Unmanned aerial vehicle trajectory prediction method fusing deep neural network and multi-dimensional geometric correction

Abstract

The present application proposes a UAV trajectory prediction method fusing deep neural network and multi-dimensional geometric correction, belonging to the technical field of UAV control. The present application is to solve the problems of strong nonlinearity, large cumulative error and insufficient generalization ability of single model in UAV trajectory prediction. It includes: S1: obtaining three-dimensional position data of the UAV, and standardizing the three-dimensional position data; S2: constructing single-step training samples based on the standardized historical trajectory data; S3: training the double-layer LSTM network fusing self-attention mechanism according to the single-step prediction training samples; S4: generating the preliminary prediction trajectory by recursive multi-step prediction using the trained double-layer LSTM network fusing self-attention mechanism; S5: post-processing the preliminary prediction trajectory based on the UAV motion attitude information, and outputting the final prediction trajectory.

Description

Technical Field

[0001] This invention relates to a method for predicting the trajectory of unmanned aerial vehicles (UAVs) that integrates deep neural networks and multidimensional geometric correction, and belongs to the field of UAV control technology. Background Technology

[0002] In typical UAV mission scenarios, UAVs need to execute mission objectives precisely within limited time and maneuverability constraints. Target UAVs are typically characterized by low flight altitude, complex penetration paths, and high maneuverability, resulting in nonlinear, time-varying, and uncertain flight trajectories. If guidance relies solely on the target's current position and velocity information, it becomes difficult to maintain effective mission execution when the target is performing high-maneuvering or evasive maneuvers, leading to decreased mission efficiency or even mission failure.

[0003] To improve mission success rates, the guidance and control system must, based on current observation information, anticipate the target's movement trends and possible trajectories over a future period—that is, predict the future trajectory of the target UAV. The trajectory prediction module, through comprehensive analysis of historical observation data and target motion characteristics, outputs a sequence of target states within a specific prediction time domain, such as the three-dimensional position, velocity, and heading angle at several future moments.

[0004] Sliding mode guidance, as a guidance method based on sliding mode variable structure control theory, has advantages such as strong robustness and insensitivity to model uncertainties and external disturbances, making it suitable for UAV missions with high target maneuverability and complex environments. Traditional sliding mode guidance laws are mostly constructed based on relative motion information at the current moment or in short-term history (such as relative distance, relative velocity, line-of-sight angle and its rate of change), failing to fully utilize information about the target's future motion trends. When the target performs large maneuvers or evasive maneuvers, traditional sliding mode guidance may exhibit response lag, leading to frequent sliding surface switching and increased control chatter, thus affecting mission execution accuracy and control quality.

[0005] Introducing trajectory prediction results into sliding mode guidance allows the trajectory prediction module to obtain the target's estimated position and velocity at several future moments during guidance. This enables the design of the sliding surface to consider the target's future relative motion, thus constructing forward-looking sliding mode variables. For example, based on the traditional sliding surface that focuses on current position and velocity errors, a predicted relative position error term can be introduced. This allows the system to react to the target's impending maneuvers before reaching the sliding surface, thereby improving the system's dynamic performance and tracking capability.

[0006] By incorporating a compensation term based on prediction error into the sliding mode control law, guidance commands can be corrected in advance, resulting in smoother attitude and speed adjustments for the UAV and effectively reducing chattering in the switching function. Predictive information allows the guidance law to adjust its trajectory early in the maneuvering phase of a sudden maneuver, rather than relying entirely on "post-mortem correction," thus shortening the overall mission execution time and reducing terminal deviation.

[0007] Even in situations where sensor noise, occlusion causing intermittent observations, or even short-term target loss exist, the trajectory prediction module can provide continuous target state estimates within a certain timeframe. This ensures the sliding mode guidance law remains effective and prevents guidance law failure due to missing observations. Furthermore, by combining state estimation methods such as extended Kalman filtering, the prediction results can be filtered and corrected, improving the reliability of the target state input and providing a more robust data foundation for robust sliding mode guidance control.

[0008] At a higher level, trajectory prediction not only serves the design of the underlying sliding mode guidance law, but can also work collaboratively with the upper-level trajectory planning module to form an integrated decision-making framework of "motion prediction—sliding mode guidance—trajectory planning". The prediction module provides the target's future trajectory, the trajectory planning module generates the optimal or suboptimal trajectory based on the prediction information, and the sliding mode guidance module is responsible for tracking the planned trajectory and resisting disturbances at the execution level. Through this layered collaborative approach, the overall intelligence level of the UAV system can be significantly improved. Summary of the Invention

[0009] To address the problems of strong nonlinearity, large cumulative error, and insufficient generalization ability of single models in UAV trajectory prediction, this invention proposes a UAV trajectory prediction method that integrates deep neural networks and multidimensional geometric correction.

[0010] The technical solution adopted by the present invention to solve the above problems is as follows: The present invention includes the following steps:

[0011] Step 1: Acquire the 3D position data of the UAV and standardize the 3D position data; Step 2: Construct single-step training samples based on standardized historical trajectory data; Step 3: Train the two-layer LSTM network with self-attention mechanism based on the single-step prediction training samples; Step 4: Use the trained two-layer LSTM network with fusion self-attention mechanism to generate the initial predicted trajectory through recursive multi-step prediction; Step 5: Post-process the preliminary predicted trajectory based on the UAV's motion attitude information and output the final predicted trajectory.

[0012] Furthermore, step 1 specifically includes: Using the reference point of the UAV mission area as the origin O, with the N-axis pointing due north to the origin O, the E-axis pointing due east to the origin O, and the D-axis pointing vertically downwards from the origin O, an inertial approximate coordinate system is established. The three-dimensional position trajectory data of the target UAV in this inertial approximate coordinate system is then acquired. Based on this three-dimensional position trajectory data, the three-dimensional position data of the target UAV is obtained. ; The difference between adjacent sampling points in the three-dimensional position trajectory of the target UAV is calculated to obtain an approximate velocity vector. The pitch angle of the target UAV is then calculated based on the approximate velocity vector. ; Obtain planar velocity components from the three-dimensional position trajectory of the UAV based on the N-axis and E-axis, and calculate the horizontal yaw angle of the target UAV based on the planar velocity components; The 3D position data of the target UAV is divided into training data and test data in chronological order, and the mean of each dimension in the training data is calculated. and standard deviation And standardize the corresponding dimensions in the training and test data; 3D position data of the target UAV The expression is: (1); In formula (1), These represent the coordinate components of the UAV in the north, east, and down directions, respectively, with T being the transpose. The pitch angle of the target drone The expression is: (2); In formula (2), For the vertical component of the drone, The horizontal velocity modulus of the drone; Yaw angle of the target drone The expression is: (3); In formula (3), Let E be the velocity component of the UAV along the E-axis. Let be the velocity component of the UAV in the N-axis direction.

[0013] Furthermore, in step 2, the single-step training samples are constructed using a sliding window, with the current state as the input and the next state as the supervisory output, forming an input-output pair; the multi-step prediction input sequence is historical trajectory window data of fixed length.

[0014] Furthermore, the two-layer LSTM network that integrates the self-attention mechanism in step 3 includes a first-layer LSTM network, a second-layer LSTM network, and a self-attention module. The first LSTM layer of the dual-layer LSTM network is used to extract high-dimensional features, and the second LSTM layer is used for feature compression and temporal inference. The self-attention module is used to model the global dependency of the historical sequence. A Dropout layer is introduced after each LSTM layer, and L2 regularization is added to the optimizer. The optimizer is used to train the dual-layer LSTM network with the self-attention mechanism. The initial learning rate is set to a preset value and decays by a fixed proportion after training reaches a preset number of rounds. At the same time, a gradient threshold is set to limit the gradient range.

[0015] Furthermore, the training steps in step 3 include: Step 3.1: Input the single-step prediction training samples into the first-layer LSTM network to extract high-dimensional temporal features, and input the high-dimensional temporal features into the second-layer LSTM network for feature compression and temporal inference to obtain the hidden state sequence for each time step. ; Step 3.2: Input the hidden state sequence into the self-attention module. By introducing a multi-head self-attention mechanism into the encoding sequence in the hidden state sequence, construct Q, K and V vectors respectively, where Q is the query vector, K is the key vector and V is the value vector. Obtain the self-attention output based on the Q, K and V vectors. Step 3.3: Decode the sequence of self-attention output and update the parameters of the two-layer LSTM network with the self-attention mechanism using the loss function. Continue until convergence, obtaining the optimal parameters. ; Hidden state sequence at each time step The expression is: (4); In formula (4), The length of the sliding window. For; column vector The expressions for vectors Q, K, and V are: (5); In formula (5), H is derived from... The matrix formed The projection matrix is ​​learnable; The expression for the self-attention output is: (6); In formula (6), T For transpose, For normalized exponential functions, is the dimension of the key vector.

[0016] Furthermore, step 4 specifically includes: The trained two-layer LSTM network is used to perform forward propagation on the current window to obtain the prediction result of the next time step. The prediction result of the next time step is used as the multi-step prediction input sequence and appended to the historical sequence. The data point of the earliest time step is removed to form the updated historical window. Based on the updated historical window, combined with the optimal parameters Repeat steps 3.1-3.3 iteratively to perform the prediction process and obtain the preliminary predicted trajectory of the multi-step future trajectory. .

[0017] Furthermore, step 5 specifically includes: The actual trajectory of the target drone By performing a difference operation, the displacement vector between adjacent sampling points is obtained. ; displacement vector between adjacent sampling points Normalization is performed to construct the unit motion direction of the target UAV at each moment. The real-time attitude direction of the UAV is obtained based on the unit motion direction of the target UAV at each moment; Preliminary trajectory prediction With the actual trajectory By comparing the results, the prediction error vector at each time point can be obtained. Calculate the projection of the prediction error vector onto the real-time attitude direction. ; Utilizing projection The initial predicted trajectory is fine-tuned along the unit movement direction of the target UAV to obtain the final predicted trajectory; Displacement vector between adjacent sampling points The expression is: (7); In formula (7), for k The drone's actual location at time +1 for k The real-time location of the drone; Unit direction of motion The calculation formula is: (8); In formula (8), ε is a small constant introduced to prevent the denominator from being zero; Prediction error vector at each time point The calculation formula is: (9); Projection The calculation formula is: (10); In formula (10), T This is a transpose.

[0018] The beneficial effects of this invention are: 1. After obtaining the instantaneous attitude direction of the target trajectory, this invention projects the prediction error onto this direction, achieving attitude-based orientation correction of multi-step predicted trajectories. Without altering the network structure, it effectively reduces systematic bias, maintains the smoothness and flightability of the three-dimensional trajectory geometry, and provides more reliable prediction input for subsequent sliding mode guidance and interception trajectory planning.

[0019] 2. Compared with other models, the dual-layer LSTM+ attitude correction model constructed in this invention performs best in the spiral trajectory prediction task. It not only significantly reduces the average error, but also achieves a stable improvement in the final displacement error. Attached Figure Description

[0020] Figure 1 A flowchart illustrating a method for predicting UAV trajectories by integrating deep neural networks and multidimensional geometric correction; Figure 2 This is a diagram of the RNN network structure. Figure 3 Here is a diagram of the LSTM network structure; Figure 4 The image shows the trajectory prediction results of the drone using an LSTM network. Figure 5 The image shows the trajectory prediction results of a drone using a two-layer LSTM network. Figure 6 This is a diagram showing the trajectory prediction results of the UAV according to the present invention. Detailed Implementation

[0021] Unmanned aerial vehicle (UAV) trajectory prediction can be viewed as a typical time series prediction problem. Its core task is to infer the position and attitude changes of a target UAV over a future period, based on historical trajectory information of a certain length. The UAV trajectory prediction problem can be modeled as single-step and multi-step trajectory prediction problems. Let's assume the target UAV is at discrete time points... The state vector is (1); In formula (1), Represents three-dimensional position coordinates. Represents the velocity component. This represents the heading angle. This invention focuses on position trajectory prediction; in actual modeling, it is typically selected as... As the primary target for time series forecasting.

[0022] Based on the different prediction time domains and application requirements, trajectory prediction can be divided into two categories: single-step prediction and multi-step prediction. In single-step prediction scenarios, the model utilizes a length of... Historical state sequence To predict the state at the next moment: in This represents the prediction model determined by the parameter θ. Single-step prediction is mainly used to model the local dynamic laws of the trajectory and provides a basis for multi-step prediction.

[0023] In interception and guidance missions, the guidance system focuses more on the motion trends at multiple future moments, requiring it to provide multi-step predictions simultaneously at the current moment. (2); Multi-step prediction can employ two typical strategies: recursive multi-step prediction, which first trains a single-step prediction model and then uses the model output as the input for the next step to perform rolling prediction; and direct multi-step prediction, which directly uses a historical sequence as input and outputs the entire future sequence.

[0024] This invention addresses the real-time requirements and complexity of UAV interception missions by employing a "single-step supervision + recursive multi-step prediction" approach: During the training phase, single-step supervised modeling is used to continuously optimize parameters through a normalized sliding window; during the testing phase, based on the latest historical window, a closed-loop rolling recursive strategy is employed to gradually generate complete future multi-step trajectories. To evaluate prediction performance, this invention uses metrics such as average displacement error and final displacement error to comprehensively evaluate the multi-step prediction results. Figure 1 As shown, the steps of the UAV trajectory prediction method integrating deep neural networks and multidimensional geometric correction described in this embodiment include: S1: Obtain the historical trajectory / status dataset of the drone; Before predicting the trajectory of a UAV, it is necessary to first define the coordinate system of the motion space and appropriately select the state variables to describe the motion state of the UAV. Commonly used coordinate systems include geographic coordinate systems, ground-fixed coordinate systems, and body coordinate systems. Considering that interception missions mostly occur in local airspace with relatively limited altitude changes, this invention adopts a North-East-Down (NED) coordinate system centered on the interception area as an inertial approximation coordinate system to describe the translational motion of the UAV within the local area.

[0025] Let O-NED be an inertial approximate coordinate system, with its origin O located at the reference point in the interception area, and the N-axis pointing due north. The E-axis points due east, and the D-axis points vertically downwards. In this coordinate system, the three-dimensional position of the UAV can be represented as: (3); In formula (3), These represent the coordinate components of the UAV in the north, east, and down directions, respectively, with T being the transpose. The corresponding velocity vector can be expressed as: (4); In obtaining the three-dimensional position trajectory Then, the difference between adjacent sampling points is calculated to obtain an approximate velocity vector. Based on this, the target's horizontal yaw angle and pitch angle, as well as the target UAV's pitch angle, can be calculated. Calculation based on vertical component and horizontal velocity modulus: (5); In formula (5), For the vertical component of the drone, The horizontal velocity modulus of the drone; Yaw angle of the target drone Calculated from planar velocity components: (6); In formula (6), Let E be the velocity component of the UAV along the E-axis. Let be the velocity component of the UAV in the N-axis direction.

[0026] Through the above steps, this invention not only obtains the target's three-dimensional position trajectory but also acquires information such as yaw angle and pitch angle, reflecting changes in motion direction and attitude. In subsequent modeling, the training of the prediction network mainly focuses on the position state. The attitude angle information is mainly used for post-processing of the prediction results to further improve the prediction accuracy.

[0027] S2: Data partitioning and standardization; To construct a trajectory dataset suitable for time-series learning, this invention divides the generated 3D position sequences into training and test sets in chronological order. Considering the need to ensure the number of training samples and the coverage of typical maneuvering processes by the test samples, this invention adopts a fixed-ratio division: the first 80% of the data points are used as training data, and the remaining 20% ​​as test data. The training set is primarily used for network parameter learning, while the test set is used to evaluate the model's predictive performance on unseen data.

[0028] To eliminate the problems of dimensional differences and numerical scale inconsistencies between different dimensions, this invention addresses the issues in the training data. The components are standardized. Specifically, the mean μ and standard deviation σ of each dimension are calculated based on the training set, and then the corresponding dimensions in both the training and test sets are standardized using the same parameters. (7); In formula (7), μ and σ are the mean and standard deviation vectors of the training set location coordinates in each dimension, respectively. This process unifies the data across dimensions to the same numerical scale, which is beneficial for stable training and gradient propagation of deep networks, preventing learning bias caused by a single dominant feature. After standardization, this invention constructs the trajectory prediction task as a time series learning problem that transitions from single-step to multi-step prediction. Taking the training set as an example, for the standardized location sequence... By constructing: (8); This involves using the current state as input and the next state as the supervised output, forming a large number of input-output pairs to train the LSTM network to learn the temporal evolution of the target trajectory. The test set uses the same method to construct the input sequence, while retaining the unnormalized true output. This allows for the direct assessment of prediction errors from the perspective of physical quantities after inverse normalization.

[0029] S3: Training of a two-layer LSTM network incorporating a self-attention mechanism; The self-attention mechanism of the two-layer LSTM network in this invention includes a two-layer LSTM network and a self-attention module. The LSTM network is a variant of the RNN algorithm, with the RNN specifically designed for sequential data. The structure of the RNN network is as follows: Figure 2 As shown, it introduces feedback into the hidden layers, combining the output of the previous time step with the current input in the computation, essentially creating a deep network unfolded in the time dimension. Therefore, it can capture the dynamic features of time series after training, enabling sequence modeling and prediction. The LSTM network serves as a fundamental time series prediction model. This model can not only connect features from the previous time step with features from the next time step, but also solve the problems of gradient explosion and gradient vanishing during training. Furthermore, LSTM effectively alleviates gradient explosion and vanishing problems by introducing three gating systems—input gate, forget gate, and output gate—into traditional recurrent neural networks, enabling it to capture the dynamic dependencies of trajectories over a longer time span. The structure of the LSTM network is shown below. Figure 3 As shown.

[0030] The formula for the forget gate in the three gating systems of LSTM is as follows: , This represents the input sequence of the LSTM neural network, which is the k-dimensional input vector of the data at time t, where k represents the dimension of the data. It is the Sigmoid function. This is the hidden state from the previous moment. This is the current input. It determines the cell state at the previous moment. Which information is retained or suppressed? The old memory is continuously scaled within the range [0,1], with values ​​closer to 0 indicating "completely ignore this" and values ​​closer to 1 indicating "completely accept this". Next, we will enter the input gate, whose formula is: (9); This step determines which new information needs to be preserved in the cellular state. Working in conjunction with the forgetting gate, it allows the network to strike a balance between "writing new memories" and "continuing old memories," enabling it to respond to sudden events or new trends. This is divided into two parts. The first part, an S-shaped network layer called the "input gate layer," determines which information needs to be updated. The second part... The shape network layer creates a new candidate value vector. This can be used to add to the cell state. In the next step, the two parts above can be combined to generate an update to the state; the formula for this step is: Multiply the old state by It's used to forget what we've decided to forget. Then we add... This is the new candidate value, scaled proportionally to the updated value we determine for each state.

[0031] Finally, the output value is determined. The output gate determines how much internal state information is output at the current moment. The formula is: (10); First, this invention runs an S-shaped network layer to determine which parts of the cell state can be output. Then, this invention inputs the cell state into tanh (adjusting the value to...). The value between 1 and 1 is then multiplied by the output value of the S-shaped network layer, allowing the present invention to output the desired portion. This also controls the amount of information the model exposes to the next layer or the next time step, avoiding the leakage of all memory at once and helping to maintain a stable temporal abstraction level.

[0032] The above introduction mainly describes the underlying mechanisms of each unit in a single LSTM neuron. However, corresponding improvements are needed to address the research content of this invention.

[0033] While standard LSTM networks perform well in modeling short- and medium-term dependencies, their ability to model long-distance temporal dependencies remains limited when dealing with UAV trajectories spanning long periods and exhibiting multi-scale maneuvering patterns. To further enhance the ability to characterize complex trajectory patterns, this invention introduces the self-attention mechanism from the Transformer architecture into a two-layer LSTM structure, constructing a Transformer-improved two-layer LSTM trajectory prediction model. The basic idea of ​​this model is to use a two-layer LSTM to initially encode the trajectory sequence and extract local temporal features; based on this, one or more self-attention modules are introduced to perform global dependency modeling on the entire historical sequence, enabling the network to automatically focus on the historical segments most critical to the current prediction, thereby improving the accuracy and stability of multi-step predictions.

[0034] In the LSTM encoding stage, the normalized 3D position sequence is first input into a two-layer stacked LSTM network to obtain the hidden state sequence at each time step: (11); In formula (11), The length of the sliding window. for; This hidden sequence preserves trajectory evolution information within the local neighborhood, providing a basic feature representation for the self-attention layer.

[0035] In the self-attention feature enhancement stage, for the obtained encoding sequence A multi-head self-attention mechanism is introduced. For each time step, a query, key, and value vector are constructed respectively: (12); In formula (12), H is derived from... The matrix formed The projection matrix is ​​learnable; the self-attention output can be written as: (13); In formula (13), T For transpose, For normalized exponential functions, is the dimension of the key vector.

[0036] Through the above operations, the representation of each time step not only includes the LSTM features of its local neighborhood, but also incorporates the time information that is highly correlated with it in the entire historical sequence, which is beneficial for characterizing trajectory dependencies over long periods of time.

[0037] The sequence representation enhanced by self-attention is then input into a second-stage LSTM or decoding network to generate multi-step predictions of future trajectories. Similar to the standard LSTM model, the output still uses fully connected layers and regression layers to map high-dimensional features to a three-dimensional location space, achieving [the desired result]. The gradual prediction.

[0038] S4: Obtain the preliminary predicted trajectory based on the trained two-layer LSTM network; In practical missions, guidance and control systems are often not concerned with single-step short-term predictions, but rather with the ability to predict trajectories over a future period given historical information. Therefore, this invention extends the prediction process to rolling multi-step prediction, building upon single-step supervised learning.

[0039] In actual processing, during the testing phase, a length of [length value] is first selected. The historical window is used as the model input: (14); The trained LSTM network is used to perform forward propagation on the current window to obtain the prediction result for the next time step. The prediction result is then appended as new input to the end of the historical sequence, and the earliest data point is removed, thus forming a new historical window: (15); Repeat the above process until a length of [length missing] is obtained. The rolling prediction method can generate multi-step future trajectories by utilizing only a limited amount of historical information, which aligns with the "continuous prediction and continuous updating" usage pattern in real-world task scenarios.

[0040] During error evaluation, this invention performs inverse normalization on the prediction results to restore them to the physical coordinate space: (16); Subsequently, the multi-step prediction performance is evaluated from both overall and final perspectives by comparing the actual trajectory with the actual trajectory for the corresponding time period, and by calculating indicators such as average displacement error (ADE) and final displacement error (FDE).

[0041] S5: Post-processing of preliminary prediction results based on attitude information; Deep LSTM networks can effectively depict the overall motion trend of UAVs when predicting their 3D trajectories in multiple steps. However, under conditions of noise interference, complex maneuvers, and limited training samples, the prediction results directly output by the network may still exhibit issues such as uneven height changes or slight deviations in spatial morphology in local segments. To improve the geometric consistency and physical plausibility of the predicted trajectory, this invention further introduces a post-processing strategy based on motion attitude information to perform targeted corrections on the prediction results, building upon the network output.

[0042] Specifically, firstly, the actual trajectory By performing a difference operation, the displacement vector between adjacent sampling points is obtained: (17); In formula (17), for k The drone's actual location at time +1 for k The real-time location of the drone; Then, normalize the data to construct the target's unit motion direction at each time step: (18); In formula (18), ε is a small constant introduced to prevent the denominator from being zero; This unit vector This describes the instantaneous motion attitude and direction of the UAV in three-dimensional space, which can be regarded as a simplified expression of the target attitude using geometric information. To maintain consistency with the length of the predicted trajectory, insufficient samples at the end are padded by repeating the attitude vector from the previous moment, thus forming a complete attitude direction sequence throughout the entire prediction interval.

[0043] After obtaining the attitude orientation, the predicted trajectory output by the two-layer LSTM is... By comparing the prediction with the actual trajectory, the prediction error vector at each time step is obtained: (19); To fully utilize attitude information, instead of directly correcting the error isotropically, we first calculate the projection of the error onto the attitude direction: (20); In formula (20), T This is a transpose.

[0044] Using this projection, the prediction results can be fine-tuned along the target's direction of motion to reduce systematic errors in the "flight direction".

[0045] In summary, this invention, after obtaining the instantaneous attitude direction of the target trajectory, projects the prediction error onto that direction, achieving attitude-based orientation correction of multi-step predicted trajectories. This method effectively reduces systematic bias without altering the network structure, maintaining the smoothness and flightability of the three-dimensional trajectory geometry, and providing more reliable predictive input for subsequent sliding mode guidance and interception trajectory planning.

[0046] In summary, the prediction of the UAV flight trajectory has been completed. To verify the accuracy of the predicted UAV flight trajectory of this invention, the following verifications were performed in this embodiment: 1. Dataset and evaluation metrics; The lack of publicly available target trajectory datasets makes it impossible to fully support trajectory prediction research. Therefore, this invention considers using the generated dataset to construct a simulation dataset while ensuring data integrity. Furthermore, to address complex real-world scenarios, a spiraling curve is considered as the dataset.

[0047] Referring to commonly used evaluation metrics in existing methods, this invention employs average displacement error and final displacement error. The average displacement error represents the point-by-point average Euclidean distance between the predicted trajectory and the true value of the predicted trajectory. The final displacement error represents the Euclidean distance between the endpoint of the predicted trajectory and the true value of the predicted trajectory endpoint. (twenty one); (twenty two); In formulas (21) and (22), When expanded, it becomes: (twenty three); In formula (23), Let represent the predicted trajectory coordinates and the true coordinates of the trajectory points at time step t, respectively.

[0048] 2. Analysis of verification results; The initial model used a single-layer LSTM with 200 hidden units, with both input and output being three-dimensional position sequences, and the final output was directly passed through a fully connected regression layer. After several experiments, a learning rate of 0.005 was found to be suitable, reducing fluctuations in the mean squared error. During training, the Adam optimizer was used with an initial learning rate of 0.005, which was decayed by a factor of 0.2 after the 100th epoch to achieve sufficient convergence over 200 epochs. A gradient threshold of 1 was set to avoid gradient explosion. After training, the network state was "warmed up" using the training set, and then closed-loop multi-step prediction was performed on the test set. The prediction results were then inversely normalized and compared with the actual trajectories.

[0049] To facilitate a clear and intuitive presentation of the results, such as Figure 4 As shown, this invention presents multi-step prediction results for 3D and XY / XZ / YZ plane projections. Overall, the predicted trajectory maintains a consistent spiral trend with the true trajectory, indicating that a single-layer LSTM can effectively capture the phase and pitch information of the trajectory. However, with the increase of the prediction step size, the light-colored dashed line (predicted) shows a slight radial expansion relative to the dark-colored solid line (true) in the XY plane, and exhibits a significant underestimation in the XZ / YZ plane. Quantitative indicators show that the average displacement error ADE = 2.5237 and the endpoint displacement error FDE = 1.9393, indicating that the model maintains meter-level accuracy within a 20-step prediction range. The endpoint error is lower than the average, indicating that although the error accumulates over time, it does not explode.

[0050] This is a modified two-layer LSTM model based on the transformer, consisting of two LSTM layers. The first layer comprises 192 hidden units, responsible for extracting high-dimensional features; the second layer comprises 96 hidden units, responsible for feature compression and temporal inference. A Dropout layer is introduced after each LSTM layer, and L2 regularization is added to the optimizer to prevent the model from overfitting on the training data and to enhance its generalization ability.

[0051] The results are as follows Figure 5 As shown, this invention presents multi-step prediction results for 3D and XY / XZ / YZ plane projections. Experimental results demonstrate that the proposed prediction model based on deep LSTM can effectively handle nonlinear trajectory prediction tasks in three-dimensional space. The dual-layer LSTM structure ensures the model's ability to extract complex dynamic features. Although there are still small cumulative errors in long-term prediction, the geometric features of the overall trajectory are accurately preserved.

[0052] To further optimize the prediction results, attitude angle correction was introduced on the basis of the two-layer LSTM. The attitude angle was obtained by instantaneous velocity change.

[0053] The results are as follows Figure 6 As shown, numerically, FDE is slightly smaller than ADE, indicating that the divergence trend at the trajectory end is effectively suppressed after post-processing correction. The model does not exhibit an exponential increase in error over time, ensuring stability in long-term time-series prediction while improving accuracy. The comparison results of the three models are shown in Table 1.

[0054] Table 1

[0055] The ADE (Advanced Depth-of-Effect) metric shows that the two-layer LSTM model (ADE=1.7189) improves upon the pure LSTM model (ADE=2.5237) by approximately 31.9%. This indicates that increasing network depth helps capture long-term dependencies in the trajectory, improving the smoothness and consistency of multi-step predictions. However, the FDE (Fixed Depth-of-Effect) metric decreases slightly (from 1.9393 to 1.8234), indicating that the local fitting ability of the deep model still fluctuates at the final time step. After introducing the attitude correction module, the ADE of the two-layer LSTM + attitude correction model further decreases to 1.3968, and the FDE decreases to 1.3547, representing a 44.7% improvement compared to the pure LSTM model. This model's predicted trajectories on the XY, XZ, and YZ planes are closer to the actual trajectories, especially showing stronger adaptability in sections with large changes in trajectory curvature. The attitude correction module effectively suppresses trajectory drift by introducing kinematic constraints, improving the physical plausibility of the predictions.

[0056] The inference time of the three models is similar, all less than 0.1s. Moreover, the double-layer LSTM improves accuracy by 44.7% while only taking 0.017s longer, still meeting the real-time requirements.

[0057] Based on the above analysis, the two-layer LSTM + attitude correction model performs best in the spiral trajectory prediction task. It not only significantly reduces the average error, but also achieves a stable improvement in the final displacement error.

[0058] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A method for predicting UAV trajectory by integrating deep neural networks and multidimensional geometric correction, characterized in that, include: Step 1: Acquire the 3D position data of the UAV and standardize the 3D position data; Step 2: Construct single-step training samples based on standardized historical trajectory data; Step 3: Train the two-layer LSTM network with self-attention mechanism based on the single-step prediction training samples; Step 4: Use the trained two-layer LSTM network with fusion self-attention mechanism to generate the initial predicted trajectory through recursive multi-step prediction; Step 5: Post-process the preliminary predicted trajectory based on the UAV's motion attitude information and output the final predicted trajectory.

2. The UAV trajectory prediction method integrating deep neural networks and multidimensional geometric correction according to claim 1, characterized in that, Step 1 specifically includes: Using the reference point of the UAV mission area as the origin O, with the N-axis pointing due north to the origin O, the E-axis pointing due east to the origin O, and the D-axis pointing vertically downwards from the origin O, an inertial approximate coordinate system is established. The three-dimensional position trajectory data of the target UAV in this inertial approximate coordinate system is then acquired. Based on this three-dimensional position trajectory data, the three-dimensional position data of the target UAV is obtained. ; The difference between adjacent sampling points in the three-dimensional position trajectory of the target UAV is calculated to obtain an approximate velocity vector. The pitch angle of the target UAV is then calculated based on the approximate velocity vector. ; Obtain planar velocity components from the three-dimensional position trajectory of the UAV based on the N-axis and E-axis, and calculate the horizontal yaw angle of the target UAV based on the planar velocity components; The 3D position data of the target UAV is divided into training data and test data in chronological order, and the mean of each dimension in the training data is calculated. and standard deviation And standardize the corresponding dimensions in the training and test data; 3D position data of the target UAV The expression is: （1）； In formula (1), These represent the coordinate components of the UAV in the north, east, and down directions, respectively, with T being the transpose. The pitch angle of the target drone The expression is: （2）； In formula (2), For the vertical component of the drone, The horizontal velocity modulus of the drone; Yaw angle of the target drone The expression is: （3）； In formula (3), Let E be the velocity component of the UAV along the E-axis. Let be the velocity component of the UAV in the N-axis direction.

3. The UAV trajectory prediction method integrating deep neural networks and multidimensional geometric correction according to claim 1, characterized in that, In step 2, the single-step training samples are constructed using a sliding window, with the current state as the input and the next state as the supervision output, forming an input-output pair; the multi-step prediction input sequence is historical trajectory window data of fixed length.

4. The UAV trajectory prediction method integrating deep neural networks and multidimensional geometric correction according to claim 1, characterized in that, The two-layer LSTM network that incorporates the self-attention mechanism in step 3 includes a first-layer LSTM network, a second-layer LSTM network, and a self-attention module; The first LSTM layer of the dual-layer LSTM network is used to extract high-dimensional features, and the second LSTM layer is used for feature compression and temporal inference. The self-attention module is used to model the global dependency of the historical sequence. A Dropout layer is introduced after each LSTM layer, and L2 regularization is added to the optimizer. The optimizer is used to train the dual-layer LSTM network with the self-attention mechanism. The initial learning rate is set to a preset value and decays by a fixed proportion after training reaches a preset number of rounds. At the same time, a gradient threshold is set to limit the gradient range.

5. The UAV trajectory prediction method integrating deep neural networks and multidimensional geometric correction according to claim 1, characterized in that, The training steps in step 3 include: Step 3.1: Input the single-step prediction training samples into the first-layer LSTM network to extract high-dimensional temporal features, and input the high-dimensional temporal features into the second-layer LSTM network for feature compression and temporal inference to obtain the hidden state sequence for each time step. ; Step 3.2: Input the hidden state sequence into the self-attention module. By introducing a multi-head self-attention mechanism into the encoding sequence in the hidden state sequence, construct Q, K and V vectors respectively, where Q is the query vector, K is the key vector and V is the value vector. Obtain the self-attention output based on the Q, K and V vectors. Step 3.3: Decode the sequence of self-attention output and update the parameters of the two-layer LSTM network with the self-attention mechanism using the loss function. Continue until convergence, obtaining the optimal parameters. ; Hidden state sequence at each time step The expression is: （4）； In formula (4), The length of the sliding window. For column vectors of the corresponding length The expressions for vectors Q, K, and V are: （5）； In formula (5), H is derived from... The matrix formed The projection matrix is ​​learnable; The expression for the self-attention output is: （6）； In formula (6), T For transpose, For normalized exponential functions, is the dimension of the key vector.

6. The UAV trajectory prediction method integrating deep neural networks and multidimensional geometric correction according to claim 1, characterized in that, Step 4 specifically includes: The trained two-layer LSTM network is used to perform forward propagation on the current window to obtain the prediction result of the next time step. The prediction result of the next time step is used as the multi-step prediction input sequence and appended to the historical sequence. The data point of the earliest time step is removed to form the updated historical window. Based on the updated historical window, combined with the optimal parameters Repeat steps 3.1-3.3 iteratively to perform the prediction process and obtain the preliminary predicted trajectory of the multi-step future trajectory. .

7. The UAV trajectory prediction method integrating deep neural networks and multidimensional geometric correction according to claim 1, characterized in that, Step 5 specifically includes: The actual trajectory of the target drone By performing a difference operation, the displacement vector between adjacent sampling points is obtained. ; displacement vector between adjacent sampling points Normalization is performed to construct the unit motion direction of the target UAV at each moment. The real-time attitude direction of the UAV is obtained based on the unit motion direction of the target UAV at each moment; Preliminary trajectory prediction With the actual trajectory By comparing the results, the prediction error vector at each time point can be obtained. Calculate the projection of the prediction error vector onto the real-time attitude direction. ; Utilizing projection The initial predicted trajectory is fine-tuned along the unit movement direction of the target UAV to obtain the final predicted trajectory; Displacement vector between adjacent sampling points The expression is: （7）； In formula (7), for k The drone's actual location at time +1 for k The real-time location of the drone; Unit direction of motion The calculation formula is: （8）； In formula (8), ε is a small constant introduced to prevent the denominator from being zero; Prediction error vector at each time point The calculation formula is: （9）； Projection The calculation formula is: （10）； In formula (10), T This is a transpose.

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