Traffic density adaptive vehicle trajectory prediction method

Abstract

The invention provides a traffic density adaptive vehicle trajectory prediction method. The method comprises two basic steps: S1, traffic state prediction; s2, traffic state adaptive track prediction is considered; s1 comprises two specific steps of traffic state variable representation and traffic state prediction by using a time convolutional neural network; and S2, trajectory prediction problem modeling, vehicle historical trajectory feature extraction, vehicle spatial-temporal feature extraction, vehicle future trajectory feature representation, latent variable acquisition and vehicle future trajectory prediction. According to the invention, the traffic density is evaluated in real time, and the parameters or the structure of the trajectory prediction model is adjusted according to different traffic densities, so that accurate prediction of vehicle trajectories under different traffic densities is realized. According to the method, track prediction is realized through efficient feature extraction and an attention mechanism, the simplicity and the high efficiency of the model are maintained, the calculation complexity is simplified, and the track prediction precision and the robustness under different traffic densities are improved.

Description

Technical Field

[0001] The invention belongs to the field of intelligent transportation, and in particular relates to a vehicle trajectory prediction method with traffic density self-adaptation. Background Art

[0002] The invention patent application with application publication number CN118419065A discloses a method for predicting trajectory of an autonomous driving vehicle based on a double crossover Transformer, which includes the following steps:

[0003] S1, collects historical trajectory data and vehicle status data of the target vehicle and surrounding vehicles as input sequence X;

[0004] S2, captures the interaction between the target vehicle and surrounding vehicles, outputs the preliminary predicted trajectories of the target vehicle and surrounding vehicles, and evaluates individual uncertainty and collaborative uncertainty;

[0005] S3, measure the prediction effect through the loss function and update the optimization parameters;

[0006] The S1 is specifically:

[0007] Vehicle historical trajectory data acquisition, including historical trajectory points in the previous three seconds, is collected once every ten frames per second, and the trajectory points are represented as (x, y);

[0008] Vehicle status data acquisition, including vehicle speed v and heading angle θ, by analyzing the trajectory, vehicle speed v and heading angle θ, the vehicle driving behavior is judged, and the trajectory of the target vehicle and surrounding vehicles is predicted; historical trajectory data and vehicle status data are used as input sequence X;

[0009] The S2 comprises the following steps:

[0010] S201, position encoding the input sequence X in S1;

[0011] S202, capturing the interaction between the target vehicle and surrounding vehicles through a bidirectional cross attention mechanism, obtaining the interaction feature Attenbidir(fs,fg), and repeatedly training;

[0012] S203, outputting the preliminary predicted trajectories of the target vehicle and its surrounding vehicles;

[0013] S204, perform individual uncertainty and collaborative uncertainty evaluation on the interactive feature Attenbidir(fs,fg).

[0014] The invention patent with the authorization announcement number CN110304075B discloses a vehicle trajectory prediction method based on a hybrid dynamic Bayesian network and a Gaussian process. The method includes the following main steps:

[0015] Step 1, building a natural driving database;

[0016] Establish a test set of surrounding vehicle-related sequence information, road-related sequence information and traffic-related sequence information collected by the autonomous driving vehicle perception system, as well as a training set for calibrating the driving intention and driving characteristics of the above information; wherein the surrounding vehicle-related sequence information includes vehicle position, vehicle speed, vehicle acceleration, vehicle yaw angular velocity, the distance of the vehicle from both sides of the road and the opening and closing status of the left and right turn taillights of the vehicle; the road-related sequence information includes the structural characteristics of the road and road signs; the traffic-related sequence information includes the surrounding traffic signs and the status of traffic lights; the test set includes a test set of a hybrid dynamic Bayesian network and a test set of a Gaussian process; the training set includes a training set of a hybrid dynamic Bayesian network and a training set of a Gaussian process;

[0017] Step 2: Using a hybrid dynamic Bayesian network, we obtain the short-term predicted trajectories of surrounding vehicles and the estimated probabilities of driving intention and driving characteristics.

[0018] A hybrid dynamic Bayesian network model is constructed using driver information, vehicle model selection, and vehicle status information as hidden variables, and surrounding vehicle-related sequence information, road-related sequence information, and traffic-related sequence information collected by the autonomous driving vehicle perception system as observation layer variables. The output of the hybrid dynamic Bayesian network is obtained through posterior probability reasoning: short-term trajectory prediction based on the vehicle model and estimated probability of driving intention and driving characteristics, and this output is used as the input of step 4.

[0019] Step 3, establishing Gaussian process functions under different driving intentions and different driving characteristics; including the following steps:

[0020] Step 3.1, setting of mean function and covariance function

[0021] With x as input, the expression of the Gaussian process function is as follows:

[0022] f(x)~GP(u(x),Σ(x,x'))

[0023] Among them, the mean function u(x) represents the vehicle trajectory trend under a certain driving intention, so the mean function can be used to represent the expected predicted trajectory; the covariance function Σ(x,x') represents both the variance of different inputs x themselves and the variance between (x,x'), so the covariance function can be used to represent the uncertainty corresponding to the expected predicted trajectory;

[0024] The corresponding mean function u(x) is set according to the vehicle trajectory under different driving intentions;

[0025] The covariance function Σ(x,x') expressed in the mean square exponential form with noise is set as follows:

[0026]

[0027] Among them, σ f is the signal standard deviation, l is the characteristic length, σ n is the standard deviation of the observation noise, δ is the Kronecker function;

[0028] Step 3.2, Learning of unknown parameters of Gaussian process function

[0029] According to the mean function u(x) and covariance function Σ(x,x') set in step 3.1, the unknown parameters involved are learned using the training set of the Gaussian process established in step 1. According to the logarithmic marginal likelihood function and its partial derivatives for each unknown parameter, the parameter learning results are obtained using a gradient-based optimization algorithm, thereby establishing Gaussian process functions under different driving intentions and driving characteristics respectively;

[0030] Step 4: Long-term trajectory prediction and uncertainty representation based on hybrid dynamic Bayesian network and Gaussian process;

[0031] According to the estimated probability of driving intention and driving characteristics output by the hybrid dynamic Bayesian network in step 2, the corresponding driving intention and driving characteristics are determined using the maximum probability principle, and then the corresponding Gaussian process function in step 3 is determined according to the driving intention and driving characteristics; the short-term predicted trajectory based on the vehicle model output by the hybrid dynamic Bayesian network in step 2 is used as the vehicle trajectory sequence information x1, and the predicted future trajectory is x2, then the Gaussian distribution of (x1, x2) is as follows:

[0032]

[0033] in, represents the normal function;

[0034]

[0035] The mean functions corresponding to x1 and x2 are u1 and u2 respectively; the covariance matrix Σ is a symmetric matrix, that is, Σ=ΣT, the covariance functions corresponding to x1 and x2 are Σ11 and Σ22 respectively, the covariance functions corresponding to x1 and x2 are Σ12 and Σ21, and Σ12=Σ21T; then the conditional probability P(x2|x1) of the possible future trajectory x2 of the vehicle under the known vehicle trajectory x1 obeys the Gaussian distribution expression as follows:

[0036]

[0037] Among them, u2|1 and Σ2|1 are the mean function and covariance function corresponding to the variable x2|1, and the expression of (u2|1,Σ2|1) is derived from the following formula:

[0038] u 2|1 =u2+∑ 12 T ∑ 11 -1 (x1-u1)

[0039] ∑ 2|1 =∑ 22 -∑ 12 T Σ 11 -1 ∑ 12

[0040] Finally, the future trajectory of the vehicle in the long time domain and its uncertainty representation are obtained based on the driving intention and driving characteristics determined by the maximum probability principle.

[0041] In general, the technical solution disclosed in the invention patent application No. CN118419065A obtains the historical trajectory data and vehicle status data of the vehicle, performs simulation training based on multiple vehicles in a vehicle-road collaborative environment, and fully considers the interaction between the target vehicle and the surrounding vehicles, thereby improving the accuracy and robustness of vehicle trajectory prediction. The technical solution disclosed in the invention patent No. CN110304075B combines vehicle models, abstract intents, and data-driven. Its MDBN and GP models are highly scalable and can be applied to different driving scenarios. It not only takes into account the short-term prediction characteristics under the vehicle physical motion model, but also can perform long-term trajectory prediction and uncertainty representation based on vehicle driver information.

[0042] However, the technical solutions disclosed in the invention patent application No. CN118419065A and the invention patent No. CN110304075B also have certain defects, which are specifically manifested in the following two aspects:

[0043] First, although both invention patent applications CN118419065A and CN110304075B consider the interaction between vehicles, they do not explicitly mention how to adapt trajectory prediction under different traffic densities. Changes in traffic density will significantly affect the interaction mode between vehicles and the accuracy of trajectory prediction, especially in high-density areas, where the interaction between vehicles is more complex.

[0044] Second, although the bidirectional cross-attention mechanism used in the invention patent CN118419065A can capture complex interactive relationships, it also increases the computational complexity and training time of the model. The model of the invention patent CN110304075B combining MDBN and GP also has high computational complexity, especially in the autonomous driving system with high real-time requirements, the calculation process is particularly complex. Summary of the invention

[0045] The purpose of the present invention is to overcome the first and second deficiencies of the above-mentioned prior art.

[0046] In order to achieve the above object, the present invention adopts the following technical solutions:

[0047] A traffic density adaptive vehicle trajectory prediction method includes the following two basic steps:

[0048] S1, traffic status prediction;

[0049] S2, trajectory prediction considering traffic state adaptation;

[0050] The S1 comprises the following specific steps:

[0051] S101, traffic state variable representation, the trajectories of all vehicles are represented by a three-dimensional one-hot vector S, where 001 represents uncrowded, 010 represents crowded, and 100 represents moderate;

[0052] S102, using temporal convolutional neural network to predict traffic status;

[0053] The S2 comprises the following specific steps:

[0054] S201, trajectory prediction problem modeling, considering the traffic state to adaptively predict the future trajectory of N vehicles in the scene, defining the input trajectory as X = X1, X2, ..., X N , the future trajectory predicted by the model is For each vehicle i, the input trajectory is the past t h The vehicle position at time step is expressed as

[0055] S202, a conditional coding prediction network based on a self-attention mechanism, including vehicle historical trajectory feature extraction, vehicle spatiotemporal feature extraction, vehicle future trajectory feature representation, latent variable acquisition and vehicle future trajectory prediction.

[0056] On the basis of the above technical solutions, the present invention may adopt the following technical means to better or more specifically solve the technical problems to be solved by the present invention:

[0057] When executing step S102, given filter F = (f1, f2, ..., f k ), sequence X=(x1,x2,...,x k ), then in x t The causal convolution at Among them, the value of time t only depends on the values ​​of the current and previous levels.

[0058] Further, when executing step S102, the dilated convolution allows the convolution input to have interval sampling, and the sampling rate is controlled by the dilation, the dilation size is d, then at x t The causal convolution at

[0059] Furthermore, when executing step S102, the input of the temporal convolutional neural network is the historical traffic flow, and the output is the traffic flow in the future period of time.

[0060] Furthermore, when executing step S202, a graph is used to represent the entire scene, in which each vehicle is represented by a node, and each node is represented by an LSTM with 4 hidden dimensions, and the vehicle is represented by the observed t h The location information and traffic status information within a time step are encoded as the node history code As shown below:

[0061]

[0062] In the formula, represents the position and state information of the vehicle at time step t, is the hidden state of LSTM, and θ is the network parameter of LSTM.

[0063] Furthermore, when executing step S202, edges are added according to the distance between the vehicle and its neighboring vehicles, each edge is represented by an LSTM, and the edge history code of the vehicle is output. As shown below:

[0064]

[0065] In the formula, represents the edge encoding between the vehicle and its neighboring vehicles at time step t, and φ is the parameter of LSTM.

[0066] Furthermore, the node history code, edge history code and traffic status are connected to obtain the node representation vector e of the vehicle. i , as shown below:

[0067]

[0068] Furthermore, when executing step S202, the Transformer model is used to extract temporal features and spatial features using a multi-head attention mechanism, as shown below:

[0069]

[0070] Where Q is the query matrix, K is the key matrix, V is the value matrix, and K T is the transpose of the value matrix K, d k is the dimension of the key vector.

[0071] Furthermore, when executing step S202, the future trajectory Y of the vehicle i The encoding is performed using a bidirectional LSTM with 64 hidden units, where the node future encoding is as follows:

[0072]

[0073] Further, when executing step S202, the training process uses the node representation vector, the node future code and the category C of the connected vehicle i To estimate the distribution parameters of the 32-dimensional latent variable z, as follows:

[0074]

[0075] z~q φ (zX i ,Y i ,f i ),

[0076] Where φ is a 2D CNN with 10 layers. The convolution kernel sizes of each layer are {5, 5, 5, 5, 3, 3, 3, 3} respectively. The convolution operation of the first 5 layers adopts a stride of 2, and the convolution operation of the last 5 layers adopts a stride of 1. The distribution q φ It is f i A parameterized categorical distribution that captures the pattern of agent trajectories associated with each traffic state;

[0077] After obtaining the distribution parameters of the 32-dimensional latent variable z, a 128-dimensional multilayer perceptron decoder is used to generate 16 component parameters for the Gaussian mixture model. Next, the future trajectory is sampled for each vehicle i from the Gaussian mixture model as follows:

[0078]

[0079] Compared with the prior art, especially compared with the prior art described in the invention patent application No. CN118419065A and the invention patent No. CN110304075B, the present invention has the following advantages:

[0080] Beneficial effects:

[0081] First, the present invention fully considers the changes in traffic density during the trajectory prediction process, evaluates the traffic density in real time through the traffic state prediction step, and adjusts the parameters or structure of the trajectory prediction model according to different traffic densities, thereby achieving more accurate prediction of vehicle trajectories under different traffic densities.

[0082] Second, the present invention realizes trajectory prediction through efficient feature extraction and attention mechanism while maintaining the simplicity and efficiency of the model, which not only simplifies the complexity of calculation, but also improves the trajectory prediction accuracy and robustness under different traffic densities. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 is a flow chart of an embodiment of the present invention;

[0084] Figure 2 4 is a working principle diagram of step S202 in this embodiment. DETAILED DESCRIPTION

[0085] In order to facilitate those skilled in the art to fully understand the technical solution of the present invention, an embodiment of the present invention is described below with reference to the accompanying drawings.

[0086] like Figure 1 As shown, a traffic density adaptive vehicle trajectory prediction method includes the following two basic steps:

[0087] S1, traffic status prediction;

[0088] S2, trajectory prediction considering traffic state adaptation;

[0089] The S1 comprises the following specific steps:

[0090] S101, traffic state variable representation, traffic state variables represent the traffic flow on the lane, which provides future information for the trajectory prediction model. The traffic state provides spatiotemporal information about adjacent vehicles and their future movements. Possible traffic states include congested, uncrowded, and moderate. The trajectories of all vehicles are represented by a three-dimensional unique hot vector S, where 001 represents uncrowded, 010 represents congested, and 100 represents moderate.

[0091] S102, using a temporal convolutional neural network (TCN) for traffic state prediction; the temporal convolutional neural network (TCN) is derived from the convolutional neural network (CNN), which can directly use the powerful function of convolution to extract features on time steps. Therefore, TCN shows better performance than LSTM and GRU in many sequence tasks. TCN mainly consists of causal convolution for processing sequences and dilated convolution and residual modules for historical data storage.

[0092] It should be noted that causal convolution is a strict time-constrained model, in which the value of time t depends only on the values ​​of the current and previous levels. k ), sequence X = (x1, x2, …, x k ), then in x t The causal convolution at

[0093] In the process of implementing the technical solution of the present invention, the dilated convolution allows the convolution input to have spaced sampling, and the sampling rate is controlled by the dilation. The higher the level, the larger the dilation size d, which makes the size of the effective window grow exponentially with the increase of the number of layers. Assume that the filter F = (f1, f2, ..., f k ), sequence X=(x1,x2,...,x k ), then in x t The causal convolution at

[0094] In this embodiment, the input of the TCN network is the historical traffic flow, and the output is the traffic flow in the future. The present invention uses the output of the TCN in subsequent trajectory prediction research to adaptively predict vehicle trajectories based on traffic conditions.

[0095] The S2 comprises the following specific steps:

[0096] S201, trajectory prediction problem modeling, considering the traffic state to adaptively predict the future trajectory of N vehicles in the scene, defining the input trajectory as X = X1, X2, ..., X N , the future trajectory predicted by the model is For each vehicle i, the input trajectory is the past t h The vehicle position at time step is expressed as The goal is to predict the future f The position of the time step, that is,

[0097] S202, a conditional coding prediction network based on self-attention mechanism, including:

[0098] (1) Vehicle historical trajectory feature extraction

[0099] See also Figure 2 , this embodiment uses a graph to represent the entire scene, where each vehicle is represented by a node. Each node is represented by an LSTM (Long Short-Term Memory) with 4 hidden dimensions, which represents the vehicle i at the observed t h The location information and traffic status information within a time step are encoded as the node history code The process can be expressed as:

[0100]

[0101] in, represents the position and state information of vehicle i at time step t, is the hidden state of LSTM, and θ is the network parameter of LSTM.

[0102] Compared to GRU networks, LSTM is more suitable for capturing long-term dependencies, which is crucial in traffic scenarios. The use of LSTM finds a good balance between model complexity and performance. This embodiment uses edges to encode the interactions between agents, and adds edges only when the distance between neighboring vehicles is within a certain range (the so-called certain range, that is, the interaction range between adjacent vehicles, can be dynamically adjusted according to the vehicle speed and driving environment. For example, in a low-speed urban environment, it can be set to 30-50 meters, and in a highway environment, it can be set to 70-100 meters). Each edge is represented by an LSTM, and the edge history encoding of vehicle i is output. The process can be described as:

[0103]

[0104] In the formula, represents the edge encoding between vehicle i and vehicle j (vehicle j is the adjacent vehicle to vehicle i) at time step t, and φ is the parameter of LSTM.

[0105] Traffic status helps to understand how many neighboring vehicles are approaching or moving away from the vehicle. Adding traffic status helps to generate future trajectories similar to the current traffic status. Concatenate the node history encoding, edge history encoding, and traffic status to obtain the node representation vector e of vehicle i. i , as shown below:

[0106]

[0107] (2) Vehicle spatiotemporal feature extraction

[0108] The future trajectory of the vehicle is affected by the interaction of time and space. This method uses Transformer to extract spatiotemporal features. The core of Transformer is the attention mechanism, which consists of query vector Q (query), key vector K (key) and value vector V (value). Through Q, K, V, the above historical embedding features are mapped to a high-dimensional space, and the attention coefficient is calculated through Q and K to extract heterogeneous interaction relationships. In this method, multi-head attention mechanisms are used to extract temporal features and spatial features, respectively, as shown below:

[0109]

[0110] In the above formula, the scaled dot product attention mechanism Q and K calculate the similarity through dot product processing, and the scaling factor sqrt(d) (used to find the square root of d) is used to avoid the situation where the variance of the inner product of Q and K is too large and difficult to learn, and the softmax function is applied to obtain the weight of value. Q, K, and V are historical encoding features obtained through the fully connected layer. Through the multi-head attention mechanism, the Transformer model can jointly pay attention to different subspace information from different positions to obtain the estimated spatiotemporal feature representation of the vehicle.

[0111] (3) Vehicle future trajectory feature representation

[0112] In the conditional variational autoencoder, the latent variable z learns the mean and variance of the underlying input trajectory distribution, which requires access to the vehicle’s past and future trajectories. Therefore, the vehicle’s future trajectory Y i The encoding is performed using a bidirectional LSTM with 64 hidden units, where the node future encoding is as follows:

[0113]

[0114] The node future encoding is only computed at training time. At test time, the node representation is used to estimate the distribution of the latent variable.

[0115] (4) Conditional latent distribution (obtaining latent variables)

[0116] The training process uses the node representation vector e i 、Node Future Coding and Category C of connected vehicles i To estimate the distribution parameters of the 32-dimensional latent variable z, as follows:

[0117]

[0118] z~q φ (zX i ,Y i ,f i ),

[0119] Where φ is a 2D CNN with 10 layers. The convolution kernel sizes of each layer are {5, 5, 5, 5, 5, 3, 3, 3, 3}. The first 5 layers use larger 5×5 convolution kernels to capture a wider range of spatial features; the last 5 layers use smaller 3×3 convolution kernels to further refine features and capture finer details. In addition, the convolution operation of the first 5 layers uses a stride of 2 to quickly reduce the spatial dimension of the feature map, while the convolution operation of the last 5 layers uses a stride of 1 to extract more abstract features while maintaining spatial information. Distribution q φ It is fi A parameterized categorical distribution that captures the pattern of agent trajectories associated with each traffic state.

[0120] (5) Future trajectory prediction

[0121] After obtaining the distribution parameters of the 32-dimensional latent variable z, a 128-dimensional multi-layer perceptron (MLP) decoder is used to generate 16 component parameters for the Gaussian mixture model. Next, the future trajectory is sampled for each vehicle i from the Gaussian mixture model (GMM):

[0122]

[0123] Vehicle dynamics features are combined to obtain future trajectories. Since it is difficult to predict the exact dynamics of different vehicles in laneless traffic, linear dynamics are used for all types of vehicles.

Claims

1. A traffic density adaptive vehicle trajectory prediction method, characterized in that: It includes the following two basic steps: S1, traffic status prediction; S2, trajectory prediction considering traffic state adaptation; The S1 comprises the following specific steps: S101, traffic state variable representation, the trajectories of all vehicles are represented by a three-dimensional one-hot vector S, where 001 represents uncrowded, 010 represents crowded, and 100 represents moderate; S102, using temporal convolutional neural network to predict traffic status; The S2 comprises the following specific steps: S201, trajectory prediction problem modeling, considering the traffic state to adaptively predict the future trajectory of N vehicles in the scene, defining the input trajectory as X = X1, X2, ..., X N , the future trajectory predicted by the model is For each vehicle i, the input trajectory is the past t h The vehicle position at time step is expressed as S202, a conditional coding prediction network based on a self-attention mechanism, including vehicle historical trajectory feature extraction, vehicle spatiotemporal feature extraction, vehicle future trajectory feature representation, latent variable acquisition and vehicle future trajectory prediction.

2. The traffic density adaptive vehicle trajectory prediction method according to claim 1, characterized in that: When executing step S102, given filter F = (f1, f2, ..., f k ), sequence X=(x1,x2,...,x k ), then in x t The causal convolution at Among them, the value of time t only depends on the values ​​of the current and previous levels.

3. The traffic density adaptive vehicle trajectory prediction method according to claim 1, characterized in that: When executing step S102, the dilated convolution allows the convolution input to have spaced sampling, and the sampling rate is controlled by the dilation, the dilation size is d, then at x t The causal convolution at 4. The traffic density adaptive vehicle trajectory prediction method according to claim 1, characterized in that: When executing step S102, the input of the temporal convolutional neural network is the historical traffic flow, and the output is the traffic flow in the future period of time.

5. The traffic density adaptive vehicle trajectory prediction method according to claim 1, characterized in that: When executing step S202, a graph is used to represent the entire scene, where each vehicle is represented by a node, and each node is represented by an LSTM with 4 hidden dimensions. h The location information and traffic status information within a time step are encoded as the node history code As shown below: In the formula, represents the position and state information of the vehicle at time step t, is the hidden state of LSTM, and θ is the network parameter of LSTM.

6. The traffic density adaptive vehicle trajectory prediction method according to claim 5, characterized in that: Add edges based on the distance between the vehicle and its neighbors. Each edge is represented as an LSTM, and the edge history encoding of the vehicle is output. As shown below: In the formula, represents the edge encoding between the vehicle and its neighboring vehicles at time step t, and φ is the parameter of LSTM.

7. The traffic density adaptive vehicle trajectory prediction method according to claim 6, characterized in that: Connect the node history code, edge history code and traffic status to obtain the node representation vector e of the vehicle i , as shown below:

8. The traffic density adaptive vehicle trajectory prediction method according to claim 1, characterized in that: When executing step S202, the Transformer model is used to extract temporal features and spatial features using a multi-head attention mechanism, as shown below: Where Q is the query matrix, K is the key matrix, V is the value matrix, and K T is the transpose of the value matrix K, d k is the dimension of the key vector.

9. The traffic density adaptive vehicle trajectory prediction method according to claim 1, characterized in that: When executing step S202, the future trajectory Y of the vehicle i The encoding is performed using a bidirectional LSTM with 64 hidden units, where the node future encoding is as follows:

10. The traffic density adaptive vehicle trajectory prediction method according to claim 1, characterized in that: When executing step S202, the training process uses the node representation vector, the node future code and the category C of the connected vehicle i To estimate the distribution parameters of the 32-dimensional latent variable z, as follows: z~q φ (z|X i ,Y i ,f i ); Where φ is a 2D CNN with 10 layers. The convolution kernel sizes of each layer are {5, 5, 5, 5, 3, 3, 3, 3} respectively. The convolution operation of the first 5 layers adopts a stride of 2, and the convolution operation of the last 5 layers adopts a stride of 1. The distribution q φ It is f i A parameterized categorical distribution that captures the pattern of agent trajectories associated with each traffic state; After obtaining the distribution parameters of the 32-dimensional latent variable z, a 128-dimensional multilayer perceptron decoder is used to generate 16 component parameters for the Gaussian mixture model. Next, the future trajectory is sampled for each vehicle i from the Gaussian mixture model as follows:

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