Unmanned aerial vehicle trajectory prediction method fusing kinematics and channel state information constraint

Abstract

The invention provides an unmanned aerial vehicle track prediction method fusing kinematics and channel state information constraint, and relates to the technical field of unmanned aerial vehicle detection and deep learning, and the method comprises the steps: collecting an original high-dimensional complex matrix sequence of the motion of an unmanned aerial vehicle, and carrying out the dimension reduction processing of a space dimension, and obtaining a real number tensor; constructing a trajectory prediction model by using a spatial feature extractor, a time sequence encoder, a time sequence decoder and a prediction head; constructing a composite loss function based on the combined kinematics and channel state information constraint, and training the trajectory prediction model by using a real number tensor to obtain a trained trajectory prediction model; and analyzing the motion data set of the unmanned aerial vehicle by using the trained trajectory prediction model to obtain a trajectory prediction result of the unmanned aerial vehicle, and completing prediction of the trajectory of the unmanned aerial vehicle. The method solves the problem that a deep learning model lacks physical authenticity and robustness when predicting a high-maneuverability trajectory.

Description

Technical Field

[0001] This specification relates to the fields of unmanned aerial vehicle (UAV) detection and deep learning technology, and in particular to a method for predicting UAV trajectories by integrating kinematic and channel state information constraints. Background Technology

[0002] With the rapid development of the low-altitude economy and the evolution of sensor-integrated communication (ISAC) technology, unmanned aerial vehicles (UAVs) are widely used in low-altitude airspace, especially in urban areas, due to their maneuverability, flexibility, and economy. Consequently, the number of UAVs in low-altitude airspace has surged. These UAVs (especially "low, small, and slow" targets) pose new challenges to public safety and airspace management. To achieve efficient beam tracking, UAV detection must shift from "passive response" to "active prediction," meaning it must not only estimate the target's current position but also accurately predict its future trajectory, thereby guiding high-gain beams towards the target in advance.

[0003] Model-based filtering methods, such as Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Probabilistic Hypothesis Density (PHD) filtering, rely on a pre-defined, accurate dynamic model. However, the high maneuverability of UAVs and their highly nonlinear and unpredictable trajectories cause these fixed-model-based filtering methods to suffer a significant drop in accuracy when faced with complex maneuvers. Data-driven methods, such as deep learning methods using Recurrent Neural Networks (RNNs) or Long Short-Term Memory Networks (LSTMs), can learn complex nonlinear motion patterns from massive amounts of data without requiring an accurate physical model. However, most existing deep learning methods are "black box" models, typically trained using simple loss functions and lacking an understanding of the physical laws. This leads to predictions that are unreasonable in terms of physical mechanisms or inconsistent with the characteristics of wireless signals, resulting in poor model robustness and weak generalization ability. Therefore, combining the powerful nonlinear modeling capabilities of deep learning with the accuracy and interpretability of physical models is a pressing technical challenge in the field of UAV trajectory prediction and beam tracking.

[0004] In existing technologies, although there are various UAV trajectory prediction and tracking methods based on filtering or data-driven approaches, these methods generally suffer from the following problems: First, traditional filtering methods rely heavily on pre-set motion models and have poor adaptability to the complex maneuvering behavior of UAVs; second, data-driven methods use only simple constraints during training and lack constraints on physical laws such as kinematics and electromagnetic wave propagation, which may lead to prediction results that violate physical laws and have insufficient robustness; third, existing methods use diverse data sources, such as optical video data that is susceptible to environmental interference, or non-endogenous sensing data such as ADS-B, or high-level fusion data such as azimuth angle and Doppler, failing to fully utilize wireless channel state information that reflects the laws of electromagnetic wave propagation for end-to-end endogenous sensing and prediction; fourth, some high-precision methods rely on multiple radars of different systems for data fusion, resulting in complex system deployment, high costs, difficulty in solving the spatiotemporal synchronization problem between multiple sensors, and difficulty in applying them to the identification and tracking tasks of "low, slow, and small" UAVs. Summary of the Invention

[0005] To address the aforementioned shortcomings in existing technologies, this invention provides a UAV trajectory prediction method that integrates kinematic and channel state information constraints, solving the problem of lack of physical realism and robustness in deep learning models when predicting highly maneuverable trajectories.

[0006] To achieve the aforementioned objectives, the present invention employs the following technical solution: a method for predicting the trajectory of a UAV by fusing kinematics and channel state information constraints, comprising: S1: Collect the original high-dimensional complex matrix sequence of the UAV motion, perform dimensionality reduction processing in the spatial dimension, and obtain a real tensor; S2: Construct a trajectory prediction model using a spatial feature extractor, a temporal encoder, a temporal decoder, and a prediction head; S3: Construct a composite loss function based on the constraints of combined kinematics and channel state information, and train the trajectory prediction model using real tensors to obtain a trained trajectory prediction model; S4: Utilize the trained trajectory prediction model to analyze the UAV motion dataset, obtain the UAV trajectory prediction results, and complete the prediction of the UAV trajectory.

[0007] Furthermore, the expression for the real tensor is: ; ; ; ; ; in, Represents a standardized real tensor. Represents a real tensor. Tensor The mean, Tensor standard deviation This represents a small constant to prevent division by zero, and its value is... , Indicates time, Indicates the first The channel components of the path, where L represents the total number of paths in multipath propagation. This represents additive white Gaussian noise. The channel matrix represents the line-of-sight path. Represents the complex channel gain. Indicates the guide vector. This represents the conjugate transpose of the guiding vector, where j represents the imaginary unit. This represents the phase delay of the antenna element in the first row and first column. This indicates the phase delay of the antenna element in row 8 and column 8. This represents the phase delay of the antenna element in the m-th row and n-th column. Represents the beam vector of electromagnetic waves. Indicates the row index of the antenna element. Indicates the spacing between antenna elements. This indicates the column index of the antenna element.

[0008] Furthermore, the trajectory prediction model includes: A spatial feature extractor is used to extract features from real tensors to obtain spatial feature sequences. A temporal encoder is used to fuse spatial feature sequences and location codes to obtain a location-aware feature representation. A temporal decoder is used to decode location-aware feature representations to obtain future feature representations. The prediction head is used to map future feature representations to obtain the drone trajectory prediction results.

[0009] Furthermore, the spatial feature extractor is used to extract high-dimensional feature vectors from the CSI spatial matrix at each time step. The model input is the CSI channel matrix at a single time step from step one. Regarding the network structure, a two-layer convolutional network was designed to extract the spatial phase distribution pattern of the antenna array. The network structure configuration is as follows: First convolutional block: Conv2d, 2 input channels, 32 output channels, 3×3 kernel, padding=1, followed by BatchNorm2d and GELU activation; Second convolutional block: Conv2d, 32 input channels, 64 output channels, 3×3 kernel, padding=1, followed by BatchNorm2d and GELU activation. Pooling and flattening: AdaptiveAvgPool2d, output size 1×1, followed by Flatten operation. Linear mapping layer: Linear, input dimension 64, output dimension 128; The temporal encoder is used to learn historical feature sequences (input dimension). The model input is a sequence of historical spatial features. Before being fed into the encoder, the input sequence is encoded using sinusoidal positional encoding to preserve temporal information. By fusing feature vectors and positional encoding, the encoding matrix PE is superimposed element-wise with the feature sequence to obtain a position-aware feature representation. The advantage of sinusoidal positional encoding is that it has extrapolation capabilities, and the relative positional relationship can be naturally expressed through the inner product of vectors.

[0010] Furthermore, the expression for the location-aware feature representation is: ; ; ; in, This represents the feature vector after adding positional encoding. Indicates the time step index. This represents the extracted original spatial feature vector. Represents the position encoding matrix, Indicates the position index in the sequence. Indicates the dimension index unit, where Indicates an even-numbered dimension index. Indicates an odd-numbered dimension index. This represents the feature dimension of the model.

[0011] Furthermore, the expression for the future feature representation is: ; ; ; ; ; ; ; in, This represents the complete future feature matrix output by the decoder. The feature vector representing the future. Indicates the index of future time steps. Indicates the time step for future prediction. Let B represent the real number field and B represent the batch size. Representing feature dimension, Indicates the first The output of the self-attention layer, Presentation layer normalization operation, Indicates the first The input feature matrix of the layer, This indicates a multi-head self-attention mechanism. The query matrix representing cross-attention. This indicates a query for the projection weight matrix. The key matrix representing cross-attention. This represents the memory matrix output by the encoder. Represents the key projection weight matrix. The value matrix representing cross-attention. The value projection weight matrix represents the total weight. This represents the cross-attention weight matrix. Indicates processing by row Normalization operation, This represents the dimension of the key vector. Indicates the number of historical time steps. Indicates the first The output of the cross-attention layer, This represents a feedforward neural network. Indicates the first The input is the first... The final output of the layer.

[0012] Furthermore, the expression for the UAV trajectory prediction result is as follows: ; ; ; ; ; ; ; ; ; in, This indicates the predicted azimuth angle, in degrees. Indicates the index of future time steps. This represents the total number of predicted future time steps. The feature vectors after layer normalization are represented. Presentation layer normalization operation, This represents the original feature vector output by the decoder. This represents the output vector of the first hidden layer. Represents the Gaussian error linear unit activation function. This represents the weight matrix of the first layer. This represents the bias vector of the first layer. Represents the real number field. Indicates the input feature dimension. This represents the output vector of the second layer. This represents the weight matrix of the second layer. This represents the bias vector of the second layer. This represents the normalized azimuth prediction value. This represents the normalized pitch angle prediction value. This represents the original predicted azimuth value. This represents the maximum value of the azimuth angle. This represents the original predicted pitch angle value. This represents the maximum pitch angle.

[0013] Furthermore, the expression for the loss function used to train the trajectory prediction model is: ; ; ; ;

[0014] ; ; ; ; in, This represents the total composite loss function value. Indicates position loss. Indicates speed loss, Indicates acceleration loss, express Physical consistency loss, The weighting coefficients representing the location loss. The weighting coefficients representing velocity loss. The weighting coefficients representing acceleration loss. express The weighting coefficients for physical consistency loss. Indicates batch size, Here, 'b' represents the number of time steps for future prediction, 't' represents the sample index in the batch, and 't' represents the time step index. Indicates the first The normalized azimuth angle predicted for each sample. Indicates the first The true normalized azimuth angle of each sample Indicates the first The predicted normalized pitch angle for each sample. Indicates the first The true normalized pitch angle of each sample Indicates the first Predicted azimuth angular velocity for each sample Indicates the first The true azimuth angular velocity of each sample. Indicates the first The predicted pitch angular velocity for each sample, Indicates the first The true pitch angular velocity of each sample Indicates the first Normalized pitch angle of each sample, Indicates the first The azimuth acceleration of each sample Indicates the first Pitch acceleration of each sample Represents the set of time steps for sampling. Indicates the first Normalized similarity of samples.

[0015] The beneficial effects of this invention are as follows: This invention provides a UAV trajectory prediction method that integrates kinematics and channel state information constraints. A trajectory prediction model is constructed using a spatial feature extractor, a temporal encoder, a temporal decoder, and a prediction head. A composite loss function is constructed based on the constraints of combined kinematics and channel state information. The trajectory prediction model is trained using real tensors to obtain a trained trajectory prediction model. (1) A dataset constructed using simulation-collected data is input into the trained model. The prediction results of the trained model are as follows: Figure 4 As shown in the figure. The evaluation metrics indicate that this method has high accuracy. Figure 4 The scatter plot on the left shows that the predicted values ​​and the actual values ​​are highly concentrated near the ideal diagonal; Figure 4The error distribution histogram on the right shows that the error of most samples is concentrated between 0.5 and 1.5 degrees, which proves the robustness of the method. (2) The high-dimensional, instantaneous channel matrix is ​​efficiently encoded into low-dimensional temporal features containing motion trends through a three-stage process, so as to decode and predict the complete motion trajectory in the future period from the features; two types of physical prior knowledge are introduced as "soft constraints" to guide the deep learning model to learn the prediction ability that conforms to physical reality during the training process. Attached Figure Description

[0016] This specification will be further described by way of exemplary embodiments, which will be described in detail with reference to the accompanying drawings. These embodiments are not limiting; in these embodiments, the same reference numerals denote the same structures, wherein: Figure 1 This is an exemplary flowchart illustrating a UAV trajectory prediction method that integrates kinematic and channel state information constraints, according to some embodiments of this specification. Figure 2 These are exemplary schematic diagrams of trajectory prediction models according to some embodiments of this specification; Figure 3 This is an exemplary schematic diagram illustrating the construction of a composite loss function according to some embodiments of this specification; Figure 4 This is an exemplary schematic diagram of a trajectory prediction model according to some embodiments of this specification. Detailed Implementation

[0017] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0018] Example Figure 1 This is an exemplary flowchart illustrating a UAV trajectory prediction method that integrates kinematic and channel state information constraints, according to some embodiments of this specification. Figure 1 As shown, the process includes the following steps. In some embodiments, the process may be executed by a processor.

[0019] In some embodiments, the processor can receive and preprocess CSI time-series data, extracting the most recent historical CSI sequence as input. Next, an Encoder-Decoder architecture trajectory prediction model is constructed to extract spatial characteristics from the historical sequence and perform global temporal modeling, generating a memory state containing historical information. This is then decoded by a Transformer decoder to generate angle prediction values ​​for multiple future time steps. This model incorporates kinematic constraints and channel state information constraints in its design, resulting in highly accurate and physically realistic predicted angle trajectories that can be directly used to guide communication systems in active, predictive beam tracking.

[0020] S1: Collect the original high-dimensional complex matrix sequence of the UAV's motion, perform dimensionality reduction processing in the spatial dimension, and obtain a real tensor.

[0021] A high-dimensional complex matrix sequence is a sequence of complex matrices representing high-dimensional wireless channel state information.

[0022] In some embodiments, the processor can generate UAV trajectory-channel state information data pairs containing real physical characteristics. First, a UAV flight trajectory simulation is performed. The simulation duration is set to 10 seconds, the sampling frequency to 1000Hz, resulting in 10,000 time points. The UAV's spatial position and three-dimensional velocity vector (velocity 5-20 m / s) are randomly initialized, and an angular trajectory sequence is obtained through coordinate transformation. and distance sequence Then, physical quantities such as radial velocity, Doppler frequency shift, and path loss are calculated. Next, a channel matrix is ​​generated based on the trajectory parameters. Configuration. Uniform planar array, element spacing For time t and angle Calculate the wave vector and construct the steering vector. Phase delay This yields a sequence of high-dimensional complex matrices.

[0023] The real tensor is a normalized single-time-step CSI channel matrix.

[0024] In some embodiments, the processor can acquire the original high-dimensional CSI complex matrix sequence and perform spatial dimension reduction on it to match the antenna array structure and reduce computational load. Then, the dimension-reduced CSI sequence is standardized and format-converted to a real tensor suitable for input to a spatiotemporal prediction model.

[0025] In some embodiments, the expression for a real tensor is: ; ; ; ; ; in, Represents a standardized real tensor. Represents a real tensor. Tensor The mean, Tensor standard deviation This represents a small constant to prevent division by zero, and its value is... , Indicates time, Indicates the first The channel components of the path, where L represents the total number of paths in multipath propagation. This represents additive white Gaussian noise. The channel matrix represents the line-of-sight path. Represents the complex channel gain. Indicates the guide vector. This represents the conjugate transpose of the guiding vector, where j represents the imaginary unit. This represents the phase delay of the antenna element in the first row and first column. This indicates the phase delay of the antenna element in row 8 and column 8. This represents the phase delay of the antenna element in the m-th row and n-th column. Represents the beam vector of electromagnetic waves. Indicates the row index of the antenna element. Indicates the spacing between antenna elements. This indicates the column index of the antenna element.

[0026] In some embodiments, the processor can, based on factors such as path loss and Doppler phase shift in the complex channel gain, further superimpose 2-4 scattering paths onto a high-dimensional complex matrix sequence to simulate multipath propagation, ultimately obtaining the channel matrix; the original channel matrix is ​​then preprocessed. Average pooling downsampling is used to separate the real and imaginary parts of the downsampled complex matrix H, forming a real tensor [H_real, H_imag]. Converting the complex data into a dual-channel real tensor naturally adapts to the multi-channel input characteristics of convolutional neural networks, without requiring modification to the standard CNN architecture; Z-score normalization is performed on the real and imaginary parts respectively to eliminate the influence of dimensions, resulting in the real tensor.

[0027] In some embodiments, standardizing the real and imaginary parts separately avoids training instability caused by the difference in magnitude between the real and imaginary parts. Traditional methods lose phase information when standardizing complex modulus values, a deficiency overcome by this method. Then, the real and imaginary parts are stacked according to the channel dimension, and the angle data used as labels is also normalized, scaling it to the range [-1, 1]. Finally, the historical window length and future prediction length are set, and the continuous data is sliced ​​into multiple data pairs [historical CSI (historical window length), future angle (future prediction length)] using a sliding window method, thus obtaining the CSI channel matrix H(t) for a single time step. Finally, the training set, validation set, and test set are divided in an 8:1:1 ratio.

[0028] S2: Construct a trajectory prediction model using a spatial feature extractor, a temporal encoder, a temporal decoder, and a prediction head.

[0029] In some embodiments, the processor can construct a multi-branch hierarchical feature fusion prediction model based on a CNN-Transformer codec, extracting and fusing low-level CSI features to predict the trajectory of the UAV. The model architecture is as follows: Figure 2 As shown. This step constructs a deep neural network model to decode the future multi-step motion trajectory from a high-dimensional, continuous historical sequence of channel information. First, a spatial feature extraction network (such as a convolutional neural network CNN) is constructed. Physically, the channel information matrix encodes the spatial phase-amplitude distribution pattern of the incident signal on the antenna array, and this distribution pattern has a deterministic physical mapping relationship with the spatial arrival angle of the target. This feature extractor uses the structure of a two-dimensional convolutional neural network, taking the channel information at each time point as input. The convolutional network compresses this spatial snapshot into a high-dimensional feature vector through layer-by-layer abstraction, thereby effectively extracting the spatial correlation of the array signal. Based on this, a time-dependent coding module (such as a Transformer Encoder) is constructed, which receives the historical feature vector sequence generated by the spatial feature extraction branch and combines it with sinusoidal position coding information to perform global information interaction across the entire historical time dimension, adaptively capturing the temporal evolution of channel features during the target's motion. Finally, a trajectory generation and decoding module (such as TransformerDecoder) is constructed. This module actively queries the historical context memory information extracted by the temporal encoding module and decodes the historical information into a feature sequence representing the future through a cross-attention mechanism. This future feature sequence is then mapped through a multilayer perceptron prediction head to generate a normalized prediction sequence of continuous angular trajectories for the next T time steps.

[0030] The trajectory prediction model employs a multi-layered architecture: a low-level local spatial feature extractor (CNN), a mid-level temporal evolution feature encoder (TransformerEncoder), and a high-level task prediction feature decoder (TransformerDecoder). This architecture constructs a multi-branch hierarchical feature fusion prediction model. Unlike methods that use only a single RNN or LSTM to process temporal data, this model explicitly extracts the spatial phase distribution patterns on the antenna array through CNN branches, and then learns their temporal evolution patterns through Transformer branches. This achieves decoupling and deep fusion of spatiotemporal features, significantly improving the model's ability to learn complex motion patterns from high-dimensional CSI. Specifically, the trajectory prediction model adopts an architecture based on spatial feature extraction and temporal encoding / decoding, with an overall CNN-encoder-decoder structure. The model is as follows: Figure 2 As shown, the model mainly consists of four parts: a spatial feature extractor using CNNs, a temporal encoder, a temporal decoder, and a prediction head. The model takes historical CSI sequences as input (dimension...). B represents the batch size, and 2 represents the real / imaginary part channel. (where T is the spatial dimension and T is the length of the historical sequence), outputting the future angular trajectory sequence (dimension). , (where 2 represents the future sequence length, and 2 represents the azimuth and elevation angles). Before being fed into the model, the input sequence undergoes dimensional rearrangement, merging the batch size and time step, resulting in a dimension of 2 for the spatial feature extractor. This architecture innovatively introduces a learnable future query vector mechanism and optimizes the network structure for the physical characteristics of CSI data.

[0031] In some embodiments, such as Figure 2 As shown, the trajectory prediction model includes: a spatial feature extractor, used to extract features from real tensors to obtain a spatial feature sequence; a temporal encoder, used to fuse the spatial feature sequence and position encoding to obtain a position-aware feature representation; a temporal decoder, used to decode the position-aware feature representation to obtain a future feature representation; and a prediction head, used to map the future feature representation to obtain the UAV trajectory prediction result.

[0032] The spatial feature extractor (CNN) is responsible for extracting high-dimensional feature vectors from the CSI spatial matrix at each time step. The model input is the CSI channel matrix from a single time step in step one. Regarding the network structure, a two-layer convolutional network was designed to extract the spatial phase distribution pattern of the antenna array. The network structure configuration is as follows: First convolutional block: Conv2d, 2 input channels, 32 output channels, 3×3 kernel, padding=1, followed by BatchNorm2d and GELU activation; Second convolutional block: Conv2d, 32 input channels, 64 output channels, 3×3 kernel, padding=1, followed by BatchNorm2d and GELU activation. Pooling and flattening: AdaptiveAvgPool2d, output size 1×1, followed by Flatten operation. Linear mapping layer: Linear, input dimension 64, output dimension 128.

[0033] The output feature dimension of the spatial feature extractor is Subsequently reshaped into This serves as the input to the timing encoder. It is processed through two layers. The convolutional cascades, with each layer having a receptive field of... After two layers, the sensory field reaches It can effectively capture the spatial phase gradient characteristics of the steering vector on the array, which is crucial for angle estimation.

[0034] The temporal encoder (TransformerEncoder) is responsible for learning the historical feature sequence (input dimension). The model input is a sequence of historical spatial features. Before being fed into the encoder, the input sequence is encoded using sinusoidal positional encoding to preserve temporal information. By fusing feature vectors and positional encoding, the encoding matrix PE is superimposed element-wise with the feature sequence to obtain a position-aware feature representation. The advantage of sinusoidal positional encoding is that it has extrapolation capabilities, and the relative positional relationship can be naturally expressed through the inner product of vectors.

[0035] In some embodiments, the network structure configuration of the timing encoder is as follows: Encoder stack: Consists of 4 stacked encoder layers. Each encoder layer has a model dimension of 128 and 4 multi-head attention heads. Residual connections and layer normalization are then performed. ; Then it passes through the feedforward network module: ; The feedforward network has a dimension of 512 (i.e.) The activation function is GELU, with the batch dimension first. ; in, Indicates the first The output feature matrix of the self-attention layer of the layer encoder. This indicates the normalization operation of the representation layer. Indicates the first The input feature matrix of the layer encoder, This represents the output of the multi-head self-attention mechanism. Indicates the layer index of the encoder. Indicates the first The final output of the layer encoder is also the first layer encoder. Layer input, This represents the output of the feedforward network. This represents the complete computation process of a feedforward neural network. This represents the input feature vector. Represents the Gaussian error linear unit activation function. First layer weight matrix, This represents the first-level bias vector. This represents the weight matrix of the second layer. This represents the second-layer bias vector.

[0036] The historical memory state sequence is obtained after processing through a 4-layer encoder, with a dimension of [missing information]. This sequence incorporates contextual information from all time steps within the historical time domain, containing a global temporal pattern of the target's motion.

[0037] In some embodiments, the expression for the location-aware feature representation is: ; ; ; in, This represents the feature vector after adding positional encoding. Indicates the time step index. This represents the extracted original spatial feature vector. Represents the position encoding matrix, Indicates the position index in the sequence. Indicates the dimension index unit, where Indicates an even-numbered dimension index. Indicates an odd-numbered dimension index. This represents the feature dimension of the model.

[0038] The TransformerDecoder introduces a set of learnable parameterized query vectors, which automatically learn during training how to extract feature patterns of future trajectories from historical memory. A learnable query matrix is ​​defined and designed. The model parameters are optimized during training. Each row of this matrix corresponds to a "question" vector at a future time step, which "questions" features relevant to the prediction at that moment in historical information through interaction with the encoded memory. The decoder consists of three stacked layers. Each decoder layer contains three sub-modules: a self-attention module, a cross-attention module, and a feedforward network module. The input to the decoder... Initialized from a learnable query matrix. For each batch of samples, the learnable query matrix is... Copy as The data is processed and integrated with location coding.

[0039] In some embodiments, the expression for future feature representation is: ; ; ; ; ; ; ; in, This represents the complete future feature matrix output by the decoder. The feature vector representing the future. Indicates the index of future time steps. Indicates the time step for future prediction. Let B represent the real number field and B represent the batch size. Representing feature dimension, Indicates the first The output of the self-attention layer, Presentation layer normalization operation, Indicates the first The input feature matrix of the layer, This indicates a multi-head self-attention mechanism. The query matrix representing cross-attention. This indicates a query for the projection weight matrix. The key matrix representing cross-attention. This represents the memory matrix output by the encoder. Represents the key projection weight matrix. The value matrix representing cross-attention. The value projection weight matrix represents the total weight. This represents the cross-attention weight matrix. Indicates processing by row Normalization operation, This represents the dimension of the key vector. Indicates the number of historical time steps. Indicates the first The output of the cross-attention layer, This represents a feedforward neural network. Indicates the first The input is the first... The final output of the layer.

[0040] In some embodiments, for the first The input to the layer decoder is first processed using a self-attention module, similar to the encoder, but since the prediction is autoregressive, a causal masking mechanism is retained to prevent future information leakage. Then, it is processed using a cross-attention module, the core of the decoder, which implements an attention mechanism for future query vectors to remember historical encodings. The attention weight matrix is ​​then... Elements represent future moments. Predictions for historical moments The degree of dependence; finally, the future feature sequence is obtained by processing through a 3-layer decoder using a feedforward network module. Through the above steps, this module is based on historical memory (dimension). ) and a set of learnable future query sequences (dimensions) This is used to generate future feature representations. Before being fed into the decoder, the query sequence is expanded in batch dimension and positional encoding is overlaid, resulting in a new dimension. This mechanism can generate predictions for all future time steps in parallel, avoiding the cumulative error of autoregressive decoding; and it can automatically learn the optimal information extraction mode from the query vector through end-to-end training.

[0041] The drone trajectory prediction result is a normalized future angular trajectory (azimuth and pitch angles), with dimensions of .

[0042] In some embodiments, the expression for the UAV trajectory prediction result is: ; ; ; ; ; ; ; ; ; in, This indicates the predicted azimuth angle, in degrees. Indicates the index of future time steps. This represents the total number of predicted future time steps. The feature vectors after layer normalization are represented. Presentation layer normalization operation, This represents the original feature vector output by the decoder. This represents the output vector of the first hidden layer. Represents the Gaussian error linear unit activation function. This represents the weight matrix of the first layer. This represents the bias vector of the first layer. Represents the real number field. Indicates the input feature dimension. This represents the output vector of the second layer. This represents the weight matrix of the second layer. This represents the bias vector of the second layer. This represents the normalized azimuth prediction value. This represents the normalized pitch angle prediction value. This represents the original predicted azimuth value. This represents the maximum value of the azimuth angle. This represents the original predicted pitch angle value. This represents the maximum pitch angle.

[0043] In some embodiments, the prediction head (MLP) introduces a layer normalization + two-layer MLP prediction head architecture. This involves taking the future feature sequence (dimension) output from the temporal decoder. ) is mapped to the final trajectory angle prediction value; where, the prediction range is [ [1,1]. The physical angle is obtained after inverse normalization.

[0044] S3: Construct a composite loss function based on the constraints of combined kinematics and channel state information, and train the trajectory prediction model using real tensors to obtain a trained trajectory prediction model.

[0045] In some embodiments, the processor can define and fuse kinematic constraint loss and channel state information constraint. This step aims to inject the laws of kinematic priors and channel state information into the model training process simultaneously through a unified composite loss function to ensure the physical authenticity of the predicted trajectory. This function innovatively integrates two types of physical constraints in addition to the standard position-supervised loss. The first type is kinematic constraints, which construct the loss term by calculating the first-order time difference (representing velocity) and second-order time difference (representing acceleration) of the predicted trajectory sequence output by the neural network. This penalizes instantaneous abrupt changes and jitter that do not conform to the law of inertia, ensuring the smoothness of the predicted trajectory's motion. The second type is channel state information consistency constraints, the core mechanism of which is that the predicted angle at higher levels must match the CSI observations at lower levels. This constraint extracts the angle predicted by the neural network, calculates its corresponding theoretical steering vector, and compares it with the vector similarity (such as the modulus of the normalized complex inner product, whose physical meaning is the energy focusing efficiency of beamforming in that direction) of the channel state information actually observed in the dataset. Finally, the two types of physical constraint losses and position losses are weighted and summed together to guide model optimization, forcing the prediction results to maintain a high degree of realism and consistency in both kinematic and channel information state dimensions.

[0046] In some embodiments, such as Figure 3 As shown, the processor can perform a weighted summation of the previously defined kinematic constraint loss and channel state information consistency loss to form the final composite total loss function. The weights of each loss term, i.e., the hyperparameters, can be adjusted according to actual needs. During the model training phase, an optimization algorithm (such as the AdamW optimization algorithm) is used to minimize this composite total loss function through backpropagation, thereby optimizing the parameters of the spatiotemporal prediction model constructed in step three. After training, the model can be deployed for actual prediction. During the inference phase, the system only needs to input the latest historical CSI sequence, and the model can predict the complete angular trajectory for a future period in one go, thus achieving proactive and advance beam tracking.

[0047] By introducing constraints on kinematic smoothness and channel state information consistency during the training phase, this mechanism prioritizes trajectory position prediction as the primary task and uses kinematic and CSI consistency as auxiliary constraints. This ensures that while maintaining high-level trajectory prediction accuracy, the network's output remains continuous and reasonable in terms of underlying physical propagation laws. This design introduces multiple constraints at the model training level, overcoming the limitations of traditional single-task optimization and further enhancing the physical consistency and prediction robustness of the network output.

[0048] Traditional trajectory prediction methods typically employ only a single mean squared error (MSE) loss function for supervised learning, or at most add an L2 regularization term to prevent overfitting. This approach lacks explicit constraints on physical laws, leading to prediction results that may violate kinematic principles or be inconsistent with actual channel observations. This paper proposes an innovative hierarchical physical constraint optimization mechanism. By incorporating kinematic constraints and channel state information constraints into the loss function as soft constraints, it guides the model to learn trajectory prediction capabilities that conform to physical laws. The structure diagram of the constructed composite physical loss function is shown below. Figure 3 As shown. The core innovation of this mechanism lies in proposing to apply four different levels of constraints simultaneously for different physical characteristics, which are complementary and non-redundant, effectively improving the model's ability to learn and predict UAV trajectories.

[0049] The composite loss function utilizes prior physical information, guided by the trajectory derivatives (velocity, acceleration) output by the neural network and the CSI physical model (guide vector), to introduce kinematic constraints and channel state information consistency constraints during training. This mechanism differs from traditional "black box" training methods that rely solely on true data values. By using physical laws to jointly guide model training, it reduces dependence on massive amounts of data and enhances the model's physical interpretability and generalization ability.

[0050] In some embodiments, the composite loss function consists of four weighted sub-items: position loss (mean squared error between predicted and true values), velocity loss (mean squared error of first-order difference), acceleration loss (smoothing penalty of second-order difference), and CSI consistency loss (obtained by calculating the similarity between the theoretical steering vector of the predicted angle and the actual CSI observation).

[0051] In some embodiments, the expression for the loss function used to train the trajectory prediction model is: ; ; ; ;

[0052] ; ; ; ; in, This represents the total composite loss function value. Indicates position loss. Indicates speed loss, Indicates acceleration loss, express Physical consistency loss, The weighting coefficients representing the location loss. The weighting coefficients representing velocity loss. The weighting coefficients representing acceleration loss. express The weighting coefficients for physical consistency loss. Indicates batch size, Here, 'b' represents the number of time steps for future prediction, 't' represents the sample index in the batch, and 't' represents the time step index. Indicates the first The normalized azimuth angle predicted for each sample. Indicates the first The true normalized azimuth angle of each sample Indicates the first The predicted normalized pitch angle for each sample. Indicates the first The true normalized pitch angle of each sample Indicates the first Predicted azimuth angular velocity for each sample Indicates the first The true azimuth angular velocity of each sample. Indicates the first The predicted pitch angular velocity for each sample, Indicates the first The true pitch angular velocity of each sample Indicates the first Normalized pitch angle of each sample, Indicates the first The azimuth acceleration of each sample Indicates the first Pitch acceleration of each sample Represents the set of time steps for sampling. Indicates the first Normalized similarity of samples.

[0053] In some embodiments, the position loss is the most basic supervised learning loss term, directly constraining the point-to-point matching accuracy between the predicted angle and the true angle label. For sample b in the batch, let the true future angle trajectory be... The model predicts the normalized angular trajectory as follows: Location loss is defined as the mean square error (MSE) between the predicted and true values.

[0054] This loss term ensures the model learns correct angle predictions by minimizing the Euclidean distance between the predicted and true trajectories at each time step. Physically, it represents the average deviation between the predicted and true trajectories in the normalized space. Because it uses mean squared error, the penalty for larger deviations increases quadratically, effectively encouraging the model to reduce outlier predictions.

[0055] The velocity consistency loss ensures the model learns the correct motion trend and continuity by constraining the consistency of the angular velocity between the predicted and actual trajectories. Angular velocity is defined as the first-order time difference of the angle between adjacent time steps. The physical meaning of this loss term is to constrain the instantaneous velocity of the predicted trajectory to be consistent with the actual velocity, preventing sudden changes in velocity or direction in the predicted trajectory. Since angular velocity reflects the local rate of change of the trajectory, this constraint ensures the continuity and smoothness of the predicted trajectory over time, consistent with the physical characteristics of the limited maneuverability of UAVs. Even if there are small deviations in the absolute position prediction at certain time points, the overall trajectory shape remains reasonable as long as the velocity trend is correct.

[0056] The physical meaning of acceleration loss is to minimize the amplitude of angular acceleration in the predicted trajectory, thus promoting a smooth, curved trajectory. Since the motion of a real UAV is limited by its mechanical structure, aerodynamics, and control system, the amplitude of angular acceleration should be kept within a reasonable range, and its changes should be gradual. This loss term, as a physical prior constraint, does not require an acceleration label from the actual trajectory; it only acts on the predicted trajectory itself, suppressing non-physical oscillations of the trajectory by penalizing the energy of the second derivative.

[0057] CSI consistency loss ensures that the prediction results are consistent with the actual physical laws of communication by establishing a physical correlation between the predicted angle and the underlying channel observations. This loss term is designed based on the following physical principle: Under far-field conditions, the spatial angle of arrival of the target... The only thing that determines the steering vector of the antenna array The channel matrix is ​​approximately a rank-one matrix when single-path dominance is involved. Therefore, if the predicted angle is correct, the theoretical steering vector calculated based on that angle should be highly correlated with the actually observed channel state information.

[0058] In some embodiments, the calculation process for the CSI consistency loss term includes the following steps: Step 1: Perform time downsampling from the predicted future trajectory. To reduce computational overhead, sampling is performed every s time steps to obtain a set of sampled time indices. .

[0059] Step 2: For each sampling time For sample b, the normalized predicted angle is denormalized to the actual physical angle (unit: degrees): Then convert to radians: .

[0060] Step 3: Calculate the theoretical steering vector based on the predicted angle and known antenna array geometric parameters. For a uniform planar array, set the element spacing... The position of the array element is According to the plane wave far-field propagation model, the first... The phase delay of each array element is:

[0061] The guide vector is defined as: .

[0062] Step 4: Obtain the true channel observations at this moment. Extract the complex channel matrix corresponding to sample b at future time t from the dataset. This matrix has been downsampled but not Z-score normalized, preserving the original amplitude and phase information. Flatten it into a one-dimensional complex vector: .

[0063] Step 5: Normalize the theoretical steering vector and the observed channel vector respectively to eliminate the influence of amplitude differences, focusing only on the similarity of spatial patterns: .

[0064] Step 6: Calculate the modulus of the normalized complex inner product as a similarity metric. This similarity reflects the degree of spatial pattern matching between the theoretical steering vector and actual channel observations. ; In the first step: This represents the set of time step indices for sampling. Indicates the time step index. express Divide by The remainder is 0, that is yes Integer multiples of, This represents the total number of time steps for future predictions. In the second step: Indicates the sample index in the batch. Indicates the first Predicted azimuth angles after inverse normalization of each sample Indicates the first Normalized azimuth prediction values ​​for each sample Indicates the first Predicted pitch angle after inverse normalization of a sample Indicates the first Normalized pitch angle prediction values ​​for each sample The value in radians represents the azimuth angle. The pitch angle in radians. In step three: Indicates the first Each sample is located at Phase delay of the antenna element, Indicates the row index of the antenna element. The column index representing the antenna element. This represents the sine value of the azimuth angle. This represents the sine value of the pitch angle. Indicates the first The theoretical guiding vector of a sample, Indicates position Complex phase response of antenna element This is a 64-dimensional complex vector space. In the fourth step: Indicates the first The observed CSI vector of each sample, This represents the matrix vectorization operation. Indicates the first The observed CSI matrix for each sample. In step five: This represents the normalized theoretical steering vector. This represents the unnormalized theoretical steering vector. This represents the normalized observation CSI vector. This represents the unnormalized observation CSI vector. This indicates the calculation of the L2 norm of the vector. In step six: Represents the theoretical guiding vector. The complex conjugate of each element The first element of the observed CSI vector represents the... One element, Represents complex conjugation. Similarity. The value reaches its maximum value of 1 when the theoretical steering vector is perfectly aligned with the observation channel.

[0065] Step 7: Define the physical inconsistency at a single moment as the negative of the similarity, and the CSI consistency loss as the average inconsistency across all sampling moments and all samples.

[0066] By minimizing The angle predictions that the model is forced to learn must not only match the position loss but also be able to physically "interpret" the underlying channel observation data. Therefore, the predicted angle must satisfy the following condition: the theoretical spatial response pattern derived from this angle must be highly consistent with the actual electromagnetic wave observation pattern on the array. This cross-domain physical constraint significantly enhances the model's generalization ability and robustness, especially in complex electromagnetic environments with multipath interference, signal-to-noise ratio fluctuations, or array calibration errors. The physical consistency constraint can effectively suppress the model's overfitting to noise and guide the model to learn a more fundamental angle-channel mapping relationship.

[0067] In some embodiments, the processor can set the loss weight hyperparameter: ; The position loss weight serves as the primary supervisory signal, set to a baseline value of 1.0 to ensure the model first learns basic point-to-point prediction capabilities. The velocity loss weight, an important auxiliary constraint, is set at 30% of the position loss, guiding trajectory continuity while maintaining position accuracy. This weight should not be too large, otherwise it may overemphasize velocity matching at the expense of position accuracy. The acceleration loss weight, a weak regularization term, is set to a small value to suppress significant non-physical oscillations and prevent over-smoothing that would prevent the model from capturing realistic maneuvers. The CSI consistency loss weight falls between velocity and acceleration, providing effective physical prior guidance without overly restricting the model's fitting degrees of freedom.

[0068] During model training, the Adaptive Moments Estimation (AdamW) algorithm is used to minimize the total composite loss function. The optimizer calculates the loss function with respect to all model parameters using the backpropagation algorithm. And update the parameters according to the gradient descent rule:

[0069] in The learning rate is dynamically adjusted by the learning rate scheduler. During training, the four sub-loss terms work together to guide the model to learn trajectory prediction capabilities that conform to both the data distribution and the laws of kinematics and radio frequency physics, thus achieving an organic unity between data-driven and physical priors.

[0070] S4: Utilize the trained trajectory prediction model to analyze the UAV motion dataset, obtain the UAV trajectory prediction results, and complete the prediction of the UAV trajectory.

[0071] In some embodiments, the prediction results of the trained trajectory prediction model are as follows: Figure 4 As shown in the figure. The evaluation metrics indicate that this method has high accuracy. Figure 4The scatter plot on the left shows that the predicted values ​​and the actual values ​​are highly concentrated near the ideal diagonal; Figure 4 The error distribution histogram on the right shows that the vast majority of sample errors are concentrated between 0.5 and 1.5 degrees, demonstrating the robustness of the method.

[0072] In some embodiments of this specification, a UAV trajectory prediction method integrating kinematics and channel state information constraints is provided. A trajectory prediction model is constructed using a spatial feature extractor, a temporal encoder, a temporal decoder, and a prediction head. A composite loss function is constructed based on the combined kinematics and channel state information constraints. The trajectory prediction model is trained using real tensors to obtain a trained trajectory prediction model. (1) The dataset constructed using simulated data is input into the trained model, which improves the robustness of the prediction. (2) The high-dimensional, instantaneous channel matrix is ​​efficiently encoded into low-dimensional temporal features containing motion trends through a three-stage process, enabling the decoding and prediction of the complete motion trajectory for a future period from these features. Two types of physical prior knowledge are introduced as "soft constraints" to guide the deep learning model to autonomously learn prediction capabilities that conform to physical reality during the training process.

Claims

1. A method of UAV trajectory prediction with fusion of kinematic and channel state information constraints, characterized in that, The method comprises the following steps: S1: Collecting a high-dimensional complex matrix sequence of original unmanned aerial vehicle motion, performing dimension reduction processing in the spatial dimension, and obtaining a real number tensor; S2: Constructing a trajectory prediction model by using a spatial feature extractor, a time sequence encoder, a time sequence decoder, and a prediction head; S3: Constructing a compound loss function based on combined kinematics and channel state information constraints, training the trajectory prediction model by using the real number tensor, and obtaining a trained trajectory prediction model; S4: Analyzing an unmanned aerial vehicle motion dataset by using the trained trajectory prediction model, obtaining an unmanned aerial vehicle trajectory prediction result, and completing the prediction of the unmanned aerial vehicle trajectory.

2. The method of claim 1, wherein, An expression of the real number tensor is as follows: ； ； ； ； ； wherein denotes a normalized real tensor, denotes a real tensor, denotes a tensor of mean values, denotes a tensor of standard deviations, denotes a small constant to prevent division by zero, and takes the value , denotes a time instant, denotes a channel component of the th path, L denotes the total number of paths of multipath propagation, denotes an additive white Gaussian noise, denotes a channel matrix of the Line-of-Sight path, denotes a complex channel gain, denotes a steering vector, denotes a conjugate transpose of the steering vector, j denotes the imaginary unit, denotes a phase delay of the antenna element in the 1st row and 1st column, denotes a phase delay of the antenna element in the 8th row and 8th column, denotes a phase delay of the antenna element in the mth row and nth column, denotes a beam vector of the electromagnetic wave, denotes a row index of the antenna element, denotes a spacing of the antenna element, denotes a column index of the antenna element.

3. The method of claim 1, wherein, The trajectory prediction model comprises: a spatial feature extractor, which is configured to perform feature extraction on the real number tensor, extract spatial phase distribution patterns of an antenna array by using a double-layer convolutional network, and obtain a spatial feature sequence; a time sequence encoder, which is configured to fuse the spatial feature sequence and position encoding, and obtain a position-aware feature representation; a time sequence decoder, which is configured to perform decoding processing on the position-aware feature representation, and obtain a future feature representation; a prediction head, which is configured to map the future feature representation, and obtain the unmanned aerial vehicle trajectory prediction result.

4. The method of claim 3, wherein, The spatial feature extractor is used to extract a high-dimensional feature vector from the CSI spatial matrix of each time step. The model input is the CSI channel matrix of a single time step in step one In terms of network structure, a double-layer convolutional network is designed to extract the spatial phase distribution pattern of the antenna array, and the network structure is configured as follows: the first convolutional block: Conv2d, input channel 2, output channel 32, convolution kernel 3*3, padding=1, followed by BatchNorm2d and GELU activation; the second convolutional block: Conv2d, input channel 32, output channel 64, convolution kernel 3*3, padding=1, followed by BatchNorm2d and GELU activation. Pooling and flattening: AdaptiveAvgPool2d, output size 1*1, followed by the Flatten operation. Linear mapping layer: Linear, input dimension 64, output dimension 128; The temporal encoder is used to learn the temporal dependency in the history feature sequence (input dimension ). The model input is the history spatial feature sequence. The input sequence is encoded with sinusoidal positional encoding to preserve the temporal information before feeding into the encoder. The encoding matrix PE is element-wise added to the feature sequence to obtain the position-aware feature representation. The advantage of sinusoidal positional encoding is that it has extrapolation ability and the relative position relationship can be naturally expressed through vector inner product.

5. The method of claim 3, wherein, An expression of the position-aware feature representation is as follows: ； ； ； wherein, denotes the feature vector after adding the positional encoding, denotes the time step index, denotes the extracted original spatial feature vector, denotes the positional encoding matrix, denotes the position index in the sequence, denotes the dimension index unit, wherein denotes the even dimension index, denotes the odd dimension index, denotes the feature dimension of the model.

6. The method of claim 3, wherein the method further comprises: An expression of the future feature representation is as follows: ； ； ； ； ； ； ； wherein, represents the complete future feature matrix output by the decoder, represents the future feature vector, represents the future time step index, represents the number of time steps of the future prediction, represents the real number domain, B represents the batch size, represents the feature dimension, represents the output of the layer self-attention layer, represents the layer normalization operation, represents the input feature matrix of the layer, represents the multi-head self-attention mechanism, represents the query matrix of the cross-attention, represents the query projection weight matrix, represents the key matrix of the cross-attention, represents the memory matrix output by the encoder, represents the key projection weight matrix, represents the value matrix of the cross-attention, represents the value projection weight matrix, represents the cross-attention weight matrix, represents the row-wise normalization operation, represents the dimension of the key vector, represents the number of history time steps, represents the output of the layer cross-attention layer, represents the feed-forward neural network, represents the input of the , i.e. the final output of the layer.

7. The method of claim 3, wherein the method further comprises: An expression of the unmanned aerial vehicle trajectory prediction result is as follows: ； ； ； ； ； ； ； ； ； wherein, denotes the predicted azimuth angle in degrees, denotes the future time step index, denotes the total number of predicted future time steps, denotes the layer normalized feature vector, denotes the layer normalization operation, denotes the original feature vector output by the decoder, denotes the output vector of the first hidden layer, denotes the Gaussian error linear unit activation function, denotes the weight matrix of the first layer, denotes the bias vector of the first layer, denotes the real number field, denotes the input feature dimension, denotes the output vector of the second layer, denotes the weight matrix of the second layer, denotes the bias vector of the second layer, denotes the normalized azimuth angle prediction, denotes the normalized elevation angle prediction, denotes the original predicted azimuth angle value, denotes the maximum value of the azimuth angle, denotes the original predicted elevation angle value, denotes the maximum value of the elevation angle.

8. The method of claim 1, wherein, An expression of a loss function of the trajectory prediction model is as follows: ； ； ； ； ； ； ； ； in, This represents the total composite loss function value. Indicates position loss. Indicates speed loss, Indicates acceleration loss, express Physical consistency loss, The weighting coefficients representing the location loss. The weighting coefficients representing velocity loss. The weighting coefficients representing acceleration loss. express The weighting coefficients for physical consistency loss. Indicates batch size, Here, 'b' represents the number of time steps for future prediction, 't' represents the sample index in the batch, and 't' represents the time step index. Indicates the first The normalized azimuth angle predicted for each sample. Indicates the first The true normalized azimuth angle of each sample Indicates the first The predicted normalized pitch angle for each sample. Indicates the first The true normalized pitch angle of each sample Indicates the first Predicted azimuth angular velocity for each sample Indicates the first The true azimuth angular velocity of each sample. Indicates the first The predicted pitch angular velocity for each sample Indicates the first The true pitch angular velocity of each sample Indicates the first Normalized pitch angle of each sample Indicates the first The azimuth acceleration of each sample Indicates the first Pitch acceleration of each sample Represents the set of time steps for sampling. Indicates the first Normalized similarity of samples.

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