Full space-time vehicle trajectory reconstruction method based on multi-source sparse detector data

Abstract

The invention relates to a full space-time vehicle trajectory reconstruction method based on multi-source sparse detector data, and belongs to the technical field of trajectory reconstruction. The method comprises the following steps: unifying formats of upstream and downstream fixed-point detector data and sparse mobile detector data to form a multi-source sparse detector data environment, and regarding a time and space range enclosed by a multi-source detector as a vehicle trajectory reconstruction area; based on multi-source sparse detector data, an initial full-space-time vehicle track is obtained through reconstruction of an intelligent driver model; and converting the full space-time vehicle trajectory data into a matrix data structure, and improving the reconstruction precision of the vehicle trajectory by using an iterative matrix singular value decomposition algorithm to obtain an optimal full space-time vehicle trajectory. Compared with an existing trajectory reconstruction technology, the method is excellent in performance and wide in application range in a multi-source sparse detector data environment.

Description

Technical Field

[0001] The present invention relates to a full-time and full-space vehicle trajectory reconstruction method based on multi-source sparse detector data, and belongs to the technical field of trajectory reconstruction. Background Art

[0002] Full-time and full-space vehicle trajectories are the basis for accurately depicting the overall situation and details of traffic flow operation. With the development of intelligent network connection technology and the construction of intelligent highways, fixed-point detectors such as radars and videos, and mobile detectors such as connected vehicles and probe vehicles have been widely used, forming a new situation of multi-source acquisition of vehicle trajectories. However, on highways or expressways, due to the high cost and limited resources of various fixed-point detectors, the layout rate of fixed-point detectors is relatively low (the distance between two fixed-point detectors is usually greater than 500 meters); mobile detectors represented by probe vehicles, connected vehicles, and intelligent driving vehicles can provide their own complete trajectory data in real time, but these mobile detectors are randomly distributed on the road network and have a low penetration rate (the penetration rate of mobile detectors is generally between 5% and 15%). The data provided by both fixed-point detectors and mobile detectors are traffic data in a single situation, and these data can only contain limited traffic information. Therefore, considering the existing types of traffic detectors, a multi-source detector data environment can be formed by fusing fixed-point detector data and mobile detector data to perform vehicle trajectory reconstruction. However, the data structures, time intervals, and acquisition accuracies of the data collected by different detectors are all different. Fusing fixed-point and mobile detector data requires comprehensive analysis of the two heterogeneous data to make the data conditions meet the basic requirements of the present invention. Fusing multi-source detector data for vehicle trajectory reconstruction can improve the accuracy and robustness of vehicle trajectory reconstruction results. Due to the low coverage rate of fixed-point detectors and the low penetration rate of mobile detectors in the real road environment, it is still challenging to directly obtain full-time and full-space vehicle trajectories using multi-source sparse detectors. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a full-time and full-space vehicle trajectory reconstruction method based on multi-source sparse detector data, aiming to solve the technical problems that the data of a single detector have limitations, and the data structures, time intervals, and acquisition accuracies of the data collected by different detectors are all different, making it difficult to ensure the accuracy and robustness of vehicle trajectory reconstruction results.

[0004] To solve the above technical problems, the technical solution of the present invention is: a full-time and full-space vehicle trajectory reconstruction method based on multi-source sparse detector data, and the specific steps are as follows:

[0005] Step S1: Unify the data formats of upstream and downstream fixed-point detector data and sparse mobile detector data to form a multi-source sparse detector data environment, and regard the time and space ranges surrounded by the multi-source sparse detectors as the vehicle trajectory reconstruction area;

[0006] Step S2: Within the vehicle trajectory reconstruction area, based on the multi-source sparse detector data, use the intelligent driver model to reconstruct the initial full-space-time vehicle trajectory;

[0007] Step S3: Construct a matrix data structure, convert the full-space-time vehicle trajectory data into a matrix data structure, and obtain the optimal full-space-time vehicle trajectory based on the iterative matrix singular value decomposition algorithm.

[0008] The unification of the data formats of the upstream and downstream fixed-point detectors and the sparse mobile detector in Step S1 is specifically as follows:

[0009] Convert the time unit and position unit in the fixed-point detector and mobile detector data to seconds and meters respectively, specifically as follows:

[0010]

[0011]

[0012] Where t is the converted time, in seconds; time is the original detector data; is the conversion coefficient; X is the converted position, in meters; is the original position of the detector, and b is the conversion coefficient.

[0013] The vehicle trajectory reconstruction area in Step S1 is specifically as follows:

[0014] During the trajectory reconstruction process, use the mobile detector and fixed-point detector to divide the full-space-time vehicle trajectory into multiple reconstruction areas. Regard the connected vehicle as a mobile detector. The time range is composed of the time when the previous connected vehicle passes the upstream fixed-point detector and the time when the non-connected vehicle before the next connected vehicle passes the downstream fixed-point detector, and the space range is composed of the distances between the upstream and downstream fixed-point detectors, thereby forming multiple separate vehicle trajectory reconstruction areas. Among them, the vehicle trajectory includes vehicle ID, timestamp, speed, and position.

[0015] Step S2 specifically includes:

[0016] Step S21: Assign values to the relevant parameters in the intelligent driver model for generating the initial full-space-time vehicle trajectory after multi-source data input. Among them, the intelligent driver model is derived from the car-following model;

[0017] Step S22: Input the multi-source sparse detector data with unified format into the intelligent driver model to obtain the initial full-space-time vehicle trajectory.

[0018] The intelligent driver model is specifically expressed as:

[0019]

[0020] Among them, is the distance interval between the following vehicle and the leading vehicle at time . is the position of the leading vehicle at time . is the position of the following vehicle at time . is the fixed minimum safety distance;

[0021]

[0022] is the relative speed between the following vehicle and the leading vehicle at time . is the speed of the leading vehicle at time . is the speed of the following vehicle at time .

[0023]

[0024] is the desired distance, is the maximum acceleration, is the comfortable deceleration, is the safety time interval, is the speed of the non-connected vehicle passing the fixed-point detector;

[0025]

[0026] is the acceleration of the non-connected vehicle at time . is the desired speed;

[0027]

[0028] is the speed of the non-connected vehicle at the next moment . is the reconstructed time step;

[0029]

[0030] is the position of the non-connected vehicle at the next moment . is the position of the non-connected vehicle passing the fixed-point detector.

[0031] Step S3 specifically includes:

[0032] Step S31: Construct a matrix data structure, store the initial full - time - space vehicle trajectory in the matrix, and obtain the initial full - time - space trajectory matrix;

[0033] Step S32: Apply the iterative singular value decomposition algorithm to the initial time - space trajectory matrix to obtain the optimal full - time - space vehicle trajectory.

[0034] Specifically, step S31 is:

[0035] The first row of the matrix data structure is the trajectory data of the connected vehicle, the second row is the trajectory data of the first non - connected vehicle, and so on until the last non - connected vehicle. Specifically:

[0036]

[0037] Where: is the trajectory vector of the th vehicle within the entire time range, is the data when the vehicle passes through the upstream fixed - point detector, is the data when the vehicle passes through the downstream fixed - point detector, is the unknown data before the vehicle reaches the upstream fixed - point detector, is the unknown data after the vehicle leaves the downstream fixed - point detector, is the unknown data within the reconstruction area;

[0038]

[0039] Among them, is the initial full - time - space trajectory matrix reconstructed by the intelligent driver model within the reconstruction area; and are the known trajectory data of the connected vehicle respectively; is the unknown data before the th non - connected vehicle reaches the upstream fixed - point detector, is the unknown data after the th non - connected vehicle leaves the downstream fixed - point detector, is the data when the th non - connected vehicle passes through the upstream fixed - point detector; is the data when the th non - connected vehicle passes through the downstream fixed - point detector; is the initial trajectory data reconstructed by the intelligent driver model of the th non - connected vehicle; is the unknown data before the th non - connected vehicle reaches the upstream fixed - point detector, is the unknown data after the th non-connected vehicle drives away from the downstream fixed-point detector, is the data when the th non-connected vehicle passes through the upstream fixed-point detector; is the data when the th non-connected vehicle passes through the downstream fixed-point detector; is the initial trajectory data reconstructed by the intelligent driver model for the th non-connected vehicle; is the unknown data before the last th non-connected vehicle arrives at the upstream fixed-point detector, is the unknown data after the last th non-connected vehicle drives away from the downstream fixed-point detector, is the data when the last th non-connected vehicle passes through the upstream fixed-point detector; is the data when the last th non-connected vehicle passes through the downstream fixed-point detector, is the data when the last th non-connected vehicle is reconstructed by the intelligent driver model to obtain the initial trajectory data.

[0040] The specific iterative singular value decomposition algorithm is as follows:

[0041]

[0042] Among them, is the initial full-space-time trajectory matrix reconstructed by the intelligent driver model in the reconstruction area, is a matrix of size , The column vector of is the eigenvector of and is the left singular value vector of the matrix is a matrix of size , The column vector of is the eigenvector of and is the right singular value vector of the matrix is a matrix of size , located on the diagonal of the matrix The elements are called singular values, and the superscript represents the transpose.

[0043] The specific step S32 is as follows:

[0044] Step S321: In the matrix singular value decomposition algorithm, the initial full-space-time trajectory matrix is denoted as , assign to the decomposition matrix , and perform singular value decomposition on the decomposition matrix , select the first largest singular values and the corresponding eigenvectors to obtain ;

[0045] Step S322: Use to update the elements at the missing positions of the non-connected vehicles between the upstream and downstream fixed-point detectors in the initial full spatio-temporal trajectory matrix , so as to obtain a new initial full spatio-temporal trajectory matrix . If the vehicle trajectory reconstruction result does not converge, continue to iteratively execute Step S321; if the vehicle trajectory reconstruction result converges, output the optimal full spatio-temporal trajectory matrix to obtain the optimal full spatio-temporal vehicle trajectory matrix.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] (1) Analyze the characteristics of the data provided by the upstream and downstream fixed-point detectors and the mobile detectors, comprehensively consider the vehicle data detected by different detectors at different times, also consider the temporal correlation of vehicle trajectories, then align the timestamps of different vehicle trajectories, and construct a spatio-temporal trajectory data structure suitable for trajectory reconstruction based on multi-source detector data, thus expanding the applicability;

[0048] (2) According to the constructed spatio-temporal trajectory data structure, fill the data provided by the low-penetration fixed-point detectors and mobile detectors into the data structure to obtain an extremely sparse trajectory matrix data structure. Then use the intelligent driver model to reconstruct the trajectories of non-connected vehicles, thereby complementing the sparse matrix to obtain an initial complete matrix, so as to enhance the robustness of vehicle trajectory reconstruction based on multi-source detector data in a low-penetration environment;

[0049] (3) Aiming at the deficiencies in the consideration of vehicle micro-motion characteristics in the current research on full spatio-temporal vehicle trajectory reconstruction and the application limitations of traditional car-following models, the present invention uses the traffic data provided by fixed-point detectors and mobile detectors as constraints, uses the matrix decomposition algorithm for the initial complete matrix, and continuously iteratively calculates to reconstruct the optimal vehicle trajectory in the full spatio-temporal domain;

[0050] (4) Both fixed-point detectors and mobile detectors can report detection data in real time. The present invention can be used in both offline and online environments, thus expanding its applications in vehicle trajectory reconstruction. Description of the Drawings

[0051] Figure 1 is the flowchart of the steps of the present invention;

[0052] Figure 2 For a sparse multi-source detector and a reconstructed target graph in a multi-source detector environment;

[0053] Figure 3 For reconstructed area division, matrix data structure, and flowchart;

[0054] Figure 4 For the real road environment and schematic diagram in the embodiment;

[0055] Figure 5 For the optimal full-time and full-space reconstruction result graph under 10% connected vehicle penetration rate in the embodiment. Specific implementation manner

[0056] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and provides a detailed implementation manner and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0057] The purpose of the present invention is to propose a method for reconstructing the full-time and full-space vehicle trajectory by using the data of fixed-point detectors with low coverage rate and the data of mobile detectors with low penetration rate on highways. The connected vehicles are regarded as mobile detectors, and the reported data includes: vehicle ID, timestamp, location, instantaneous speed, etc., so that the vehicle trajectory data of the connected vehicles can be obtained in real time; the fixed-point detectors on the road can record the timestamp, speed, vehicle ID, vehicle license plate, etc. when all vehicles pass through the fixed-point detectors. First, the data detected by different detectors form a multi-source sparse detector data environment, then, the traffic flow theory and data-driven are combined, and finally, the multi-source sparse detector data is input into the established model - data-driven algorithm, so as to reconstruct the full-time and full-space vehicle trajectory. The present invention designs a complete process from multi-source sparse detector data to establishing an intelligent driver model to obtain the initial full-time and full-space vehicle trajectory, and then to reconstructing the optimal full-time and full-space vehicle trajectory by using the iterative matrix singular value decomposition algorithm.

[0058] Embodiment 1: As Figure 1 shown, a method for reconstructing the full-time and full-space vehicle trajectory based on multi-source sparse detector data is specifically as follows:

[0059] Step S1: Unify the data formats of the upstream and downstream fixed-point detector data and the sparse mobile detector data to form a multi-source sparse detector data environment, and regard the time and space range enclosed by the multi-source sparse detectors as the vehicle trajectory reconstruction area;

[0060] Specifically, since the data formats of the fixed-point detectors and the mobile detectors are not unified, it is necessary to unify the heterogeneous data formats of the multi-source detectors. The time unit in the fixed-point detector and the sparse mobile detector data is set to seconds (s), and the unit of position is set to meters (m), as shown in Equations (1) and (2):

[0061] (1)

[0062] (2)

[0063] where t is the converted time in seconds; time is the original data of the detector; is the conversion coefficient; X is the converted position in m; is the original position of the detector, and b is the conversion coefficient.

[0064] During the trajectory reconstruction process, the full-time and full-space vehicle trajectories are divided into multiple reconstruction regions by using the mobile detectors and the fixed-point detectors. The connected vehicles are regarded as mobile detectors. The time range is composed of the time when the previous connected vehicle passes through the upstream fixed-point detector and the time when the non-connected vehicle before the next connected vehicle passes through the downstream fixed-point detector, and the space range is composed of the distances between the upstream and downstream fixed-point detectors, thus forming multiple separate vehicle trajectory reconstruction regions, denoted as reconstruction region n. Among them, the vehicle trajectory includes vehicle ID, timestamp, speed, and position. The original data of the connected vehicle contains vehicle ID, timestamp, and position, that is, ( , , ), ( , , ), …, ( , , ), is the connected vehicle ID in reconstruction region n, and are the timestamp and position of the connected vehicle at the L-th trajectory point respectively; the original data when the non-connected vehicle passes through the upstream fixed-point detector contains vehicle ID, timestamp, and position, that is, ( , , ), ( , , ), …, ( , , ), is the ID of the i-th non-connected vehicle passing through the upstream fixed-point detector, is the time when the i-th non-connected vehicle passes through the upstream fixed-point detector, is the position of the upstream fixed-point detector; the original data when a non-connected vehicle passes the downstream fixed-point detector includes the vehicle ID, timestamp, and position, i.e., ( , , ), ( , , ), …, ( , , ), is the ID of the i-th non-connected vehicle passing the downstream fixed-point detector, is the time when the i-th non-connected vehicle passes the downstream fixed-point detector, is the position of the downstream fixed-point detector. Plot the trajectory points of all vehicles on the same spatio-temporal graph, as shown in Figure 2 .

[0065] Step S2: In the vehicle trajectory reconstruction area, based on multi-source sparse detector data, use the intelligent driver model to reconstruct the initial full spatio-temporal vehicle trajectory;

[0066] Step S21: Assign values to the relevant parameters in the intelligent driver model for generating the initial full spatio-temporal vehicle trajectory after multi-source data input, where the intelligent driver model is derived from the car-following model;

[0067] Step S22: Input the multi-source sparse detector data with unified format into the intelligent driver model to obtain the initial full spatio-temporal vehicle trajectory.

[0068] Specifically, for each reconstruction area, use the intelligent driver model in the car-following model to reconstruct the missing trajectory of non-connected vehicles between the upstream and downstream fixed-point detectors. The intelligent driver model can calculate the distance and relative speed between the following vehicle n and the preceding vehicle n-1 at time t to obtain the expected distance between the two vehicles, and then obtain the acceleration of the non-connected vehicle at time t. Finally, use the position and speed of the non-connected vehicle passing the fixed-point detector to obtain its speed and position at the next moment . As shown in Eqs. (3)~(8):

[0069] (3)

[0070] (4)

[0071] (5)

[0072] (6)

[0073] (7)

[0074] (8)

[0075] In Equation (3), is the distance interval between the following vehicle and the leading vehicle at time . is the position of the leading vehicle at time . is the position of the following vehicle at time . is the fixed minimum safety distance; In Equation (4), is the relative speed between the following vehicle and the leading vehicle at time . is the speed of the leading vehicle at time . is the speed of the following vehicle at time ; In Equation (5), is the desired distance, is the maximum acceleration, is the comfortable deceleration, is the safety time interval, is the speed of the non-connected vehicle passing the fixed-point detector; In Equation (6), is the acceleration of the non-connected vehicle at time . is the desired speed; In Equation (7), is the speed of the non-connected vehicle at the next moment . is the reconstructed time step; In Equation (8), is the position of the non-connected vehicle at the next moment . is the position of the non-connected vehicle passing the fixed-point detector.

[0076] In this embodiment, ; , , , , .

[0077] Specifically, the obtained multi-source sparse detector data is input into the established intelligent driver model to obtain the initial full-space and full-time vehicle trajectory within the reconstruction area, as Figure 3 shown.

[0078] Step S3: Construct a matrix data structure, convert the full-space and full-time vehicle trajectory data into a matrix data structure, and obtain the optimal full-space and full-time vehicle trajectory based on the iterative matrix singular value decomposition algorithm;

[0079] Specifically, the iterative matrix singular value decomposition algorithm is used to further improve the reconstruction accuracy of the vehicle trajectory to obtain the optimal full-space and full-time vehicle trajectory, which specifically includes:

[0080] Step S31: Construct a matrix data structure, store the initial full-space and full-time vehicle trajectory in the matrix to obtain the initial full-space and full-time trajectory matrix;

[0081] Step S32: Apply the iterative singular value decomposition algorithm to the initial space-time trajectory matrix to obtain the optimal full-space and full-time vehicle trajectory.

[0082] Specifically, through the analysis of the vehicle trajectory, a space-time matrix data structure is constructed, and then the reconstructed initial full-space and full-time vehicle trajectory is stored in this space-time matrix, as shown in Equations (9) and (10):

[0083] (9)

[0084] Where: is the trajectory vector of the th vehicle within the entire time range, is the data when the vehicle passes through the upstream fixed-point detector, is the data when the vehicle passes through the downstream fixed-point detector, is the unknown data before the vehicle reaches the upstream fixed-point detector, is the unknown data after the vehicle leaves the downstream fixed-point detector, is the unknown data within the reconstruction area;

[0085] (10)

[0086] Where, is the initial full-space and full-time trajectory matrix reconstructed by the intelligent driver model within the reconstruction area; and are the known connected vehicle trajectory data respectively; is the unknown data before the th non-connected vehicle reaches the upstream fixed-point detector, is the unknown data after the th non-connected vehicle leaves the downstream fixed-point detector, is the Data of the \(n\)th non-connected vehicle passing through the upstream fixed-point detector; is the Data of the \(n\)th non-connected vehicle passing through the downstream fixed-point detector; is the Initial trajectory data of the \(n\)th non-connected vehicle reconstructed by the intelligent driver model; is the Unknown data of the \(n\)th non-connected vehicle before reaching the upstream fixed-point detector, is the Unknown data of the \(n\)th non-connected vehicle after leaving the downstream fixed-point detector, is the Data of the \(m\)th non-connected vehicle passing through the upstream fixed-point detector; is the Data of the \(m\)th non-connected vehicle passing through the downstream fixed-point detector; is the Initial trajectory data of the \(m\)th non-connected vehicle reconstructed by the intelligent driver model; is the last Unknown data of the last non-connected vehicle before reaching the upstream fixed-point detector, is the last Unknown data of the last non-connected vehicle after leaving the downstream fixed-point detector, is the last Data of the last non-connected vehicle passing through the upstream fixed-point detector; is the last Data of the last non-connected vehicle passing through the downstream fixed-point detector, is the last Initial trajectory data of the last non-connected vehicle reconstructed by the intelligent driver model.

[0087] Specifically, within the reconstruction region, the initial full-time and space vehicle trajectory reconstructed based on the intelligent driver model is input into the sparse vehicle trajectory matrix data structure to obtain the initial full-time and space vehicle trajectory matrix, where the amount of data in the sparse matrix is significantly increased. Among various matrix decomposition methods, singular value decomposition has a wide range of applications and relatively reliable decomposition results. Therefore, the present invention selects the matrix singular value decomposition algorithm to reconstruct the unknown part of the vehicle trajectory. Then, by using the strong ability of the iterative matrix singular value decomposition algorithm to capture the correlation between the rows and columns of the matrix data, the iterative singular value decomposition algorithm is applied to the initial full-time and space vehicle trajectory matrix to improve the accuracy of the reconstructed trajectory. Among them, matrix singular value decomposition is to decompose a matrix of size into three matrices, and then multiply the three matrices to obtain a complete matrix again, achieving the purpose of reproducing the known and unknown values in the matrix, as shown in Equation (11).

[0088] ​ (11)

[0089] Among them, is the initial full - space - time trajectory matrix reconstructed by the intelligent driver model within the reconstruction area, is a matrix of size , The column vector of is 's eigenvector and is the left singular value vector of matrix ; is a matrix of size , The column vector of is 's eigenvector and is the right singular value vector of matrix ; is a matrix of size , and the elements on the diagonal of matrix are called singular values, and the superscript represents the transpose.

[0090] Specifically, in order to improve the accuracy of the method, enhance the accuracy of the reconstructed trajectory and the robustness of the model, an iterative matrix singular value decomposition algorithm is used to further enhance the effect of full - space - time vehicle trajectory reconstruction, so as to complete the full - space - time non - connected vehicle trajectory reconstruction within the reconstruction area and obtain the optimal full - space - time vehicle trajectory. The following operations are performed on the initial matrix filled:

[0091] Step S321: In the matrix singular value decomposition algorithm, denote the initial full - space - time trajectory matrix as , assign to the decomposition matrix , and perform singular value decomposition on the decomposition matrix , select the first largest singular values and the corresponding eigenvectors to obtain ;

[0092] Step S322: Use to update the elements of the missing positions of non - connected vehicles between the upstream and downstream fixed - point detectors in the initial full - space - time trajectory matrix , so as to obtain a new initial full - space - time trajectory matrix . If the vehicle trajectory reconstruction result does not converge, continue to iteratively execute Step S321; if the vehicle trajectory reconstruction result converges, output the optimal full - space - time trajectory matrix to obtain the optimal full - space - time vehicle trajectory matrix

[0093] The elements of the new matrix obtained by using the matrix singular value decomposition algorithm are different from those of the original matrix at the missing points of the non-connected vehicle trajectories. As the iteration progresses, the vehicle trajectory reconstruction result will eventually converge, and then the optimal complete matrix will be output. , so as to obtain the full-time and full-space vehicle trajectories of non-connected vehicles in the reconstruction area.

[0094] The above embodiments are the detailed steps for reconstructing the full-time and full-space vehicle trajectories by using the multi-source sparse detector data. The steps are applicable to any direction of the highway. Therefore, the full-time and full-space vehicle trajectories of the highway can be obtained through reconstruction.

[0095] Taking the vehicles in the leftmost lane of the highway in the NGSIM dataset as the experimental objects, 10% of the vehicles are randomly selected as virtual connected vehicles, that is, the penetration rate of the mobile detector is 10%. And a suitable spacing is selected as the trajectory missing section, and two virtual fixed-point detectors are set at the head and tail of the trajectory missing section as the upstream and downstream fixed-point detectors. Using the connected vehicle trajectory data and the data of non-connected vehicles passing through the upstream and downstream fixed-point detectors as the input, the full-time and full-space vehicle trajectories are reconstructed.

[0096] The real environment and schematic diagram of the highway section in the embodiment are as Figure 4 shown.

[0097] First, the time unit in the dataset is converted from milliseconds to seconds, and the position is converted from feet to meters. Part of the original data in the NGSIM dataset is shown in Table 1:

[0098] Table 1 Part of the original trajectory data in the NGSIM dataset

[0099] Vehicle ID Time (ms) Location (feet) 1 1113433136100.00 48.21 1 1113433136200.00 49.46 1 1113433136300.00 50.71 1 1113433136400.00 51.96 1 1113433136500.00 53.21 1 1113433136600.00 54.46 1 1113433136700.00 55.71 1 1113433136800.00 56.96 1 1113433136900.00 58.20 1 1113433137000.00 59.46 1 1113433137100.00 60.78 1 1113433137200.00 62.16 1 1113433137300.00 63.59 1 1113433137400.00 65.05 1 1113433137500.00 66.53 1 1113433137600.00 67.99 1 1113433137700.00 69.46 1 1113433137800.00 70.91 1 1113433137900.00 72.37 1 1113433138000.00 73.81 1 1113433138100.00 75.21 1 1113433138200.00 76.56

[0100] The conversion formulas for time and position units are formulas (12) and (13) respectively, that is

[0101] (12)

[0102] (13)

[0103] Secondly, the selected upstream fixed-point detector is located at 50 m, that is = 50 m, and the selected downstream fixed-point detector is located at 300 m, that is = 300 m. After unifying the data format, the time range is composed of the time when the previous connected vehicle passes through the upstream fixed-point detector and the time when the non-connected vehicle before the next connected vehicle passes through the downstream fixed-point detector, and the space range is composed of the distances between the upstream and downstream fixed-point detectors, forming the reconstruction area of the present invention. Part of the original trajectory data in the NGSIM dataset is plotted into a spatio-temporal diagram.

[0104] Next, select the intelligent driver model in the car-following model as the model of the present invention, and assign values to various parameters in the intelligent driver model. In this embodiment, the parameter values are , , , , , ; Select the first largest singular values and their corresponding eigenvectors in the iterative singular value decomposition algorithm.

[0105] Finally, the optimal full-time and full-space vehicle trajectory reconstruction result in the reconstruction area is obtained according to the steps of the present invention as shown in Figure 5 . Since the trajectory data is microscopic data, the mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE) are used to quantify the reconstruction accuracy of the non-connected vehicles in the present invention. In the reconstruction areas i and i+1, the spatial range of the reconstruction area is 250m, and the penetration rate of connected vehicles is 10%. The quantization indexes MAE, MAPE, and RMSE are 6.71m, 4.04%, and 9.51m respectively.

[0106] Similarly, for other reconstruction areas in this embodiment, the unknown trajectories of non-connected vehicles can all be reconstructed according to the method of the present invention. The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the knowledge scope of those of ordinary skill in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A full spatio-temporal vehicle trajectory reconstruction method based on multi-source sparse detector data, characterized in that The specific steps are as follows: Step S1: Unify the data formats of the upstream and downstream fixed-point detectors and the sparse mobile detector data to form a multi-source sparse detector data environment, and regard the time and space ranges enclosed by the multi-source sparse detectors as the vehicle trajectory reconstruction area; Step S2: In the vehicle trajectory reconstruction area, based on the multi-source sparse detector data, use the intelligent driver model to reconstruct the initial full-time and full-space vehicle trajectory; Step S3: Construct a matrix data structure, convert the full-time and full-space vehicle trajectory data into a matrix data structure, and obtain the optimal full-time and full-space vehicle trajectory based on the iterative matrix singular value decomposition algorithm.

2. The full-space-time vehicle trajectory reconstruction method based on multi-source sparse detector data according to claim 1, characterized in that In step S1, the unification of the data formats of the upstream and downstream fixed-point detectors and the sparse mobile detector data is specifically as follows: Convert the time unit and position unit in the fixed-point detector and mobile detector data to seconds and meters respectively, specifically as follows: ； ； where t is the converted time in seconds; time is the original data of the detector; is the conversion coefficient; X is the converted position in meters; is the original position of the detector, and b is the conversion coefficient.

3. A full - spatio - temporal vehicle trajectory reconstruction method based on multi - source sparse detector data according to claim 1, characterized in that, In step S1, the vehicle trajectory reconstruction area is specifically as follows: During the trajectory reconstruction process, use the mobile detector and the fixed-point detector to divide the full-time and full-space vehicle trajectory into multiple reconstruction areas. Regard the connected vehicle as a mobile detector. The time range is composed of the time when the previous connected vehicle passes the upstream fixed-point detector and the time when the non-connected vehicle before the next connected vehicle passes the downstream fixed-point detector, and the space range is composed of the distances between the upstream and downstream fixed-point detectors, so as to form multiple separate vehicle trajectory reconstruction areas. Among them, the vehicle trajectory includes vehicle ID, timestamp, speed, and position.

4. A full-space-time vehicle trajectory reconstruction method based on multi-source sparse detector data according to claim 1, characterized in that Step S2 specifically includes: Step S21: Assign values to the relevant parameters in the intelligent driver model for generating the initial full-time and full-space vehicle trajectory after multi-source data input. Among them, the intelligent driver model is derived from the car-following model; Step S22: Input the unified multi-source sparse detector data into the intelligent driver model to obtain the initial full-time and full-space vehicle trajectory.

5. A full-space and full-time vehicle trajectory reconstruction method based on multi-source sparse detector data according to claim 4, characterized in that The intelligent driver model is specifically expressed as: ； Among them, is the distance between the following vehicle and the preceding vehicle at time , and is the position of the preceding vehicle at time , is the position of the following vehicle at time , and is the fixed minimum safety distance; ； is the following vehicle and the leading vehicle at time relative speed of, is the leading vehicle at time speed of, is the following vehicle at time speed of; ； is the expected distance, is the maximum acceleration, is the comfortable deceleration, is the safety time interval, is the speed of the non-connected vehicle passing through the fixed detector; ； is the acceleration of the non-connected vehicle at time , is the desired speed; ； The speed of the non-connected vehicle at the next moment is the reconstructed time step; ； is the position of the non-connected vehicle at the next moment and is the position where the non-connected vehicle passes the fixed-point detector.

6. A full spatio-temporal vehicle trajectory reconstruction method based on multi-source sparse detector data according to claim 1, characterized in that Step S3 specifically includes: Step S31: Construct a matrix data structure, store the initial full-time and full-space vehicle trajectory in the matrix to obtain the initial full-time and full-space trajectory matrix; Step S32: Apply the iterative singular value decomposition algorithm to the initial space-time trajectory matrix to obtain the optimal full-time and full-space vehicle trajectory.

7. A full spatio-temporal vehicle trajectory reconstruction method based on multi-source sparse detector data according to claim 6, characterized in that Step S31 is specifically as follows: The first row of the matrix data structure is the connected vehicle trajectory data, the second row is the trajectory data of the first non-connected vehicle, and so on to the last non-connected vehicle. Specifically: ； Wherein: is the trajectory vector of the th vehicle within the entire time range, is the data when the vehicle passes through the upstream fixed-point detector, is the data when the vehicle passes through the downstream fixed-point detector, is the unknown data before the vehicle arrives at the upstream fixed-point detector, is the unknown data after the vehicle leaves the downstream fixed-point detector, is the unknown data within the reconstruction area; ； Among them, is the initial full-time and space trajectory matrix reconstructed by the intelligent driver model within the reconstruction area; and are the known connected vehicle trajectory data respectively; is the unknown data before the th non-connected vehicle arrives at the upstream fixed-point detector, is the unknown data after the th non-connected vehicle leaves the downstream fixed-point detector, is the data when the th non-connected vehicle passes through the upstream fixed-point detector; is the data when the th non-connected vehicle passes through the downstream fixed-point detector; is the initial trajectory data reconstructed by the intelligent driver model for the th non-connected vehicle; is the unknown data before the th non-connected vehicle arrives at the upstream fixed-point detector, is the unknown data after the th non-connected vehicle leaves the downstream fixed-point detector, is the data when the th non-connected vehicle passes through the upstream fixed-point detector; is the data when the th non-connected vehicle passes through the downstream fixed-point detector; is the initial trajectory data reconstructed by the intelligent driver model for the th non-connected vehicle; is the unknown data before the last th non-connected vehicle arrives at the upstream fixed-point detector, is the unknown data after the last th non-connected vehicle leaves the downstream fixed-point detector, is the data when the last th non-connected vehicle passes through the upstream fixed-point detector; is the data when the last th non-connected vehicle passes through the downstream fixed-point detector, is the data when the last th non-connected vehicle passes through the downstream fixed-point detector, is the initial trajectory data reconstructed by the intelligent driver model for the last th non-connected vehicle.

8. A full spatio-temporal vehicle trajectory reconstruction method based on multi-source sparse detector data according to claim 6, characterized in that The iterative singular value decomposition algorithm is specifically as follows: ； Among them, is the initial full-time and space trajectory matrix reconstructed by the intelligent driver model within the reconstruction area, is a matrix with a size of ; The column vector of is 's eigenvector and is the left singular value vector of matrix ; is a matrix with a size of ; The column vector of is 's eigenvector and is the right singular value vector of matrix ; is a matrix with a size of . The elements located on the diagonal of matrix are called singular values, and the superscript represents the transpose.

9. A full spatio-temporal vehicle trajectory reconstruction method based on multi-source sparse detector data according to claim 8, characterized in that, Step S32 is specifically as follows: Step S321: In the matrix singular value decomposition algorithm, denote the initial full spatio-temporal trajectory matrix as , and assign to the decomposition matrix , and perform singular value decomposition on the decomposition matrix , select the first largest singular values and the corresponding eigenvectors to obtain ; Step S322: Use to update the elements of the missing positions between the upstream and downstream fixed-point detectors in the initial full spatio-temporal trajectory matrix to obtain a new initial full spatio-temporal trajectory matrix . If the vehicle trajectory reconstruction result does not converge, continue to iteratively execute Step S321; if the vehicle trajectory reconstruction result converges, output the optimal full spatio-temporal trajectory matrix to obtain the optimal full spatio-temporal vehicle trajectory matrix.

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