the one or more processors, and the programs include steps for performing the aircraft trajectory prediction method based on spatial gridding and heuristic search as described in the first aspect.

[0048] As can be seen from the above, this application provides a method and system for predicting aircraft trajectories based on spatial gridding and heuristic search. By relying on large-capacity memory and high-performance processing equipment, it can adaptively adjust the grid resolution for high-speed aircraft trajectory prediction and quickly calculate possible high-probability trajectories according to the aircraft type. This solves the problems of inflexible coordination of computing resources, insensitive perception of aircraft type, and low physical constraints in the current high-speed aircraft trajectory prediction, and provides support for subsequent ground analysis. This method and system achieve the following technical effects: (1) Adaptive grid partitioning, increasing the flexibility of computing resource scheduling. The spatial grid is discretized using an intelligent agent and dynamically adjusted according to the target state to adapt to the current flight environment. While retaining key details, the consumption of computing resources is minimized. (2) Intelligent trajectory search, simultaneously acquiring multiple high-probability trajectories. By introducing physical models, information theory, and optimal control theory, the traditional cost function is upgraded to a prediction engine with physical perception, and possible trajectories are searched based on physical constraints. First, the cost of the aircraft's current state to the target state is calculated using the cost function of the embedded physical model built into the algorithm. Then, a heuristic function is used to search for the cost of state changes based on physical constraints. Finally, several high-probability flight trajectories are output, achieving high-probability prediction of the aircraft's flight trajectory. (3) Target type matching increases computational accuracy. By training the captured target motion characteristics through machine learning algorithms, the rapid perception and scientific judgment of the target maneuvering mode are achieved, enabling trajectory calculation to make reasonable predictions based on the target maneuvering mode. Thus, the time-deep integration of dynamic grid partitioning and improved heuristic search algorithm improves the accuracy and flexibility of flight trajectory prediction, providing a reference for improving aerospace security defense. Attached Figure Description

[0049] To more clearly illustrate the technical solutions of this embodiment, the accompanying drawings used in the embodiment will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this embodiment and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1This is a flowchart illustrating the steps of the aircraft trajectory prediction method based on spatial gridding and heuristic search disclosed in this embodiment.

[0051] Figure 2 This is a flowchart illustrating the process of finding the optimal trajectory for an aircraft to reach a target area, as disclosed in this embodiment.

[0052] Figure 3 This is a schematic diagram of the structure of the aircraft trajectory prediction system based on spatial gridding and heuristic search disclosed in this embodiment;

[0053] Figure 4 This is a schematic diagram of the operation process of the aircraft trajectory prediction system based on spatial gridding and heuristic search disclosed in this embodiment. Detailed Implementation

[0054] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which these embodiments belong; the terminology used herein and in the specification of the application is for the purpose of describing particular embodiments only and is not intended to limit these embodiments; the terms "comprising" and "having," and any variations thereof, in the specification of these embodiments and the foregoing drawings, are intended to cover non-exclusive inclusion. The terms "first," "second," etc., in the specification of these embodiments and the foregoing drawings are used to distinguish different objects, not to describe a particular order.

[0055] The implementation details of the technical solution in this embodiment are described below:

[0056] This application proposes a method for predicting aircraft trajectories based on spatial gridding and heuristic search, such as... Figure 1 As shown, the method includes:

[0057] S101, the continuous six-dimensional state space information of the aircraft is discretized into grid points of different resolutions at each grid level, and the prior probability distribution of each grid point is determined; the six-dimensional state space information includes three-dimensional spatial position information and three-dimensional velocity components.

[0058] Specifically, in this embodiment, resolution grid construction is a preprocessing step performed by the grid construction module. This step discretizes the state space, providing a basic data structure for subsequent searches. The aim of this step is to construct a multi-level, multi-resolution discrete state space system to support subsequent search tasks with varying accuracy and efficiency requirements.

[0059] First, the continuous six-dimensional state space information of the spacecraft is discretized into grid points of different resolutions at each grid level. Prior to this, the method further includes constructing L grid levels with different resolutions; wherein the resolution Δl of the l-th grid level satisfies the geometric series relationship: Δl = Δ0·ρ (l-1) Δ0 is the base resolution, and ρ is the scaling factor.

[0060] That is, before step S101, mesh hierarchy generation is performed first. L mesh levels with different resolutions are constructed, forming a pyramid-shaped mesh system from coarse to fine. The resolution Δl of the l-th mesh layer satisfies the geometric series relationship: Δl = Δ0·ρ (l-1) Where Δ0 is the base resolution and ρ is the scaling factor. Each mesh layer is spatially aligned to ensure that every cell in the coarse mesh is completely covered by multiple cells in the fine mesh. The coarse mesh layer (smaller l) covers the global space and is used for fast, low-computational-cost global trend exploration and potential region locking; the fine mesh layer (larger l) is used for refined state description and trajectory optimization in critical or high-uncertainty regions. The total number of mesh layers L and the base resolution Δ0 can be preset or dynamically configured based on the task space, computational resource limits, and the required minimum resolvable feature scale.

[0061] The continuous six-dimensional state space information of the spacecraft is discretized into grid points of different resolutions at each grid level, including:

[0062] Based on the preset three-dimensional spatial boundary and the resolution Δl of each grid level, the three-dimensional spatial position information is uniformly divided into several cubic grid units. The center point or vertex of each cubic grid unit represents a discrete position state, thereby forming a discrete position grid that includes the position state.

[0063] Based on the preset velocity range and the resolution Δl of each grid level, the three-dimensional velocity components are discretized to form a velocity discrete grid that includes the velocity state.

[0064] The position discrete grid and the velocity discrete grid are combined by Cartesian product to form a complete discrete state point, with each point representing a specific combination of position and velocity.

[0065] Specifically, in this embodiment, the continuous six-dimensional state space information of the aircraft (including three-dimensional position coordinates x, y, z and three-dimensional velocity components v) is used. x , v y , v zDiscretization is performed at each grid level. For the position dimension, based on the preset 3D spatial boundary (e.g., spatial range) and the resolution Δl of each layer, it is uniformly divided into several cubic grid cells, with the center point or vertex of each cell representing a discrete position state. For the velocity dimension, it is similarly discretized based on the preset velocity range (e.g., minimum and maximum velocities) and resolution, forming a discrete set of velocity states. The position discrete grid and the velocity discrete grid are combined through a Cartesian product to form a complete discrete state point, with each point representing a specific "position-velocity" combination state.

[0066] Furthermore, for each discrete state point at each grid level, its prior probability distribution at the prediction start time is calculated. This probability reflects the likelihood that the target is in that state in the absence of real-time observation data, and integrates mission prior knowledge, geographical environment information, and tactical intent. For each grid point, its prior probability distribution is calculated.

[0067] Determine the prior probability distribution for each grid point, including:

[0068]

[0069] Where r is the position vector of the current grid point; summation iterates through all known or preset target regions of interest n; w n The priority weight for this target region is determined by the importance of the task; f n (z) is the altitude preference function, reflecting the target's activity altitude layer in the region; α is the range attenuation coefficient; r is the distance from the current grid point to the target region. n The distance. P lijk Z represents the prior probability of the ijk-th grid point; ijk The height of grid point ijk is given; N is the number of all grid points; i,j,k are the three-dimensional coordinates of the grid points.

[0070] This calculation integrates spatial proximity, high degree of matching, and regional importance to form a non-uniform probability field covering the entire space, which guides the subsequent search process to focus on high-probability regions.

[0071] S102, obtain the current state parameters of the aircraft, dynamically select the optimal grid level from multiple grid levels according to the state parameters, and map the state vector of the aircraft to the optimal grid level; the state parameters include the magnitude of velocity and the magnitude of acceleration; the state vector includes position and velocity.

[0072] Specifically, in this embodiment, adaptive grid selection is a key step in the search process, executed by the grid selection module. It dynamically adjusts the grid resolution used for representation and searching based on the real-time status of the aircraft, aiming to balance search efficiency with the accuracy of state description in real time. This includes the following sub-steps:

[0073] (2-1) State Parameter Extraction. Key parameters of the current aircraft's motion state are obtained through external radar detection. These mainly include: velocity magnitude ||v||, calculated by the velocity vector v = (v... x , v y , v z The Euclidean norm of |v|| is obtained, i.e., ||v|| = √(v) x ² + v y ² + v z ²); The magnitude of acceleration ||a|| is obtained by differentiating the velocity vectors at consecutive moments and dividing by the time interval, i.e., a = (v t - v t-1 These parameters, Δt and Δt, are direct indicators of the intensity (maneuverability) of a target's motion.

[0074] (2-2) Hierarchical decision calculation. Based on the extracted state parameters, the optimal grid level index l is dynamically calculated using an online learned decision function. optimal .

[0075] Furthermore, dynamically selecting the optimal grid level from multiple grid levels based on the state parameters includes: dynamically calculating the optimal grid level index l based on the state parameters using an online learned decision function. optimal The decision function is:

[0076] l optimal = floor( L * (λ * (||a|| / a max ) + (1-λ) * (||v|| / v scale ) ) )

[0077] Where L is the total number of grid layers; a max This is the reference value for maximum acceleration; v scale λ is the speed reference threshold; λ is the maneuver intensity weighting factor, 0≤λ≤1, used to adjust the relative importance of acceleration and speed in decision-making.

[0078] The function's purpose is to: when the target is in a high-speed (high v) or high-maneuverability (high a) state, l optimal Tend to larger values ​​(select a finer grid) to accurately capture rapidly changing state details; when the target is in a low-speed, stable flight state, loptimal The algorithm tends towards smaller values ​​(choosing a coarser grid) to save computational resources. The floor operation in the function ensures that the level index is an integer.

[0079] (2-3) Mesh mapping switching. Based on the calculated optimal level index l optimal This maps the current continuous state vector (position and velocity) of the aircraft to a discrete grid space at that level. For a position coordinate x, its index i in the grid at that level... x The calculation formula is: i x = floor( (x - x min ) / Δl ), where x min Let Δl be the minimum boundary of space in the x-direction, and let Δl be the l-th... optimal The resolution of the layered mesh in the x-direction. Similar calculations are performed for the y and z coordinates to obtain a complete set of discrete mesh indices. The velocity mapping is the same as the coordinate mapping; the velocity components in the x, y, and z directions are respectively calculated using v... x =floor( (v x - v xmin ) / Δl ).

[0080] This process achieves a "quantization" mapping from a continuous state space to a discrete grid space with a specific resolution. During the execution of the search algorithm, the algorithm will mainly expand and evaluate the current state at the selected grid level. When the target state changes significantly (triggered by monitoring changes in velocity or acceleration exceeding a threshold), steps (2-1) and (2-2) will be re-executed to dynamically switch to a new optimal grid level, achieving adaptive adjustment of the search granularity.

[0081] S103, Based on the type of the current aircraft, determine the maneuver mode from the pre-built maneuver mode library, and generate candidate trajectories based on the preset kinematic integral model;

[0082] Furthermore, the pre-built maneuver pattern library includes multiple maneuver patterns; each maneuver pattern is associated with a trigger probability; the trigger probability is determined by a base probability and an adjustment amount based on the aircraft type.

[0083] Furthermore, based on the type of the aircraft, a maneuvering mode is determined from a pre-built maneuvering mode library, and candidate trajectories are generated based on a preset kinematic integral model, including:

[0084] Based on the current aircraft type, multiple candidate maneuver commands are generated from the corresponding maneuver mode library according to the action commands of each maneuver mode and their associated trigger probabilities, through a weighted random selection method.

[0085] Preferably, for each candidate maneuver command, a constraint acceleration is determined; the constraint acceleration is a function of aerodynamic constraints, control capability constraints, and fuel consumption constraints.

[0086] Based on the constrained acceleration, a preset kinematic integral model is used to recursively calculate the current state and generate the predicted state for the next time step.

[0087] The process of iteratively executing the maneuver extension, physical constraint correction, and constraint state recursion generates a continuous sequence of state points over a future period starting from the current state, and generates multiple candidate trajectories.

[0088] Specifically, in this embodiment, probabilistic maneuver pattern construction and trajectory generation are the core steps in generating candidate trajectories. These steps are executed by the maneuver pattern library and the trajectory generation module, generating maneuvers with probability distributions based on the aircraft type and calculating state transition costs. Specifically, this includes the following sub-steps:

[0089] (3-1) Construction of the maneuver mode library.

[0090] For different types of aircraft, a structured probabilities library of maneuver patterns is pre-built. Each maneuver pattern m is defined as a basic motion unit, associated with the prior probability P(m) of that pattern being triggered in the current context. The calculation of the trigger probability P(m) considers the base probability and type adjustment:

[0091]

[0092] Among them, P m base It is the basic maneuver probability common to all types of targets, reflecting general motion laws; Δ m type It is a probability offset based on the currently identified target type.

[0093] It should be noted that in the trajectory prediction method, the trigger probability is used in the subsequent trajectory cost evaluation and decision-making process. This probability is pre-configured based on the correlation between aircraft type and preset maneuvering modes, forming a priori maneuvering mode-probability mapping library. Specifically, the system assigns corresponding preset trigger probability values ​​to various possible maneuvers (such as left turn, right turn, climb, descent, etc.) based on the known aircraft type. In the trajectory prediction stage, the system generates multiple candidate trajectories corresponding to different maneuvering modes in parallel based on the aforementioned preset probabilities. For example, if the current aircraft is determined to have a 10% probability of performing a left turn and a 90% probability of performing a right turn, the system will perform kinematic integration along the left turn and right turn maneuvering assumptions respectively, generating two corresponding future trajectory segments. Subsequently, in the cost evaluation stage, the system will comprehensively calculate the cost of each candidate trajectory (such as the degree of fit with the prior probability field, maneuver smoothness, constraint compliance, etc.). Finally, by weighing the trigger probability of each trajectory against its computational cost, the trajectory with the best comprehensive evaluation is selected as the prediction output. Following the previous example, the right-turn trajectory, due to its high trigger probability and low overall cost, will be identified as a high-probability event and used as the final output trajectory. The correspondence between the above-mentioned aircraft types, maneuver modes, and their trigger probabilities is all predefined during system initialization through manual settings or configuration files, serving as a priori knowledge base for trajectory prediction.

[0094] (3-2) Candidate trajectory generation.

[0095] Since the velocity and position of the aircraft change over time, the trajectory of the target can be obtained by performing Euler integrals on the moving physical quantities (such as velocity and position). Let the target be at position r at time t and have velocity v, then the velocity and position of the target after Δt are:

[0096]

[0097] Where Δt is the time step. To introduce a physical feasibility constraint layer, this embodiment embeds an acceleration constraint α into the aforementioned traditional Euler integral. c This constrained acceleration a c It is not a fixed constant, but a function that dynamically adjusts with respect to target aerodynamic parameters, controllability, and fuel consumption factors. This model can adaptively adjust based on target type and flight phase to ensure that the generated trajectory physics is more reasonable. Therefore, the above equation becomes:

[0098]

[0099] Among them, a c = γ1· Φ_aerodynamic + γ2· Φ_control + γ3· Φ_fuel and Φ_aerodynamic represent aerodynamic constraint potential energy; Φ_control represents control capability constraint potential energy; and Φ_fuel represents fuel consumption constraint potential energy.

[0100] It should be noted that Φ_aerodynamic, Φ_control, and Φ_fuel are all solved in advance. In the aforementioned aircraft trajectory prediction method based on spatial gridding and heuristic search, multiple constraint potential energy terms are introduced during trajectory optimization or cost evaluation to generate feasible trajectories that conform to physical laws and mission constraints. These potential energy terms, as penalty functions, collectively constitute part of the comprehensive cost function, guiding the search algorithm to avoid infeasible regions. The determination method for each constraint potential energy term is explained below:

[0101] Regarding the determination of the aerodynamic constraint potential energy (Φ_aerodynamic). This aerodynamic constraint potential energy term characterizes the degree of conformity between the predicted trajectory and the aerodynamic performance envelope of the target aircraft, aiming to ensure that the trajectory state remains within a safe flight envelope. The determination of this potential energy term is based on the aerodynamic parameter envelope data of the target aircraft. Specifically, the aerodynamic safety boundaries of the aircraft, as specified in the manual, verified by wind tunnel testing, or numerical simulation, are first obtained. These include, but are not limited to, the maximum and minimum permissible airspeeds (V_max, V_min), the maximum permissible angle of attack (α_max) and sideslip angle (β_max), and the maximum normal and axial overload coefficients. In the algorithm implementation, a potential energy function Φ_aerodynamic is constructed, whose function value monotonically increases as the flight state quantities (such as instantaneous airspeed V, angle of attack α) at ​​the trajectory points approach or exceed the safety boundaries. As an exemplary implementation, the potential energy function can take the form of a quadratic penalty, and its expression is exemplarily: Φ_aerodynamic = k_v · max(0, V - V_max)^2 + k_α · max(0, |α| - α_max)^2, where k_v and k_α are preset weight coefficients used to adjust the strictness of various constraints.

[0102] Regarding the determination of the control capability constraint potential energy (Φ_control). In the aircraft trajectory prediction method, the control capability constraint potential energy term Φ_control can be constrained based on the minimum allowable turning radius of the aircraft. This is achieved by directly imposing a constraint on the geometric curvature of the predicted trajectory, based on the existence of a defined minimum turning radius R_{min}Rmin due to aerodynamic and structural limitations. Specifically, the instantaneous curvature κ(t) of the predicted trajectory is first calculated, where κ(t) is the reciprocal of the trajectory curvature radius R(t), i.e., κ(t) = 1 / R(t). Subsequently, a potential energy function of the following form is constructed:

[0103] .

[0104] Regarding the determination of the fuel consumption constraint potential energy (Φ_fuel): This fuel consumption constraint potential energy term characterizes the estimated fuel cost of completing the predicted trajectory. Its purpose is to optimize or constrain the fuel economy of the trajectory, ensuring that the mission is completed within the fuel budget. The determination of this potential energy term is based on the aircraft's engine fuel consumption model. Typically, a thrust-specific fuel consumption rate (TSFC) parameter is introduced, which can be a function of engine thrust and flight conditions (altitude, Mach number). Alternatively, a simplified fuel flow model can be used to represent the instantaneous fuel consumption rate. _fuel is expressed as a function of engine throttle setting and flight state. The potential energy function Φ_fuel is constructed to measure or constrain fuel consumption accumulated along the trajectory. In one embodiment, it can be directly taken as the predicted total fuel consumption: Φ_fuel = ∫ _fuel(t) dt, where the integration interval is the duration of the predicted trajectory. In another implementation, it can be set as a penalty function for when the remaining fuel amount at the end of the trajectory is lower than a safety threshold, thereby indirectly achieving fuel constraint.

[0105] The weight coefficients of the above constraint potential energy terms can be manually configured according to task priority during algorithm initialization or determined through optimization and debugging, together forming a comprehensive trajectory evaluation system that takes into account safety, feasibility and economy.

[0106] This mathematical model system extends the traditional, simple Euler integral into a modified model that senses changes in physical quantities, enabling it to more accurately simulate the dynamic evolution of a target over time in a real environment.

[0107] S104, calculate the state transition cost of the candidate trajectory based on the state transition cost function; and estimate the time cost from the current state to the target region based on the heuristic function;

[0108] Furthermore, the state transition cost is composed of a weighted sum of physical feasibility cost, speed cost, altitude cost, and probability cost;

[0109] The heuristic time cost from the current state to the target region includes:

[0110] h(s) = (κ type / v avg ) · d scaled (s, G)

[0111] h(s) is the heuristic time cost from the current state to the target region; κ type The adjustment factor corresponding to the current type of aircraft; v avgd represents the average speed of the current type of aircraft in the current environment. scaled (s, G) represents the scaled distance from state s to the target region G.

[0112] Specifically, in this embodiment, the integrated cost calculation and heuristic search are the core steps for efficient optimization in the discrete grid space, executed by the cost calculation module and the search algorithm module. It guides the search on the grid through a carefully designed cost function and heuristic information, quickly finding high-quality trajectories. Specifically, it includes the following sub-steps:

[0113] (4-1) Design of the comprehensive cost function. To evaluate the cost function design from state s... i Transition to state s j To determine the cost, design a multi-factor integrated cost function C(s). i , s j Define the state transition cost function:

[0114]

[0115] in, As a physical feasibility cost, it is responsible for measuring whether the state transition conforms to physical laws; As a cost to speed, they are responsible for assessing whether the speed status after the transfer is reasonable; At a significant cost, they are responsible for assessing whether the new altitude is appropriate after the relocation. The probability cost is determined based on the prior probability of the grid point where the transfer endpoint is located; α, β, γ, and δ are weighting coefficients that can be adaptively adjusted according to the aircraft type.

[0116] (4-2) Heuristic Function Design. Design a heuristic function:

[0117] h(s) = (κ type / v avg ) · d scaled (s, G)

[0118] This is used to estimate the minimum time cost from the current state to the target region, where κ type Adjustment factor for target type; v avg d represents the average velocity of this type of target in the current environment. scaled (s, G) is the "scaling distance" from state s to target region G. This function takes into account the influence of grid level on distance estimation, and different distance scaling factors are used for different levels.

[0119] Regarding the scaling distance d scaled The determination of (s, G). In some embodiments, this can be achieved by first defining a hierarchical, independent fundamental geometric distance function:

[0120]

[0121] Where pos(S) is the position coordinate (x, y, z) of the extracted state, pos(S) is the coordinate of the grid point in the region, and G is the set of all discrete grid points in the target region; specifically, pos(s) is the specific coordinate of the aircraft in space; pos(g) is the coordinate of the grid point, and G is the set of grid point coordinates pos(g). To perform grid scaling, the coordinates of the target point and the coordinates of the grid points need to be obtained. For example, in a 4×4 two-dimensional plane, there is a point (1, 1). If the grid is densified by one time, the coordinates of (1, 1) become (2, 2), but its original position remains unchanged.

[0122] Then, the scaling factor ζ(l) is introduced, and its design principle is as follows: l is an integer representing the grid division level, and L is the total number of levels. Based on this, d can be determined. scaled (s, G):

[0123] .

[0124] For example, suppose the total number of levels L=3, and the base distance d base =100km, in a coarse grid l=2, ζ(l)=0.5, then d scaled =50km; In a fine grid with l=1, ζ(l)=0.25, then d scaled =25km.

[0125] S105, the sum of the state transition cost and time cost is used as the total cost, and a heuristic search is performed on the discretized grid space based on the candidate trajectory to find the optimal trajectory for the aircraft to reach the target area.

[0126] Furthermore, a heuristic search is performed on the discretized grid space based on the candidate trajectories to find the optimal trajectory for the aircraft to reach the target area, including:

[0127] Starting from the search origin, multiple candidate trajectory segments are generated in each iteration; the sum of the state transition cost and heuristic time cost of each segment is calculated as the total cost of that segment;

[0128] Select the candidate trajectory segment with the minimum total cost for path expansion to obtain a new state node; repeat the above iterative process until the target area is reached; backtrack all selected candidate trajectory segments and connect them to form the optimal trajectory.

[0129] Specifically, in this embodiment, a heuristic search based on the A* algorithm framework is performed on the constructed discrete grid space. The total cost is the sum of the comprehensive cost function in step (4-1) and the heuristic search function in step (4-2):

[0130]

[0131] Where f l (s) represents the cumulative cost from the starting point to the current state. By executing the standard steps of the A* algorithm, the trajectory with the lowest cost, or multiple trajectories with costs within a certain range, can be output.

[0132] Specifically, this application further proposes a heuristic search based on candidate trajectories in a discretized grid space to find the optimal trajectory for the aircraft to reach the target area, such as... Figure 2 ,include:

[0133] Step S201: Search Iteration and Optimal Expansion. Taking the current state of the aircraft as the starting point of the search, at the optimal discretized grid level, starting from this starting point, in each iteration of the heuristic search algorithm (e.g., A* algorithm), multiple candidate trajectory segments are generated starting from the currently expanded state node; the sum of the state transition cost and the heuristic time cost from the end point of the segment to the target region for each candidate trajectory segment is calculated as the total cost estimate for that segment; from all the candidate segments generated this time, the segment with the smallest total cost estimate is selected, and its end point is taken as the new state node, completing this path expansion.

[0134] Step S202: Termination Condition Determination and Optimal Path Backtracking. Repeat step S201, iteratively expanding new state nodes until the spatial position of a certain expanded state node is determined to fall into the preset target area, at which point the search process terminates; subsequently, the algorithm starts from the endpoint node and backtracks along the "parent node-child node" connection relationship recorded during the search process until it backtracks to the search starting point; connect all state nodes on the backtracking path in sequence to form a complete flight trajectory from the starting point to the target area, which is the optimal predicted trajectory with the minimum total cost.

[0135] Specifically, using the aircraft's current state as the search starting point means using the discretized state of the aircraft (i.e., its position and velocity indices at the optimal grid level) obtained after processing by the "adaptive grid selection" module as the initial state node of the heuristic search algorithm. At the discretized optimal grid level, starting from this starting point, in each iteration of the heuristic search algorithm, multiple candidate trajectory segments are generated from the currently expanded state node. This means that in the algorithm's main loop (taking A* as an example), after each time the node with the smallest total cost estimate is selected from the "open set" as the "current expanded node," the "probabilistic maneuvering pattern construction and trajectory generation" module is immediately invoked. Based on the state information of this node (including its corresponding aircraft type, position, and velocity), this module, according to a pre-built maneuvering pattern library, generates multiple candidate commands representing short-term (e.g., the next few seconds) maneuvers through a weighted random selection mechanism. Each command is calculated using a modified kinematic integral model that incorporates physical constraints (aerodynamics, control, fuel), thereby obtaining a physically feasible trajectory segment starting from the current node state. The endpoint of this segment, after calculation, is remapped and quantized to a specific discrete state point on the same optimal grid level, thus becoming a new candidate state node.

[0136] The calculation of the sum of the state transition cost and the heuristic time cost from the endpoint of the segment to the target region for each candidate trajectory segment, as the total cost estimate for that segment, refers to the instantaneous and parallel quantitative evaluation of each generated candidate trajectory segment. The state transition cost is calculated using the comprehensive cost function C(s_i, s_j), which quantifies the cost required to execute the maneuver represented by the segment. Its calculation incorporates multiple dimensions, including physical feasibility, velocity constraints, altitude preference, and the prior probability of the endpoint grid point. The heuristic time cost is estimated using the heuristic function h(s), which optimistically estimates the minimum time cost required to fly from the segment endpoint to the target region based on the aircraft type, the average speed in the current environment, and the distance from the segment endpoint to the target region (considering grid level scaling). Adding the two together yields the estimated total cost (i.e., the f-value in the A* algorithm) of the complete path from the search starting point, through the current extended node, along the candidate segment to the new node, and finally to the target region. This f-value is assigned to the new state node corresponding to the candidate segment.

[0137] In practical applications, selecting the segment with the smallest estimated total cost from all generated candidate segments and using its endpoint as a new state node to complete the current path expansion means that in one iteration, the algorithm compares the f-values ​​of the new nodes corresponding to all candidate segments expanded from the current node. The node with the smallest f-value means that among all known options to be explored, the estimated total cost of reaching the target from the starting point via it is the lowest. Therefore, this node is selected by the algorithm, and its corresponding candidate trajectory segment becomes the optimal local action adopted in this iteration. This node is then added to the open set for subsequent expansion, and the algorithm records its connection relationship with the current expansion node (i.e., its parent node). Step S201 is repeated until the spatial position of an expanded state node is determined to fall into the preset target area, at which point the search process terminates. This means that the algorithm continuously performs the "generation-evaluation-selection-expansion" loop. Each loop selects the node with the smallest global f-value from the open set for expansion, which ensures that the search always moves in the globally most promising direction. When the physical coordinates of an expanded node meet the conditions for entering the target region (e.g., the distance to the center of the target region is less than a threshold), the algorithm considers it to have successfully found a path to the target and stops searching. Subsequently, the algorithm starts from the endpoint node and backtracks along the "parent-child node" connections recorded during the search process. This means using the pointers to the parent nodes saved when expanding each child node. Starting from the endpoint, it sequentially finds its parent node, grandparent node, and so on, until it backtracks to the initial starting node. This series of nodes connected by pointers represents the endpoints of the candidate trajectory segments with the minimum total cost estimates selected in each iteration. Connecting their positions and states in chronological order naturally forms a continuous and physically feasible complete flight trajectory from the starting point to the endpoint, with the globally minimum total cost in the discrete grid space. This is the optimal predicted trajectory, which is the final output of the system.

[0138] In some embodiments, a trajectory visualization and output step is also included. Trajectory visualization and output is the result display step in this embodiment, performed by the visualization module, which displays the searched trajectory in a multi-dimensional visualization. Specifically, it includes the following sub-steps:

[0139] (5-1) Generation of 3D Spatial Trajectory Map. Displays the complete path of the trajectory in 3D space, including the start point, end point, target area marker, and velocity vector arrow. Multiple candidate trajectories are distinguished by different colors, and the confidence level of the displayed trajectory is adjusted by controlling the transparency.

[0140] (5-2) Generation of 2D Plane Projection Views. Three orthogonal projection views are provided: XY plane, XZ plane, and YZ plane, displaying the trajectory projection in different dimensions. Each planar view is displayed independently while maintaining consistent coordinate axis scale, facilitating multi-angle analysis of trajectory characteristics.

[0141] (5-3) Velocity profile generation. Displays the time-varying curves of velocity magnitude and components, as well as the acceleration curve. Multiple subplots show the temporal variations of velocity magnitude, velocity components, acceleration magnitude, and altitude, providing a detailed analysis of the trajectory dynamics.

[0142] (5-4) Parameter Statistics and Report Generation. Calculate statistical parameters for each trajectory, including average speed, maximum speed, minimum altitude, maximum altitude, average turning rate, etc., and generate a text report. Summarize comparative information from multiple trajectories in tabular form to support decision analysis.

[0143] Secondly, this embodiment also proposes an aircraft trajectory prediction system based on spatial gridding and heuristic search, such as... Figure 3 As shown, it includes:

[0144] The construction module 301 is used to discretize the continuous six-dimensional state space information of the aircraft into grid points of different resolutions at each grid level, and determine the prior probability distribution of each grid point; the six-dimensional state space information includes three-dimensional spatial position information and three-dimensional velocity components.

[0145] The selection and mapping module 302 is used to obtain the current state parameters of the aircraft, dynamically select the optimal grid level from multiple grid levels according to the state parameters, and map the state vector of the aircraft to the optimal grid level; the state parameters include the magnitude of velocity and the magnitude of acceleration; the state vector includes position and velocity;

[0146] The generation module 303 is used to determine the maneuvering mode from a pre-built maneuvering mode library according to the type of the current aircraft, and generate candidate trajectories based on a preset kinematic integral model;

[0147] The cost calculation module 304 is used to calculate the state transition cost of the candidate trajectory based on the state transition cost function; and to estimate the time cost from the current state to the target region based on a heuristic function.

[0148] The search module 305 is used to perform a heuristic search in a discretized grid space based on the sum of the state transition cost and the time cost as the total cost, in order to find the optimal trajectory for the aircraft to reach the target area.

[0149] Thirdly, this embodiment also proposes an electronic device comprising: one or more processors, and a memory for storing one or more computer programs; characterized in that the computer programs are configured to be executed by the one or more processors, and the programs include steps for performing the aircraft trajectory prediction method based on spatial gridding and heuristic search as described in the first aspect.

[0150] In some embodiments, a specific implementation method is also provided. This embodiment takes the evasive maneuver trajectory of a high-speed aircraft in a complex terrain area as an example to introduce the operation process of an aircraft trajectory prediction system based on spatial gridding and heuristic search, such as... Figure 4 As shown. The system's software is deployed on a high-performance computing cluster equipped with multiple high-performance multi-core CPUs, high-speed, high-capacity memory, solid-state drive arrays, and multiple professional graphics processing units, exchanging data via a high-speed internal network. For example... Figure 4 As shown, the system includes signal input, terminal agent, a spacecraft trajectory prediction system based on spatial gridding and heuristic search, and data output. It is supported by hardware, including a high-performance parallel computing server, large-capacity storage devices, and a dedicated graphics processing unit. The specific implementation steps are as follows:

[0151] Step 1: System initialization and multi-resolution grid space construction.

[0152] In the task planning area of ​​the system's graphical interface, the operator defines a warning airspace with dimensions of 200km x 200km x 20km x 20km as the analysis range. The grid base resolution Δ0 is set to 1km, the total number of levels L=5, and the scaling factor ρ=2, thus forming a five-layer grid pyramid with resolutions ranging from 1km to 16km. Simultaneously, three potential high-value target areas (main target, target 1, target 2) are marked on the electronic map, and priority weights w1=0.7, w2=0.5, and w3=0.3, respectively, along with corresponding preference functions, are assigned.

[0153] Further, mesh construction is performed. a) Mesh generation: The multi-resolution mesh space construction module generates a 5-level mesh data structure in parallel based on the input parameters. The first level (coarsest) mesh size is 16km, and the fifth level (fineest) mesh size is 1km. b) Prior probability field calculation: The module calculates the prior probability field based on the formula P... prior (r) = Σn [w n * f n (z) * exp(-α * ||r- r nThe prior probability is calculated for each grid point. For example, a grid point located 10km away from the main target (weight 0.7) and at low altitude will receive a higher prior probability value. Ultimately, a prior probability field with a non-uniform probability distribution covering the entire warning airspace is formed and stored in memory for subsequent searches.

[0154] Step 2: Target detection, type recognition, and parameter adaptation.

[0155] First, data input is performed. The phased array radar continuously tracks the target and sends real-time data streams, such as the target's position, velocity vector (e.g., v=(300m / s, 0, 0)), and radar cross-section (RCS), to the system.

[0156] Secondly, the target type identification and adaptation are performed. a) Type identification: The target type identification and parameter adaptation module receives the radar data stream. Its built-in lightweight convolutional neural network analyzes the target's RCS sequence and velocity profile, identifying the target features that match the "high-speed aircraft" type library with the highest degree of matching (92% confidence). b) Parameter adaptation: The module then retrieves the parameter set preset for this type from the database: the maneuver intensity weight factor λ is set to 0.6 (focusing more on acceleration), the cost function weight is adjusted to (α,β,γ,δ) = (0.4, 0.2, 0.2, 0.2), and the "high-speed aircraft" dedicated maneuver mode probability library is loaded.

[0157] Step 3: Adaptive mesh selection and state mapping.

[0158] Dynamic adjustment is performed as follows: a) State extraction: The module calculates the current velocity magnitude ||v|| = 300 m / s and the acceleration magnitude ||a|| = 15 m / s² from the data stream. b) Hierarchical decision-making: Based on the decision model l optimal = floor( L * (λ * (||a|| / a max ) + (1-λ) * (||v|| / v scale Substituting the parameters (L=5, λ=0.6, a) max =50m / s², v scale =340m / s), calculated to yield l optimal = 3. The system decides to switch to the third-level grid (4km resolution) for the current stage of the search to balance capturing maneuver details and computational efficiency. c) State mapping: Mapping the continuous states (x, y, z, v) of the target. x , v y ,v z The index is mapped to the discrete index of the 3rd layer grid, serving as the starting state node for the current search.

[0159] Step 4: Probabilistic trajectory generation and physical constraint embedding.

[0160] a) Maneuver selection: The trajectory generation and physical constraint embedding module expands multiple candidate actions from the current state in a weighted random manner based on the "high-speed aircraft" maneuver mode library, such as: "maintain current heading and accelerate", "dodge 20 degrees to the left and climb", "dodge 30 degrees to the right".

[0161] b) Physical constraint integration: For each candidate action, the module does not simply use s k+1 = s k + Δt * v k Instead of performing extrapolation, it calls the embedded physical model to calculate the constraint acceleration 'a'. c = γ1· Φ aerodynamic + γ2· Φ control +γ3· Φ fuel For example, calculations show that a sharp ascent results in an aerodynamic potential energy Φ. aerodynamic The acceleration increases dramatically (exceeding the angle-of-attack capability of the high-speed aircraft), thus generating a reverse corrective acceleration α. c To "flatten" the trajectory, ensuring that the generated candidate trajectory segments are physically feasible.

[0162] c) State update: using the modified Euler integral formula s k+1 = s k + Δt * v k + 0.5 * Δt² * (a k +a c This generates a series of continuous state points for the next few seconds, forming candidate trajectory segments.

[0163] Step 5: Comprehensive Cost Calculation and Heuristic Search. The system performs a search and optimization process, including:

[0164] a) Cost Evaluation: For each candidate trajectory segment generated in step four, the heuristic search module uses the comprehensive cost function C(s) to evaluate the cost. i , s j Calculate its cost. For example, a trajectory heading towards a known air defense position, its cost C prob The (probabilistic cost) would be extremely high; a trajectory exceeding the speed limit of this type of high-speed aircraft would have a C... vel The cost of speed will become infinitely large, leading to its elimination.

[0165] b) Heuristic Guidance: The module simultaneously calculates the heuristic estimate h(s) from each candidate state to the preset target region = (κ) type / v avg) * d scaled (s, G), where κ type Adjustments were made for high-speed aircraft, d scaled Distance estimation is currently performed at the 3rd layer of the grid.

[0166] c) A* Algorithm Search: The module uses the A* algorithm framework to continuously select the state with the minimum total cost f(s) = g(s) + h(s) within a dynamically maintained open and closed set for expansion (step four), and evaluation (step five a) until the target region is found or the maximum number of expansion steps is reached. The entire process is a "generation-evaluation-expansion" loop. For example, in this search iteration of 1000 times, the final output is the 3 trajectories with the lowest cumulative cost, forming a trajectory solution set.

[0167] Step Six: Trajectory Visualization and Decision Support. The system performs visualization presentation:

[0168] a) Multi-dimensional display: The trajectory visualization and analysis module receives three candidate trajectory data obtained from the search. These are then simultaneously rendered on the command center's large screen.

[0169] 3D spatial trajectory map: Three trajectories are clearly displayed on the 3D terrain as curves of different colors: red, blue, and green. The red trajectory has the highest confidence and is presented with a darker color and thicker line width. The predicted arrival time is marked on the trajectory.

[0170] Two-dimensional projection diagram: In a separate sub-window, the trajectory is projected onto the horizontal plane (XY) and the elevation plane (XZ), which facilitates the analysis of its horizontal avoidance route and elevation changes.

[0171] Velocity / Acceleration Profile: Displays the changes in velocity magnitude, vertical velocity, and acceleration over time for three trajectories in the form of a curve, allowing for a direct comparison of the intensity of their maneuvers.

[0172] b) Parameter report: The module automatically generates a comparison report, listing the key indicators of the three trajectories: Trajectory 1 (red): predicted arrival time T+120s, average speed 320m / s, maximum overload 6G; Trajectory 2 (blue): arrival time T+135s, average speed 310m / s, maximum overload 4G, minimum ground clearance 50m (clear terrain following characteristics).

[0173] Step 7: Dynamic Updates and Closed-Loop Corrections.

[0174] The system continuously runs steps two through six as a closed loop. When the next frame of radar data arrives, showing that the target acceleration has increased to 25 m / s², the system recalculates in step S301, possibly dynamically switching the grid level to a finer 4th layer (2 km resolution). Under the new accuracy, it continues to search and optimize trajectory prediction, achieving adaptive refinement of prediction as the target state evolves.

[0175] Through the seven logically rigorous steps outlined above, this embodiment fully demonstrates how the method and system described herein begin with spatial grid construction, drive parameter adaptation through real-time target recognition, generate candidate trajectories by fusing physical constraints within a dynamically adjusted multi-resolution grid, and quickly identify multiple high-probability, physically feasible predicted trajectories using an improved cost function and heuristic search. Finally, it assists command and control decisions through rich visualization methods. The entire process represents a leap from "fixed grid, single model" to "dynamic perception, physical embedding, and intelligent search," effectively solving the three major challenges mentioned in the background technology: rigid computing resources, insufficient physical feasibility, and insensitivity to target types. This fully demonstrates the technical superiority and practical value of this embodiment.

[0176] The technical solution provided in this embodiment, through deep integration of dynamic multi-resolution mesh construction, trajectory generation with embedded physical constraints, and intelligent search and evaluation mechanism that adapts to target types, brings significant and multifaceted benefits compared to existing technologies, specifically reflected in the following aspects:

[0177] 1. Dynamically adjusting grid resolution enables intelligent dynamic optimization of computing resources. Based on target speed and maneuver intensity, the optimal grid level is dynamically determined. A coarse grid is used for rapid global exploration when the target is flying smoothly, while a fine grid is used for detailed depiction during violent maneuvers. This mechanism, combined with a multi-level search strategy from coarse to fine, ensures that computing resources are always focused on key areas, avoiding redundant calculations caused by a globally uniform fine grid. This significantly improves search efficiency while maintaining accuracy, meeting the needs of high-real-time air defense and missile defense scenarios.

[0178] 2. The cost function is deeply bound to physical constraints, enabling intelligent search for high-probability trajectories. The system deeply embeds aerodynamic, maneuvering, and physical constraints into trajectory generation. Physical correction terms ensure that candidate trajectories conform to dynamic laws, while adjusting cost function weights and heuristic parameters. This design integrates prior tactical behaviors of specific target types into the prediction model, making trajectory prediction not only kinematic but also capable of tactical behavior inference, allowing the algorithm to search for mathematically and physically "optimal" trajectories.

[0179] 3. Enhanced predictive targeting and adaptability for different types of threats. This embodiment achieves personalized configuration of the prediction model by constructing a maneuver pattern library. By utilizing prior knowledge, the predicted trajectory is made to better match the actual behavioral logic of specific types of targets, reducing systematic prediction errors caused by unclear target types and realizing personalized output of the prediction model.

[0180] The above description is merely an embodiment of this application and is not intended to limit the scope of protection of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for predicting aircraft trajectories based on spatial gridding and heuristic search, characterized in that, include: The continuous six-dimensional state space information of the aircraft is discretized into grid points of different resolutions at each grid level, and the prior probability distribution of each grid point is determined. The six-dimensional state space information includes three-dimensional spatial position information and three-dimensional velocity components; Obtain the current state parameters of the aircraft, dynamically select the optimal grid level from multiple grid levels based on the state parameters, and map the state vector of the aircraft to the optimal grid level; The state parameters include the magnitude of velocity and the magnitude of acceleration; the state vector includes position and velocity. Based on the type of the aircraft, a maneuvering mode is determined from a pre-built maneuvering mode library, and a candidate trajectory is generated based on a preset kinematic integral model. The state transition cost of the candidate trajectory is calculated based on the state transition cost function; Furthermore, the time cost from the current state to the target region is estimated based on heuristic functions; The sum of the state transition cost and time cost is used as the total cost. Based on the candidate trajectory, a heuristic search is performed on the discretized grid space to find the optimal trajectory for the aircraft to reach the target area. The method further includes discretizing the continuous six-dimensional state space information of the spacecraft into grid points of different resolutions at each grid level. Construct L mesh levels with different resolutions; where the resolution Δl of the l-th mesh level satisfies the geometric series relationship: Δl = Δ0·ρ (l-1)； Δ0 is the base resolution, and ρ is the scaling factor; The continuous six-dimensional state space information of the spacecraft is discretized into grid points of different resolutions at each grid level, including: Based on the preset three-dimensional spatial boundary and the resolution Δl of each grid level, the three-dimensional spatial position information is uniformly divided into several cubic grid units. The center point or vertex of each cubic grid unit represents a discrete position state, thereby forming a discrete position grid that includes the position state. Based on the preset velocity range and the resolution Δl of each grid level, the three-dimensional velocity components are discretized to form a velocity discrete grid that includes the velocity state. The position discrete grid and the velocity discrete grid are combined by Cartesian product to form a complete discrete state point, with each point representing a specific combination of position and velocity.

2. The aircraft trajectory prediction method based on spatial gridding and heuristic search according to claim 1, characterized in that, Determine the prior probability distribution for each grid point, including: Where r is the position vector of the current grid point; summation is performed to traverse all known regions of interest n; w n f represents the priority weight for the target region. n (z) is the height preference function; α is the distance decay coefficient; r is the distance from the current grid point to the target region. n The distance; Let be the prior probabilities of the i, j, k-th grid points; The height of grid point i,j,k is given by ; N is the total number of grid points; and i,j,k are the three-dimensional coordinates of the grid points.

3. The aircraft trajectory prediction method based on spatial gridding and heuristic search according to claim 2, characterized in that, Dynamically selecting the optimal grid level from multiple grid levels based on the state parameters includes: Based on the aforementioned state parameters, the optimal grid level index l is dynamically calculated using an online-learned decision function. optimal The decision function is: l optimal = floor( L* (λ* (||a|| / a max ) + (1-λ)* (||v|| / v scale ) ) ) Where L is the total number of grid layers; a max This is the reference value for maximum acceleration; v scale λ is the speed reference threshold; λ is the maneuver intensity weighting factor, 0≤λ≤1, used to adjust the relative importance of acceleration and speed in decision-making; ||v|| is the speed magnitude, and ||a|| is the acceleration magnitude.

4. The aircraft trajectory prediction method based on spatial gridding and heuristic search according to claim 3, characterized in that, The pre-built maneuver pattern library includes multiple maneuver patterns; each maneuver pattern is associated with a trigger probability; the trigger probability is determined by a base probability and an adjustment based on the aircraft type.

5. The aircraft trajectory prediction method based on spatial gridding and heuristic search according to claim 4, characterized in that, Based on the type of the aircraft, a maneuver mode is determined from a pre-built maneuver mode library, and candidate trajectories are generated based on a preset kinematic integral model, including: Based on the current aircraft type, multiple candidate maneuver commands are generated from the corresponding maneuver mode library according to the action commands of each maneuver mode and their associated trigger probabilities, through a weighted random selection method. For each candidate maneuver command, a constraint acceleration is determined; the constraint acceleration is a function of aerodynamic constraints, control capability constraints, and fuel consumption constraints. Based on the constrained acceleration, a preset kinematic integral model is used to recursively calculate the current state and generate the predicted state for the next time step. The process of iteratively executing the maneuver extension, physical constraint correction, and constraint state recursion generates a continuous sequence of state points over a future period starting from the current state, and generates multiple candidate trajectories.

6. The aircraft trajectory prediction method based on spatial gridding and heuristic search according to any one of claims 1-5, characterized in that, The state transition cost is composed of a weighted sum of physical feasibility cost, speed cost, altitude cost, and probability cost. The heuristic time cost from the current state to the target region includes: h(s) = (κ type / v avg ) · d scaled (s, G) h(s) is the heuristic time cost from the current state to the target region; κ type The adjustment factor corresponding to the current type of aircraft; v avg d represents the average speed of the current type of aircraft in the current environment. scaled (s, G) represents the scaled distance from state s to the target region G.

7. The aircraft trajectory prediction method based on spatial gridding and heuristic search according to claim 6, characterized in that, Heuristic search is performed on a discretized grid space based on candidate trajectories to find the optimal trajectory for the aircraft to reach the target area, including: Starting from the search origin, multiple candidate trajectory segments are generated in each iteration; the sum of the state transition cost and heuristic time cost of each segment is calculated as the total cost of that segment; Select the candidate trajectory segment with the minimum total cost for path expansion to obtain a new state node; Repeat the above iterative process until the target area is reached; backtrack all selected candidate trajectory segments and connect them to form the optimal trajectory.

8. A spacecraft trajectory prediction system based on spatial gridding and heuristic search, characterized in that, include: The module is used to discretize the continuous six-dimensional state space information of the aircraft into grid points of different resolutions at each grid level, and determine the prior probability distribution of each grid point; The six-dimensional state space information includes three-dimensional spatial position information and three-dimensional velocity components; The selection and mapping module is used to obtain the current state parameters of the aircraft, dynamically select the optimal grid level from multiple grid levels according to the state parameters, and map the state vector of the aircraft to the optimal grid level. The state parameters include the magnitude of velocity and the magnitude of acceleration; the state vector includes position and velocity. The generation module is used to determine the maneuvering mode from a pre-built maneuvering mode library according to the type of the current aircraft, and generate candidate trajectories based on a preset kinematic integral model; The cost calculation module is used to calculate the state transition cost of the candidate trajectory based on the state transition cost function. Furthermore, the time cost from the current state to the target region is estimated based on heuristic functions; The search module is used to perform a heuristic search in a discretized grid space based on the sum of the state transition cost and the time cost as the total cost, in order to find the optimal trajectory for the aircraft to reach the target area. The construction module is also used to construct L mesh levels with different resolutions; wherein the resolution Δl of the l-th mesh level satisfies the geometric series relationship: Δl = Δ0·ρ (l-1)； Δ0 is the base resolution, and ρ is the scaling factor; The discretization of the continuous six-dimensional state space information of the aircraft into grid points of different resolutions at each grid level includes: uniformly dividing the three-dimensional spatial position information into several cubic grid units according to the preset three-dimensional spatial boundary and the resolution Δl of each grid level, wherein the center point or vertex of each cubic grid unit represents a discrete position state, thereby forming a position discrete grid including the position state; discretizing the three-dimensional velocity components according to the preset velocity range and the resolution Δl of each grid level, forming a velocity discrete grid including the velocity state; and combining the position discrete grid and the velocity discrete grid through a Cartesian product to form a complete discrete state point, wherein each point represents a specific position and velocity combination state.

9. An electronic device, the electronic device comprising: One or more processors, a memory for storing one or more computer programs; characterized in that the computer programs are configured to be executed by the one or more processors, the programs including steps for performing the aircraft trajectory prediction method based on spatial gridding and heuristic search as described in any one of claims 1-7.

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