Full Spatiotemporal Vehicle Trajectory Reconstruction Method Based on Multi-Source Sparse Detector Data

Abstract

The present invention relates to a method for reconstructing full-time and space-time vehicle trajectories based on multi-source sparse detector data, and belongs to the field of trajectory reconstruction technology. The method comprises: unifying the 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 the time and space range enclosed by the multi-source detectors as the vehicle trajectory reconstruction area; based on the multi-source sparse detector data, reconstructing the initial full-time and space-time vehicle trajectory using an intelligent driver model; converting the full-time and space-time vehicle trajectory data into a matrix data structure, and utilizing an iterative matrix singular value decomposition algorithm to improve the reconstruction accuracy of the vehicle trajectory, thereby obtaining the optimal full-time and space-time vehicle trajectory. Compared with existing trajectory reconstruction technologies, the present invention has excellent performance in a multi-source sparse detector data environment and a wide range of applications.

Description

Technical Field

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

[0002] Full-time and spatiotemporal vehicle trajectories are essential for accurately capturing the full picture and details of traffic flow. With the development of intelligent connected technologies and the construction of smart highways, fixed-point sensors such as radar and video cameras, as well as mobile sensors such as connected vehicles and probe vehicles, have become widely used, creating a new era for multi-source vehicle trajectory acquisition. However, on highways and expressways, the high cost and limited resources of various fixed-point sensors have led to a low deployment rate (the distance between two fixed-point sensors is typically greater than 500 meters). Mobile sensors, such as probe vehicles, connected vehicles, and autonomous vehicles, can provide complete trajectory data in real time, but these mobile sensors are randomly distributed across the road network and have a low penetration rate (typically 5% to 15%). Both fixed-point and mobile sensors provide traffic data from a single instance, containing only limited traffic information. Therefore, considering the existing types of traffic sensors, a multi-source data environment can be created by fusing fixed-point and mobile sensor data to reconstruct vehicle trajectories. However, the data structure, time interval, and accuracy of data collected by different sensors vary. Fusion of fixed-point and mobile detector data requires comprehensive analysis of both heterogeneous data types to ensure that the data conditions meet the fundamental requirements for the present invention. Fusion of multi-source detector data for vehicle trajectory reconstruction can improve the accuracy and robustness of the resulting trajectory reconstruction. However, due to the low coverage of fixed-point detectors and the low penetration of mobile detectors in real-world road environments, directly acquiring full-time and spatiotemporal vehicle trajectories using multi-source sparse detectors remains challenging. Summary of the Invention

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

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

[0005] Step S1: Unify the 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 range surrounded by the multi-source sparse detectors as the vehicle trajectory reconstruction area;

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

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

[0008] In step S1, the formats of the upstream and downstream fixed-point detector data and the sparse mobile detector data are unified as follows:

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

[0010]

[0011]

[0012] 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.

[0013] The vehicle trajectory reconstruction area in step S1 is specifically:

[0014] During the trajectory reconstruction process, the full-time and space vehicle trajectory is divided into multiple reconstruction areas using mobile detectors and fixed-point detectors. The connected vehicles are regarded as mobile detectors. The time range is composed of the time when the previous connected vehicle passed the upstream fixed-point detector and the time when the non-connected vehicle before the next connected vehicle passed the downstream fixed-point detector. The spatial range is composed of the distance between the upstream and downstream fixed-point detectors, thereby forming multiple separate vehicle trajectory reconstruction areas, where the vehicle trajectory includes vehicle ID, timestamp, speed and position.

[0015] The step S2 specifically includes:

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

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

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

[0019]

[0020] in, It's the car behind With the car in front In time The interval distance, It's the car in front In time location, It's the car behind In time location, is a fixed minimum safety distance;

[0021]

[0022] It's the car behind With the car in front In time The relative speed, It's the car in front In time speed, It's the car behind In time speed;

[0023]

[0024] is the expected distance, is the maximum acceleration, For comfortable deceleration, For a safe time interval, The speed of non-connected vehicles passing through fixed-point detectors;

[0025]

[0026] Is it a non-connected car in time? The acceleration of is the expected speed;

[0027]

[0028] Is it a non-connected car in the next moment? speed, is the reconstruction time step;

[0029]

[0030] Is it a non-connected car in the next moment? location, This is the location where a non-connected vehicle passes a fixed-point detector.

[0031] The step S3 specifically includes:

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

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

[0034] The step S31 is specifically as follows:

[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 to the last non-connected vehicle, specifically:

[0036]

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

[0038]

[0039] in, It is the initial full-time and space trajectory matrix reconstructed by the intelligent driver model in the reconstruction area; and They are the known connected vehicle trajectory data; It is The unknown data before the non-connected vehicle reaches the upstream fixed-point detector, It is Unknown data after a non-connected vehicle leaves the downstream fixed-point detector, It is Data from a non-connected vehicle passing an upstream fixed-point detector; It is Data from a non-connected vehicle passing a downstream fixed-point detector; It is The initial trajectory data of a non-connected vehicle reconstructed by the intelligent driver model; It is The unknown data before the non-connected vehicle reaches the upstream fixed-point detector, It is Unknown data after a non-connected vehicle leaves the downstream fixed-point detector, It is Data from a non-connected vehicle passing an upstream fixed-point detector; It is Data from a non-connected vehicle passing a downstream fixed-point detector; It is The initial trajectory data of a non-connected vehicle reconstructed by the intelligent driver model; It's the last The unknown data before the non-connected vehicle reaches the upstream fixed-point detector, It's the last Unknown data after a non-connected vehicle leaves the downstream fixed-point detector, It's the last Data from a non-connected vehicle passing an upstream fixed-point detector; It's the last The data of a non-connected vehicle passing through the downstream fixed-point detector, It's the last The initial trajectory data of a non-connected vehicle is reconstructed by the intelligent driver model.

[0040] The iterative singular value decomposition algorithm is specifically:

[0041]

[0042] in, It is the initial full-time and space trajectory matrix reconstructed by the intelligent driver model in the reconstruction area, Is the size of The matrix, Column vector of yes The eigenvectors of the matrix The left singular value vector of ; Is the size of The matrix, Column vector of yes The eigenvectors of the matrix The right singular value vector of ; Is the size of The matrix, located in the matrix The elements on the diagonal are called singular values, and the superscript Indicates transpose.

[0043] The step S32 is specifically as follows:

[0044] Step S321: In the matrix singular value decomposition algorithm, the initial full-time and space trajectory matrix is recorded as ,Will Assign to the decomposition matrix , and decompose the matrix Perform singular value decomposition and select The largest singular value and the corresponding eigenvector are obtained ;

[0045] Step S322: Use Update the initial full-time and space trajectory matrix The elements of the missing position between the upstream and downstream fixed-point detectors of the connected vehicle in China and Africa are used to obtain the new initial full-time and space trajectory matrix If the vehicle trajectory reconstruction result does not converge, continue to iterate and execute step S321; if the vehicle trajectory reconstruction result converges, output the optimal full-time and space trajectory matrix to obtain the optimal full-time and space vehicle trajectory matrix.

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

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

[0048] (2) According to the constructed spatiotemporal trajectory data structure, the data provided by the low-penetration fixed-point detectors and mobile detectors are filled into the data structure to obtain an extremely sparse trajectory matrix data structure. The trajectories of non-connected vehicles are then reconstructed using the intelligent driver model to complete the sparse matrix and obtain an initial complete matrix to enhance the robustness of vehicle trajectory reconstruction based on multi-source detector data in low-penetration environments;

[0049] (3) In view of the current lack of consideration of vehicle microscopic motion characteristics in the research on full-time and space vehicle trajectory reconstruction and the application limitations of the traditional car-following model, the present invention uses the traffic data provided by fixed-point detectors and mobile detectors as constraints, applies a matrix decomposition algorithm to the initial complete matrix, and continuously iterates the calculation to reconstruct the optimal vehicle trajectory in full time and space;

[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, thereby expanding its application in vehicle trajectory reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 is a flow chart of the steps of the present invention;

[0052] Figure 2 Sparse multi-source detectors and reconstructed target maps in multi-source detector environments;

[0053] Figure 3 To reconstruct the region partitioning, matrix data structure and flow chart;

[0054] Figure 4 The actual road environment and schematic diagram in the embodiment;

[0055] Figure 5 This is the optimal full-time and space reconstruction result diagram of the embodiment under 10% connected vehicle penetration rate. DETAILED DESCRIPTION

[0056] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method 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 full-time and full-space vehicle trajectories using fixed-point detector data with low coverage and mobile detector data with low penetration on highways. The connected vehicle is regarded as a mobile detector, and the reported data includes: vehicle ID, timestamp, position and instantaneous speed, etc., so that the vehicle trajectory data of the connected vehicle can be obtained in real time; the fixed-point detectors on the road can record the timestamp, speed, vehicle ID and vehicle license plate of all vehicles passing 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 to reconstruct the full-time and full-space vehicle trajectory. The present invention designs a complete process from multi-source sparse detector data to the establishment of an intelligent driver model to obtain the initial full-time and full-space vehicle trajectory, and then uses the iterative matrix singular value decomposition algorithm to reconstruct the optimal full-time and full-space vehicle trajectory.

[0058] Example 1: Figure 1 As shown in Figure 1, a full-time and space vehicle trajectory reconstruction method based on multi-source sparse detector data is as follows:

[0059] Step S1: Unify the 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 range surrounded by the multi-source sparse detectors as the vehicle trajectory reconstruction area;

[0060] Specifically, since the data formats of fixed-point detectors and mobile detectors are not unified, it is necessary to unify the heterogeneous data formats of multi-source detectors. The time unit in the fixed-point detector and sparse mobile detector data is set to seconds (s), and the position unit 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 position after conversion, the unit is m; is the original position of the detector, and b is the conversion coefficient.

[0064] During the trajectory reconstruction process, the full spatiotemporal vehicle trajectory is divided into multiple reconstruction regions using mobile detectors and fixed-point detectors. The connected vehicle is regarded as a mobile detector. The time range is composed of the time when the previous connected vehicle passed the upstream fixed-point detector and the time when the non-connected vehicle before the next connected vehicle passed the downstream fixed-point detector. The spatial range is composed of the distance between the upstream and downstream fixed-point detectors, thereby forming multiple separate vehicle trajectory reconstruction regions, which are recorded as reconstruction regions n. The vehicle trajectory includes vehicle ID, timestamp, speed and position. The original data of the connected vehicle includes vehicle ID, timestamp and position, that is, ( , , ), ( , , ),…,( , , ), is the ID of the connected car in the reconstructed region n, and are respectively the timestamp and position of the connected vehicle at the Lth trajectory point; the raw data of the non-connected vehicle when passing the upstream fixed-point detector contains the 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 the upstream fixed-point detector, is the location of the upstream fixed-point detector; the raw data of the non-connected vehicle passing the downstream fixed-point detector contains the vehicle ID, timestamp and location, that is ( , , ), ( , , ),…,( , , ), is the ID of the i-th non-connected vehicle passing through 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 in the same space-time graph, such as Figure 2 shown.

[0065] Step S2: In the vehicle trajectory reconstruction area, based on the multi-source sparse detector data, the intelligent driver model is used to reconstruct the initial full-time and space vehicle trajectory;

[0066] Step S21: Assigning values to relevant parameters in the intelligent driver model for generating an initial full-time and space vehicle trajectory after multi-source data input, wherein the intelligent driver model is derived from the car-following model;

[0067] Step S22: Input the multi-source sparse detector data in a unified format into the intelligent driver model to obtain the initial full-time and space vehicle trajectory.

[0068] Specifically, for each reconstruction area, the intelligent driver model in the car-following model is used to reconstruct the missing tracks of the non-connected vehicles in the area between the two fixed-point detectors upstream and downstream. The intelligent driver model can calculate the distance between the following vehicle n and the preceding vehicle n-1 at time t. and relative speed Get the expected distance between the two cars , and then get the acceleration of the non-connected vehicle at time t , and finally the location of the non-connected vehicle passing through the fixed-point detector and speed Get it at the next moment Speed and location As shown in formulas (3) to (8):

[0069] (3)

[0070] (4)

[0071] (5)

[0072] (6)

[0073] (7)

[0074] (8)

[0075] In formula (3), It's the car behind With the car in front In time The interval distance, It's the car in front In time location, It's the car behind In time location, is a fixed minimum safety distance; in formula (4), It's the car behind With the car in front In time The relative speed, It's the car in front In time speed, It's the car behind In time The speed of; In formula (5), is the expected distance, is the maximum acceleration, For comfortable deceleration, For a safe time interval, is the speed of the non-connected vehicle passing the fixed-point detector; in formula (6), Is it a non-connected car in time? The acceleration of is the expected speed; in formula (7), Is it a non-connected car in the next moment? speed, is the reconstruction time step; in formula (8), Is it a non-connected car in the next moment? location, This is the location where a non-connected vehicle passes a 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-time and space vehicle trajectory in the reconstruction area, such as Figure 3 shown.

[0078] Step S3: Constructing a matrix data structure, converting the full-time and full-time vehicle trajectory data into a matrix data structure, and obtaining the optimal full-time and full-time vehicle trajectory based on an iterative matrix singular value decomposition algorithm;

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

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

[0081] Step S32: Apply an iterative singular value decomposition algorithm to the initial spatiotemporal trajectory matrix to obtain the optimal full spatiotemporal vehicle trajectory.

[0082] Specifically, by analyzing the vehicle trajectory, a spatiotemporal matrix data structure is constructed, and then the reconstructed initial full spatiotemporal vehicle trajectory is stored in the spatiotemporal matrix, as shown in Equations (9) and (10):

[0083] (9)

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

[0085] (10)

[0086] in, It is the initial full-time and space trajectory matrix reconstructed by the intelligent driver model in the reconstruction area; and They are the known connected vehicle trajectory data; It is The unknown data before the non-connected vehicle reaches the upstream fixed-point detector, It is Unknown data after a non-connected vehicle leaves the downstream fixed-point detector, It is Data from a non-connected vehicle passing an upstream fixed-point detector; It is Data from a non-connected vehicle passing a downstream fixed-point detector; It is The initial trajectory data of a non-connected vehicle reconstructed by the intelligent driver model; It is The unknown data before the non-connected vehicle reaches the upstream fixed-point detector, It is Unknown data after a non-connected vehicle leaves the downstream fixed-point detector, It is Data from a non-connected vehicle passing an upstream fixed-point detector; It is Data from a non-connected vehicle passing a downstream fixed-point detector; It is The initial trajectory data of a non-connected vehicle reconstructed by the intelligent driver model; It's the last The unknown data before the non-connected vehicle reaches the upstream fixed-point detector, It's the last Unknown data after a non-connected vehicle leaves the downstream fixed-point detector, It's the last Data from a non-connected vehicle passing an upstream fixed-point detector; It's the last The data of a non-connected vehicle passing through the downstream fixed-point detector, It's the last The initial trajectory data of a non-connected vehicle is reconstructed by the intelligent driver model.

[0087] Specifically, within the reconstruction area, the initial full-time and space vehicle trajectory obtained by reconstruction 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, wherein the amount of data in the sparse matrix is significantly increased. Among the various matrix decomposition methods, singular value decomposition has a wider range of applications and more reliable decomposition results, so the present invention selects the matrix singular value decomposition algorithm to reconstruct the unknown part of the vehicle trajectory. Then, using the iterative matrix singular value decomposition algorithm's strong ability to capture the correlation between rows and columns of 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, the matrix singular value decomposition is to convert a matrix of size Matrix Decompose it into three matrices, and then multiply the three matrices to obtain a complete matrix, so as to achieve the purpose of reproducing the known and unknown values in the matrix, as shown in formula (11).

[0088] (11)

[0089] in, It is the initial full-time and space trajectory matrix reconstructed by the intelligent driver model in the reconstruction area, Is the size of The matrix, Column vector of yes The eigenvectors of the matrix The left singular value vector of ; Is the size of The matrix, Column vector of yes The eigenvectors of the matrix The right singular value vector of ; Is the size of The matrix, located in the matrix The elements on the diagonal are called singular values, and the superscript Indicates transpose.

[0090] Specifically, in order to improve the accuracy of the method, improve the precision of the reconstructed trajectory and the robustness of the model, the iterative matrix singular value decomposition algorithm is used to further enhance the effect of full-time and space vehicle trajectory reconstruction, thereby completing the full-time and space non-connected vehicle trajectory reconstruction in the reconstruction area and obtaining the optimal full-time and space vehicle trajectory. Do the following:

[0091] Step S321: In the matrix singular value decomposition algorithm, the initial full-time and space trajectory matrix is recorded as ,Will Assign to the decomposition matrix , and decompose the matrix Perform singular value decomposition and select The largest singular value and the corresponding eigenvector are obtained ;

[0092] Step S322: Use Update the initial full-time and space trajectory matrix The elements of the missing position between the upstream and downstream fixed-point detectors of the connected vehicle in China and Africa are used to obtain the new initial full-time and space trajectory matrix If the vehicle trajectory reconstruction result does not converge, continue to iterate and execute step S321; if the vehicle trajectory reconstruction result converges, output the optimal full-time and space trajectory matrix to obtain the optimal full-time and space vehicle trajectory matrix

[0093] The new matrix obtained by using the matrix singular value decomposition algorithm has different elements from the original matrix at the missing parts of the non-connected vehicle trajectory. As the iteration proceeds, the vehicle trajectory reconstruction result will eventually converge, and then the optimal complete matrix will be output. , thus obtaining the full-time and space vehicle trajectories of non-connected vehicles in the reconstructed area.

[0094] The above embodiment is a detailed step for reconstructing the full-time and space vehicle trajectory using multi-source sparse detector data. The steps are applicable to any direction on the highway. Therefore, the full-time and space vehicle trajectory on the highway can be obtained through reconstruction.

[0095] The following experiment uses vehicles in the leftmost lane of a highway from the NGSIM dataset as the experimental subjects. We randomly select 10% of these vehicles as virtual connected vehicles, meaning that the penetration rate of mobile detectors is 10%. We also select appropriate intervals to define missing segments, and set two virtual fixed-point detectors at the beginning and end of each missing segment as upstream and downstream fixed-point detectors. Using the trajectory data of connected vehicles and the data of non-connected vehicles passing through the upstream and downstream fixed-point detectors as input, we reconstruct vehicle trajectories across the entire space and time.

[0096] The real environment and schematic diagram of the highway section in the embodiment are as follows 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. Some of the original data in the NGSIM dataset are shown in Table 1:

[0098] Table 1. Some original trajectory data in the NGSIM dataset

[0099] Vehicle ID Time (ms) Position (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 time and position unit conversion formulas are formulas (12) and (13), namely

[0101] (12)

[0102] (13)

[0103] Secondly, the upstream fixed-point detector selected is located at 50m, that is, =50m, select the downstream fixed-point detector at 300m, that is = 300 m. After unifying the data format, the time range is composed of the time when the previous connected vehicle passed the upstream fixed-point detector and the time when the non-connected vehicle before the next connected vehicle passed the downstream fixed-point detector. The spatial range is composed of the distance between the upstream and downstream fixed-point detectors. This forms the reconstruction area of the present invention, and a portion of the original trajectory data in the NGSIM dataset is plotted into a time-space diagram.

[0104] Next, the intelligent driver model in the car-following model is selected as the model of the present invention, and various parameters in the intelligent driver model are assigned values. In this embodiment, the parameter values are , , , , , ; Select the previous The largest singular values and their corresponding eigenvectors.

[0105] Finally, according to the steps of the present invention, the optimal full-time and space vehicle trajectory reconstruction result in the reconstruction area is obtained as follows: Figure 5 As shown in Figure 2. Since trajectory data is microscopic, the reconstruction accuracy of non-connected vehicles in this invention is quantified using mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE). For reconstruction regions i and i+1, where the spatial extent of the reconstruction region is 250 meters and the penetration rate of connected vehicles is 10%, the MAE, MAPE, and RMSE are 6.71 meters, 4.04%, and 9.51 meters, respectively.

[0106] Similarly, other reconstructed areas and unknown trajectories of non-connected vehicles in this embodiment can be reconstructed using the method of the present invention. The above describes the specific embodiments of the present invention in detail with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various modifications can be made within the scope of knowledge possessed by ordinary technicians in this field without departing from the spirit of the present invention.

Claims

1. A method for reconstructing full-time and space-time vehicle trajectories based on multi-source sparse detector data, characterized in that: The specific steps are: Step S1: Unify the 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 range surrounded 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, the intelligent driver model is used to reconstruct the initial full-time and space vehicle trajectory; Step S3: Constructing a matrix data structure, converting the full-time and full-time vehicle trajectory data into a matrix data structure, and obtaining the optimal full-time and full-time vehicle trajectory based on an iterative matrix singular value decomposition algorithm; The vehicle trajectory reconstruction area in step S1 is specifically: During the trajectory reconstruction process, the full spatiotemporal vehicle trajectory is divided into multiple reconstruction areas using mobile detectors and fixed-point detectors. The connected vehicles are regarded as mobile detectors. The time range is composed of the time when the previous connected vehicle passed the upstream fixed-point detector and the time when the non-connected vehicle before the next connected vehicle passed the downstream fixed-point detector. The spatial range is composed of the distance between the upstream and downstream fixed-point detectors, thereby forming multiple separate vehicle trajectory reconstruction areas. The vehicle trajectory includes vehicle ID, timestamp, speed and position. The step S3 specifically includes: Step S31: construct a matrix data structure, store the initial full-time and full-space vehicle trajectory into the matrix, and obtain the initial full-time and full-space trajectory matrix; Step S32: applying an iterative singular value decomposition algorithm to the initial spatiotemporal trajectory matrix to obtain the optimal full spatiotemporal vehicle trajectory; The step S31 is specifically as follows: 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 to the last non-connected vehicle, specifically: ； in: It is The trajectory vector of the vehicle in the entire time range, is the data when the vehicle passes the upstream fixed-point detector, is the data when the vehicle passes the downstream fixed-point detector, It is the unknown data before the vehicle reaches the upstream fixed-point detector. It is the unknown data after the vehicle leaves the downstream fixed-point detector. is the unknown data within the reconstruction area; ； in, It is the initial full-time and space trajectory matrix reconstructed by the intelligent driver model in the reconstruction area; and They are the known connected vehicle trajectory data; It is The unknown data before the non-connected vehicle reaches the upstream fixed-point detector, It is Unknown data after a non-connected vehicle leaves the downstream fixed-point detector, It is Data from a non-connected vehicle passing an upstream fixed-point detector; It is Data from a non-connected vehicle passing a downstream fixed-point detector; It is The initial trajectory data of a non-connected vehicle reconstructed by the intelligent driver model; It is The unknown data before the non-connected vehicle reaches the upstream fixed-point detector, It is Unknown data after a non-connected vehicle leaves the downstream fixed-point detector, It is Data from a non-connected vehicle passing an upstream fixed-point detector; It is Data from a non-connected vehicle passing a downstream fixed-point detector; It is The initial trajectory data of a non-connected vehicle reconstructed by the intelligent driver model; It's the last The unknown data before the non-connected vehicle reaches the upstream fixed-point detector, It's the last Unknown data after a non-connected vehicle leaves the downstream fixed-point detector, It's the last Data from a non-connected vehicle passing an upstream fixed-point detector; It's the last The data of a non-connected vehicle passing through the downstream fixed-point detector, It's the last The initial trajectory data of a non-connected vehicle is reconstructed by the intelligent driver model.

2. The method for reconstructing full-space-time vehicle trajectories based on multi-source sparse detector data according to claim 1, characterized in that: In step S1, the formats of the upstream and downstream fixed-point detector data and the sparse mobile detector data are unified as follows: Convert the time unit in the fixed-point detector and mobile detector data to seconds, and the position unit to meters, specifically: ； ； 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. The method for reconstructing full-time and space-time vehicle trajectories based on multi-source sparse detector data according to claim 1, characterized in that: The step S2 specifically includes: Step S21: Assigning values to relevant parameters in the intelligent driver model for generating an initial full-time and space vehicle trajectory after multi-source data input, wherein the intelligent driver model is derived from the car-following model; Step S22: Input the multi-source sparse detector data in a unified format into the intelligent driver model to obtain the initial full-time and space vehicle trajectory.

4. The method for reconstructing full-time and space-time vehicle trajectories based on multi-source sparse detector data according to claim 3, characterized in that: The intelligent driver model is specifically expressed as follows: ； in, It's the car behind With the car in front In time The interval distance, It's the car in front In time location, It's the car behind In time location, is a fixed minimum safety distance; ； It's the car behind With the car in front In time The relative speed, It's the car in front In time speed, It's the car behind In time speed; ； is the expected distance, is the maximum acceleration, For comfortable deceleration, For a safe time interval, The speed of non-connected vehicles passing through fixed-point detectors; ； Is it a non-connected car in time? The acceleration of is the expected speed; ； Is it a non-connected car in the next moment? speed, is the reconstruction time step; ； Is it a non-connected car in the next moment? location, This is the location where a non-connected vehicle passes a fixed-point detector.

5. The method for reconstructing full-time and space-time vehicle trajectories based on multi-source sparse detector data according to claim 1, characterized in that: The iterative singular value decomposition algorithm is specifically: ； in, It is the initial full-time and space trajectory matrix reconstructed by the intelligent driver model in the reconstruction area, Is the size of The matrix, Column vector of yes The eigenvectors of the matrix The left singular value vector of ; Is the size of The matrix, Column vector of yes The eigenvectors of the matrix The right singular value vector of ; Is the size of The matrix, located in the matrix The elements on the diagonal are called singular values, and the superscript Indicates transpose.

6. The method for reconstructing full-time and space-time vehicle trajectories based on multi-source sparse detector data according to claim 5, characterized in that: The step S32 is specifically as follows: Step S321: In the matrix singular value decomposition algorithm, the initial full-time and space trajectory matrix is recorded as ,Will Assign to the decomposition matrix , and decompose the matrix Perform singular value decomposition and select g , g ≤ min ( m , n ) largest singular values and corresponding eigenvectors, we get ; Step S322: Use Update the initial full-time and space trajectory matrix The elements of the missing position between the upstream and downstream fixed-point detectors of the connected vehicle in China and Africa are used to obtain the new initial full-time and space trajectory matrix If the vehicle trajectory reconstruction result does not converge, continue to iterate and execute step S321; if the vehicle trajectory reconstruction result converges, output the optimal full-time and space trajectory matrix to obtain the optimal full-time and space vehicle trajectory matrix.

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