Vehicle trajectory reconstruction method considering physical constraints

Abstract

The invention discloses a vehicle trajectory reconstruction method considering physical constraints, and the method comprises the steps: S1, building a vehicle trajectory data set based on the observation records of an upstream fixed detector and a downstream virtual detector; s2, processing the trajectory data of each vehicle into time sequence data; s3, introducing an overtaking behavior as a physical constraint condition, estimating overtaking point information of the vehicle through a time consumption curve, and obtaining an overtaking behavior constraint condition of the target vehicle; and S4, introducing a speed space-time distribution diagram based on a shock wave theory as physical information to represent the operation state of the traffic flow where the target vehicle is located, and obtaining the speed space-time distribution constraint condition of the target vehicle. And S5, constructing and training based on the car-following model and the GRU model to obtain a fusion model, and correcting the reconstructed trajectory by adopting two constraint conditions. And S6, carrying out smoothing processing on the corrected vehicle track. According to the method, the traffic flow state can be accurately controlled, and the method has important application value for refining traffic state evaluation.

Description

Technical Field

[0001] The present invention belongs to the field of traffic perception and big data analysis, and specifically relates to a vehicle trajectory reconstruction method considering physical constraints. Background Art

[0002] Vehicle trajectories contain rich spatiotemporal information about traffic flows, which is of great significance for traffic flow simulation modeling, traffic signal optimization, and traffic operation status evaluation. Obtaining complete vehicle trajectories and analyzing their spatiotemporal information play a key role in describing the operation status of traffic flows. Therefore, how to supplement more trajectory information based on limited and partially continuous trajectory data has become a research hotspot in recent years.

[0003] Current vehicle trajectory detection devices can be divided into two categories based on their motion characteristics: fixed detectors (such as automatic vehicle identification and loop detectors) and mobile detectors (such as probe vehicles and connected autonomous vehicles). Fixed detectors are installed at specific locations and can perform high-precision vehicle point detection, but they cannot record the motion information of vehicle trajectories. Mobile detectors can obtain the motion data of vehicles and other traffic participants within a certain range through sensing and positioning devices installed on vehicles. Probe vehicles can provide their own position, acceleration, and velocity characteristics; however, due to their low penetration rate, it is difficult to fully reconstruct the missing trajectories of other vehicles. In contrast, connected autonomous vehicles can collect information about vehicles within their detection range, and the amount of trajectory data generated is several times that of probe vehicles. Making full use of this information helps to reconstruct high-precision vehicle trajectories. With these advantages, connected autonomous vehicles have made progress in the simulation of following behavior, the establishment of basic graphs, and the study of overtaking behavior. However, due to their low penetration rate, connected autonomous vehicles can only provide fragmented observation data rather than complete traffic trajectory information.

[0004] Current trajectory reconstruction methods are mainly divided into data-driven methods and traffic flow theory-based methods. For data-based methods, the focus is on inferring the spatiotemporal distribution pattern of trajectory points based on the characteristics of trajectory data. In trajectory reconstruction research, data-based methods can be divided into several categories: statistical models (such as maximum likelihood estimation, particle filtering), interpolation methods (such as linear interpolation, Hermite interpolation, Lagrange interpolation, adaptive smoothing spline, local weighted polynomial regression) and machine learning-based methods. Although machine learning-based methods perform well in short-term trajectory prediction, their prediction errors tend to increase with the increase in the length of the trajectory segment to be reconstructed. Data-based methods do not consider traffic flow effects, while methods based on traffic flow theory use traffic flow models to estimate the spatiotemporal distribution of vehicle trajectories. Traffic flow theory includes a variety of methods, such as variational theory, safety-based theory, following models, overtaking behavior, and the establishment of basic graphs. Traffic flow theory-based methods have good interpretability of driving behavior, but the reconstruction accuracy is not as high as that based on data-driven methods. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention provides a vehicle trajectory reconstruction method considering physical constraints. Taking highways as the research object, the vehicle number, speed, position and passing time of vehicles passing through fixed detectors are extracted, and the physical constraints of the overtaking point of the vehicle trajectory are calculated based on the time consumption curve; considering the influence of the traffic flow running state on the vehicle trajectory, a linear assumption is adopted in the shock wave theory to simplify the shock wave model, and the time-space distribution constraints of the vehicle speed are calculated; according to the two major physical constraints, the trajectory reconstruction result of the hybrid model is adjusted, and the reconstructed result is smoothed by a Savitzky-Golay filter, so that the reconstructed vehicle trajectory is not only more accurate but also more reasonable.

[0006] In order to solve the above technical problems, the present invention provides the following technical solutions: a vehicle trajectory reconstruction method considering physical constraints, comprising the following steps:

[0007] S1. Based on the observation records of the upstream fixed detector and the downstream virtual detector, a vehicle trajectory dataset is constructed, including the target vehicle number, as well as the target vehicle's location information, speed, acceleration, and time information;

[0008] S2, according to the sequence length and the prediction length, processing the trajectory data of each vehicle in the vehicle trajectory data set in step S1 into time series data, and dividing it into a training set, a test set and a validation set;

[0009] S3, introducing overtaking behavior as a physical constraint condition, estimating the overtaking point information of the vehicle through the time consumption curve, and obtaining the overtaking behavior constraint condition of the target vehicle;

[0010] S4. Introduce the speed space-time distribution diagram based on shock wave theory as physical information to characterize the running state of the traffic flow where the target vehicle is located, and obtain the speed space-time distribution constraint conditions of the target vehicle;

[0011] S5. Construct and train a fusion model based on the car-following model and the GRU model, specifically: input the original vehicle trajectory data into the car-following model and the GRU model, fuse the reconstruction results of the car-following model and the GRU model to obtain a reconstructed vehicle trajectory, and use the overtaking behavior constraint of the target vehicle and the speed spatiotemporal distribution constraint of the target vehicle to correct the reconstructed trajectory;

[0012] S6. Smoothing the corrected vehicle trajectory to eliminate the influence of abnormal speed and acceleration points, and obtaining the final reconstructed vehicle trajectory.

[0013] Furthermore, the aforementioned step S1 constructs a vehicle trajectory dataset, specifically: through the upstream detector, the license plate number of the vehicle passing through the target section is used as the vehicle ID, and the time when vehicle n passes the upstream detector position of section k is recorded as a k,n , the time to pass the end of the target section is a k+1,n , the observation set of vehicle n upstream of road segment k is {s(a k,n ),v(a k,n ),a k,n}, the observation set of vehicle n downstream of road segment k is {s(a k+1,n ),v(a k+1,n ),a k+1,n}, where s(a k,n ) is the longitudinal position of vehicle n passing the upstream detector of section k, v(a k,n ) is the speed of vehicle n passing the upstream detector of section k, s(a k+1,n ) is the longitudinal travel position of vehicle n passing the virtual detector downstream of section k, v(a k+1,n ) is the speed of vehicle n passing the virtual detector downstream of section k.

[0014] Furthermore, the aforementioned step S2 includes the following sub-steps:

[0015] S2.1, the vehicle trajectory is divided by sliding window, and the length of the selected historical sequence is l h , the reconstruction length is l p , the time segments of the historical sequence Seq(i) and the reconstructed sequence P(i) of the i-th sample are as shown in formulas (1) and (2) respectively; the vehicle's position, speed, acceleration, lane and other information are all within this segment, that is, the time series data Tra:

[0016] Seq(i)∈[t start ,tstart +l h ](26)

[0017] P(i)∈[t start +l h +1,t start +l h +l p ](27)

[0018] where t start is the start time of each sample;

[0019] S2.2. According to the stratified sampling principle, the time series data is divided into training set, validation set and test set according to the preset ratio, where Train_set, Val_set, Test_set represent the training set, validation set and test set respectively, and Tra is all the vehicle trajectory samples obtained in step S2.1:

[0020] Train_set = m1*Tra (28)

[0021] Val_set=m2*Tra (29)

[0022] Test_set = m3*Tra (30)

[0023] m1, m2, m3 are preset scaling factors.

[0024] Furthermore, the aforementioned step S3 includes the following sub-steps:

[0025] S3.1. Calculate the travel time t of each vehicle passing through the target road section k based on the time when vehicle n passes through the upstream detector and the downstream virtual detector position. k,n , and then obtain the travel time observation set of n vehicles on the target road section in the data set:

[0026] S3.2. By drawing a distribution diagram of the observed time and performing a Kolmogorov-Smirnov test, the expected travel time of the vehicle passing through the section k is obtained based on the fact that the travel time of the vehicle on the section k conforms to the normal distribution when the traffic flow is stable. As follows:

[0027] t k,n =a k+1,n -a k,n (31)

[0028]

[0029] Among them, t k,n is the travel time of vehicle n through road segment k, is the variance of the travel time of vehicle n through road segment k, a k,n is the time when vehicle n passes the upstream detector position of road segment k, a k+1,n is the time when vehicle n passes the end of the target section;

[0030] S3.3. Based on the calculated expected travel time Based on the uniform speed of vehicle n, the time it takes for vehicle n to pass the end of the study section k is: Then calculate the vehicle's position and time as shown in formula (9),

[0031]

[0032] in, is the average speed of vehicle n passing through section k, l k is the length of section k, s′ k,n,t is the longitudinal distance travelled by vehicle n on road section k,

[0033] S3.4. Obtain the estimated overtaking point based on the trajectory position and time expressions of different vehicles The reconstructed vehicle trajectory is adjusted according to formulas (11)-(12):

[0034]

[0035] Where (t k ″ ,n ,s′ k ' ,n,t ) represents the actual overtaking point position, s k ″′ ,n,t is the position of the vehicle trajectory point after adjustment. Further, the aforementioned step S4 includes the following sub-steps:

[0036] S4.1. Based on the linear assumption introduced by shock wave theory, the spatiotemporal distribution of speed in each lane is calculated:

[0037]

[0038] Among them, v fv represents the velocity at the intersection point A of the shock wave path and the preceding vehicle trajectory, v r ' efer represents the speed at any reference point between the front and rear vehicles, v nfv represents the velocity at the intersection point B of the rear vehicle trajectory and the shock wave path, l1, l2 represent the distances between the reference point and A, B respectively;

[0039] S4.2, adjust the reconstructed vehicle trajectory according to the spatiotemporal distribution of vehicle speed calculated in step S4.1: consider the influence of speed fluctuations,

[0040] The upper and lower limits of the speed threshold of the vehicle trajectory point are calculated by formula (14). If the lower and upper limits of the speed fluctuation are exceeded, the vehicle trajectory is adjusted, as shown in formula (15):

[0041]

[0042] v lower =v r ' efer -u*v r ' efer (41)

[0043] v upper =v r ' efer +u*v r ' efer (42)

[0044] where v lower ,v upper They represent the lower and upper limits of speed fluctuation respectively, and u is the speed fluctuation factor.

[0045] Furthermore, the aforementioned step S5 includes the following sub-steps:

[0046] S5.1. Input the corrected vehicle trajectory data into the car-following model and output the result s IDM,i ;

[0047] S5.2. Input the corrected vehicle trajectory data into the GRU model for training. The GRU model includes two gate structures: reset gate and update gate. The core expression of the GRU model is as shown in formula (18) to formula (21).

[0048] r t =σ(W r ·[h t-1 ,x t ]+b r ) (43)

[0049] z t =σ(W z ·[h t-1 ,x t ]+b z ) (44)

[0050]

[0051] Among them, h t is the current hidden state, is a candidate hidden state, x t Represents the input data, W r is the weight matrix of the reset gate, W z is the weight matrix of the update gate, W h is the weight matrix of the candidate state, b r is the bias term for the reset gate, b z is the bias term of the update gate, b h is the bias term of the candidate state, z t is the update gate vector, σ is the sigmoid activation function, r t is the reset gate vector;

[0052] S5.3. Output result of the car-following model s IDM,i It is fused with the reconstruction result of the GRU model, and the average MAE loss of the GRU model is calculated to enhance the training process of the GRU model. The model fusion process is shown in expression (22):

[0053]

[0054] w IDM,i +w GRU,i =1 (49)

[0055] where s GRU,i Represents the trajectory points i, w reconstructed by the GRU model IDM,i ,w GRU,i They represent the weight coefficients of the car-following model and the GRU model respectively, characterizing the credibility of different models. The sum of the two is 1, and loss is the training MAE loss of the GRU model.

[0056] Furthermore, the aforementioned step S6 includes the following sub-steps:

[0057] S6.1, input the vehicle trajectory data reconstructed by the hybrid model into the Savitzky-Golay filter, and filter out the noise in the velocity and acceleration based on the local polynomial least squares fitting in the time domain, keep the shape and width of the signal unchanged, and obtain different filtering results by selecting different window widths;

[0058] S6.2, using the speed and acceleration obtained in step S6.1, further adjust the reconstructed vehicle trajectory position as shown in formula (25) to obtain the final reconstructed vehicle trajectory, so that the reconstructed vehicle trajectory is more reasonable.

[0059]

[0060] in represents the position of the vehicle at time t after adjustment, v f,t ,v f,t-1They represent the speed of the vehicle at time t or time t-1 after passing through the Savitzky-Golay filter.

[0061] Compared with the prior art, the beneficial technical effects of the present invention using the above technical solution are as follows:

[0062] The present invention fully exploits the key data such as vehicle license plate, speed, time, acceleration recorded by fixed detectors on the road section, introduces two major physical constraints, namely overtaking behavior and speed spatiotemporal distribution, and adjusts the vehicle trajectory reconstructed by the trajectory reconstruction model; the time consumption curve is used to calculate the overtaking point distribution constraints between different vehicles, providing additional information for reconstructing the vehicle trajectory; based on the shock wave theory, linear constraints are introduced to calculate the speed spatiotemporal distribution between the front floating vehicle and the rear floating vehicle, and the speed fluctuation of the vehicle trajectory is adjusted; the following model and the GRU model are integrated, combined with the two major physical constraints, and finally the trajectory is smoothed through the Savitzky-Golay filter, and the reconstructed vehicle trajectory is closer to the actual situation. The vehicle trajectory reconstruction method considering physical constraints proposed by the present invention has higher reconstruction accuracy, and the MAPE error of trajectory reconstruction is only 3.33%, which is about 45% and 37% less than the estimation errors of the two classic models of trajectory reconstruction, respectively. In summary, the method of the present invention can accurately control the traffic flow state, which is an important condition for further ensuring the smooth operation of highways and monitoring vehicle exhaust emissions, and has important academic significance and application value for refining traffic state evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 is a schematic diagram of travel time distribution; (a) is a schematic diagram of travel time distribution under low traffic density conditions; (b) is a schematic diagram of travel time distribution under high traffic density conditions;

[0064] Figure 2 is a spatiotemporal distribution diagram of velocity under an embodiment;

[0065] Figure 3 is a spatiotemporal distribution diagram of vehicle trajectories according to an embodiment of the present invention;

[0066] Figure 4 3 are three types of vehicle trajectory reconstruction result diagrams, wherein (a) is the vehicle trajectory reconstruction result diagram of the following model; (b) is the vehicle trajectory reconstruction result diagram of the GRU model; (c) is the vehicle trajectory reconstruction result diagram of the method of the present invention taking into account physical constraints;

[0067] Figure 5 It is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0068] In order to better understand the technical content of the present invention, specific embodiments are given and described as follows in conjunction with the accompanying drawings.

[0069] Various aspects of the invention are described herein with reference to the accompanying drawings, in which many illustrative embodiments are shown. The embodiments of the invention are not limited to those described in the accompanying drawings. It should be understood that the invention is implemented by any of the various concepts and embodiments described above, as well as the concepts and embodiments described in detail below, because the concepts and embodiments disclosed in the invention are not limited to any implementation. In addition, some aspects disclosed in the invention may be used alone or in any appropriate combination with other aspects disclosed in the invention.

[0070] Figure 1 This is the travel time distribution diagram of the research section calculated in the present invention. (a) is a schematic diagram of the travel time distribution under low traffic density conditions; (b) is a schematic diagram of the travel time distribution under high traffic density conditions. It can be found from the figure that the travel time of vehicles passing through the target section under low traffic density and high traffic density conditions conforms to the normal distribution. The overtaking point calculated based on the time consumption curve can be used as a spatiotemporal physical constraint for vehicle trajectory reconstruction; Figure 2 The figure in the figure is an example of calculating the spatiotemporal distribution of the speed of the road. The spatiotemporal distribution of the speed between the two vehicles can be calculated by two floating vehicles, and the vehicle trajectory can be corrected by considering the speed fluctuation range. Through two physical constraints, the method proposed by the present invention can significantly reduce the error of trajectory reconstruction.

[0071] refer to Figure 5 , the present invention provides a vehicle trajectory reconstruction method considering physical constraints, comprising the following steps:

[0072] S1. Based on the observation records of the upstream fixed detector and the downstream virtual detector, a vehicle trajectory dataset is constructed, including the target vehicle number, as well as the target vehicle's location information, speed, acceleration, and time information;

[0073] S2, according to the sequence length and the prediction length, processing the trajectory data of each vehicle in the vehicle trajectory data set in step S1 into time series data, and dividing it into a training set, a test set and a validation set;

[0074] S3, introducing overtaking behavior as a physical constraint condition, estimating the overtaking point information of the vehicle through the time consumption curve, and obtaining the overtaking behavior constraint condition of the target vehicle;

[0075] S4. Introduce the speed space-time distribution diagram based on shock wave theory as physical information to characterize the running state of the traffic flow where the target vehicle is located, and obtain the speed space-time distribution constraint conditions of the target vehicle;

[0076] S5. Construct and train a fusion model based on the car-following model and the GRU model, specifically: input the original vehicle trajectory data into the car-following model and the GRU model, fuse the reconstruction results of the car-following model and the GRU model to obtain a reconstructed vehicle trajectory, and use the overtaking behavior constraint of the target vehicle and the speed spatiotemporal distribution constraint of the target vehicle to correct the reconstructed trajectory;

[0077] S6. Smoothing the corrected vehicle trajectory to eliminate the influence of abnormal speed and acceleration points, and obtaining the final reconstructed vehicle trajectory.

[0078] As a preferred embodiment of the present invention, step S1 constructs a vehicle trajectory data set, specifically: through the upstream detector, the license plate number of the vehicle passing through the study section is used as the vehicle ID, and the time when vehicle n passes the upstream detector position of section k is recorded as a k,n , the time to pass the end of the target section is a k+1,n , the observation set of vehicle n upstream of road segment k is {s(a k,n ),v( , a kn )}, , a, the observation set of vehicle n downstream of road segment k is {s(a k+1,n ),v(a k+1,n ),a k+1,n}, where s(a k,n ) is the longitudinal position of vehicle n passing the upstream detector of section k, v(a k,n ) is the speed of vehicle n passing the upstream detector of section k, s(a k+1,n ) is the longitudinal travel position of vehicle n passing the virtual detector downstream of section k, v(a k+1,n ) is the speed of vehicle n passing the virtual detector downstream of section k.

[0079] As a preferred embodiment of the present invention, step S2 includes the following sub-steps:

[0080] S2.1, the vehicle trajectory is divided by sliding window, and the length of the selected historical sequence is l h , the reconstruction length is l p , the time segments of the historical sequence Seq(i) and the reconstructed sequence P(i) of the i-th sample are as shown in formulas (1) and (2) respectively; the vehicle's position, speed, acceleration, lane and other information are all within this segment, that is, the time series data Tra:

[0081] Seq(i)∈[t start ,t start +l h ](51)

[0082] P(i)∈[tstart +l h +1,t start +l h +l p ] (52)

[0083] where t start is the start time of each sample;

[0084] S2.2. According to the stratified sampling principle, the time series data is divided into training set, validation set and test set in a ratio of 7:1:2, where Train_set, Val_set, Test_set represent the training set, validation set and test set respectively, and Tra is all the vehicle trajectory samples obtained in step S2.1:

[0085] Train_set = 0.7*Tra (53)

[0086] Val_set=0.1*Tra (54)

[0087] Test_set = 0.2*Tra (55)

[0088] As a preferred embodiment of the present invention, step S3 includes the following sub-steps:

[0089] S3.1. Calculate the travel time t of each vehicle passing through the target road section k based on the time when vehicle n passes through the upstream detector and the downstream virtual detector position. k,n , and then obtain the travel time observation set of n vehicles on the target road section in the data set: T k ={t k,1 ,t k,2 ,t k,3 ,t k,4 ,…t k,n-2 ,t k,n-1 ,t k,n}.

[0090] S3.2. By drawing a distribution diagram of the observed time and performing a Kolmogorov-Smirnov test, the expected travel time of the vehicle passing through the section k is obtained based on the fact that the travel time of the vehicle on the section k conforms to the normal distribution when the traffic flow is stable. As follows:

[0091] t k,n =a k+1,n -a k,n (56)

[0092]

[0093] Among them, t k,nis the travel time of vehicle n through road segment k, is the variance of the travel time of vehicle n through road segment k, a k,n is the time when vehicle n passes the upstream detector position of road segment k, a k+1,n is the time when vehicle n passes the end of the target section.

[0094] S3.3. Based on the calculated expected travel time Based on the uniform speed of vehicle n, the time it takes for vehicle n to pass the end of the study section k is: Then calculate the vehicle's position and time as shown in formula (9),

[0095]

[0096]

[0097] in, is the average speed of vehicle n passing through section k, l k is the length of section k, s′ k,n,t is the longitudinal distance travelled by vehicle n on road section k,

[0098] S3.4. Obtain the estimated overtaking point based on the trajectory position and time expressions of different vehicles The reconstructed vehicle trajectory is adjusted according to formulas (11)-(12):

[0099]

[0100] Where (t k ″ ,n ,s′ k ' ,n,t ) represents the actual overtaking point position, s k ″′ ,n,t is the position of the vehicle trajectory point after adjustment.

[0101] As a preferred embodiment of the present invention, step S4 includes the following sub-steps:

[0102] S4.1. Based on the linear assumption introduced by shock wave theory, the spatiotemporal distribution of speed in each lane is calculated:

[0103]

[0104] Among them, v fv represents the velocity at the intersection point A of the shock wave path and the preceding vehicle trajectory, v r ' efer represents the speed at any reference point between the front and rear vehicles, v nfvrepresents the velocity at the intersection point B of the rear vehicle trajectory and the shock wave path, l1, l2 represent the distances between the reference point and A, B respectively;

[0105] S4.2, adjust the reconstructed vehicle trajectory according to the spatiotemporal distribution of vehicle speed calculated in step S4.1: consider the influence of speed fluctuations,

[0106] The upper and lower limits of the speed threshold of the vehicle trajectory point are calculated by formula (14). If the lower and upper limits of the speed fluctuation are exceeded, the vehicle trajectory is adjusted, as shown in formula (15):

[0107]

[0108] v lower =v r ' efer -u*v r ' efer (66)

[0109] v upper =v r ' efer +u*v r ' efer (67)

[0110] where v lower ,v upper They represent the lower and upper limits of speed fluctuation respectively, and u is the speed fluctuation factor.

[0111] As a preferred embodiment of the present invention, step S4 includes the following sub-steps:

[0112] S5.1. Input the corrected vehicle trajectory data into the car-following model and output the result s IDM,i ;

[0113] S5.2. Input the corrected vehicle trajectory data into the GRU model for training. The GRU model can consider the long-term dependency problem. The GRU model includes two gate structures: reset gate and update gate. The core expression of the GRU model is as shown in formula (18) to formula (21).

[0114] r t =σ(W r ·[h t-1 ,x t ]+b r ) (68)

[0115] z t =σ(W z ·[h t-1 ,x t ]+b z ) (69)

[0116]

[0117] Among them, h t is the current hidden state, is a candidate hidden state, x t Represents the input data, W r is the weight matrix of the reset gate, W z is the weight matrix of the update gate, W h is the weight matrix of the candidate state, b r is the bias term for the reset gate, b z is the bias term of the update gate, b h is the bias term of the candidate state, z t is the update gate vector, σ is the sigmoid activation function, r t is the reset gate vector;

[0118] S5.3. Output result of the car-following model s IDM,i It is fused with the reconstruction result of the GRU model, and the average MAE loss of the GRU model is calculated to enhance the training process of the GRU model. The model fusion process is shown in expression (22):

[0119]

[0120] w IDM,i +w GRU,i =1 (74)

[0121] where s GRU,i Represents the trajectory points i, w reconstructed by the GRU model IDM,i ,w GRU,i They represent the weight coefficients of the car-following model and the GRU model respectively, characterizing the credibility of different models. The sum of the two is 1, and loss is the training MAE loss of the GRU model.

[0122] As a preferred embodiment of the present invention, step S6 includes the following sub-steps:

[0123] S6.1, input the vehicle trajectory data reconstructed by the hybrid model into the Savitzky-Golay filter, and filter out the noise in the velocity and acceleration based on the local polynomial least squares fitting in the time domain, keep the shape and width of the signal unchanged, and obtain different filtering results by selecting different window widths;

[0124] S6.2, using the speed and acceleration obtained in step S6.1, further adjust the reconstructed vehicle trajectory position as shown in formula (25) to obtain the final reconstructed vehicle trajectory, so that the reconstructed vehicle trajectory is more reasonable.

[0125]

[0126] in represents the position of the vehicle at time t after adjustment, v f,t ,v f,t-1 They represent the speed of the vehicle at time t or time t-1 after passing through the Savitzky-Golay filter.

[0127] The data collected in the embodiment of the present invention is collected on the highway section of US 101 (Hollywood Freeway) in Los Angeles, California. The direction of camera detection is from south to north. The section is about 640m long, the main road has 5 lanes, and the data sampling interval is 1Hz. In this study, based on real data, a genetic algorithm is used to calibrate the car-following model.

[0128] First, the trajectory data is processed and analyzed. The data is preprocessed, including the processing of missing values ​​and outliers. The segments with outliers are deleted, and the missing values ​​are filled by interpolation. The sampling interval in the original data is 1Hz. The present invention downsamples it to 10Hz to improve the efficiency of model operation. Based on the data processing, the vehicle trajectory map is drawn. The vehicle trajectory map is as follows: Figure 3 As shown, it can be found that there is a shock wave path in the vehicle trajectory, which also shows that it is reasonable for the present invention to use shock waves to calculate the spatiotemporal distribution of velocity.

[0129] Then the sliding window is used to process the time series data, and the data set is divided into training set, validation set and test set.

[0130] Based on the constructed data set and input parameters, the overtaking point distribution of each sample is calculated based on the time consumption curve and the speed time-space distribution is calculated based on the shock wave theory. Figure 1 It can be found that when the traffic operation state is stable, the travel time intuitively conforms to the normal distribution. Kolmogorov-Smirnov (KS) is used to perform a non-parametric test on the observed data to determine whether the population obeys the normal distribution. Since the p value is greater than 0.05, the travel time in this case also obeys the normal distribution empirically. This provides theoretical support for the subsequent calculation of overtaking points. Figure 2 In the present invention, two floating vehicles are used to calculate the spatiotemporal distribution of the speed between the two vehicles, and considering that the speed may fluctuate within a certain range, a speed fluctuation factor is introduced to adjust the speed of the reconstructed vehicle trajectory. The two physical constraints proposed by the present invention are helpful to reconstruct the vehicle trajectory with high precision.

[0131] The vehicle trajectory on the study section is reconstructed according to the hybrid algorithm of the trajectory reconstruction algorithm based on physical constraints of the present invention. The three evaluation indicators of MAE, MAPE, and RMSE are used to comprehensively evaluate the accuracy of vehicle trajectory reconstruction. In general, the smaller the three evaluation indicators, the higher the overall accuracy of the algorithm. The trajectory reconstruction results of the three algorithms based on the following model, the GRU model and the method of the present invention (hybrid method based on physical constraints) at a penetration rate of 5%-15% of autonomous driving vehicles are shown in Table 1, a comparison table of trajectory reconstruction results of the present invention and the traditional method.

[0132] Table 1

[0133]

[0134] As can be seen from Table 1, the vehicle trajectory reconstructed by the method of the present invention has a smaller error. At a penetration rate of 5%, the MAE index is improved by 37.01% and 40.59% compared with the GRU and the car-following model, respectively. This shows that even at a low penetration rate, the proposed model considering physical constraints still has a good performance, which plays an important role in the reconstruction of the trajectory of connected vehicles at low penetration rates in the future.

[0135] Furthermore, Figure 4 Figures (a), (b), and (c) in the figure show the comparison of the trajectories reconstructed by the three algorithms. The reconstructed vehicle trajectory points under the method of the present invention are closer to the actual situation. There are large deviations to varying degrees for both the car-following model and the GRU model, and there are local aggregations and sudden changes in vehicle trajectories, which are inconsistent with actual driving behavior. These results further demonstrate the superiority of the algorithm proposed in the present invention and confirm the necessity of considering physical constraints in trajectory estimation.

[0136] Finally, the present invention explores the relationship between sequence length and reconstruction length and finds that when the sequence length is close to the reconstruction length, the reconstructed vehicle trajectory has higher accuracy. The corresponding error is shown in Table 2, which tests the relationship between reconstruction length and sequence length.

[0137] Table 2

[0138]

[0139]

[0140] Although the present invention has been described above with preferred embodiments, it is not intended to limit the present invention. A person skilled in the art of the present invention may make various modifications and improvements without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be determined by the definition of the claims.

Claims

1. A vehicle trajectory reconstruction method considering physical constraints, characterized in that: The steps include: S1. Based on the observation records of the upstream fixed detector and the downstream virtual detector, a vehicle trajectory dataset is constructed, including the target vehicle number, as well as the target vehicle's location information, speed, acceleration, and time information; S2, according to the sequence length and the prediction length, processing the trajectory data of each vehicle in the vehicle trajectory data set in step S1 into time series data, and dividing it into a training set, a test set and a validation set; S3, introducing overtaking behavior as a physical constraint condition, estimating the overtaking point information of the vehicle through the time consumption curve, and obtaining the overtaking behavior constraint condition of the target vehicle; S4. Introduce the speed space-time distribution diagram based on shock wave theory as physical information to characterize the running state of the traffic flow where the target vehicle is located, and obtain the speed space-time distribution constraint conditions of the target vehicle; S5. Construct and train a fusion model based on the car-following model and the GRU model, specifically: input the original vehicle trajectory data into the car-following model and the GRU model, fuse the reconstruction results of the car-following model and the GRU model to obtain a reconstructed vehicle trajectory, and use the overtaking behavior constraint of the target vehicle and the speed spatiotemporal distribution constraint of the target vehicle to correct the reconstructed trajectory; S6. Smoothing the corrected vehicle trajectory to eliminate the influence of abnormal speed and acceleration points, and obtaining the final reconstructed vehicle trajectory.

2. A vehicle trajectory reconstruction method considering physical constraints according to claim 1, characterized in that: Step S1 constructs a vehicle trajectory dataset, specifically: through the upstream detector, the license plate number of the vehicle passing through the target section is used as the vehicle ID, and the time when vehicle n passes the upstream detector position of section k is recorded as a k,n , the time to pass the end of the target section is a k+1,n , the observation set of vehicle n upstream of road segment k is {s(a k,n ),v(a k,n ),a k,n }, the observation set of vehicle n downstream of road segment k is {s(a k+1,n ),v(a k+1,n ),a k+1,n }, where s(a k,n ) is the longitudinal position of vehicle n passing the upstream detector of section k, v(a k,n ) is the speed of vehicle n passing the upstream detector of section k, s(a k+1,n ) is the longitudinal travel position of vehicle n passing the virtual detector downstream of section k, v(a k+1,n ) is the speed of vehicle n passing the virtual detector downstream of section k.

3. The vehicle trajectory reconstruction method considering physical constraints according to claim 1 is characterized in that: Step S2 includes the following sub-steps: S2.1, the vehicle trajectory is divided by sliding window, and the length of the selected historical sequence is l h , the reconstruction length is l p , the time segments of the historical sequence Seq(i) and the reconstructed sequence P(i) of the i-th sample are as shown in formulas (1) and (2) respectively; the vehicle's position, speed, acceleration, lane and other information are all within this segment, that is, the time series data Tra: Seq(i)∈[t start ,t start +l h ](1) P(i)∈[t start +l h +1,t start +l h +l p ](2) where t start is the start time of each sample; S2.

2. According to the stratified sampling principle, the time series data is divided into training set, validation set and test set according to the preset ratio, where Train_set, Val_set, Test_set represent the training set, validation set and test set respectively, and Tra is all the vehicle trajectory samples obtained in step S2.1: Train_set=m1*Tra (3) Val_set=m2*Tra (4) Test_set = m3*Tra (5) m1, m2, m3 are preset scaling factors.

4. The vehicle trajectory reconstruction method considering physical constraints according to claim 2 is characterized in that: Step S3 includes the following sub-steps: S3.

1. Calculate the travel time t of each vehicle passing through the target road section k based on the time when vehicle n passes through the upstream detector and the downstream virtual detector position. k,n , and then obtain the travel time observation set of n vehicles on the target road section in the data set: T k ={t k,1 ,t k,2 ,t k,3 ,t k,4 ,…t k,n-2 ,t k,n-1 ,t k,n }; S3.

2. By drawing a distribution diagram of the observed time and performing a Kolmogorov-Smirnov test, the expected travel time of the vehicle passing through the section k is obtained based on the fact that the travel time of the vehicle on the section k conforms to the normal distribution when the traffic flow is stable. As follows: t k,n =a k+1,n -a k,n (6) Among them, t k,n is the travel time of vehicle n through road segment k, is the variance of the travel time of vehicle n through road segment k, a k,n is the time when vehicle n passes the upstream detector position of road segment k, a k+1,n is the time when vehicle n passes the end of the target section; S3.

3. Based on the calculated expected travel time Based on the uniform speed of vehicle n, the time it takes for vehicle n to pass the end of the study section k is: Then calculate the vehicle's position and time as shown in formula (9), in, is the average speed of vehicle n passing through section k, l k is the length of section k, s′ k,n,t is the longitudinal distance travelled by vehicle n on road section k, S3.

4. Obtain the estimated overtaking point based on the trajectory position and time expressions of different vehicles The reconstructed vehicle trajectory is adjusted according to formulas (11)-(12): Where (t k ″ ,n ,s′ k ' ,n,t ) represents the actual overtaking point position, s k ″′ ,n,t is the position of the vehicle trajectory point after adjustment.

5. The vehicle trajectory reconstruction method considering physical constraints according to claim 2, characterized in that: Step S4 includes the following sub-steps: S4.

1. Based on the linear assumption introduced by shock wave theory, the spatiotemporal distribution of speed in each lane is calculated: Among them, v fv represents the velocity at the intersection point A of the shock wave path and the preceding vehicle trajectory, v r ' efer represents the speed at any reference point between the front and rear vehicles, v nfv represents the velocity at the intersection point B of the rear vehicle trajectory and the shock wave path, l1, l2 represent the distances between the reference point and A, B respectively; S4.2, adjust the reconstructed vehicle trajectory according to the spatiotemporal distribution of vehicle speed calculated in step S4.1: Considering the influence of speed fluctuation, the upper and lower limits of the speed threshold of the vehicle trajectory point are calculated by formula (14). If the lower and upper limits of the speed fluctuation are exceeded, the vehicle trajectory is adjusted, as shown in formula (15) v lower =v r ′ efer -u*v r ′ efer (16) v upper =v r ′ efer +u*v r ′ efer (17) where v lower ,v upper They represent the lower and upper limits of speed fluctuation respectively, and u is the speed fluctuation factor.

6. The vehicle trajectory reconstruction method considering physical constraints according to claim 2, characterized in that: Step S5 includes the following sub-steps: S5.

1. Input the corrected vehicle trajectory data into the car-following model and output the result s IDM,i ; S5.

2. Input the corrected vehicle trajectory data into the GRU model for training. The GRU model includes two gate structures: reset gate and update gate. The core expression of the GRU model is as shown in formula (18) to formula (21). r t =σ(W r ·[h t-1 ,x t ]+b r ) (18) z t =σ(W z ·[h t-1 ,x t ]+b z ) (19) Among them, h t is the current hidden state, is the candidate hidden state, x t Represents the input data, W r is the weight matrix of the reset gate, W z is the weight matrix of the update gate, W h is the weight matrix of the candidate state, b r is the bias term for the reset gate, b z is the bias term of the update gate, b h is the bias term of the candidate state, z t is the update gate vector, σ is the sigmoid activation function, r t is the reset gate vector; S5.

3. Output result of the car-following model s IDM,i It is fused with the reconstruction result of the GRU model, and the average MAE loss of the GRU model is calculated to enhance the training process of the GRU model. The model fusion process is shown in expression (22): In IDM,i +in GRU,i =1 (24) where s GRU,i Represents the trajectory points i, w reconstructed by the GRU model IDM,i ,w GRU,i They represent the weight coefficients of the car-following model and the GRU model respectively, characterizing the credibility of different models. The sum of the two is 1, and loss is the training MAE loss of the GRU model.

7. The vehicle trajectory reconstruction method considering physical constraints according to claim 6, characterized in that: Step S6 includes the following sub-steps: S6.1, input the vehicle trajectory data reconstructed by the hybrid model into the Savitzky-Golay filter, and filter out the noise in the velocity and acceleration based on the local polynomial least squares fitting in the time domain, keep the shape and width of the signal unchanged, and obtain different filtering results by selecting different window widths; S6.2, using the speed and acceleration obtained in step S6.1, further adjust the reconstructed vehicle trajectory position as shown in formula (25) to obtain the final reconstructed vehicle trajectory, so that the reconstructed vehicle trajectory is more reasonable. in represents the position of the vehicle at time t after adjustment, v f,t ,v f,t-1 They represent the speed of the vehicle at time t or time t-1 after passing through the Savitzky-Golay filter.

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