A multi-type aircraft state prediction method fusing physical constraints

Abstract

The application discloses a kind of multi-type aircraft state prediction methods of fusion physical constraint, specifically for different types of low-altitude aircraft, obtain respective historical original data;Then, the kinematics and dynamics constraints of each aircraft are established, and one-hot coding is carried out according to type type, to generate respective condition vector;Then, a deep learning model is constructed with the basic framework of encoder-decoder as the core prediction unit of neural ODE;Total loss function is constructed using explicit regularization strategy;Optimal parameters are solved by iterative updating of back propagation.In the prediction phase, the optimal parameters are used by the deep learning model to encode and decode, and the original action features of the aircraft to be tested are output;Finally, a physical correction layer is connected in series after the output layer of the decoder, and implicit regularization is used to trim the original action feature sequence to generate the final action feature, and the flight trajectory is predicted by kinematic integration;The application improves the reliability, generalization ability and safety of aircraft trajectory prediction.

Description

Technical Field

[0001] This invention belongs to the field of artificial intelligence and air traffic management, and relates to aircraft trajectory prediction technology, specifically a method for predicting the state of multiple types of aircraft that integrates physical constraints. Background Technology

[0002] With the booming development of the global low-altitude economy, applications such as drone logistics, urban air traffic (UAM), aerial mapping, and emergency rescue are increasing, leading to a sharp rise in the number and density of aircraft in low-altitude airspace. This poses unprecedented challenges to the surveillance, management, and security of low-altitude airspace. Among these challenges, accurate and reliable prediction of the future trajectories and maneuvers of low-altitude aircraft is a core technological prerequisite for achieving conflict detection and mitigation, intelligent traffic management, and dynamic risk assessment. It is also the cornerstone for building a modern and intelligent low-altitude traffic management (UTM) system.

[0003] Currently, aircraft trajectory prediction technology is mainly divided into two categories: model-based methods and data-driven methods.

[0004] Model-based methods, such as Kalman filtering and its variants (Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), rely on accurate modeling of aircraft dynamics. These methods have the advantages of clear physical meaning and strong interpretability. However, they also have significant limitations: First, establishing an accurate flight dynamics model requires a large number of aerodynamic parameters, which are costly and difficult to obtain for the diverse and frequently modified low-altitude aircraft. Second, these models are weak in modeling pilot intentions and sudden environmental factors (such as gusts and obstacle avoidance), resulting in insufficient prediction accuracy in complex maneuvering scenarios.

[0005] In recent years, with breakthroughs in deep learning, data-driven trajectory prediction methods have become a research hotspot. Deep sequence models such as Long Short-Term Memory (LSTM), Gated Recurrent Units (GRU), and Transformers can automatically learn complex spatiotemporal dependencies and driver behavior patterns from massive amounts of historical trajectory data, demonstrating great potential in prediction accuracy. However, these purely data-driven methods also have inherent limitations, specifically:

[0006] Lack of physical consistency: Deep learning models are essentially complex function fitters whose learning objective is to minimize prediction errors rather than to understand physical laws. Therefore, when dealing with extreme or rare maneuvers not adequately covered in the training data, the model may generate trajectories that violate fundamental physical laws. For example, predicting a fixed-wing aircraft making a near 90-degree instantaneous turn in a short time, or generating overloads far exceeding its structural and physiological limits. Such "physically impossible" predictions are fatal in safety-critical air traffic management, severely misleading subsequent decisions.

[0007] Limited generalization ability: The performance of purely data-driven models is highly dependent on the distribution of training data. When faced with a novel aircraft whose dynamic characteristics differ significantly from all aircraft in the training set, or when the aircraft performs a maneuver that is extremely rare in the training set, the model's predictive performance drops sharply, exhibiting severe overfitting. This "knowing what but not why" characteristic limits its practical deployment and application in open, dynamic low-altitude environments.

[0008] Poor interpretability: The "black box" nature of deep learning models makes their prediction and decision-making processes difficult to understand. When predictions fail, it is difficult to trace which step or factor caused the error, which poses a significant obstacle to model debugging, optimization, and building trust.

[0009] In summary, existing technologies either struggle to capture complex behavioral patterns or lack physical common sense and generalization ability. Therefore, how to construct a trajectory prediction model that can fully utilize the powerful fitting capabilities of data-driven approaches, ensure that the prediction results conform to physical laws, and possess good generalization and interpretability is a pressing technical challenge in the field of low-altitude airspace management. Summary of the Invention

[0010] To address the issues of poor physical consistency, weak generalization ability, and insufficient interpretability in purely data-driven models, this invention provides a multi-type aircraft state prediction method that integrates physical constraints. This method achieves deep integration of deep learning data-driven models with prior knowledge of flight dynamics, enabling prediction results to strictly follow physical laws while fitting data patterns. This significantly improves the reliability, generalization ability, and safety of aircraft trajectory prediction.

[0011] The specific steps are as follows:

[0012] Step 1: For different types of low-altitude aircraft, each aircraft acquires its own historical flight trajectory raw data from its multi-source sensing devices and performs preprocessing.

[0013] Multi-source sensing devices include radar, ADS-B, GPS, etc.

[0014] The raw data includes timestamps, three-dimensional spatial location (longitude, latitude, altitude), and dynamic state parameters such as velocity and acceleration.

[0015] Preprocessing includes data cleaning, spatiotemporal alignment, and feature engineering.

[0016] Step 2: Establish a set of simplified flight kinematics and dynamic constraints for each type of aircraft, store them in structured data format, and index them by aircraft type.

[0017] The kinematic constraints include: maximum / minimum flight speed Maximum / Minimum Climb Rate Maximum turning angular velocity ;

[0018] The dynamic constraints include maximum normal overload. , maximum tangential acceleration Minimum turning radius (This value can be obtained from) and Export).

[0019] Step 3: Perform one-hot encoding on each aircraft type to generate its own condition vector;

[0020] Let the set of aircraft types be ,in This represents the total number of aircraft types.

[0021] Aircraft type The generated condition vector for A dimensional vector, its formula is:

[0022]

[0023] in: The condition vector is represented by the first... There are 1 component, j∈{1,2,...,K}.

[0024] That is, the condition vector c is the one-hot encoded vector of the aircraft type type.

[0025] Step 4: Using the conditional vectors of each aircraft and the preprocessed raw data, construct a deep learning model with an encoder-decoder framework and a neural ODE as the core prediction unit.

[0026] The encoder employs a 4-layer Transformer structure to extract deep temporal features of historical trajectories; the decoder uses Neural ODE (Neural ODE) as the core prediction unit, utilizing its continuous-time modeling characteristics to describe the dynamic evolution of the aircraft.

[0027] The specific principles of deep learning models are as follows:

[0028] Step I: For the current aircraft S, the encoder receives the preprocessed raw data sequence. The augmented input sequence is obtained by fusing the conditional vector c. ;

[0029] The formula for incorporating splicing is:

[0030] Step II: Through the self-attention mechanism within the Transformer layer, combined with the pooling layer, the input sequence is processed. Encode as a high-dimensional context vector The output is sent to the decoder;

[0031]

[0032] Step III: The decoder receives the context vector output by the encoder and initializes the hidden state:

[0033]

[0034] Step IV: Convert the condition vector of aircraft S Through the embedding layer, it is mapped to a conditional embedding vector. Input encoder;

[0035]

[0036] This is the embedding layer mapping function, with a total of 64 dimensions;

[0037] Step V, Conditional Embedding Vector The inputs and outputs of each layer of the encoder are broadcast and added together:

[0038]

[0039] in, For encoder number The input or output characteristics of the layer Features are those obtained after fusing conditional information.

[0040] Step VI: Discretize the number of layers of the encoder Treat as continuous variables Discrete changes between layers are transformed into changes in the continuous "time / depth" dimension. Differential equation:

[0041]

[0042] in Total number of layers corresponding to the encoder , Corresponding encoder This indicates continuous "depth". The hidden state of the location. The parameter is Neural network functions, Random initialization.

[0043] Step VII: Using a numerical solver, along the "depth / time" dimension From 0 to Integrating the above differential equation forward yields the sequence of future hidden states:

[0044]

[0045] Step VIII, at depth At this point, the neural ODE completes the forward integral and outputs the final hidden state. After mapping through a fully connected layer, the original predicted action feature sequence for the initial iteration is obtained. :

[0046]

[0047] This is the weight matrix of the fully connected layer; This is the bias vector for the fully connected layer.

[0048] Step 5: Combining kinematic and dynamic constraints, construct the total loss function using an explicit regularization strategy. ;

[0049] Total loss is defined as the weighted sum of prediction error and physical loss:

[0050]

[0051] in: For the predicted original action feature sequence The mean squared error between the sequence and the actual action feature sequence. The physical loss term, i.e., the prediction result. Penalty terms for violating dynamic constraints. is the regularization coefficient.

[0052] Step 6: Using the Adam optimizer, iteratively update the algorithm through backpropagation to solve for the solution that minimizes the total loss. Minimal optimal parameters for deep learning model .

[0053] Step 7: In the prediction phase, input the dynamic state sequence and type of the aircraft's historical time. The deep learning model uses the optimal parameters... After encoding and decoding, the original action features are output. ;

[0054] Step 8: Connect a physical correction layer after the output layer of the decoder to receive the original action feature sequence predicted by the deep learning model. Then, implicit regularization is used to prune the data according to the corresponding dynamic constraints to generate the final motion features that meet the physical limits. The flight trajectory is predicted by kinematic integral.

[0055] Implicit regularization enforces strong pruning of out-of-bounds values, specifically:

[0056] For original action characteristics The Dimensional original action characteristics The "prune" function is used to force it back into the physically feasible region:

[0057] The formula for the "Clip" function is: ;

[0058] in and Corresponding to the first of aircraft S Minimum and maximum values ​​of dimensional dynamic constraints;

[0059] The advantages of this invention are:

[0060] (1) The present invention integrates the guarantee mechanism of explicit and implicit dual physical constraints, which fundamentally solves the problem of lack of physical consistency of pure data-driven models, eliminates the generation of absurd predictions, and greatly improves the reliability and interpretability of prediction results.

[0061] (2) The present invention adopts a parameterized, pluggable dynamic constraint and condition adaptation mechanism to abstract the physical constraints of different aircraft types into a configurable parameter set, and realizes the compatibility of a single model with multiple types of aircraft through condition embedding. This design brings two major advantages: First, it has a strong generalization ability. When encountering a new aircraft type, it is only necessary to configure a new set of physical parameters for it, without retraining the entire model, which greatly reduces the cost of model deployment and maintenance. Second, it has flexibility and scalability. This "pluggable" design enables the system to easily adapt to new aircraft that will continue to emerge in the future, and has good application prospects.

[0062] (3) This invention uses neural ODE as the core prediction unit, taking advantage of its continuous-time modeling characteristics, making it naturally suitable for describing continuous dynamic systems such as aircraft. Compared with traditional discrete-time models, neural ODE has advantages in processing irregular sampled data and generating smooth trajectories, further improving the accuracy and naturalness of prediction. Attached Figure Description

[0063] Figure 1 This is a flowchart of a multi-type aircraft state prediction method that integrates physical constraints according to the present invention.

[0064] Figure 2 This is a schematic diagram of a neural network structure incorporating physical constraints provided in an embodiment of the present invention;

[0065] Figure 3 is a schematic diagram of the multi-type aircraft condition adaptation mechanism provided in the embodiment of the present invention. Detailed Implementation

[0066] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Obviously, the described embodiments are merely some, not all, embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort should fall within the scope of protection of the present invention.

[0067] This invention provides a method for predicting the state of multiple types of aircraft by integrating physical constraints. By constructing a deep learning model that combines explicit and implicit physical regularization, and employing a combination of a parameterized physical constraint library and a conditional embedding mechanism, a physical loss function is introduced during the training phase of the deep learning model, and a physical correction layer is used for forced projection during the prediction phase. This ensures that the model's prediction output strictly follows the laws of flight dynamics while fitting the data pattern, providing high-fidelity and high-reliability prediction input for low-altitude traffic management systems, which is of great significance for ensuring the safe operation of low-altitude airspace.

[0068] like Figure 1 As shown, it includes the following steps:

[0069] Step 1: For different types of low-altitude aircraft, each aircraft acquires its own historical flight trajectory raw data from its multi-source sensing devices and performs preprocessing.

[0070] Multi-source sensing devices include radar, ADS-B, GPS, etc.

[0071] The raw data includes timestamps, three-dimensional spatial location (longitude, latitude, altitude), and dynamic state parameters such as velocity and acceleration.

[0072] Preprocessing includes data cleaning, spatiotemporal alignment, and feature engineering.

[0073] Step 2: Establish a set of simplified flight kinematics and dynamic constraints for each type of aircraft, store them in structured data format, and index them by aircraft type.

[0074] The kinematic constraints include: maximum / minimum flight speed Maximum / Minimum Climb Rate Maximum turning angular velocity ;

[0075] The dynamic constraints include maximum normal overload. , maximum tangential acceleration Minimum turning radius (This value can be obtained from) and Export).

[0076] Structured storage includes writing physical constraints as JSON or storing them as dictionaries indexed by type;

[0077] Step 3: Perform one-hot encoding on each aircraft type to generate its own condition vector;

[0078] Let the set of aircraft types be ,in This represents the total number of aircraft types.

[0079] Aircraft type The generated condition vector for A dimensional vector, its formula is:

[0080]

[0081] in: The condition vector is represented by the first... There are 1 component, j∈{1,2,...,K}.

[0082] That is, the condition vector c is the one-hot encoded vector of the aircraft type type.

[0083] Step 4: Using the conditional vectors of each aircraft and the preprocessed raw data, construct a deep learning model with an encoder-decoder framework and a neural ODE as the core prediction unit.

[0084] This invention constructs an Encoder-Decoder architecture. The encoder adopts a 4-layer Transformer structure to extract deep temporal features of historical trajectories. The decoder uses a Neural ODE as the core prediction unit, utilizing its continuous-time modeling characteristics to describe the dynamic evolution of the aircraft. The Neural ODE can output prediction results at arbitrary time resolution, and its internal state evolution is highly consistent with the form of differential equations, providing an ideal mathematical framework for incorporating prior knowledge of dynamics.

[0085] like Figure 2 As shown, the encoder concatenates / fused the original historical data and encodes it into a high-dimensional context vector through a self-attention mechanism. The output is fed to the decoder; the decoder uses the neural ODE for continuous state evolution; the hidden state is initialized from the context vector output by the encoder, and the neural ODE evolves the future hidden state by integrating forward in the time dimension according to the following differential equation, thereby obtaining the predicted action features; the total loss function is constructed using an explicit regularization strategy. And based on dynamic constraints, implicit regularization is used for pruning, and finally the predicted flight trajectory is output.

[0086] Physical loss and physical constraint library

[0087] The specific principles of deep learning models are as follows:

[0088] Step I: For the current aircraft S, the encoder receives a pre-processed raw historical data sequence of length T. The augmented input sequence is obtained by fusing the conditional vector c. ;

[0089] The formula for incorporating splicing is:

[0090] Step II: Through the self-attention mechanism within the Transformer layer, combined with the pooling layer, the input sequence is processed. Encode as a high-dimensional context vector The output is sent to the decoder;

[0091] Self-attention mechanism captures sequences The long-range spatiotemporal dependencies in the data ultimately encode the input sequence into a high-dimensional context vector, which encapsulates the dynamic characteristics of the historical flight states.

[0092] Meanwhile, by incorporating the conditional vector of the aircraft type into the encoding process through a conditional embedding mechanism, the context vector becomes aircraft-specific.

[0093]

[0094] Step III: The decoder receives the context vector output by the encoder and initializes the hidden state:

[0095]

[0096] Step IV: Convert the condition vector of aircraft S Through the embedding layer, it is mapped to a conditional embedding vector. Input encoder;

[0097]

[0098] This is the embedding layer mapping function, with a total of 64 dimensions;

[0099] Step V, Conditional Embedding Vector The inputs and outputs of each layer of the encoder are broadcast and added together:

[0100]

[0101] in, For encoder number The input or output characteristics of the layer Features are those obtained after fusing conditional information.

[0102] Step VI: Discretize the number of layers of the encoder Treat as continuous variables Discrete changes between layers are transformed into changes in the continuous "time / depth" dimension. Differential equation:

[0103] In traditional discrete deep networks, the propagation of hidden states between layers is represented as follows: In neural ODEs, the number of discrete layers... Treat as continuous variables At this point, the discrete variations between layers are transformed into variations concerning continuous "time / depth". The derivative of is the following differential equation:

[0104]

[0105] in Total number of layers corresponding to the encoder , Corresponding encoder This indicates continuous "depth". The hidden state of the location. The parameter is The neural network function is used to characterize the rate of change of the hidden state with "depth". Random initialization is performed before training begins. : Continuous-time variables that evolve from the original discrete layer number.

[0106] Step VII: The neural ODE receives the context vector output by the encoder as the initial hidden state. Using a numerical solver, along the "depth / time" dimension From 0 to Integrating the above differential equation forward yields the sequence of future hidden states:

[0107]

[0108] In this process Continuous evolution, no longer limited by the number of discrete layers, and parameters Shared throughout the entire continuous interval.

[0109] Step VIII, at depth At (or any desired time resolution node), the neural ODE completes the forward integration and outputs the final hidden state. After mapping through a fully connected layer, the original predicted action feature sequence for the initial iteration is obtained. :

[0110]

[0111] This is the weight matrix of the fully connected layer; This is the bias vector for the fully connected layer. The original predicted action feature sequence generated for mapping.

[0112] Numerical solvers (such as the Runge-Kutta method) can output prediction results at any time resolution, which are then mapped to future action feature sequences (such as acceleration and rate of change of angular velocity) through a fully connected layer.

[0113] Step 5: To evaluate the current parameters (as well as , The quality of the loss function is determined by combining kinematic and dynamic constraints, and an explicit regularization strategy is used to construct the total loss function. ;

[0114] The explicit regularization in the loss function of the deep learning model Introducing physical loss terms This allows the model to learn physical laws; the total loss is defined as the weighted sum of prediction error and physical loss:

[0115]

[0116] in: For the predicted original action feature sequence The mean squared error between the sequence and the actual action feature sequence. The physical loss term, i.e., the prediction result. Penalties for violating dynamic constraints (such as exceeding normal overload limits). This is the regularization coefficient, used to balance prediction accuracy and physical consistency.

[0117] Step 6: Using the Adam optimizer, iteratively update the algorithm through backpropagation to solve for the solution that minimizes the total loss. Minimal optimal parameters for deep learning model .

[0118] Minimize the total loss function This allows the model to learn to obey physical laws while fitting data.

[0119] Since the state evolution in the transformation differential equation depends on the parameters The loss calculation depends on the evolution results. These two elements constitute a complete closed-loop optimization process. To solve for the total loss... Minimum optimal parameters It employs the Adam optimizer and performs iterative updates using the backpropagation algorithm.

[0120] Since solving the neural ODE involves a large number of intermediate time steps, explicitly storing all states would exhaust memory. Therefore, the adjoint method is introduced to efficiently compute the gradient. The specific mathematical solution process is as follows:

[0121] Define the accompanying state and the accompanying ODE:

[0122] Define the accompanying state According to variational methods and integrals by parts, the adjoint state satisfies the adjoint ODE of reverse evolution:

[0123]

[0124] Its boundary conditions (terminal time) The initial value of is the gradient of the loss with respect to the terminal state:

[0125]

[0126] Inverse solution with ODE:

[0127] from arrive By reversing the above-mentioned adjoint ODE, the adjoint state sequence is obtained. .

[0128] Calculate the loss against the parameters gradient:

[0129] Yes The results obtained from the forward process The loss function with respect to the parameters can be calculated using the following integral. gradient:

[0130]

[0131] Iteratively update parameters using the Adam optimizer:

[0132] Calculate the gradient Then, it is input into the Adam optimizer to update the parameters. Let the current iteration number be... The learning rate is The parameter update formula is:

[0133]

[0134] Through multiple iterations of the above "forward computation" Assess the loss Accompanied by inverse gradient update The process of "fitting data" allows the model to learn to obey physical laws. When the loss function converges to its minimum, the final optimal parameters are obtained. .

[0135] Step 7: In the prediction phase, input the dynamic state sequence and type of the aircraft's historical time. The deep learning model uses the optimal parameters. After encoding and decoding, trajectory prediction is performed to output the original action features. ;

[0136] Step 8: Connect a physical correction layer after the output layer of the decoder to receive the original action feature sequence predicted by the deep learning model. Then, implicit regularization is used to prune the data according to the corresponding dynamic constraints to generate the final motion features that conform to the physical limits. The flight trajectory is predicted by kinematic integral.

[0137] Implicit regularization is applied to the decoder output during the prediction phase, followed by strong clipping of out-of-bounds values, specifically:

[0138] For original action characteristics The Dimensional original action characteristics The "prune" function is used to force it back into the physically feasible region:

[0139] The formula for the "Clip" function is: ;

[0140] in and Corresponding to the first of aircraft S Minimum and maximum values ​​of dimensional dynamic constraints;

[0141] Finally, the original action features in all dimensions are "trimmed" dimension by dimension to obtain the physically feasible domain:

[0142] .

[0143] and These represent the lower and upper bounds of the physical limits for each dimension, respectively. The original action features are of any dimension;

[0144] Step 6: Input the dynamic state sequence and type of the aircraft under test in the past time. The deep learning model encodes and decodes the original motion features. After being clipped by the physical correction layer, the final motion features (such as acceleration and rate of change of angular velocity) of the future prediction window are obtained. The physically consistent motion feature sequence within the next prediction window is calculated by kinematic integration, which is the predicted flight trajectory.

[0145] This invention deeply integrates physical knowledge into the model by adding a physical loss term (explicit) to the loss function and a physical correction layer (implicit) to the network structure. Explicit constraints guide the model to learn physical laws during training, while implicit constraints enforce the physical feasibility of the output during prediction. Its working principle is as follows: Figure 3 As shown, this is achieved by projecting the original prediction onto the physically feasible region.

[0146] Example:

[0147] This embodiment was conducted in a simulated low-altitude traffic management (UTM) system environment. The hardware platform used a high-performance server equipped with an NVIDIA A100 GPU, and the software environment was based on the Ubuntu 20.04 operating system, using the Python 3.8 programming language and the PyTorch 1.12 deep learning framework. The training and testing data were derived from the publicly available ADS-B dataset and simulated flight trajectories, with a data sampling frequency of 10Hz.

[0148] The specific steps are as follows:

[0149] Step 1: Multi-source heterogeneous data acquisition and preprocessing

[0150] The goal of this step is to transform raw, multi-source trajectory data into clean, aligned sequence data rich in dynamic features, providing high-quality input for model training.

[0151] First, raw historical flight trajectory data of low-altitude aircraft from multi-source sensing devices such as radar, ADS-B, and GPS are acquired, including timestamps, longitude, latitude, and altitude. Then, preprocessing is performed:

[0152] (1.1) Data cleaning: The moving average filter is used to remove instantaneous outliers. For data segments with fewer than 3 consecutive missing points, cubic spline interpolation is used to fill them in. For longer missing segments, the trajectory of that segment is discarded directly.

[0153] (1.2) Spatiotemporal alignment: All location data are converted to the WGS-84 geocentric rectangular coordinate system (ECEF), and timestamps are uniformly converted to Coordinated Universal Time (UTC).

[0154] (1.3) Feature Engineering: Based on the aligned position sequence The core dynamic state is calculated using central difference:

[0155] Velocity vector:

[0156]

[0157] Acceleration vector:

[0158]

[0159] Heading angle and turning angular velocity:

[0160]

[0161]

[0162] Climb rate:

[0163]

[0164] This ultimately forms the feature vector for each time step. .

[0165] Step 2: Construct parameterized, pluggable, differentiated dynamic constraint modules

[0166] For different types of aircraft, a parameterized set of simplified flight kinematics and dynamics constraints is established, which constitutes a "physics plugin library" that can be called by neural networks. The constraint set is stored in the form of structured data (such as JSON or XML files) and categorized by aircraft type. Perform indexing.

[0167] This step aims to establish a structured "physics plugin library" that allows the model to dynamically invoke appropriate physical constraints based on the aircraft type. This module is stored in JSON file format, for example:

[0168] {

[0169] "fixed_wing": {

[0170] "v_max": 80.0, "v_min": 20.0,

[0171] "n_z_max": 3.5, "a_t_max": 5.0

[0172] },

[0173] "multirotor": {

[0174] "v_max": 20.0, "v_min": 0.0,

[0175] "n_z_max": 2.0, "a_t_max": 8.0

[0176] }

[0177] }

[0178] The advantage of this design is that when a new type of aircraft is introduced, only the corresponding JSON configuration items need to be added or modified, without changing the model code or retraining, which greatly improves the scalability and maintenance efficiency of the system.

[0179] Step 3: Design a neural network that integrates explicit and implicit regularization

[0180] We construct a deep learning model with an encoder-decoder framework and a neural ODE (Ordinary Differential Equation) as the core prediction unit, and innovatively integrate two physical regularization strategies.

[0181] Specifically:

[0182] (3.1) Network architecture: The encoder uses a 4-layer Transformer to process the historical state sequence of length T. Encoded as context vector The decoder employs a neural ODE, whose state evolution follows the differential equation:

[0183]

[0184] Neural ODE from Initialize, and continuously evolve to the future state.

[0185] (3.2) Explicit Regularization Strategy: During training, for normal overload constraints, the penalty function can be defined as follows:

[0186]

[0187] By minimizing During training, the model is guided to learn not to produce outputs that violate the laws of physics.

[0188] (3.3) Implicit Regularization Strategy (Key Innovation): During prediction, the original acceleration of the neural ODE output. There may still be minor out-of-bounds errors. To address this, a physical correction layer is designed to perform a mathematical projection operation. The core idea is to find the point within the physically feasible region C that is closest to the original prediction, achieved through the following optimization formula:

[0189]

[0190] To specifically implement this projection, when the feasible region C is defined by simple upper and lower bounds (such as maximum tangential acceleration) and maximum normal acceleration This projection operation can be efficiently performed using a dimension-by-dimensional "clipping" function, the specific formula of which is as follows:

[0191]

[0192]

[0193] in, .

[0194] The significance of this formula lies in the fact that it forces any non-compliant predictions to be rejected. By "pulling back" to the physical limits in every dimension, the generation of absurd predictions is fundamentally eliminated, which is the key to ensuring physical consistency in this invention.

[0195] Step 4: Achieve condition adaptation for multiple aircraft types

[0196] The aircraft type is one-hot encoded to generate a conditional vector. The condition vector The historical dynamic state sequence is input into the encoder along with the input concatenation and conditional embedding.

[0197] Input concatenation is to... It is concatenated with the dynamic state vector at each time step to form an augmented input vector.

[0198] Conditional embedding is to Mapped to a conditional embedding vector through an embedding layer. Then It is added to the input or output of each layer of the encoder, or used to generate the initial state of the decoder neural ODE.

[0199] Through conditional embedding, the model is guided to make predictions based on... The value is activated from the "Physics Plugin Library" and the dynamic constraint parameters corresponding to the type are applied.

[0200] This step enables a single model to handle multiple aircraft types by performing one-hot encoding on the aircraft type (e.g., "fixed_wing") to obtain a vector. Do not use directly Instead, it maps it to a 64-dimensional conditional embedding vector through an embedding layer. Then, It is broadcast and added to the input of each layer of the encoder.

[0201] The advantage of this approach is that the embedding layer can learn the potential similarities between different device models, while the addition operation is an efficient and gentle way of fusing information. It guides the model to calculate attention based on... The value of adapts to adjust the weights of different dynamic characteristics, thereby activating and applying the correct constraint parameters from the "Physics Plugin Library".

[0202] Step 5: Model Training and Prediction

[0203] The neural network was trained end-to-end using 100,000 labeled historical data points. An optimizer such as Adam was employed, with an initial learning rate of 1e-4, and a cosine annealing strategy was used to decay the learning rate to 0 over 100 epochs. The gradient was minimized using the backpropagation algorithm to minimize the total loss function. This allows the model to learn to update all network parameters in accordance with physical laws while fitting data. Even if the physical correction layer itself has no parameters, the gradient can still penetrate it, thus affecting the learning of the neural ODE. During prediction, the input is the dynamic state sequence of the aircraft over the most recent 5 seconds (50 time steps) and its type. The model outputs a physically consistent sequence of motion features (such as acceleration and rate of change of angular velocity) for the next 10 seconds. This sequence can be integrated to obtain a smooth future trajectory.

[0204] To verify the superiority of this invention, it was compared with a pure LSTM prediction model on the same test set. The test scenario included a rare maneuver involving a fixed-wing aircraft performing a sharp turn to avoid an obstacle. The results clearly demonstrate that this invention, by incorporating physical constraints, effectively suppresses the "illusion" of data-driven models in sparse data regions, generating reliable predictions that conform to both data patterns and physical common sense, proving its significant advantages in improving safety and reliability.

Claims

1. A method for predicting the state of multiple types of aircraft by incorporating physical constraints, characterized in that, The specific steps are as follows: Step 1: For different types of low-altitude aircraft, each aircraft acquires its own historical flight trajectory raw data from its multi-source sensing devices and performs preprocessing. Step 2: Establish a set of parameterized simplified flight kinematics and dynamic constraints for each type of aircraft, store them in structured data format, and index them by aircraft type; Step 3: Perform one-hot encoding on each aircraft type to generate its own condition vector; Step 4: Using the conditional vectors of each aircraft and the preprocessed raw data, construct a deep learning model with an encoder-decoder framework and a neural ODE as the core prediction unit. The encoder employs a 4-layer Transformer structure to receive the preprocessed raw data sequence and extract deep temporal features, encoding them into a high-dimensional context vector. The output is fed to the decoder; the decoder uses a neural ODE as the core prediction unit, utilizing its continuous-time modeling characteristics to describe the dynamic evolution of the aircraft, and obtains the original predicted action feature sequence. ; Step 5: Combining kinematic and dynamic constraints, construct the total loss function using an explicit regularization strategy. ; Total loss is defined as the weighted sum of prediction error and physical loss: in: For the predicted original action feature sequence The mean squared error between the actual action feature sequence and the actual action feature sequence; The physical loss term, i.e., the prediction result. Penalty terms for violating dynamic constraints; The regularization coefficient is used. Step 6: Using the Adam optimizer, iteratively update the algorithm through backpropagation to solve for the solution that minimizes the total loss. Minimal optimal parameters for deep learning model ; Step 7: In the prediction phase, input the dynamic state sequence and type of the aircraft's historical time. The deep learning model uses the optimal parameters. After encoding and decoding, the original action features are output. ; Step 8: Connect a physical correction layer after the output layer of the decoder to receive the original action feature sequence predicted by the deep learning model. Then, implicit regularization is used to prune the data according to the corresponding dynamic constraints to generate the final motion features that conform to the physical limits. Flight trajectory is predicted by kinematic integral; Implicit regularization enforces strong pruning of out-of-bounds values, specifically: For original action characteristics The Dimensional original action characteristics The "prune" function is used to force it back into the physically feasible region: The formula for the "Clip" function is: ; in and Corresponding to the first of aircraft S Minimum and maximum values ​​of dimensional dynamic constraints.

2. The method as described in claim 1, characterized in that, In step one, the raw data includes timestamps, three-dimensional spatial location (i.e., longitude, latitude, and altitude), velocity, and acceleration; preprocessing includes data cleaning, spatiotemporal alignment, and feature engineering.

3. The method as described in claim 1, characterized in that, In step two, the kinematic constraints include: maximum / minimum flight speed. Maximum / Minimum Climb Rate Maximum turning angular velocity ; Dynamic constraints include maximum normal overload , maximum tangential acceleration Minimum turning radius .

4. The method as described in claim 1, characterized in that, In step three, the set of aircraft types is as follows: in The total number of aircraft types; Aircraft type The generated condition vector for A dimensional vector, its formula is: in: The condition vector is represented by the first... There are 1, 2, ..., K components; that is, the condition vector c is the one-hot encoded vector of the aircraft type type.

5. The method as described in claim 1, characterized in that, In step four, the specific principle of the deep learning model is as follows: Step I: For the current aircraft S, the encoder receives the preprocessed raw data sequence. The augmented input sequence is obtained by fusing the conditional vector c. ; The formula for incorporating splicing is: Step II: Through the self-attention mechanism within the Transformer layer, combined with the pooling layer, the input sequence is processed. Encode as a high-dimensional context vector The output is sent to the decoder; Step III: The decoder receives the context vector output by the encoder and initializes the hidden state: Step IV: Convert the condition vector of aircraft S Through the embedding layer, it is mapped to a conditional embedding vector. Input encoder; This is the embedding layer mapping function, with a total of 64 dimensions; Step V, Conditional Embedding Vector The inputs and outputs of each layer of the encoder are broadcast and added together: in, For encoder number The input or output characteristics of the layer Features after fusing conditional information; Step VI: Discretize the number of layers of the encoder Treat as continuous variables Discrete changes between layers are transformed into changes in the continuous "time / depth" dimension. Differential equation: in Total number of layers corresponding to the encoder , Corresponding encoder This indicates continuous "depth". The hidden state; The parameter is Neural network functions, Random initialization; Step VII: Using a numerical solver, along the "depth / time" dimension From 0 to Integrating the above differential equation forward yields the sequence of future hidden states: Step VIII, at depth At this point, the neural ODE completes the forward integral and outputs the final hidden state. After mapping through a fully connected layer, the original predicted action feature sequence for the initial iteration is obtained. : This is the weight matrix of the fully connected layer; This is the bias vector for the fully connected layer.

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