Space-time coding and decoding vehicle track prediction method based on dynamic kinematics constraint embedding

Abstract

The invention provides a space-time coding and decoding vehicle track prediction method based on dynamic kinematics constraint embedding. The method comprises the following steps of: encoding historical track sequences of a target vehicle and surrounding vehicles by using a peep hole long short-term memory network (Peehole LSTM) to obtain a time dependence feature; capturing local interaction information between vehicles by adopting an expansion convolution social pooling module, capturing global interaction information through a multi-head self-attention mechanism, and fusing local and global interaction features; a proper kinematic model is dynamically selected based on driving intention recognition, kinematic constraints are embedded in a decoding stage, a predicted trajectory is corrected in real time, and a target vehicle future trajectory conforming to a physical law and a driving intention is output, so that the trajectory prediction accuracy and physical consistency in a complex traffic scene are improved, and the method is suitable for popularization and application.

Description

Technical Field

[0001] This invention relates to the fields of intelligent transportation and autonomous driving technology, specifically to a spatiotemporal encoding and decoding method for predicting vehicle trajectories based on dynamic kinematic constraint embedding. Background Technology

[0002] By predicting the trajectories of surrounding vehicles, intelligent vehicles can react in advance to changes in the motion of those vehicles, make accurate and proactive decisions about future traffic conditions, and plan safe, easily controllable, comfortable, and not overly conservative driving trajectories. Existing vehicle trajectory prediction methods can be broadly categorized into three types: physics-based methods, data-driven methods, and hybrid methods based on physics-data fusion.

[0003] Physical model-based vehicle trajectory prediction methods rely on vehicle kinematics and physical laws for motion prediction, typically incorporating parameters such as speed, acceleration, and steering angle, as well as environmental factors like road geometry and traffic rules. These models offer advantages such as strong interpretability, high computational efficiency, and good stability under physical constraints. However, they often struggle to capture the complex spatiotemporal dependencies between interacting vehicles, leading to decreased reliability in long-term predictions (e.g., exceeding one second). While dynamic models require internal vehicle parameters that are difficult to observe through external sensors, kinematic models (such as CV, CA, and CTRV) are more commonly used. However, these methods cannot fully account for road-related factors and vehicle state uncertainties, limiting long-term prediction accuracy.

[0004] Data-driven approaches abandon explicit physical formulas, learning complex interaction patterns and nonlinear behaviors directly from empirical data. This typically leads to higher prediction accuracy and greater adaptability to various traffic scenarios. Deep learning techniques demonstrate unique advantages in modeling complex interactions among traffic participants. Recurrent Neural Networks (RNNs) and their variants (LSTM, GRU) have been widely used for trajectory prediction, and subsequent models combining Convolutional Neural Networks (CNNs) and Graph Convolutional Networks (GCNs) have emerged to better capture spatial relationships. However, these methods often lack physical interpretability, their performance heavily depends on the scope, quality, and diversity of the training dataset, and some models fail to adequately capture multi-vehicle interactions and potential spatiotemporal dependencies.

[0005] Hybrid approaches based on physics-data fusion aim to integrate the interpretability of physical models with the adaptability and learning capabilities of machine learning, maintaining physical feasibility while considering the influence of environmental and behavioral factors. For example, some methods directly fuse the short-term outputs of the physical model in the final stage of the data-driven predictor, or incorporate the trajectory sequences generated by the physical model as auxiliary inputs into the decoding step through iterative mechanisms. However, most existing hybrid schemes treat the iterative processes of the physical and learning components as independent processes, which easily propagates accumulated physical model errors and ultimately reduces overall prediction performance. At the same time, many data-driven modules still fail to fully capture multi-vehicle interactions and spatiotemporal dependencies, and lack real-time dynamic adjustments to physical constraints, resulting in predicted trajectories that may violate vehicle dynamics characteristics. Summary of the Invention

[0006] To address the problems of existing technologies, this invention provides a spatiotemporal encoding and decoding vehicle trajectory prediction method based on dynamic kinematic constraint embedding. The method aims to capture time-dependent features using a Peephole Long Short-Term Memory (LSTM) network, fuse local and global interaction information through dilated convolutional social pooling and multi-head self-attention mechanisms, and dynamically embed kinematic constraints based on driving intention during the decoding stage to correct the predicted trajectory in real time. This solves the problems of insufficient physical interpretability, error accumulation, and inadequate capture of interaction information in existing methods, thereby improving the accuracy and physical consistency of trajectory prediction.

[0007] To achieve the above objectives, the specific solution of the present invention is as follows:

[0008] A spatiotemporal encoding and decoding method for vehicle trajectory prediction based on dynamic kinematic constraint embedding includes the following steps:

[0009] S1, Peephole LSTM is used to encode the historical observation data HT of the target vehicle and its surrounding vehicles to obtain time-dependent features, resulting in the hidden state sequence h and the cell state sequence c.

[0010] S2 employs a dilated convolutional social pooling module to capture local interaction information between the target vehicle and its nearby vehicles, resulting in a local interaction vector. ;

[0011] S3 uses a multi-head self-attention mechanism to capture global interaction information between all vehicles in the scene, and obtains the global interaction vector Ca.

[0012] S4, Fusing Local Interaction Vectors With global interaction vector The comprehensive interactive feature vector is obtained. ;

[0013] S5, based on comprehensive interactive feature vector Recognize driving intentions and dynamically select the corresponding kinematic model;

[0014] S6 will integrate the interactive feature vector Input the Peephole LSTM decoder, embed the selected kinematic model as a constraint during the decoding process, correct the prediction results in real time, and iteratively output the future trajectory Y of the target vehicle.

[0015] Furthermore, the expression for the historical observation data HT is as follows:

[0016]

[0017] In the formula, N represents the total number of the target vehicle and the vehicles around it; Let represent the sequence of observed states of the nth vehicle at discrete time steps t=1,2,...,T;

[0018]

[0019] Where x and y are position coordinates; t is time; T is total time; v is velocity; a is acceleration; θ is heading angle; ω is turning angle; Let represent the observed state of the nth vehicle at time t.

[0020] The PeepholeLSTM used in this invention is a variant of the standard LSTM, which provides direct access to the cell state for each gating unit (forget gate, input gate, and output gate). Therefore, at each time step, the gating unit receives not only the previous hidden state... and current input It also receives information from the cell state via a viewing hole. This architectural improvement enables the network to more sensitively track and regulate the evolution of its internal memory.

[0021] When computing the gated activation at time t, the peephole LSTM combines the previous cell state, the hidden state, and the current input to enhance temporal dependency modeling. The gated activation function is defined as follows:

[0022]

[0023]

[0024]

[0025] Among them, the forgetting gate f t Determines the cell state at the previous moment How much information is retained in the current cell state? In the middle. Input gate i t Decide to input X at the current moment tHow much information is written into the cell state at the current moment? Middle. Output gate o t Determines the cell state at the current moment How much information is output to the hidden state at the current moment? Then, at time t, the forward computation of the peephole LSTM network can be expressed as:

[0026]

[0027]

[0028]

[0029] Among them, candidate cell state Ĉ t Is the input X at the current time? t Hidden state from the previous moment The function represents new information that may be written into the cell state. Current cell state. It is the cell state at the previous moment. With the Gate of Oblivion t The weighted sum, and the candidate cell state K t With input gate i t The weighted sum. The hidden state at the current moment. It is an output gate. t Current cell state The product of hyperbolic tangent functions. When the input is a historical trajectory sequence HT, the final output of the peephole LSTM network can be expressed as:

[0030]

[0031] Where h and c are the final hidden state sequence and final cell state sequence obtained by each vehicle in the traffic scene after being processed by the peephole LSTM network, respectively.

[0032] Furthermore, the steps of the dilated convolutional social pooling module in capturing local interaction information are as follows:

[0033] S21, construct the scene social tensor by combining the hidden state sequence h and the cell state sequence c according to the spatial positional relationship of the vehicle;

[0034] S22 uses two 3×3 dilated convolutional layers (dilation rate of 2 and padding length of 1) to extract features from the social tensor;

[0035] S23, compresses the dimension of the feature map through an adaptive average pooling layer;

[0036] S24 uses a 3×1 dilated convolutional layer (dilution ratio 2, padding length (1,0)) to optimize features, and obtains the local interaction vector after adaptive average pooling. .

[0037] Furthermore, the steps of the multi-head self-attention mechanism in capturing global interaction information are as follows:

[0038] S31, dimensionality reduction of the social tensor to generate a one-dimensional sequence vector;

[0039] S32 embeds sequence position information through positional encoding. Specifically, it uses standard fixed sine and cosine functions to generate a unique and distinguishable code for each position.

[0040]

[0041]

[0042] Where PE is the position code; pos is the position index; i is the embedding dimension index; and d is the embedding dimension.

[0043] S33, generate query vector Q, key vector K, and value vector V.

[0044]

[0045] in is the output feature vector of the spatiotemporal coding module; j is the index of the "head" in the multi-head attention mechanism, used to distinguish different attention heads; , , The weight matrix is ​​a learnable weight matrix;

[0046] S34, Calculate the attention score:

[0047]

[0048] in d is the attention score of the j-th attention head, used to quantify the association priority between different vehicles (or trajectory features); k Let K be the dimension of the key vector.

[0049] S35, by calculating headⱼ=αⱼ×Vⱼ through multi-head attention, concatenating the outputs of multiple attention heads and mapping them back to the original dimension, we obtain the global interaction vector:

[0050]

[0051] in This is a vector that captures global interaction features through self-attention; Let j be the output feature vector of the j-th attention head; The weight matrix is ​​a learnable weight matrix;

[0052] Furthermore, the comprehensive interaction feature vector-based The steps for identifying driving intentions and selecting a kinematic model are as follows:

[0053] S51, integrate the interactive feature vector The input to the fully connected layer yields six categories of driving intent ( , , , , , The logit score;

[0054] S52, the log odds fraction is converted into the intention probability distribution MP by the Softmax function;

[0055] S53: Select the driving intention category with the highest probability, and dynamically select the kinematic model according to the mapping rules. Corresponding to the constant velocity (CV) model, Corresponding to the constant acceleration (CA) model, or Corresponding to the constant angle and constant speed (CTRV) model, or This corresponds to the Constant Rotation and Constant Acceleration (CTRA) model.

[0056] Furthermore, the step of embedding kinematic constraints in the decoding stage is as follows:

[0057] S61, starting with the single-step state vector generated by the kinematic model, combine this vector with the comprehensive interaction feature vector. They are input together into the Peephole LSTM decoder unit;

[0058] S62, each subsequent decoder unit inherits the previous hidden state. and cell state ;

[0059] S63, the predicted state vector of step k = =[x,y,v,a, ,ω], together and It propagates through kinematic equations;

[0060] For CV models:

[0061]

[0062] For the CA model:

[0063]

[0064] For the CTRV model:

[0065]

[0066] For the CTRA model:

[0067]

[0068] S64, the final output is the corrected state. Then, the corrected state Together and Input into the decoder, generate By iterating through this process, the model generates a complete predicted trajectory.

[0069] Furthermore, the expression for the kinematic model is as follows:

[0070] CV model:

[0071]

[0072]

[0073] CA model:

[0074]

[0075]

[0076]

[0077] CTRV model:

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] CTRA model:

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094] Where x and y are the vehicle's lateral and longitudinal coordinates; λ represents the horizontal and vertical coordinates at t=0; v represents the instantaneous velocity of the vehicle. ρ is the initial velocity; a is the instantaneous acceleration of the vehicle; θ represents the initial acceleration; θ represents the vehicle heading angle; t represents the prediction time interval; k, k+1 represent the time step indices. =25 is the maximum prediction time step; Δt=0.2s is the fixed time interval between adjacent time steps; ω is the vehicle steering angular velocity; These are the velocity components of the vehicle in the x and y directions; These are the velocity components along the x and y axes at time step k+1. Let be the turning angular velocity at time step k.

[0095] The technical effects of this invention are as follows:

[0096] 1. This invention proposes a hybrid prediction method that integrates physical and data fusion. By encoding the temporal dependency features of historical trajectories using Peephole LSTM, it captures local and global interaction information using dilated convolutional social pooling and multi-head self-attention mechanisms, respectively, thereby achieving effective fusion of multi-scale interaction features and overcoming the shortcomings of traditional methods in not considering interaction information.

[0097] 2. Unlike existing hybrid methods, this invention dynamically embeds kinematic constraints based on driving intention during the decoding stage, avoids error accumulation through real-time physical correction, ensures that the predicted trajectory conforms to the vehicle's dynamic characteristics, and improves physical interpretability and prediction stability.

[0098] 3. The combination of driving intention recognition and dynamic selection mechanism of kinematic model can adapt to various driving behaviors such as straight driving, acceleration and deceleration, and lane changing, and has stronger adaptability in complex traffic scenarios. At the same time, the experimental results of the model on NGSIM and HighD datasets show that its prediction accuracy is significantly better than the existing baseline model, while maintaining good computational efficiency. Attached Figure Description

[0099] Figure 1 This is a diagram illustrating the overall architecture of the vehicle trajectory prediction method in this specific embodiment.

[0100] Figure 2 The overall architecture of the proposed spatiotemporal coding-decoding model with embedded dynamic kinematic constraints (STE-DKC) for vehicle trajectory prediction is presented.

[0101] Figure 3 This is a schematic diagram of the Peephole LSTM encoder in this specific embodiment.

[0102] Figure 4 This is a schematic diagram of the encoding process of the multi-head self-attention mechanism in this specific embodiment.

[0103] Figure 5 This is a diagram showing the coupling mapping relationship between driving intention and kinematic model in this specific embodiment.

[0104] Figure 6 This is a flowchart illustrating the dynamic embedding of kinematic constraints during the decoding stage in this specific embodiment.

[0105] Figure 7 This is a visualization of the prediction effects of different models under various driving conditions in this specific embodiment.

[0106] Figure 8 and Figure 9 This is a diagram showing the ablation experiment results of the kinematic model combination in this specific embodiment.

[0107] Figure 10 This is a visualization analysis diagram of the impact of kinematic constraints on trajectory prediction in this specific embodiment.

[0108] Figure 11 This is one of the visualization analysis diagrams showing the influence of surrounding vehicles on the trajectory prediction of the target vehicle in this specific embodiment.

[0109] Figure 12 This is the second visualization analysis diagram of the influence of surrounding vehicles on the trajectory prediction of the target vehicle in this specific embodiment.

[0110] Figure 13 This is the third visualization analysis diagram showing the impact of surrounding vehicles on the trajectory prediction of the target vehicle in this specific embodiment. Detailed Implementation

[0111] The present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. It should be noted that the specific embodiments are not intended to limit the scope of the present invention.

[0112] like Figure 1 As shown in the figure, this specific embodiment provides a spatiotemporal encoding and decoding vehicle trajectory prediction method based on dynamic kinematic constraint embedding, including the following steps:

[0113] S1, Peephole LSTM is used to encode the historical observation data HT of the target vehicle and its surrounding vehicles to obtain time-dependent features, resulting in the hidden state sequence h and the cell state sequence c; specifically, the historical observation data... N is the total number of the target vehicle and its surrounding vehicles. This represents the sequence of observed states of the nth vehicle at time steps t=1,2,...,T. It covers parameters such as position coordinates, velocity, acceleration, heading angle, and turning angle. For example... Figure 3 The Peephole LSTM shown is a variant of the standard LSTM, where each gate unit (forget gate, input gate, output gate) can directly access the cell state, in addition to receiving the hidden state h from the previous time step. t ₋1 and the current input X t In addition, cell status is obtained through a viewing hole. This information allows for more sensitive tracking and regulation of the evolution of internal memory. Its forward computation process is as follows: Forget gate f t Determines the cell state C at the previous moment t ₋1 Retain the cell state C at the current moment t Information content; input gate i t Decide to input X at the current moment t Write cell state C t Information content; candidate cell state The current input is X t and the hidden state h from the previous moment t A function of ₋1 represents new information that may be written into the cell state; the current cell state. Output gate o t Determining cell state C t Output to hidden state h t The amount of information, Through this encoding process, the hidden state sequence h and cell state sequence c of each vehicle are obtained.

[0114] S2 employs a dilated convolutional social pooling module to capture local interaction information between the target vehicle and its nearby vehicles, resulting in a local interaction vector. Since the Peephole LSTM encoder primarily captures temporal dependencies and struggles to directly capture motion correlations between vehicles, a dilated convolutional social pooling module is employed to extract local interaction features. First, a scene social tensor is constructed based on the spatial relationships between the hidden states and cell states of all vehicles. Then, a social pooling module is built, consisting of two 3×3 dilated convolutional layers (dilation rate of 2, padding length of 1), an adaptive average pooling layer, a 3×1 dilated convolutional layer (dilation rate of 2, padding length of (1,0)), and an adaptive average pooling layer. Dilated convolutions can expand the receptive field without increasing parameters or computational cost, integrating broader contextual information and ultimately outputting local interaction vectors. This reflects how each vehicle is affected by nearby vehicles.

[0115] S3 employs a multi-head self-attention mechanism to capture global interaction information between all vehicles in the scene, resulting in a global interaction vector. The social pooling layer, limited by the convolutional kernel, can only capture local features and cannot fully capture the global interaction features between vehicles. Therefore, it is designed as follows: Figure 4 A global interaction feature capture module based on a multi-head self-attention mechanism is proposed. First, the social tensor is reduced in dimensionality to generate a one-dimensional sequence vector, and then positional encoding is performed using fixed sine and cosine functions. , Embed sequence position information; then, generate a query vector. Key vector Value vector ( , , (For the learnable weight matrix), calculate the attention score. (d) k (where the key vector dimension is used); the multi-head attention output is obtained by concatenating the results of multiple attention heads and mapping them back to the original dimension, i.e. ( (This is a learnable weight matrix), and the vector aggregates the global interaction features of all vehicles.

[0116] S4, Fusing Local Interaction Vectors With global interaction vector The comprehensive interactive feature vector is obtained. By splicing together local and global interactive features, that is... This vector contains both short-range local interactions between vehicles and long-range global dependencies, providing a rich contextual basis for subsequent driving intention recognition and trajectory prediction.

[0117] S5, based on comprehensive interactive feature vector Recognize driving intentions and dynamically select the corresponding kinematic model; integrate interactive feature vectors After processing by a fully connected layer, log-odds scores for six driving intent categories are generated. , , , , , ), which is converted into a probability distribution MP=[ using the Softmax function. , , , , , Based on the driving intention category with the highest probability, the kinematic model is selected according to the following mapping rule: Corresponding to the CV (constant velocity) model, Corresponding to the CA (constant acceleration) model, or Corresponding to the CTRV (constant angle, constant speed) model, or This corresponds to the CTRA (Constant Acceleration and Steering) model. The selected kinematic model closely matches the driving intention and accurately reflects the vehicle's motion characteristics, such as... Figure 5 As shown.

[0118] S6, such as Figure 6 Starting with the single-step state vector generated by the kinematic model, this vector is combined with the comprehensive interaction feature vector. The input is a Peephole LSTM decoder. During decoding, a selected kinematic model is embedded as a constraint to correct the prediction results in real time, iteratively outputting the future trajectory Y of the target vehicle. The decoder employs a Peephole LSTM structure mirrored in the encoder, fully utilizing the hidden states and cell states generated by the encoder. During decoding, the integrated interaction feature vector is first... Input to decoder to generate initial prediction state X k =[x,y,v,a,θ,ω]; then, X k Input the kinematic model selected in step S5, and calculate the physically corrected state X. k+1 To ensure that each prediction step conforms to the laws of vehicle dynamics; the corrected X k+1 With the hidden state h of the decoder k Cell state c k The common input is used to the next decoding unit to generate X. k+2 Repeat the above iterative process until a complete trajectory Y with 25 time steps (total prediction duration of 5 seconds) is generated.

[0119] This invention uses publicly available NGSIM and HighD datasets for comparative experiments. The I-80 and US-101 subsets of NGSIM contain vehicle trajectories recorded at a frequency of 10Hz in real-world highway environments, covering 45 minutes of data under light, medium, and heavy traffic conditions. This data provides diverse scenarios for evaluating the robustness and effectiveness of the proposed network. The HighD dataset contains measurement data from approximately 110,000 vehicles at six different highway locations, totaling 16.5 hours, and includes 5,600 complete lane change events. To ensure a fair comparison, the original NGSIM and HighD data were downsampled to 5Hz, and each trajectory was divided into 8-second segments, with the first 3 seconds used as the observation time range and the remaining 5 seconds used as the prediction time domain. The datasets were divided into training, validation, and test sets in a 7:1:2 ratio.

[0120] To measure the difference between the predicted trajectory and the actual trajectory using root mean square error (RMSE) and average displacement error (ADE), the evaluation metrics were calculated for prediction ranges F = 1s, 2s, 3s, 4s, and 5s.

[0121] RMSE formula:

[0122]

[0123] in Let be the root mean square error at time t; t is the prediction time step. and These represent the predicted trajectory and the actual trajectory at time t, respectively; N is the number of vehicles.

[0124] ADE formula:

[0125]

[0126] Where ADE is the average displacement error over the entire prediction time domain; F is the prediction duration; and T is the last time step of the observation duration. and These represent the predicted trajectory and the actual trajectory at time t, respectively; N is the number of vehicles.

[0127] It reflects the average deviation of the entire predicted trajectory.

[0128] Experimental Results and Analysis:

[0129] Table 1. Analysis of experimental results for different models

[0130]

[0131] Comparison results with baseline methods such as S-LSTM, CS-LSTM, S-GAN, NLS-LSTM, WSIP, DRBP, TCN-SA, and TFE-PID on the NGSIM and HighD datasets show that the model proposed in this invention exhibits superior prediction performance.

[0132] Table 1 summarizes the prediction results of all models, with the lowest RMSE for each prediction time domain highlighted in bold. It is worth noting that, due to the higher data collection quality and more comprehensive scene coverage of the HighD dataset, all models outperform the NGSIM dataset overall.

[0133] On the NGSIM dataset, the proposed model achieves state-of-the-art performance across all prediction time domains, with RMSEs of 0.52 m, 1.13 m, 1.83 m, 2.72 m, and 3.82 m at 1 sec, 2 sec, 3 sec, 4 sec, and 5 sec, respectively. The mean RMSE (AVE) reaches 2.01 m, approximately 7.2% higher than the second-best method (TCN-SA). This improvement demonstrates that fusing dynamic kinematic constraints and intent recognition enables the model to more effectively capture motion patterns and physical dynamics. Notably, models such as WSIP and NLS-LSTM, which primarily focus on spatial interactions, perform well in the short term, but their long-term prediction errors accumulate due to limited consideration of physical feasibility. On the HighD dataset, STE-DKC achieved the lowest RMSE at 2 seconds (0.55 m, 1.8% better than TCN-SA's 0.56 m) and 5 seconds (2.80 m, 2.4% better than TCN-SA's 2.87 m), and was tied for best with other models at 1 second (0.19 m). However, in the 3-second and 4-second time domains, DRBP performed better, with RMSEs of 1.11 m and 1.40 m, respectively, while STE-DKC's RMSEs were 1.12 m and 1.90 m, respectively. DRBP also had the lowest mean RMSE (AVE) (0.93 m), but this value was only calculated based on the 1–4 second time domain, as results for 5 seconds were not available. Therefore, comparisons of mean RMSE should be interpreted with caution. Considering the methods that report results across the full 1–5 second range, STE-DKC offers the best long-term prediction accuracy and competitive mid-to-short-term performance.

[0134] Further comparative analysis shows that: (1) S-LSTM, CS-LSTM and NLS-LSTM exhibit similar performance, which is consistent with their shared LSTM backbone network; (2) Although S-GAN can generate multimodal trajectories through a generative adversarial framework with social constraints, its sequence modeling ability is weak, resulting in low overall accuracy; (3) TCN-SA captures temporal dependencies with higher parallelism and long-distance modeling capabilities by employing a temporal convolutional network, achieving better results than traditional LSTM-based methods; (4) The WSIP model introduces a wave superposition mechanism and improves interpretability through phase difference analysis, but it fails to outperform the proposed method, indicating that modeling interactions solely through physical wave analogy is insufficient to capture the complex spatiotemporal dependencies and kinematic constraints in real-world driving; (5) DRBP combines intent prediction with trajectory generation through a dual Transformer structure, performing well in the mid-temporal domain of the HighD dataset, highlighting the advantages of intent-aware modeling, but long-term predictions show inconsistencies due to the lack of embedded physical constraints. Similarly, although TFE-PID combines physical modeling with data-driven learning, its accuracy is limited due to neglecting vehicle interaction and environmental context. The proposed STE-DKC model effectively addresses these limitations by embedding kinematic constraints in a unified physics-data driven framework and utilizing a peephole LSTM network for robust sequence modeling, achieving excellent overall performance on both datasets.

[0135] Table 2. Comparison and evaluation of mean absolute error (ADE) and inference time for each method on the NGSM dataset.

[0136]

[0137] As shown in Table 2, the model was further compared using ADE and inference time metrics on the NGSIM dataset. The proposed method demonstrates a significant advantage in trajectory prediction accuracy, especially in the mid-to-long-term time domain (3 to 5 seconds). In the 5-second prediction time domain, the model achieved an ADE of 1.70 meters, significantly lower than the 2.44–2.89 meters of other baseline methods. This substantial reduction in displacement error (reflecting the average deviation across the entire predicted trajectory) indicates that the proposed framework possesses superior capabilities in modeling the complete spatiotemporal evolution of vehicle motion. Therefore, the model can generate more accurate and dynamically consistent trajectories over extended prediction intervals.

[0138] From a computational efficiency perspective, the inference time comparison reveals the different architectural characteristics. S-LSTM, employing fully connected interaction modeling, has a higher latency (0.275 ms) than CS-LSTM (0.248 ms), while CS-LSTM benefits from efficient convolutional social pooling. WSIP requires a moderate inference time (0.282 ms) due to its wave superposition mechanism, which needs to compute phase and amplitude information for interaction modeling. TCN-SA has the highest latency among the baseline methods (0.351 ms) because its attention mechanism involves constructing and processing the adjacency matrix to capture global dependencies. Notably, TPE-PID achieves the fastest inference speed (0.216 ms) by relying solely on master vehicle data, significantly reducing computational complexity. In contrast, the proposed STE-DKC maintains a good balance between accuracy and efficiency with an inference time of 0.302 ms. This is achieved by directly applying self-attention to the flattened social tensor, eliminating the need for explicit adjacency matrix construction, effectively reducing computational complexity while preserving representational power. The combination of peephole LSTM optimization and dynamically embedded kinematic constraints further enhances the model's temporal inference capability and physical consistency. Overall, the proposed framework achieves an excellent trade-off between prediction accuracy and computational efficiency across two datasets and multiple evaluation metrics.

[0139] Figure 7 This presentation showcases a comprehensive visual comparison of vehicle trajectory predictions from different models under various driving operations. The chart consists of three rows and two columns, with each column corresponding to a specific driving condition (normal driving and speed changes), and each row representing a driving action (going straight, changing lanes to the left, and changing lanes to the right). Within each sub-chart, six trajectory representations are displayed: blue squares represent the historical trajectories of surrounding vehicles (Nbrs hist), providing contextual information about the traffic environment; black solid lines represent the target vehicle's true future trajectory (GT fut), serving as an accuracy benchmark; cyan dashed lines represent the target vehicle's historical trajectory (Tar hist); red solid lines represent the predicted trajectory of the CS-LSTM model; yellow solid lines represent the predicted trajectory of the TFE-PID model; and green solid lines represent the predicted trajectory of the proposed model.

[0140] Visualization results demonstrate that the proposed model consistently delivers superior predictive performance regardless of whether the vehicle maintains a constant speed or accelerates or decelerates. Especially... Figure 7In the lower subfigure of (b), the proposed model (solid green line) demonstrates a significant advantage in complex scenarios involving simultaneous lane changes and speed adjustments. It accurately predicts the initiation of lane change operations and the corresponding acceleration trajectory during the transition phase. In contrast, the CS-LSTM model (solid red line) fails to capture these dynamic changes in acceleration and lateral displacement. Although the TFE-PID model takes short-term predictions from the physical model as input, it does not dynamically embed physical constraints in the long term; therefore, it cannot update these constraints in real time during the prediction process. Furthermore, since the TFE-PID model does not consider interactions with surrounding vehicles, its prediction accuracy is lower than that of the proposed model and the CS-LSTM model. This improvement of the proposed model stems from its ability to adaptively select an appropriate kinematic model based on the predicted driving intent and apply dynamically embedded kinematic constraints at each prediction step. This mechanism ensures real-time physical consistency of the predicted trajectory, enabling it to better align with real driving intent and achieve higher accuracy in complex scenarios. Overall, compared to traditional models, the proposed method exhibits superior adaptability and prediction accuracy, contributing to improved safety and reliability in autonomous driving applications.

[0141] Intent recognition analysis

[0142] The proposed STE-DKC model incorporates a driving intent recognition task, and comprehensive experiments were conducted to evaluate its effectiveness. While both CS-LSTM and TFE-PID include intent recognition modules, TFE-PID relies solely on the master vehicle's state information, neglecting environmental context. Therefore, the comparative analysis focuses only on the proposed STE-DKC model and the CS-LSTM baseline method. To construct a balanced dataset, 4,800 samples were randomly selected from six operation categories: acceleration or deceleration, left lane change (…). ), constant speed left lane change ( ), acceleration or deceleration lane keeping ( ), constant speed lane keeping ( ), accelerate or decelerate when changing lanes to the right ( ) and constant speed right lane change ( A total of 28,800 samples were collected.

[0143] Performance evaluation uses three key metrics: precision, recall, and F1 score. Precision measures the proportion of correctly predicted positive instances out of all predicted positive instances; recall quantifies the proportion of correctly predicted positive instances out of all actual positive instances. The F1 score is the harmonic mean of precision and recall, providing a balanced assessment of model performance. The formal definitions of these metrics are as follows:

[0144] Precision = TP / (TP + FP)

[0145] xiRecall = TP / (TP + FN)

[0146] F1-Score=2×(Precision×Recall) / (Precision+ Recall)

[0147] TP represents a true positive, FP represents a false positive, and FN represents a false negative.

[0148] Table 3. Performance Comparison of Intent Recognition Based on Precise Metrics

[0149]

[0150] As shown in Table 3, the proposed STE-DKC model achieved excellent performance across all evaluation metrics, with an average precision of 94.0%, recall of 94.3%, and an F1 score of 0.940, significantly outperforming the CS-LSTM baseline method (precision 85.5%, recall 87.6%, F1 score 0.859). This improvement is consistent across all operation categories, particularly in lane-keeping scenarios involving acceleration or deceleration. In lane keeping operations, the improvement in accuracy is particularly significant: STE-DKC achieved an accuracy of 95.8%, while CS-LSTM achieved 85.4%, an improvement of 10.4 percentage points. STE-DKC's superior performance is attributed to its integration of multi-head attention and social pooling during scene encoding, enabling the model to effectively capture spatial dependencies and temporal motion dynamics between vehicles. In contrast, CS-LSTM relies solely on social pooling of neighboring vehicle features, limiting its understanding of context. Detailed analysis of the results for each category further highlights STE-DKC's ability to distinguish fine-grained operational patterns. In lane keeping operations, STE-DKC, under constant speed conditions (… It achieved a precision of 95.6% and a recall of 98.2%, with an F1 score of 0.969, while CS-LSTM achieved a precision of 88.0%, a recall of 94.1%, and an F1 score of 0.908. Under acceleration or deceleration conditions ( STE-DKC maintained a precision of 95.8% and a recall of 95.6% (F1 score: 0.957), significantly outperforming CS-LSTM's 85.4% precision and 84.3% recall (F1 score: 0.848). In lane-changing scenarios, STE-DKC performed robustly, maintaining a steady speed while changing lanes to the left. The accuracy rate was 95.3%, the recall rate was 94.8%, and the acceleration of left lane change ( The precision of STE-DKC was 92.8%, and the recall was 92.1%, consistently outperforming CS-LSTM across all corresponding categories. Similar improvements were observed for right lane changes, with STE-DKC achieving a precision of 91.9% (…). ) and 92.6% These results demonstrate the generality of the proposed method. They comprehensively validate the effectiveness of the STE-DKC framework in identifying complex driving intentions, providing a reliable foundation for subsequent trajectory predictions with higher accuracy and physical consistency.

[0151] Table 4 Ablation experiments on the NGSIM dataset

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[0153] Ablation experiment:

[0154] Three sets of ablation experiments were conducted to investigate the contribution of key components to the overall model performance. Specifically, the experiments included: (1) removing the convolution and pooling modules; (2) removing the attention-based interaction module; and (3) omitting the kinematic constraints of the dynamic embedding and using a standard unfolded peephole LSTM for single-step decoding prediction. The results are summarized in Table 4, clearly showing the performance contribution of each module.

[0155] When the dynamic embedding kinematic constraints are removed and predictions are made using standard peephole LSTM single-step decoding, the model fails to account for the physical properties of vehicle motion, resulting in consistently higher prediction errors across all time domains compared to the full model. This observation definitively demonstrates that the dynamic embedding of physical constraints is crucial for ensuring predictions conform to fundamental physical laws. Without this key module, the model's predictive ability is significantly impaired. When the attention interaction module is removed, the model fails to adequately capture the complex interactions between vehicles in the global scene. This directly leads to a significant drop in model performance and a substantial impact on prediction accuracy. The impact is evident because the model struggles to understand complex global vehicle interactions, thus hindering accurate predictions. Removing the dilated convolution module causes the model to lose its ability to understand local interaction information, thereby reducing accuracy. However, this reduction is less pronounced compared to removing the attention interaction module. This indicates that the attention-based global interaction module plays a crucial role in integrating vehicle interactions. It is argued that relying solely on single interaction features (whether local or global) extracted by the social pooling module or the attention interaction module is insufficient to fully reflect the dynamics of real-world interactions. Therefore, fusing local and global interaction features is essential for significantly improving the overall performance of the model. This finding indirectly demonstrates that utilizing additional auxiliary information is an effective strategy for improving the performance of predictive models, and highlights the complementarity of local and global interaction features. Ablation experiments show that the model's key contributions—dynamically embedded kinematic constraints and the synergistic combination of extended social pooling and self-attention for extracting information about surrounding vehicles—are functionally validated.

[0156] To verify the effectiveness of the multi-model kinematic framework, an ablation study was conducted on the model components, and the results are as follows: Figure 8 and Figure 9As shown, in single-model configurations, the CA model achieved the best performance (RMSE: 4.20 m at 5 seconds), followed by the CV model (4.35 m), while the steering models (CTRV: 5.09 m, CTRA: 4.92 m) produced higher errors in general applications. This ranking is further confirmed by the ADE index at 5 seconds, where the CA model (2.02 m) and CV model (2.15 m) also outperformed the CTRV model (2.34 m) and CTRA model (2.22 m). This trend is consistent with real-world highway driving behavior, where straight-line motion is dominant, and indiscriminate use of steering models introduces significant inaccuracies. Combining kinematic models resulted in cumulative improvements in RMSE and ADE. An intent-based selection mechanism was employed, dynamically assigning models according to the predicted driving intent. The CV+CA configuration reduced the 5-second RMSE to 4.12 m and the ADE to 1.98 m, indicating that distinguishing between constant speed and acceleration helps improve predictive performance. Adding steering models further reduced errors: CV+CA+CTRV achieved an RMSE of 4.01 meters and an ADE of 1.92 meters, while CV+CA+CTRA achieved an RMSE of 3.99 meters and an ADE of 1.87 meters. Ultimately, the complete STE-DKC framework achieved the best results—an RMSE of 3.82 meters and an ADE of 1.70 meters at 5 seconds—a 9.1% improvement in ADE compared to the strongest baseline. This significant improvement validates that, although steering maneuvers are not frequent, accurately modeling them when they occur through appropriate intent-based model assignment is crucial for improving the overall system accuracy in trajectory-level and point-level evaluation metrics.

[0157] Visual analysis of the impact of kinematic constraints on trajectory prediction

[0158] A typical lane-change scenario was selected to visualize and compare the predicted trajectories generated by different models. In this scenario, the CTRA kinematic model was dynamically embedded into the decoder of the proposed framework. Figure 10 As shown, a comparative analysis was conducted on the following trajectories: the true trajectory (GT), the predicted trajectory of the proposed model (Fut pred), the predicted trajectory of the model without kinematic constraints (Without CTRA pred), and the intermediate trajectory points obtained after applying kinematic constraints at each prediction step (CTRA-refined points)—these points are used as inputs to the PLSTM in the next prediction step. The results clearly demonstrate that incorporating kinematic constraints enables the model to more accurately infer driving intentions and guides the predicted trajectory closer to the true trajectory, thereby significantly improving prediction accuracy.

[0159] In-depth analysis of the amplified prediction results revealed the following: First, the kinematic constraint model effectively corrects prediction biases at the initial time step and uses the adjusted output as input to the decoder, significantly enhancing the consistency of subsequent prediction sequences. Second, as the vehicle completes a lane change and enters a straight-line driving phase, the model's predicted yaw angle gradually converges to zero, causing the kinematic constraint model's output to naturally approximate a straight trajectory. This correction mechanism ensures that the entire prediction process conforms to the physical laws of actual driving behavior.

[0160] The visualization results clearly demonstrate that the kinematic constraint model consistently guides the predicted trajectory to converge in a manner consistent with the vehicle's dynamic characteristics. In addition to ensuring prediction accuracy, it significantly improves the reasonableness and interpretability of the prediction results.

[0161] Visual analysis of the impact of surrounding vehicles on the trajectory prediction of the target vehicle:

[0162] To further analyze multi-vehicle interactions, the impact of surrounding vehicles on the trajectory prediction of the target vehicle was visually studied, such as... Figures 11 to 13 As shown in the figure, this diagram combines a driving scenario map, an attention weight heatmap, and predicted trajectories for straight-ahead, left lane change, and right lane change. It reveals that the model continuously focuses on vehicles directly ahead, reflecting the need for human drivers to monitor road conditions for safety. Furthermore, in lane change scenarios, the attention mechanism dynamically adjusts: when changing lanes to the left, it strengthens its attention to vehicles in the adjacent left lane to assess distance; when changing lanes to the right, attention shifts to vehicles in the right lane; and when going straight, attention focuses on the target vehicle's own motion, as lateral assessment is not required. These observations confirm that attention-based encoding can effectively capture scenario-related interactions and closely simulate the decision-making logic of human drivers.

[0163] This invention proposes a spatiotemporal encoding-decoding model (STE-DKC) incorporating dynamic kinematic constraints for vehicle trajectory prediction. By integrating real-time trajectory correction during the decoding stage, STE-DKC ensures physical plausibility and enhances stability and responsiveness in complex high-speed scenarios. To capture interactive effects, an expanded convolutional social pooling module modeling local spatial interactions is combined with a multi-head self-attention mechanism that learns global dependencies; this approach incorporates the proximity and long-distance effects of surrounding vehicles into each prediction.

[0164] Empirical analysis yielded three key findings: First, the dynamic embedding of motion constraints enabled the model to correct its output in real time, ensuring physically plausible trajectories and improving reliability under complex conditions. Second, the two interactive modules jointly considered detailed and global environmental factors, resulting in a significant improvement in prediction accuracy compared to baseline methods. Third, the visualization of attention weights and trajectory correction provided clear interpretability: quantifying how kinematic feedback pulls predictions back to feasible regions and illustrating how attention dynamically adapts to different traffic environments.

[0165] In conclusion, STE-DKC has made significant progress in trajectory prediction for straight-ahead and lane-changing maneuvers. Future work will explore richer kinematic formulas and integrate multimodal data (such as sensor fusion and traffic signal information) to extend its application to more complex urban environments, such as intersections, congested areas, and severe weather, to further improve prediction stability.

Claims

1. A spatiotemporal encoding and decoding vehicle trajectory prediction method based on dynamic kinematic constraint embedding, characterized in that, Includes the following steps: S1, Peephole LSTM is used to encode the historical observation data HT of the target vehicle and its surrounding vehicles to obtain time-dependent features, resulting in the hidden state sequence h and the cell state sequence c. S2 employs a dilated convolutional social pooling module to capture local interaction information between the target vehicle and its nearby vehicles, resulting in a local interaction vector. ; S3 uses a multi-head self-attention mechanism to capture global interaction information between all vehicles in the scene, and obtains the global interaction vector Ca. S4, Fusing Local Interaction Vectors With global interaction vector The comprehensive interactive feature vector is obtained. ; S5, based on comprehensive interactive feature vector Recognize driving intentions and dynamically select the corresponding kinematic model; S6 will integrate the interactive feature vector Input the Peephole LSTM decoder, embed the selected kinematic model as a constraint during the decoding process, correct the prediction results in real time, and iteratively output the future trajectory Y of the target vehicle.

2. The spatiotemporal encoding and decoding vehicle trajectory prediction method based on dynamic kinematic constraint embedding according to claim 1, characterized in that, The expression for the historical observation data HT is as follows: ； In the formula, N represents the total number of the target vehicle and the vehicles around it; Let represent the sequence of observed states of the nth vehicle at discrete time steps t=1,2,...,T; The observed state of vehicle n at time t in the scenario is represented as follows: ； Where x and y are the positions; t is the time, T is the total time; v is the velocity; a is the acceleration; θ is the heading angle; and ω is the turning angle. Let n be the observed state of the nth vehicle at time t; The PeepholeLSTM used is a variant of the standard LSTM, which provides each gating unit with direct access to the cell state. At each time step, the gating unit receives not only the previous hidden state, but also... and current input It also receives information from the cell state via a viewing hole. Information; When calculating the gated activation at time t, the peephole LSTM combines the previous cell state, the hidden state, and the current input to enhance time-dependent modeling; the gated activation function is defined as follows: ； ； ； Among them, the forgetting gate f t Determines the cell state at the previous moment How much information is retained in the current cell state? Middle; Input gate i t Decide to input X at the current moment t How much information is written into the cell state at the current moment? Middle; Output gate o t Determines the cell state at the current moment How much information is output to the hidden state at the current moment? Then, at time t, the forward computation of the peephole LSTM network can be expressed as: ； ； ； Among them, candidate cell state Ĉ t Is the input X at the current time? t Hidden state from the previous moment The function represents new information that may be written into the cell state; the current cell state. It is the cell state at the previous moment. With the Gate of Oblivion t The weighted sum, and the candidate cell state K t With input gate i t The weighted sum; the hidden state at the current moment. It is an output gate. t Current cell state The product of hyperbolic tangent functions; when the input is a historical trajectory sequence HT, the final output of the peephole LSTM network can be expressed as: ； Where h and c are the final hidden state sequence and final cell state sequence obtained by each vehicle in the traffic scene after being processed by the peephole LSTM network, respectively.

3. The spatiotemporal encoding and decoding vehicle trajectory prediction method based on dynamic kinematic constraint embedding according to claim 1, characterized in that, S2 specifically includes the following sub-steps: S21, construct the scene social tensor by combining the hidden state sequence h and the cell state sequence c according to the spatial positional relationship of the vehicle; S22 uses two 3×3 dilated convolutional layers to extract features from the social tensor; the dilation rate is 2 and the padding length is 1. S23, compresses the dimension of the feature map through an adaptive average pooling layer; S24 uses a 3×1 dilated convolutional layer to optimize features, and then obtains the local interaction vector after adaptive average pooling. The expansion rate is 2, and the fill length is (1,0).

4. The spatiotemporal encoding and decoding vehicle trajectory prediction method based on dynamic kinematic constraint embedding according to claim 1, characterized in that, S3 includes the following sub-steps: S31, dimensionality reduction of the social tensor to generate a one-dimensional sequence vector; S32 embeds sequence position information through position encoding; specifically, it uses standard fixed sine and cosine functions to generate a unique and distinguishable code for each position. ； ； Where PE is the position code; pos is the position index; i is the embedding dimension index; d is the embedding dimension; S33, Generate query vector Key vector Value vector ,in , , The weight matrix is ​​a learnable weight matrix; ； in is the output feature vector of the spatiotemporal coding module; j is the index of the "head" in the multi-head self-attention mechanism; used to distinguish different attention heads; S34, Calculate the attention score: ； in The attention score of the j-th attention head is used to quantify the association priority between different vehicles (or trajectory features); Key vector The dimension; S35, calculates the weight matrix headⱼ=αⱼ×Vⱼ through multi-head attention, concatenates the outputs of multiple attention heads and maps them back to the original dimension to obtain the global interaction vector: ； in This is a vector that captures global interaction features through self-attention; Let j be the output feature vector of the j-th attention head; This is a learnable weight matrix.

5. The spatiotemporal encoding and decoding vehicle trajectory prediction method based on dynamic kinematic constraint embedding according to claim 1, characterized in that, S4 specifically includes the following sub-steps: S41, and Fusion is achieved through splicing: ； in This is a comprehensive interactive feature vector; Global interaction feature vector; This is a local interactive feature vector.

6. The spatiotemporal encoding and decoding vehicle trajectory prediction method based on dynamic kinematic constraint embedding according to claim 1, characterized in that, S5 specifically includes the following sub-steps: S51, integrate the interactive feature vector Inputting into a fully connected layer yields logit scores for six driving intent categories; The six driving intention categories are: , , , , , ; S52, the log odds fraction is converted into the intention probability distribution MP by the Softmax function; S53: Select the driving intention category with the highest probability, and dynamically select the kinematic model according to the mapping rules. Corresponding to the constant-rate CV model, Corresponding to the constant acceleration CA model, or Corresponding to the constant angle and constant speed CTRV model, or The corresponding constant angle and constant acceleration CTRA model; specifically, the CV model represents the main uniform linear motion, the CA model considers acceleration and deceleration in longitudinal motion, the CTRV model characterizes stable steering operations such as lane changes, and the CTRA model effectively describes the coupled dynamics of steering and acceleration in complex operations.

7. The spatiotemporal encoding and decoding vehicle trajectory prediction method based on dynamic kinematic constraint embedding according to claim 1, characterized in that, S6 specifically includes the following sub-steps: S61, starting with the single-step state vector generated by the kinematic model, combine this vector with the comprehensive interaction feature vector. They are input together into the Peephole LSTM decoder unit; S62, each subsequent decoder unit inherits the previous hidden state. and cell state ; S63, the predicted state vector of step k = =[x,y,v,a, ,ω], together and It propagates through kinematic equations; For CV models: ； For the CA model: ； For the CTRV model: ； For the CTRA model: ； in and Let be the vehicle's state vector at time steps k and k+1; x and y are the vehicle's lateral and longitudinal coordinates; v is the vehicle's instantaneous velocity; a is the vehicle's instantaneous acceleration; θ is the vehicle's heading angle; t is the prediction time interval; and k and k+1 are the time step indices. =25 is the maximum prediction time step; Δt=0.2s is the fixed time interval between adjacent time steps; ω is the vehicle steering angular velocity; S64, the final output is the corrected state. Then, the corrected state Together and Input into the decoder, generate ; By iterating through this process, the model generates a complete predicted trajectory.

8. The spatiotemporal encoding and decoding vehicle trajectory prediction method based on dynamic kinematic constraint embedding according to claim 1, characterized in that, The expression for the kinematic model is as follows: CV model: ； ； CA Model: ； ； ； CTRV model: ； ； ； ； ； ； ； CTRA model: ； ； ； ； ； ； ； ； Where x and y are the vehicle's lateral and longitudinal coordinates; λ represents the horizontal and vertical coordinates at t=0; v represents the instantaneous velocity of the vehicle. ρ is the initial velocity; a is the instantaneous acceleration of the vehicle; θ represents the initial acceleration; θ is the vehicle heading angle; t is the prediction time interval; k and k+1 are time step indices. =25 is the maximum prediction time step; Δt=0.2s is the fixed time interval between adjacent time steps; ω is the vehicle steering angular velocity; These are the velocity components of the vehicle in the x and y directions; These are the velocity components along the x and y axes at time step k+1. Let be the turning angular velocity at time step k.

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