A vehicle trajectory prediction method considering step-by-step bidirectional interaction

Abstract

The application provides a vehicle trajectory prediction method considering step-by-step bidirectional interaction, constructs a network model capable of fully extracting bidirectional interaction information between vehicles, extracts trajectory and spatial position information of the predicted vehicle and other surrounding vehicles as input by steps, uses an encoding architecture to perform motion encoding on the vehicle trajectory, accurately predicts the future trajectory of the vehicle in combination with the step-by-step bidirectional interaction relationship between the vehicles, fully considers the complex mutual influence between the vehicles, constructs different observation tensors for the predicted vehicle and the surrounding vehicles according to respective conditions, uses a convolutional pooling network to extract spatial information between the vehicles, reasonably processes the interaction information between different vehicles, finally inputs the extracted interaction information into a decoder, obtains the future trajectory of the predicted vehicle in multiple segments, fully considers the influence of the future trajectory of the predicted vehicle and the surrounding vehicles on each other, and improves the precision of trajectory prediction.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of vehicle trajectory prediction, and provides a vehicle trajectory prediction method considering step-by-step bidirectional interaction. BACKGROUND

[0002] When talking about the intelligence and automation of modern traffic systems, vehicle trajectory prediction is one of the key research fields, but due to the influence of technology, society and ethics, the coexistence of automatic driving and manual driving vehicles on the road will be the norm for a long time in the future; in the traffic scene, vehicle spatial interaction is very important, vehicles are not just isolated entities, they often need to interact with other vehicles around them on the road, and these interactions not only affect the driving path of each vehicle, but also directly determine the efficiency and safety of the overall traffic system; the core of bidirectional interaction is to understand and predict the mutual influence between traffic participants and its influence on behavior, for example, when a vehicle intends to change lanes, it needs to consider the speed and position of other vehicles on the current lane, and whether the space on the adjacent lane is sufficient, this multi-aspect spatial interaction needs an accurate prediction model to analyze, so that the model can accurately predict the trajectory of the target vehicle; therefore, how to ensure the prediction accuracy of the future trajectory of the predicted vehicle under the continuous mutual influence of the predicted vehicle and the surrounding vehicles is the research difficulty to be solved at present. SUMMARY

[0003] The application provides a vehicle trajectory prediction method considering step-by-step bidirectional interaction, which fully extracts bidirectional interaction information between vehicles by gradually extracting trajectory and spatial position information of the predicted vehicle and other surrounding vehicles and inputting the built network model to accurately predict the future trajectory of the vehicle in multiple sections.

[0004] The application is implemented by adopting the following technical solutions:

[0005] The application provides a vehicle trajectory prediction method considering step-by-step bidirectional interaction, which fully extracts bidirectional interaction information between vehicles by gradually extracting trajectory and spatial position information of the predicted vehicle and other surrounding vehicles and inputting the built network model to accurately predict the future trajectory of the vehicle in multiple sections.

[0006] Step one, process the vehicle trajectory data set:

[0007] First, the position information of the vehicle in the data set is extracted in time sequence, that is, the absolute coordinates (x, y) of the horizontal and vertical position of the vehicle; then, all vehicle coordinates are further processed, and the processing steps include vehicle trajectory extraction, observation tensor construction and conversion of relative coordinates between vehicles;

[0008] In vehicle trajectory extraction, the absolute coordinates of the predicted vehicle's historical trajectory TargHist and the absolute coordinates of the predicted vehicle's future real trajectory TargFut are defined as follows:

[0009]

[0010] wherein, is the lateral and longitudinal absolute coordinates of the predicted vehicle at time t, is the lateral absolute coordinates of the predicted vehicle at time t, is the longitudinal absolute coordinates of the predicted vehicle at time t, t∈{1,2,...,T obs}, T obs is the observation time length of the predicted vehicle's historical trajectory, which is also the current time, is the real lateral and longitudinal absolute coordinates of the predicted vehicle at future time k, which is used to calculate the loss value of the model, is the lateral absolute coordinates of the predicted vehicle at future time k, is the longitudinal absolute coordinates of the predicted vehicle at future time k, k∈{1,2,...,T pred}, T pred is the prediction time length of the predicted vehicle's future trajectory;

[0011] The absolute coordinates of the predicted vehicle's surrounding vehicle's historical trajectory NbrsHist and the absolute coordinates of the predicted vehicle's surrounding vehicle's future real trajectory NbrsFut are defined as follows:

[0012]

[0013] wherein, n∈N is the number of surrounding vehicles of the predicted vehicle, N is a positive integer greater than 0, and the surrounding vehicles of the predicted vehicle will be referred to as surrounding vehicles hereinafter; is the set of lateral and longitudinal absolute coordinates of n surrounding vehicles at time t, specifically, is the set of lateral absolute coordinates of n surrounding vehicles at time t, is the set of longitudinal absolute coordinates of n surrounding vehicles at time t, t∈{1,2,...,T obs}, T obs is the observation time length of the surrounding vehicle's historical trajectory, because the model requires the observation time length of the predicted vehicle and the surrounding vehicle's historical trajectory to be the same, so is the set of real lateral and longitudinal absolute coordinates of n surrounding vehicles at future time k, specifically, is the set of real lateral absolute coordinates of n surrounding vehicles at future time k, is the set of real longitudinal absolute coordinates of n surrounding vehicles at future time k, k∈{1,2,...,T pred}, Tpred The prediction time length of the future trajectory of the surrounding vehicle, because the model requires the prediction time length of the future trajectory of the predicted vehicle and the surrounding vehicle to be the same, so T pred pred ;

[0014] In the construction of the observation tensor, the environment within 30 meters before and after the predicted vehicle and within 5 meters on the left and right is taken, a 5x25 two-dimensional space grid is established with the center of mass of the predicted vehicle as the center, 5 in 5x25 represents the observation range of the predicted vehicle in the lateral direction, 25 in 5x25 represents the observation range of the predicted vehicle in the longitudinal direction, the center of mass of the predicted vehicle is located at the centermost position of the two-dimensional space grid, i.e. the third grid in the lateral direction and the thirteenth grid in the longitudinal direction, the length of each small grid in the two-dimensional space grid is defined as 2.4 meters and the width is 2 meters, and the position of the surrounding vehicle is recorded in the two-dimensional space grid; in this 5x25 two-dimensional space grid, the small grid with a vehicle is set to TRUE, and the small grid without a vehicle is set to FALSE, the number of surrounding vehicles is n, and then the observation tensor of the position of the surrounding vehicle represented by TRUE and FALSE is obtained CentGrid∈R 5×25 The spatial interaction features between the predicted vehicle and the surrounding vehicles can be extracted through the observation tensor CentGrid∈R 5×25 ;

[0015] In the conversion of the relative coordinates between the vehicle and the vehicle, the absolute coordinates of the historical trajectory TargHist and the absolute coordinates of the future real trajectory TargFut of the predicted vehicle are respectively subtracted from the lateral and longitudinal absolute coordinates of the predicted vehicle at the current time T obs The converted relative historical trajectory coordinates TargCentHist of the predicted vehicle and the converted relative future trajectory coordinates TargCentFut of the predicted vehicle are obtained:

[0016]

[0017]

[0018] Among them, TargCentHist is used for the input of the model, TargCentFut is used for the model to calculate the loss value, is the converted relative historical trajectory coordinates of the predicted vehicle at time t, is the lateral and longitudinal absolute coordinates of the predicted vehicle at time t, is the lateral and longitudinal absolute coordinates of the predicted vehicle at the current time T obs , t∈{1,2,...,T obs}, ​​the converted relative future trajectory coordinate of the predicted vehicle at time k in the future, the converted relative future trajectory horizontal coordinate of the predicted vehicle at time k in the future, the converted relative future trajectory vertical coordinate of the predicted vehicle at time k in the future, k e {1, 2,..., T} pred};

[0019] the absolute historical trajectory coordinates NbrsHist of the surrounding vehicles and the absolute future trajectory coordinates NbrsFut of the surrounding vehicles are respectively subtracted from the absolute horizontal and vertical coordinates of the predicted vehicle at time T obs to obtain the converted relative historical trajectory coordinates NbrsCentHist of the surrounding vehicles and the converted relative future trajectory coordinates NbrsCentFut of the surrounding vehicles:

[0020]

[0021] wherein the converted relative historical trajectory coordinates NbrsCentHist are used as the input of the model, and the converted relative future trajectory coordinates NbrsCentFut are used for the model to calculate the loss value, the converted relative historical trajectory coordinates of the surrounding vehicle at time t, t' e {1, 2,..., T} obs}; the converted relative future trajectory coordinates of the surrounding vehicle at time k' in the future, the converted relative future trajectory horizontal coordinate of the surrounding vehicle at time k' in the future, the converted relative future trajectory vertical coordinate of the surrounding vehicle at time k' in the future, k' e {1, 2,..., T} pred};

[0022] Step two, designing a trajectory prediction model of the vehicle

[0023] The trajectory prediction model comprises a predicted vehicle trajectory prediction model TargModel and a surrounding vehicle trajectory prediction model NbrsModel. The model structures of the predicted vehicle trajectory prediction model TargModel and the surrounding vehicle trajectory prediction model NbrsModel are the same, but the parameters in the models are different. Both the predicted vehicle trajectory prediction model TargModel and the surrounding vehicle trajectory prediction model NbrsModel comprise a vehicle motion trajectory information extraction module and a vehicle trajectory prediction module:

[0024] For the vehicle motion trajectory information extraction module, the dimensions of the relative historical trajectory coordinates of the predicted vehicle and the relative historical trajectory coordinates of the surrounding vehicles are respectively converted to and the​ input to a one-dimensional convolutional neural network Conv1D3 to extract the motion information of the predicted vehicle, and input to another one-dimensional convolutional neural network Conv1D3' to extract the motion information of the surrounding vehicles, to obtain the motion embedding TargCentHist of the predicted vehicle emb and the motion embedding NbrsCentHist of the surrounding vehicles emb :

[0025]

[0026] wherein, is the motion encoding information of the predicted vehicle, is the motion encoding information of the surrounding vehicles, Conv1D3 and Conv1D3' are both one-dimensional convolutional layers with a convolution kernel size of 3, an input channel number of 2, an output feature number of 32, and a step size of 1, is the weight parameter of Conv1D3, is the weight parameter of Conv1D3', is the bias parameter of Conv1D3, is the bias parameter of Conv1D3';

[0027] the dimension of the motion encoding information of the predicted vehicle is converted to the dimension of the motion encoding information of the surrounding vehicles is converted to and then input to the encoder to obtain the encoding information of the predicted vehicle and the encoding information of the surrounding vehicles

[0028]

[0029] wherein, is the hidden state of the predicted vehicle, is the hidden state of the surrounding vehicles, Encoder is the motion encoder of the predicted vehicle, and Encoder' is the motion encoder of the surrounding vehicles, the encoder is composed of a Long Short-Term Memory (LSTM) network, the input feature number of the LSTM network in the encoder is 32, the hidden feature number is 64, and the number of layers is 1, is the weight parameter of Encoder, is the weight parameter of Encoder', is the bias parameter of Encoder, is the bias parameter of Encoder';

[0030] Encoding information of the predicted vehicle's motion The encoding information is aggregated through a fully connected layer:

[0031]

[0032] wherein, is the encoding of the predicted vehicle's motion information with a feature number of 32, and φ is an embedding function of the fully connected layer, is a weight parameter of the fully connected layer for aggregating the encoding information of the predicted vehicle, is a bias parameter of the fully connected layer for aggregating the encoding information of the predicted vehicle;

[0033] Encoding information of the surrounding vehicles' motion The observation tensor CentGrid∈R 5×25 in step one is filled in order according to its position in the grid 5×25 , that is, filling into the position of CentGrid∈R 5×25 wherein TRUE, and filling 0 into the position where FALSE, if there is only one position TRUE in the grid, the position relationship of the vehicle in the grid is not considered, and is directly filled into the position, and is filled into CentGrid∈R 5×25 to obtain the observation feature tensor CentGridH, and then using two-dimensional graph convolution Conv2D 3×3 to extract the feature of the spatial interaction between the predicted vehicle and the surrounding vehicles:

[0034]

[0035] wherein NbrsGridConv∈R 64×5×25 is the spatial interaction feature between vehicles, Conv2D 3×3 is a two-dimensional convolution layer with a convolution kernel size of 3×3, the input feature number and the output feature number are both 64, and the step is 1, is a weight parameter of Conv2D 3×3 , is a bias parameter of Conv2D 3×3 ;

[0036] The spatial interaction feature NbrsGridConv between vehicles is subjected to a pooling operation to reduce the dimension, reserve key information, and improve the generalization degree of the model:

[0037]

[0038] wherein NbrsGridPool∈R 64×9×1MaxPool 3×3 It is a max-pooling layer with a 3×3 pooling core and a step size of 2. For weight parameters, These are bias parameters;

[0039] To further enhance the prediction network's ability to understand and model spatial feature data, NbrsGridPool undergoes further reconvolution and repooling steps. Specifically, NbrsGridPool is input into a 2D convolutional layer with a 3×1 kernel, and then into a max-pooling layer with a 2×1 kernel, ultimately yielding spatial interaction information between vehicles. And transform the dimension into

[0040] The vehicle trajectory prediction module predicts future time intervals of T by acquiring vehicle motion information and spatial information between vehicles. pred Vehicle trajectory within; specific operation is as follows: encoding the motion information of the vehicle to be predicted. Spatial interaction information between vehicles Perform splicing and copying T pred This yields a vehicle information aggregation feature with 112 features. This aggregation feature The input is fed into the trajectory prediction module to obtain the predicted future trajectory Pred for the vehicle being predicted.

[0041]

[0042] In the formula,

[0043] For the predicted vehicle at T obs+m The relative predicted trajectory coordinates at time. For the predicted vehicle at T obs+m The relative x-coordinate of the predicted trajectory at time. For the predicted vehicle at T obs+m The relative predicted trajectory ordinate at time m, m∈{1,2,...,T} pred The decoder is composed of a Long Short-Term Memory (LSTM) network. The LSTM network in the decoder has 112 input features, 128 hidden features, and one layer. These are the weight parameters of the decoder. Here, φ represents the bias parameters of the decoder, and φ is the embedding function of the fully connected layer. These are the weight parameters of the fully connected layer. The bias parameters for the fully connected layer are 128 input features and 2 output dimensions.

[0044] Step 3: Construct the loss function

[0045] The expression for the loss function Loss is:

[0046]

[0047] in, Let x be the x-coordinate of the predicted vehicle's relative true trajectory at time p. Let be the ordinate of the predicted vehicle's relative true trajectory at time p. The x-coordinate of the predicted trajectory of the vehicle at time p is the output of the model. The ordinate of the predicted trajectory of the vehicle at time p is the output of the model.

[0048] Step 4: Stepwise two-way interactive trajectory prediction

[0049] The predicted vehicle will be denoted as Car. targ Set prediction Car targ The duration of the future trajectory is T, and the duration of the predicted future trajectories of surrounding vehicles is T', because the model requires the duration of the predicted future trajectories of surrounding vehicles to be Car. targ Half of, so Car targ The historical observation duration is T obs The historical observation duration for surrounding vehicles is T. obs ', because the model requires the input Car targ The observation duration is the same as that of surrounding vehicles, so T obs '=T obs ;

[0050] The model predicts Car in two stages. targ Future trajectory:

[0051] In stage 1, the model outputs Car. targ future The relative predicted trajectory in the time domain and the relative predicted trajectory of surrounding vehicles in the future time domain from 0 to T';

[0052] In stage 2, the model outputs Car. targ future Relative predicted trajectory in the time domain;

[0053] Finally, the predicted time domain is... and The relative predicted trajectories of the two predicted vehicles are spliced ​​together in chronological order to obtain Car. targ The complete future relative prediction trajectory with a duration of T;

[0054] First, obtain the first segment of the predicted trajectory for the vehicle being predicted:

[0055] Car targ The observation tensor CentGrid∈R 5×25 Car targ The relative historical trajectory coordinates TargCentHist and the relative historical trajectory coordinates NbrsCentHist of surrounding vehicles are input into the vehicle trajectory prediction model TargModel to obtain Car. targ future Predicted trajectory TargPred in the time domain:

[0056]

[0057] in, For Car targ At the T obs The predicted trajectory coordinates at time +a For Car targ At the T obs The predicted x-axis at time +a For Car targ At the T obs The predicted ordinate at time +a

[0058] Next, regarding Car targ Perform relative coordinate transformation with surrounding vehicles:

[0059] Select all surrounding vehicles in turn, and denote the selected surrounding vehicles as Cars. g Where g∈N represents the surrounding vehicles of the g-th vehicle, let Car g The original relative historical trajectory coordinates SelHist are:

[0060]

[0061] in, For Car g The original relative historical trajectory coordinates at time b, b∈{1,2,...,T} obs'}, Car g The current time T obs 'Lower position' Set Car as the origin and establish a new reference coordinate system. g The historical trajectory coordinates are converted to coordinates in the new reference coordinate system to obtain Car. g New relative historical trajectory coordinates TurnHist:

[0062]

[0063] Cartarg the original relative historical trajectory coordinates of Car

[0064]

[0065] where TargCentHist is the new relative historical trajectory coordinates of Car targ in the new reference coordinate system;

[0066] Then, the observation tensor SelCentGrid of Car g is obtained:

[0067] Based on the observation tensor CentGrid of Car targ , Centgrid ∈ R 5×25 , the small grid where Car g is located is set to TRUE, and the contents of the remaining small grids are all set to FALSE, obtaining the observation tensor SelCentGrid of Car g , SelCentGrid ∈ R 5×25 ;

[0068] Secondly, all surrounding vehicles are selected in turn and their next segment of predicted trajectory is obtained respectively:

[0069] The number of surrounding vehicles of Car targ is n, and one surrounding vehicle Car g is selected in turn in order each time, and the surrounding vehicle trajectory prediction process is performed:

[0070] The observation tensor SelCentGrid of Car g , SelCentGrid ∈ R 5×25 , the new relative historical trajectory coordinates TurnHist of Car g , and the new relative historical trajectory coordinates TargNewHist of Car targ obtained by the above step are input into the surrounding vehicle trajectory prediction model NbrsModel, obtaining the predicted trajectory of Car g in the future 0-T' time domain with the center of mass as the reference system origin;

[0071] After the above surrounding vehicle trajectory prediction process is performed n' times, the predicted trajectory coordinates SelNbrsPred of all surrounding vehicles in the new reference system with the center of mass as the reference system origin can be obtained, because the surrounding vehicle trajectory prediction process needs to be performed as many times as the number of vehicles, so n' = n:

[0072]

[0073] wherein, is the predicted trajectory coordinates of the surrounding vehicle at the future c time, is the predicted trajectory x-coordinate of the surrounding vehicle at future time c, is the predicted trajectory y-coordinate of the surrounding vehicle at future time c, c e {1, 2,..., T'} ;

[0074] Continuing, SelNbrsPred is converted to the predicted trajectory coordinates in the Car targ frame of reference:

[0075] SelNbrsPred is the trajectory coordinates in the Car g frame of reference with the center at the origin. To convert it to the coordinates in the Car targ frame of reference, one simply adds SelNbrsPred directly to to obtain the next predicted trajectory coordinates of the surrounding vehicle in the Car targ frame of reference, NbrsPred:

[0076]

[0077] where, is the original relative historical trajectory coordinates of Car g at time T obs ' ;

[0078] Finally, the next predicted trajectory coordinates of the predicted vehicle and the surrounding vehicle are substituted into the respective old historical trajectories to obtain the new historical trajectory coordinates:

[0079] The first trajectory points in the old historical trajectory TargCentHist are discarded, and TargPred is added to TargCentHist as the latest trajectory point at time, to obtain the updated new historical trajectory TargRepHist:

[0080]

[0081] where, is the predicted trajectory point of the predicted vehicle at the latest time, is the new historical trajectory of the predicted vehicle at time d,

[0082] and the latest trajectory point of the predicted vehicle, is taken as the new origin of the reference frame and a new reference coordinate system is established, to obtain the new relative historical trajectory of the predicted vehicle, TargCentHist2:

[0083]

[0084] where, is the new relative history trajectory coordinate of the surrounding vehicle at the e-th time in the new reference coordinate system, and

[0085] Similarly, the first 0~T' trajectory points in the old history trajectory NbrsCentHist are replaced by the predicted trajectory NbrsPred of the surrounding vehicle, to obtain the updated new history trajectory NbrsRepHist:

[0086]

[0087] wherein, is the predicted trajectory point of the surrounding vehicle at the latest T' time, is the new history trajectory of the surrounding vehicle at the f-th time, f∈{T'+1,T'+2...,T obs '-1,T obs ',T obs '+1,...,T obs '+T'}.

[0088] and the latest trajectory point of the predicted vehicle is taken as the new origin coordinate, to obtain the new relative history trajectory NbrsCentHist2 of the surrounding vehicle in the new reference coordinate system:

[0089]

[0090] wherein, is the new relative history trajectory coordinate of the surrounding vehicle at the l-th time with the origin at , and l∈[T'+1,T'+2,...,T obs '+T'-1,T obs '+T'].

[0091] The obtained new relative history trajectory TargCentHist2 of the predicted vehicle, the new relative history trajectory NbrsCentHist2 of the surrounding vehicle, and the observation tensor CentGrid are input into the trajectory prediction model TargModel of the predicted vehicle, to obtain the predicted trajectory TargPred2 of the predicted vehicle in the future time domain:

[0092]

[0093] wherein, is the predicted trajectory coordinate of the predicted vehicle at the T obs +p-th time, is the predicted horizontal coordinate of the predicted vehicle at the T obs +p-th time, is the predicted vertical coordinate of the predicted vehicle at the Tobs a predicted longitudinal coordinate of the predicted vehicle at the T+q moment,

[0094] Finally, the first stage predicted trajectory TargPred and the second stage predicted trajectory TargPred2 of the predicted vehicle are spliced to obtain a complete predicted trajectory Pred of the predicted vehicle:

[0095]

[0096] wherein, is a predicted trajectory coordinate of the predicted vehicle at the T+q moment, obs a predicted longitudinal coordinate of the predicted vehicle at the T+q moment, a predicted longitudinal coordinate of the predicted vehicle at the T+q moment, obs a predicted longitudinal coordinate of the predicted vehicle at the T+q moment, a predicted longitudinal coordinate of the predicted vehicle at the T+q moment, obs a predicted longitudinal coordinate of the predicted vehicle at the T+q moment,

[0097] Compared with the prior art, the present application has the following beneficial effects:

[0098] The vehicle trajectory prediction method provided by the present application considers step-by-step bidirectional interaction, constructs a network model that can fully extract bidirectional interaction information between vehicles, extracts the trajectory and spatial position information of the predicted vehicle and other surrounding vehicles as input by steps, uses an encoding architecture to motion encode the vehicle trajectory, combines the step-by-step bidirectional interaction relationship between vehicles, accurately predicts the future trajectory of the vehicle, fully considers the complex mutual influence between vehicles, constructs different observation tensors for the predicted vehicle and surrounding vehicles according to their respective situations, uses a convolution pooling network to extract spatial information between vehicles, reasonably processes the interaction information between different vehicles, finally inputs the extracted interaction information into a decoder, obtains the future trajectory of the predicted vehicle in multiple segments, fully considers the influence of the future trajectory of the predicted vehicle and surrounding vehicles on each other, and improves the accuracy of trajectory prediction. BRIEF DESCRIPTION OF DRAWINGS

[0099] The present application will be further described below in conjunction with the drawings:

[0100] Figure 1 The present application provides a general flowchart of a vehicle trajectory prediction method considering step-by-step bidirectional interaction.

[0101] Figure 2 The present application provides a framework schematic diagram of a vehicle trajectory prediction model in step two of a vehicle trajectory prediction method considering step-by-step bidirectional interaction. DETAILED DESCRIPTION

[0102] The present application will be further described below in conjunction with the drawings:

[0103] The application provides a vehicle trajectory prediction method considering step-by-step bidirectional interaction, which fully extracts bidirectional interaction information between vehicles by step-by-step extraction of trajectory and spatial position information of a predicted vehicle and other surrounding vehicles and input into a built network model, and accurately predicts future trajectories of the vehicles in multiple sections, and the specific steps of the method are as follows:

[0104] Step one, processing of the vehicle trajectory data set:

[0105] First, the position information of the vehicles in the data set is extracted in time sequence, that is, the absolute coordinates (x, y) of the vehicles in the horizontal and vertical directions; then, all vehicle coordinates are further processed, and the processing steps include vehicle trajectory extraction, construction of observation tensors and conversion of relative coordinates between vehicles;

[0106] In the vehicle trajectory extraction, the absolute coordinates of the historical trajectory TargHist of the predicted vehicle and the absolute coordinates of the future real trajectory TargFut are defined as follows:

[0107]

[0108] Wherein, is the absolute coordinate of the predicted vehicle in the horizontal and vertical directions at t time, is the absolute coordinate of the predicted vehicle in the horizontal direction at t time, is the absolute coordinate of the predicted vehicle in the vertical direction at t time, t∈{1,2,...,T obs},T obs is the observation time length of the historical trajectory of the predicted vehicle, and is also the current time, is the real absolute coordinate of the predicted vehicle in the horizontal and vertical directions at future k time, which is used to calculate the loss value of the model, is the absolute coordinate of the predicted vehicle in the horizontal direction at future k time, is the absolute coordinate of the predicted vehicle in the vertical direction at future k time, k∈{1,2,...,T pred},T pred is the future trajectory prediction time length of the predicted vehicle;

[0109] The absolute coordinates of the historical trajectory NbrsHist and the absolute coordinates of the future real trajectory NbrsFut of the surrounding vehicles of the predicted vehicle are defined as follows:

[0110]

[0111]

[0112] Wherein, n∈N is the number of surrounding vehicles of the predicted vehicle, N is a positive integer greater than 0, and the surrounding vehicles of the predicted vehicle are referred to as surrounding vehicles. is the set of lateral and longitudinal absolute coordinates of n surrounding vehicles at time t, specifically, is the set of lateral absolute coordinates of n surrounding vehicles at time t, is the set of longitudinal absolute coordinates of n surrounding vehicles at time t, t e {1, 2,..., T obs ', T obs ' is the observation time length of the surrounding vehicle historical trajectory, because the model requires the observation time length of the predicted vehicle and the surrounding vehicle to be the same, so T obs ' = T obs , is the set of real lateral and longitudinal absolute coordinates of n surrounding vehicles at future time k, specifically, is the set of real lateral absolute coordinates of n surrounding vehicles at future time k, is the set of real longitudinal absolute coordinates of n surrounding vehicles at future time k, k e {1, 2,..., T pred ', T pred ' is the future trajectory prediction time length of the surrounding vehicle, because the model requires the future trajectory prediction time length of the predicted vehicle and the surrounding vehicle to be the same, so T pred ' = T pred ;

[0113] In the construction of the observation tensor, the environment within 30 meters before and 5 meters on the left and right of the predicted vehicle is taken, and a 5x25 two-dimensional space grid is established with the center of mass of the predicted vehicle as the center. The 5 in 5x25 represents the observation range of the predicted vehicle in the lateral direction, and the 25 in 5x25 represents the observation range of the predicted vehicle in the longitudinal direction. The center of mass of the predicted vehicle is located at the centermost position of the two-dimensional space grid, i.e., the third grid in the lateral direction and the thirteenth grid in the longitudinal direction. The length of each small square in the two-dimensional space grid is defined as 2.4 meters, and the width is 2 meters. The two-dimensional space grid records the position of the surrounding vehicles; in this 5x25 two-dimensional space grid, the small squares with vehicles are set to TRUE, and the small squares without vehicles are set to FALSE. The number of surrounding vehicles is n, and the observation tensor of the position of the surrounding vehicles represented by TRUE and FALSE is obtained. 5×25 Through the observation tensor CentGrid e R 5×25 , the spatial interaction features between the predicted vehicle and the surrounding vehicles can be extracted;

[0114] In the conversion of the relative coordinates between vehicles, the historical trajectory absolute coordinates TargHist of the predicted vehicle and the future real trajectory absolute coordinates TargFut are respectively subtracted from the lateral and longitudinal absolute coordinates of the predicted vehicle at the current time T obs ​The converted relative historical trajectory coordinates of the predicted vehicle TargCentHist and the converted relative future trajectory coordinates of the predicted vehicle TargCentFut are obtained:

[0115]

[0116] Wherein, TargCentHist is used for the input of the model, and TargCentFut is used for the model to calculate the loss value, The converted relative historical trajectory coordinates of the predicted vehicle at time t are The horizontal and vertical absolute coordinates of the predicted vehicle at time t, The horizontal and vertical absolute coordinates of the predicted vehicle at time T obs under the current time T, t∈{1,2,...,T obs} are obtained. The converted relative future trajectory coordinates of the predicted vehicle at future time k are The converted relative future trajectory horizontal coordinates of the predicted vehicle at future time k are The converted relative future trajectory vertical coordinates of the predicted vehicle at future time k are k∈{1,2,...,T pred};

[0117] The historical trajectory absolute coordinates NbrsHist and the future trajectory absolute coordinates NbrsFut of the surrounding vehicle are respectively subtracted from the horizontal and vertical absolute coordinates of the predicted vehicle at time T obs under the current time T The converted relative historical trajectory coordinates NbrsCentHist of the surrounding vehicle and the converted relative future trajectory coordinates NbrsCentFut of the surrounding vehicle are obtained:

[0118]

[0119] Wherein, NbrsCentHist is used for the input of the model, and NbrsCentFut is used for the model to calculate the loss value, The converted relative historical trajectory coordinates of the surrounding vehicle at time t are t'∈{1,2,...,T obs '}; The converted relative future trajectory coordinates of the surrounding vehicle at future time k' are The converted relative future trajectory horizontal coordinates of the surrounding vehicle at future time k' are The converted relative future trajectory vertical coordinates of the surrounding vehicle at future time k' are k'∈{1,2,...,T pred '};

[0120] Step two, design a trajectory prediction model of the vehicle

[0121] In Figure 2 , a framework diagram of a trajectory prediction model is shown, which includes a predicted vehicle trajectory prediction model TargModel and a surrounding vehicle trajectory prediction model NbrsModel. The model structures of the predicted vehicle trajectory prediction model TargModel and the surrounding vehicle trajectory prediction model NbrsModel are the same, but the parameters in the models are different. Both the predicted vehicle trajectory prediction model TargModel and the surrounding vehicle trajectory prediction model NbrsModel include a vehicle motion trajectory information extraction module and a vehicle trajectory prediction module:

[0122] For the vehicle motion trajectory information extraction module, the relative historical trajectory coordinates of the predicted vehicle and the relative historical trajectory coordinates of the surrounding vehicle are converted into and respectively. The is input into a one-dimensional convolutional neural network Conv1D3 to extract the motion information of the predicted vehicle, and the emb is input into another one-dimensional convolutional neural network Conv1D3' to extract the motion information of the surrounding vehicle, to obtain the motion embedding TargCentHist of the predicted vehicle emb and the motion embedding NbrsCentHist of the surrounding vehicle

[0123]

[0124] wherein, is the motion encoding information of the predicted vehicle, is the motion encoding information of the surrounding vehicle, Conv1D3 and Conv1D3' are one-dimensional convolutional layers with a convolution kernel size of 3, an input channel number of 2, an output feature number of 32, and a step of 1, is the weight parameter of Conv1D3, is the weight parameter of Conv1D3', is the bias parameter of Conv1D3, is the bias parameter of Conv1D3';

[0125] The dimension of the motion encoding information of the predicted vehicle is converted into The dimension of the motion encoding information of the surrounding vehicle is converted into Then input into the encoder to obtain the encoding information of the predicted vehicle and the encoding information of the surrounding vehicle

[0126]

[0127] wherein, is the hidden state of the predicted vehicle, is the hidden state of the surrounding vehicles, Encoder is the motion encoder of the predicted vehicle, Encoder' is the motion encoder of the surrounding vehicles, the encoder is composed of a Long Short-Term Memory (LSTM) network, the input feature number of the LSTM network in the encoder is 32, the hidden feature number is 64, and the number of layers is 1, is the weight parameter of the Encoder, is the weight parameter of the Encoder', is the bias parameter of the Encoder, is the bias parameter of the Encoder';

[0128] The motion encoding information of the predicted vehicle is aggregated by a fully connected layer:

[0129]

[0130] wherein, is the motion information encoding of the predicted vehicle with a feature number of 32, and φ is an embedding function of the fully connected layer, is the weight parameter of the fully connected layer for aggregating the encoding information of the predicted vehicle, is the bias parameter of the fully connected layer for aggregating the encoding information of the predicted vehicle;

[0131] The motion encoding information of the surrounding vehicles is filled into the observation tensor CentGrid ∈ R 5×25 in step one according to their positions in the grid in turn, is filled into CentGrid ∈ R 5×25 where TRUE, and 0 is filled into the position where False, if there is only one position TRUE in the grid, the position relationship of the vehicle in the grid is not considered, and is directly filled into the position, and is filled into CentGrid ∈ R 5×25 After that, the observation feature tensor CentGridH is obtained, and then CentGridH is used as input to use two-dimensional graph convolution Conv2D 3×3 to extract the features of the spatial interaction information between the predicted vehicle and the surrounding vehicles:

[0132]

[0133] where NbrsGridConv ∈ R 64×5×25 is the spatial interaction feature between vehicles, Conv2D 3×3 is a two-dimensional convolution layer with a kernel size of 3x3, the input feature number and the output feature number are both 64, and the step is 1, is the weight parameter of Conv2D 3×3 , is the bias parameter of Conv2D 3×3 ;

[0134] The spatial interaction feature NbrsGridConv between vehicles is subjected to a pooling operation to reduce the dimension, retain key information, and improve the generalization degree of the model:

[0135]

[0136] where NbrsGridPool ∈ R 64×9×1 , MaxPool 3×3 is a maximum pooling layer with a kernel size of 3x3 and a step of 2, is the weight parameter, is the bias parameter;

[0137] In order to further enhance the understanding and modeling ability of the prediction network for spatial feature data, the NbrsGridPool is further subjected to a re-convolution and re-pooling step, that is, the NbrsGridPool is input into a two-dimensional convolution layer with a kernel size of 3x1, and then input into a maximum pooling layer with a kernel size of 2x1, and finally the spatial interaction information between vehicles is obtained and the dimension is changed to

[0138] The vehicle trajectory prediction module predicts the vehicle trajectory in the future time length T pred by obtaining the vehicle motion information and the spatial information between vehicles; the specific operation is as follows: the motion information of the vehicle to be predicted is encoded and the spatial interaction information between vehicles is spliced and copied T pred times to obtain a vehicle information aggregation feature with a feature number of 112 The aggregation feature is input into the trajectory prediction module to obtain the future prediction trajectory Pred of the vehicle to be predicted:

[0139]

[0140] wherein,

[0141] is the future prediction trajectory of the vehicle to be predicted in T obs+mthe relative predicted trajectory coordinate of the predicted vehicle at time t, the relative predicted trajectory horizontal coordinate of the predicted vehicle at time t, obs+m the relative predicted trajectory vertical coordinate of the predicted vehicle at time t, the relative predicted trajectory coordinate of the predicted vehicle at time t, obs+m the relative predicted trajectory horizontal coordinate of the predicted vehicle at time t, pred}, the Decoder is a decoder composed of a long short-term memory (LSTM) network, the input feature number of the LSTM network in the decoder is 112, the hidden feature number is 128, and the number of layers is 1, the weight parameter of the decoder, the bias parameter of the decoder, and φ is an embedding function of a fully connected layer, the weight parameter of the fully connected layer, the bias parameter of the fully connected layer, the input feature number is 128, and the output dimension is 2;

[0142] Step three, constructing a loss function

[0143] The expression of the loss function Loss is:

[0144]

[0145] wherein, the relative true trajectory horizontal coordinate of the predicted vehicle at time p, the relative true trajectory vertical coordinate of the predicted vehicle at time p, the relative predicted trajectory horizontal coordinate of the predicted vehicle at time p output by the model, the relative predicted trajectory vertical coordinate of the predicted vehicle at time p output by the model;

[0146] Step four, step-by-step bidirectional interactive trajectory prediction

[0147] The step-by-step bidirectional interactive trajectory prediction method flow is as shown in Figure 1 , the predicted vehicle is denoted as Car targ , the time length of predicting the future trajectory of Car targ is set to T, the time length of predicting the future trajectory of the surrounding vehicle is set to T', because the model requires the time length of the predicted future trajectory of the surrounding vehicle to be half of Car targ , so the historical observation time length of Car targ is T obs , and the historical observation time length of the surrounding vehicle is T obs ', because the model requires the historical observation time length of Car targ and the surrounding vehicle to be the same, so T obs ' = T obs ;

[0148] The model predicts Car in two stages. targ Future trajectory:

[0149] In stage 1, the model outputs Car. targ future The relative predicted trajectory in the time domain and the relative predicted trajectory of surrounding vehicles in the future time domain from 0 to T';

[0150] In stage 2, the model outputs Car. targ future Relative predicted trajectory in the time domain;

[0151] Finally, the predicted time domain is... and The relative predicted trajectories of the two predicted vehicles are spliced ​​together in chronological order to obtain Car. targ The complete future relative prediction trajectory with a duration of T;

[0152] First, obtain the first segment of the predicted trajectory for the vehicle being predicted:

[0153] Car targ The observation tensor CentGrid∈R 5×25 Car targ The relative historical trajectory coordinates TargCentHist and the relative historical trajectory coordinates NbrsCentHist of surrounding vehicles are input into the vehicle trajectory prediction model TargModel to obtain Car. targ future Predicted trajectory TargPred in the time domain:

[0154]

[0155] in, For Car targ At the T obs The predicted trajectory coordinates at time +a For Car targ At the T obs The predicted x-axis at time +a For Car targ At the T obs The predicted ordinate at time +a

[0156] Next, regarding Car targ Perform relative coordinate transformation with surrounding vehicles:

[0157] Select all surrounding vehicles in turn, and denote the selected surrounding vehicles as Cars. g Where g∈N represents the surrounding vehicles of the g-th vehicle, let Car gThe original relative historical trajectory coordinates SelHist are:

[0158]

[0159] in, For Car g The original relative historical trajectory coordinates at time b, b∈{1,2,...,T} obs'}, Car g The current time T obs 'Lower position' Set Car as the origin and establish a new reference coordinate system. g The historical trajectory coordinates are converted to coordinates in the new reference coordinate system to obtain Car. g New relative historical trajectory coordinates TurnHist:

[0160]

[0161] Car targ The original relative historical trajectory coordinates are converted to new relative historical trajectory coordinates in the new reference coordinate system, TargNewHist:

[0162]

[0163] Where TargCentHist is Car targ The original relative historical trajectory coordinates;

[0164] Then, obtain the Car. g The observation tensor SelCentGrid:

[0165] In Car targ The observation tensor Centgrid∈R 5×25 Based on this, the Car in the grid g Set the cell containing the current cell to TRUE, and set the contents of all other cells to FALSE to get Car. g The observation tensor SelCentGrid∈R 5×25 ;

[0166] Secondly, select all surrounding vehicles in turn and obtain their next predicted trajectory segment for each:

[0167] Car targ The number of surrounding vehicles is n. Each time, one surrounding vehicle, Car, is selected in turn. g The process of predicting the trajectories of surrounding vehicles:

[0168] The Car obtained from the previous step g The observation tensor SelCentGrid∈R5×25 Car g New relative historical trajectory coordinates TurnHist, Car targ The new relative historical trajectory coordinates, TargNewHist, are input into the surrounding vehicle trajectory prediction model, NbrsModel, to obtain the Car... g The predicted trajectory in the future time domain from 0 to T' with its own center of mass as the origin of the reference frame;

[0169] After performing the above surrounding vehicle trajectory prediction process n' times, the predicted trajectory coordinates SelNbrsPred of all surrounding vehicles in a new reference frame with their respective centroids as the origin of the reference frame can be obtained. Since the number of surrounding vehicle trajectory prediction processes is equal to the number of vehicles, n' = n.

[0170]

[0171] in, Let c be the predicted trajectory coordinates of surrounding vehicles at time c in the future. Let x be the x-coordinate of the predicted trajectory of the surrounding vehicles at time c in the future. Let c be the predicted ordinate of the trajectory of the surrounding vehicles at time c in the future, where c∈{1,2,...,T'};

[0172] Continue, convert SelNbrsPred to Car targ The predicted trajectory coordinates for the reference frame:

[0173] SelNbrsPred is based on Car g The trajectory coordinates in a reference frame centered at the origin need to be converted into Car coordinates. targ The coordinates in the reference frame can be obtained by directly connecting SelNbrsPred to... Adding them together, we can get Car. targ The coordinates of the next segment of the predicted trajectory of surrounding vehicles in the reference frame, NbrsPred:

[0174]

[0175] in, For Car g In T obs 'The original relative historical trajectory coordinates at that moment;'

[0176] Finally, the coordinates of the next predicted trajectory segment of the predicted vehicle and surrounding vehicles are replaced with their respective old historical trajectories to obtain the new historical trajectory coordinates:

[0177] Discarding the old historical trajectory in TargCentHist a latest trajectory point of the predicted vehicle, TargPred, is added to TargCentHist as the newest a new history trajectory TargRepHist of the predicted vehicle is obtained:

[0178]

[0179] wherein, TargPred is a latest trajectory point of the predicted vehicle, TargPred is a new history trajectory of the predicted vehicle at d,

[0180] and a new relative history trajectory TargCentHist2 of the predicted vehicle is obtained by taking the latest trajectory point TargPred of the predicted vehicle as the new origin of the reference frame and establishing a new reference coordinate system:

[0181]

[0182] wherein, TargPred is a new relative history trajectory coordinate of the predicted vehicle at e in the new reference coordinate system, and

[0183] Similarly, the prediction trajectory NbrsPred of the surrounding vehicle is used to replace the first 0~T' trajectory points in the old history trajectory NbrsCentHist, and a new history trajectory NbrsRepHist is obtained:

[0184]

[0185] wherein, NbrsPred is a latest trajectory point of the surrounding vehicle at T' time points, NbrsPred is a new history trajectory of the surrounding vehicle at f, f∈{T'+1,T'+2...,T obs '-1,T obs ',T obs '+1,...,T obs '+T'}.

[0186] and a new relative history trajectory NbrsCentHist2 of the surrounding vehicle in the new reference coordinate system is obtained by taking the latest trajectory point NbrsPred of the predicted vehicle as the new origin coordinate:

[0187]

[0188] wherein, NbrsPred is a new relative history trajectory of the surrounding vehicle in the new reference coordinate system, ​TargCentHist2, NbrsCentHist2, CentGrid) = TargModel(TargCentHist1, NbrsCentHist1, CentGrid) where TargCentHist1 is the new relative history trajectory of the target vehicle at time l for the origin, and l ∈ [T'+1, T'+2,..., T obs '+T'-1, T obs '+T'].

[0189] The obtained new relative history trajectory of the target vehicle TargCentHist2, new relative history trajectory of the surrounding vehicles NbrsCentHist2 and observation tensor CentGrid are input into the target vehicle trajectory prediction model TargModel to obtain the predicted trajectory TargPred2 of the target vehicle in the future time domain:

[0190]

[0191] wherein, TargPred2 is the predicted trajectory coordinate of the target vehicle at time T obs +p, TargPred2 is the predicted horizontal coordinate of the target vehicle at time T obs +p, TargPred2 is the predicted vertical coordinate of the target vehicle at time T obs +p,

[0192] Finally, the first-stage predicted trajectory TargPred and the second-stage predicted trajectory TargPred2 of the target vehicle are spliced to obtain the complete predicted trajectory Pred of the target vehicle:

[0193]

[0194] wherein, TargPred is the predicted trajectory coordinate of the target vehicle at time T obs +q, TargPred is the predicted horizontal coordinate of the target vehicle at time T obs +q, TargPred is the predicted vertical coordinate of the target vehicle at time T obs +q, ​

Claims

1. A vehicle trajectory prediction method considering progressive two-way interaction, which fully extracts the trajectory and spatial location information of the vehicle being predicted and other surrounding vehicles by progressively extracting these information and inputting them into a constructed network model to fully extract the two-way interaction information between vehicles, and accurately predicts the future trajectory of the vehicle in multiple segments, characterized in that... The specific steps of this method are as follows: Step 1: Process the vehicle trajectory dataset: First, the location information of the vehicles in the dataset is extracted in chronological order, that is, the absolute coordinates (x, y) of the vehicle's horizontal and vertical positions. Then, all vehicle coordinates are further processed, including vehicle trajectory extraction, observation tensor construction, and relative coordinate transformation between vehicles. In vehicle trajectory extraction, the historical trajectory absolute coordinates TargHist and the future true trajectory absolute coordinates TargFut of the predicted vehicle are defined as follows: in, Let be the absolute coordinates of the vehicle being predicted at time t. Let be the absolute lateral coordinate of the vehicle being predicted at time t. Let be the absolute longitudinal coordinate of the vehicle being predicted at time t, where t∈{1,2,...,T} obs }, T obs The observation duration of the predicted vehicle's historical trajectory, and also the current moment. Let k be the true absolute coordinates of the vehicle in the future at time k. Let be the absolute lateral coordinate of the vehicle to be predicted at time k in the future. Let K be the absolute longitudinal coordinate of the vehicle to be predicted at time k in the future, k∈{1,2,...,T} pred }, T pred Predicting the duration of the future trajectory of the vehicle being predicted; Define the historical trajectory absolute coordinates NbrsHist of the vehicles surrounding the predicted vehicle and the future true trajectory absolute coordinates NbrsFut as follows: Where n∈N is the number of vehicles surrounding the vehicle being predicted, and N is a positive integer greater than 0. Hereafter, the vehicles surrounding the vehicle being predicted will be referred to as: surrounding vehicles. Let be the set of absolute horizontal and vertical coordinates of n surrounding vehicles at time t. Specifically, Let be the set of absolute lateral coordinates of n surrounding vehicles at time t. Let be the set of absolute longitudinal coordinates of n surrounding vehicles at time t, where t∈{1,2,...,T} obs '}, T obs 'T' represents the observation duration of the historical trajectories of surrounding vehicles. Because the model requires the historical trajectory observation duration of the input vehicle being predicted to be the same as that of the surrounding vehicles, T... obs '=T obs , Let n be the set of the true horizontal and vertical absolute coordinates of the surrounding vehicles at time k in the future. Specifically, Let n be the set of the true lateral absolute coordinates of the surrounding vehicles at time k in the future. Let n be the set of the true longitudinal absolute coordinates of n surrounding vehicles at time k in the future, k∈{1,2,...,T} pred '}, T pred 'Predict the future trajectory prediction duration for surrounding vehicles. Because the model requires the predicted trajectory prediction duration for the predicted vehicle to be the same as that for surrounding vehicles, T...' pred '=T pred ; In constructing the observation tensor, the environment within 30 meters in front of and behind the predicted vehicle, and 5 meters to the left and right, is considered. A 5×25 two-dimensional spatial grid is constructed with the centroid of the predicted vehicle as the center. The 5 in 5×25 represents the lateral observation range of the predicted vehicle, and the 25 represents the longitudinal observation range. The centroid of the predicted vehicle is located at the very center of the two-dimensional spatial grid, specifically the 3rd horizontal and 13th vertical cell. Each small square in the two-dimensional spatial grid is defined as 2.4 meters long and 2 meters wide. The orientation of surrounding vehicles is recorded in the two-dimensional spatial grid. In this 5×25 two-dimensional spatial grid, squares with vehicles are marked TRUE, and squares without vehicles are marked FALSE. The number of surrounding vehicles is n. Thus, the observation tensor CentGrid∈R, representing the orientation of surrounding vehicles, is obtained using TRUE and FALSE. 5×25 By observing the tensor CentGrid∈R 5×25 It can extract spatial interaction features between the predicted vehicle and surrounding vehicles; In the transformation of relative coordinates between vehicles, the absolute coordinates of the predicted vehicle's historical trajectory (TargHist) and the absolute coordinates of its future true trajectory (TargFut) are respectively subtracted by the current time T. obs The absolute coordinates of the predicted vehicle in the lateral and longitudinal directions The transformed relative historical trajectory coordinates of the predicted vehicle, TargCentHist, and the transformed relative future trajectory coordinates of the predicted vehicle, TargCentFut, are obtained as follows: TargCentHist is used as the input to the model, and TargCentFut is used to calculate the loss value of the model. The coordinates of the predicted vehicle's relative historical trajectory at time t are the converted coordinates. The absolute coordinates of the vehicle in the horizontal and vertical directions at time t. Let T be the current time. obs The absolute coordinates of the predicted vehicle in the horizontal and vertical directions, t∈{1,2,...,T} obs }, Let be the transformed relative future trajectory coordinates of the predicted vehicle at time k. Let x be the x-coordinate of the predicted relative future trajectory of the vehicle at time k after the transformation. Let be the ordinate of the relative future trajectory of the predicted vehicle at time k, where k∈{1,2,...,T}. pred }; Subtract the current time T from the historical absolute coordinates NbrsHist and the future true absolute coordinates NbrsFut of the surrounding vehicles. obs The predicted absolute coordinates of the vehicle in the horizontal and vertical directions Obtain the converted relative historical trajectory coordinates NbrsCentHist of surrounding vehicles and the converted relative future trajectory coordinates NbrsCentFut of surrounding vehicles: Where NbrsCentHist is used as the input to the model, and NbrsCentFut is used to calculate the loss value of the model. Let be the relative historical trajectory coordinates of the surrounding vehicles at time t, where t'∈{1,2,...,T} obs '}; Let be the relative future trajectory coordinates of the surrounding vehicles at time k' after the transformation. Let x be the x-coordinate of the relative future trajectory of the surrounding vehicles at time k' after the transformation. The transformed relative future trajectory ordinates of surrounding vehicles at time k', where k'∈{1,2,...,T} pred '}; Step 2: Design the vehicle trajectory prediction model The trajectory prediction model includes the predicted vehicle trajectory prediction model (TargModel) and the surrounding vehicle trajectory prediction model (NbrsModel). The predicted vehicle trajectory prediction model (TargModel) and the surrounding vehicle trajectory prediction model (NbrsModel) have the same model structure, but different parameters. Both the predicted vehicle trajectory prediction model (TargModel) and the surrounding vehicle trajectory prediction model (NbrsModel) include a vehicle motion trajectory information extraction module and a vehicle trajectory prediction module. For the vehicle trajectory information extraction module, firstly, the relative historical trajectory coordinates of the predicted vehicle from step one are... Relative historical trajectory coordinates of vehicles and surrounding vehicles The dimensions are respectively transformed into and Will The input is fed into a one-dimensional convolutional neural network Conv1D3 to extract the motion information of the vehicle being predicted. The input is fed into another one-dimensional convolutional neural network, Conv1D3', to extract motion information of surrounding vehicles, resulting in the motion embedding of the predicted vehicle, TargCentHist. emb The motion of surrounding vehicles is embedded in NbrsCentHist emb : in, The motion coding information of the vehicle being predicted. To encode motion information for surrounding vehicles, Conv1D3 and Conv1D3' are both one-dimensional convolutional layers with a kernel size of 3, 2 input channels, 32 output features, and a stride of 1. For the weight parameters of Conv1D3, For Conv1D3', the parameters are weights. These are the bias parameters for Conv1D3. For the bias parameters of Conv1D3'; The motion coding information of the vehicle to be predicted Dimensions converted Motion coding information of surrounding vehicles Dimensions converted Then the information is input into the encoder to obtain the encoded information of the vehicle being predicted. Coding information of surrounding vehicles in, The hidden state of the predicted vehicle. The hidden state of the surrounding vehicles is represented by Encoder, which is the motion encoder of the vehicle being predicted, and Encoder' is the motion encoder of the surrounding vehicles. The encoder is composed of a Long Short-Term Memory (LSTM) network. The LSTM network in the encoder has 32 input features, 64 hidden features, and 1 layer. These are the weight parameters for the Encoder. The weight parameters for Encoder' These are the bias parameters for the Encoder. For the bias parameter of Encoder'; The motion coding information of the vehicle to be predicted The encoded information is aggregated through a fully connected layer: in, This is the encoding of the motion information of the predicted vehicle with 32 features, and φ is the embedding function of the fully connected layer. To aggregate the weight parameters of the fully connected layer that contain the predicted vehicle coding information, The bias parameters of the fully connected layer that aggregate the predicted vehicle coding information; Motion coding information of surrounding vehicles Fill in the observation tensors from step one, CentGrid∈R, according to their positions in the grid. 5×25 That is to say, Fill to CentGrid∈R 5×25 The positions marked as TRUE are filled with 0, while positions marked as False are filled with 0. If only one position in the grid is TRUE, then the vehicle's position in the grid is disregarded, and the position is directly set to TRUE. Fill in this position, Fill to CentGrid∈R 5×25 The observed feature tensor CentGridH is then obtained, and CentGridH is used as input to perform a 2D graph convolution Conv2D. 3×3 To extract features for spatial interaction information between the predicted vehicle and its surrounding vehicles: Where NbrsGridConv∈R 64×5×25 Conv2D is used to define the spatial interaction features between vehicles. 3×3 It is a two-dimensional convolutional layer with a kernel size of 3×3, 64 input features and 64 output features, and a stride of 1. For Conv2D 3×3 The weight parameters, For Conv2D 3×3 The bias parameter; Pooling is performed on the spatial interaction features NbrsGridConv between vehicles to reduce dimensionality, preserve key information, and improve the model's generalization ability. Where NbrsGridPool∈R 64×9×1 MaxPool 3×3 It is a max-pooling layer with a 3×3 pooling core and a step size of 2. For weight parameters, These are bias parameters; To further enhance the prediction network's ability to understand and model spatial feature data, NbrsGridPool undergoes further reconvolution and repooling steps. Specifically, NbrsGridPool is input into a 2D convolutional layer with a 3×1 kernel, and then into a max-pooling layer with a 2×1 kernel, ultimately yielding spatial interaction information between vehicles. And transform the dimension The vehicle trajectory prediction module predicts future time intervals of T by acquiring vehicle motion information and spatial information between vehicles. pred Vehicle trajectory within; specific operation is as follows: encoding the motion information of the vehicle to be predicted. Spatial interaction information between vehicles Perform splicing and copying of T pred This yields a vehicle information aggregation feature with 112 features. This aggregation feature The input is fed into the trajectory prediction module to obtain the predicted future trajectory Pred for the vehicle being predicted. In the formula, For the predicted vehicle at T obs+m The relative predicted trajectory coordinates at time. For the predicted vehicle at T obs+m The relative x-coordinate of the predicted trajectory at time. For the predicted vehicle at T obs+m The relative predicted trajectory ordinate at time m, m∈{1,2,...,T} pred The decoder is composed of a Long Short-Term Memory (LSTM) network. The LSTM network in the decoder has 112 input features, 128 hidden features, and one layer. These are the weight parameters of the decoder. Here, φ represents the bias parameters of the decoder, and φ is the embedding function of the fully connected layer. These are the weight parameters of the fully connected layer. The bias parameters for the fully connected layer are 128 input features and 2 output dimensions. Step 3: Construct the loss function The expression for the loss function Loss is: in, Let x be the x-coordinate of the predicted vehicle's relative true trajectory at time p. Let be the ordinate of the predicted vehicle's relative true trajectory at time p. The x-coordinate of the predicted trajectory of the vehicle at time p is the output of the model. The ordinate of the predicted trajectory of the vehicle at time p is the output of the model. Step 4: Stepwise two-way interactive trajectory prediction The predicted vehicle will be denoted as Car. targ Set up predictive Car targ The duration of the future trajectory is T, and the duration of the predicted future trajectories of surrounding vehicles is T', because the model requires the duration of the predicted future trajectories of surrounding vehicles to be Car. targ Half of, so Car targ The historical observation duration is T obs The historical observation duration for surrounding vehicles is T. obs ', because the model requires the input Car targ The observation duration is the same as that of surrounding vehicles, so T obs '=T obs ; The model predicts Car in two stages. targ Future trajectory: In stage 1, the model outputs Car. targ future The relative predicted trajectory in the time domain and the relative predicted trajectory of surrounding vehicles in the future time domain from 0 to T'; In stage 2, the model outputs Car. targ future Relative predicted trajectory in the time domain; Finally, the predicted time domain is... and The relative predicted trajectories of the two predicted vehicles are spliced ​​together in chronological order to obtain Car. targ The complete future relative prediction trajectory with a duration of T; First, obtain the first segment of the predicted trajectory for the vehicle being predicted: Car targ The observation tensor CentGrid∈R 5×25 Car targ The relative historical trajectory coordinates TargCentHist and the relative historical trajectory coordinates NbrsCentHist of surrounding vehicles are input into the vehicle trajectory prediction model TargModel to obtain Car. targ future Predicted trajectory TargPred in the time domain: in, For Car targ At the T obs The predicted trajectory coordinates at time +a For Car targ At the T obs The predicted x-coordinate at time +a For Car targ At the T obs The predicted ordinate at time +a Next, regarding Car targ Perform relative coordinate transformation with surrounding vehicles: Select all surrounding vehicles in turn, and denote the selected surrounding vehicles as Cars. g Where g∈N represents the surrounding vehicles of the g-th vehicle, let Car g The original relative historical trajectory coordinates SelHist are: in, For Car g The original relative historical trajectory coordinates at time b, b∈{1,2,...,T} obs' }, Car g The current time T obs 'Lower position' Set Car as the origin and establish a new reference coordinate system. g The historical trajectory coordinates are converted to coordinates in the new reference coordinate system to obtain Car. g New relative historical trajectory coordinates TurnHist: Car targ The original relative historical trajectory coordinates are converted to new relative historical trajectory coordinates in the new reference coordinate system, TargNewHist: Where TargCentHist is Car targ The original relative historical trajectory coordinates; Then, obtain the Car. g The observation tensor SelCentGrid: In Car targ The observation tensor Centgrid∈R 5×25 Based on this, the Car in the grid g Set the cell containing the current cell to TRUE, and set the contents of all other cells to FALSE to get Car. g The observation tensor SelCentGrid∈R 5×25 ; Secondly, select all surrounding vehicles in turn and obtain their next predicted trajectory segment for each: Car targ The number of surrounding vehicles is n. Each time, one surrounding vehicle, Car, is selected in turn. g The process of predicting the trajectories of surrounding vehicles: The Car obtained from the previous step g The observation tensor SelCentGrid∈R 5×25 Car g New relative historical trajectory coordinates TurnHist, Car targ The new relative historical trajectory coordinates, TargNewHist, are input into the surrounding vehicle trajectory prediction model, NbrsModel, to obtain the Car... g The predicted trajectory in the future time domain from 0 to T' with its own center of mass as the origin of the reference frame; After performing the above surrounding vehicle trajectory prediction process n' times, the predicted trajectory coordinates SelNbrsPred of all surrounding vehicles in a new reference frame with their respective centroids as the origin of the reference frame can be obtained. Since the number of surrounding vehicle trajectory prediction processes is equal to the number of vehicles, n' = n. in, Let c be the predicted trajectory coordinates of surrounding vehicles at time c in the future. Let x be the x-coordinate of the predicted trajectory of the surrounding vehicles at time c in the future. Let c be the predicted ordinate of the trajectory of the surrounding vehicles at time c in the future, where c∈{1,2,...,T'}; Continue, convert SelNbrsPred to Car targ The predicted trajectory coordinates for the reference frame: SelNbrsPred is based on Car g The trajectory coordinates in a reference frame centered at the origin need to be converted into Car coordinates. targ The coordinates in the reference frame can be obtained by directly connecting SelNbrsPred to... Adding them together, we can get Car. targ The coordinates of the next segment of the predicted trajectory of surrounding vehicles in the reference frame, NbrsPred: in, For Car g In T obs The original relative historical trajectory coordinates at that moment; Finally, the coordinates of the next predicted trajectory segment of the predicted vehicle and surrounding vehicles are replaced with their respective old historical trajectories to obtain the new historical trajectory coordinates: Discarding the old historical trajectory in TargCentHist For each trajectory point, add TargPred to TargCentHist as the latest. The trajectory points at each moment are used to obtain the updated historical trajectory TargRepHist: in, For the latest The predicted trajectory points of the vehicle at each time point. The new historical trajectory of the vehicle at time d is to be predicted. And based on the latest trajectory point of the predicted vehicle Using the new origin of the reference frame as the origin and establishing a new reference coordinate system, we obtain the new relative historical trajectory TargCentHist2 of the predicted vehicle: in, Let e ​​be the new relative historical trajectory coordinates of the vehicle being predicted at time e in the new reference coordinate system, and Similarly, the first 0 to T' trajectory points in the old historical trajectory NbrsCentHist are replaced with the predicted trajectories NbrsPred of surrounding vehicles to obtain the updated new historical trajectory NbrsRepHist: in, The predicted trajectory points of surrounding vehicles at the latest time T' are given. Let f be the new historical trajectory of the surrounding vehicles at time f, where f∈{T'+1,T'+2,…,T obs '-1,T obs ',T obs '+1,…,T obs '+T'}; And based on the latest trajectory point of the predicted vehicle As the new origin coordinates, the new relative historical trajectories of the surrounding vehicles in the new reference coordinate system, NbrsCentHist2, are obtained: in, For surrounding vehicles Let l be the coordinates of the new relative historical trajectory at time l, where l ∈ [T'+1, T'+2, ..., T]. obs '+T'-1,T obs '+T']; The new relative historical trajectory TargCentHist2 of the predicted vehicle, the new relative historical trajectories NbrsCentHist2 of surrounding vehicles, and the observation tensor CentGrid are input into the predicted vehicle trajectory prediction model TargModel to obtain the predicted future trajectory of the vehicle. Predicted trajectory TargPred2 in the time domain: in, For the predicted vehicle at T obs Predicted trajectory coordinates at time +p For the predicted vehicle at T obs The predicted x-axis at time +p For the predicted vehicle at T obs The predicted ordinate at time +p Finally, the first-stage predicted trajectory TargPred and the second-stage predicted trajectory TargPred2 of the predicted vehicle are concatenated to obtain the complete predicted trajectory Pred of the predicted vehicle: in, For the predicted vehicle at T obs The predicted trajectory coordinates at time +q For the predicted vehicle at T obs The predicted x-axis at time +q For the predicted vehicle at T obs The predicted ordinate at time +q

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