Vehicle track sub-second reconstruction method based on high-frequency satellite positioning data

Abstract

The invention belongs to the technical field of traffic science and big data, and discloses a vehicle track sub-second reconstruction method based on high-frequency satellite positioning data, which utilizes the self-similarity feature of a vehicle track signal to perform encryption, can well capture the self-similarity and local details of the track, is low in calculation complexity, reduces the demand for priori knowledge, and improves the reconstruction efficiency. According to the method, satellite positioning system errors, vehicle motion consistency and physical consistency constraints are considered in parameter selection, the adaptability is high, and reliable performance can be achieved without correction of a large amount of training data and multi-source sensing data; therefore, the method is an economical, efficient, accurate and reliable data encryption method for solving a space-time large-range trajectory under a high-frequency sampling rate.

Description

Technical Field

[0001] This application belongs to the technical field of traffic science and big data, and specifically relates to a method for sub-second reconstruction of vehicle trajectories based on high-frequency satellite positioning data. Background Art

[0002] In recent years, vehicle trajectory information has provided great potential and broad prospects in various applications. Vehicle trajectories provide key information for various traffic applications, including the construction of high-precision digital maps, traffic safety analysis, and mobility-related applications. With the improvement of satellite positioning accuracy, sampling frequency, and acquisition convenience, mobile sensor trajectory data is more reliable and can cover any required time and space range. However, the quality of mobile sensor data should be the first factor to consider because the data source has a decisive impact on the scope and accuracy limits of traffic state recognition and prediction in intelligent transportation systems.

[0003] Although mobile sensors have made significant improvements in positioning accuracy and sampling frequency, for example, GPS trajectory data with a sampling rate of 1 Hz has been widely collected and utilized. Although it is high-frequency trajectory data, the distance between adjacent trajectory points is approximately 20 - 30 m, which is too far for the safety of many road and traffic flow analyses based on trajectories. Currently, road management departments or highway management companies have collected a large amount of trajectory data, and their demand for detecting sub-second or sub-meter ground displacement signals is increasing. Therefore, it is necessary to further improve the sensitivity of GPS solutions and the resolution of trajectory data.

[0004] The trajectory data collected by GNSS still has some signal noises, such as satellite and receiver clock errors and orbital errors. These noises are random, so the algorithm needs to denoise while improving the resolution of trajectory data. On the other hand, the reconstruction algorithm needs to consider economic costs. Collecting a necessary number of labeled training or using multi-source sensing devices is costly for big data. Developing a successful artificial intelligence or trajectory model requires access to a large amount of data. Therefore, it is necessary to develop an economical and effective method to improve data resolution and accuracy. Summary of the Invention

[0005] The purpose of this application is to solve the problems of the prior art and provide a method for sub-second reconstruction of vehicle trajectories based on high-frequency satellite positioning data.

[0006] To solve the technical problems, the technical solution of this application is: A method for sub-second reconstruction of vehicle trajectories based on high-frequency satellite positioning data, including the following steps: Step 1: Acquisition of electronic map data; Step 2: Acquisition of large-scale satellite positioning vehicle trajectories and processing of large-scale satellite positioning vehicle trajectories; Step 2-1: Group vehicle trajectories; Step 2-2: Adjust the format of vehicle trajectories; Step 2-3: Remove abnormal points from vehicle trajectories; Step 3: Match the processed vehicle trajectories with geographical information; Step 3-1: Projection transformation to convert the longitude and latitude coordinates of vehicle trajectories into a projected coordinate system; Step 3-2: Map matching to match the vehicle trajectories in the projected coordinate system with the electronic map data obtained in Step 1; Step 3-3: Frenet coordinate transformation to obtain the longitudinal position S and lateral position D coordinates of the vehicle trajectories in the Frenet coordinates based on the electronic map data matching; Step 4: Sub-second reconstruction of vehicle trajectories; Step 4-1: Trajectory segmentation. Segment the vehicle trajectories processed in Step 3 based on the statistic of the Hurst exponent to obtain multiple sub-trajectories; Step 4-2: Fractal interpolation to encrypt the trajectories. Encrypt multiple sub-trajectories through fractal interpolation and insert interpolation points between the original trajectory points of the vehicle trajectories processed in Step 3; Step 4-3: Denoise and smooth the interpolation points; Step 4-4: Align and interpolate the interpolation points with the original trajectory points, and align the interpolation points at equal intervals; Step 4-5: Repeat Steps 4-1 to 4-4 to obtain the reconstructed satellite positioning trajectories; Step 5: Reverse-transform the reconstructed satellite positioning trajectories to the Cartesian coordinate system, re-match the electronic map data, and calculate the vehicle motion characteristics.

[0007] Preferably, the vehicle trajectory grouping in Step 2-1 is specifically: Group the large-scale satellite positioning vehicle trajectories by vehicle ID, and sort each group by timestamp.

[0008] Preferably, the removal of abnormal points from vehicle trajectories in Step 2-3 is specifically: The abnormal points of vehicle trajectories include position jump abnormal points, time interval abnormal points, and trajectory deviation abnormal points. First, remove the position jump abnormal points and time interval abnormal points, then use the outlier factor algorithm to remove the trajectory deviation abnormal points, and finally save each group as a separate data file; The specific process of removing the trajectory deviation abnormal points by the outlier factor algorithm is: First, find the k nearest neighbors for each original trajectory point of the vehicle trajectory, calculate the density between the original trajectory point and the neighbors. If the density of a certain original trajectory point is significantly lower than that of the surrounding neighbors, it will be marked as an abnormal point, and the trajectory deviation abnormal points that are significantly deviated from the normal trajectory are screened out.

[0009] Preferably, step 3-1 is specifically as follows: According to the EPSG code of the data coordinate system, use the pyproj library to convert the longitude and latitude coordinates of the vehicle trajectory into a projected coordinate system; Step 3-2 is specifically as follows: Perform map matching. Use the KD-tree algorithm to construct a binary tree from the road centerline point coordinates in the electronic map data obtained in step 1 to accelerate the query of the nearest neighbor road coordinates; Step 3-3 is specifically as follows: Traverse the vehicle trajectory to query the nearest neighbor road coordinates of the original trajectory points, so as to obtain the midpoint of the two nearest neighbor road coordinates corresponding to the original trajectory points; Based on the midpoint coordinates, calculate the longitudinal position S and lateral position D coordinates of the original trajectory points in the Frenet coordinate system.

[0010] Preferably, step 3-3 is specifically as follows: For each original trajectory point in the vehicle trajectory set Match the node pair of the nearest neighbor road coordinates and to establish a node vector Use the node vector to calculate the perpendicular distance from the original trajectory point to the local sub-segment ; For each current subset, define the vector from the original trajectory point to the node pair , then calculate the perpendicular distance and the longitudinal incremental distance , obtain the road boundary stake number according to the electronic map data in step 1 , and obtain the longitudinal position S and lateral position D coordinates of the original trajectory point in the Frenet coordinate system: ; ; In the formula: is the road boundary stake number.

[0011] Preferably, step 4-1 is specifically as follows: Select the smallest time window for sliding, and identify the extreme point sequence of the statistic through the first derivative method as the candidate points for segmentation. Set a threshold to judge the extreme points less than the threshold, exclude the extreme points less than the threshold from the candidate points for segmentation, obtain the final candidate points for segmentation, and then obtain multiple sub-trajectories, and use the list index to mark the original point positions of the sub-trajectories after segmentation; The formula for the statistic is as follows: ; In the above formula and The calculation formula is: ; ; ; ; ; In the formula: is the length of the sub-trajectory, that is, the time span; is the mean-adjusted sequence, representing the deviation between the original value and the mean m; is the original value, the observed value at the i-th moment in the original trajectory points; is the time series The arithmetic mean of, the time series is The set of; n is the total length of the time series ;

[0012] Preferably, in step 4-2, multiple sub-trajectories are encrypted by fractal interpolation, and inserting interpolation points between the original trajectory points is specifically: Let the interpolation points be expressed as {S, D} = , the point set is linearly sorted by its abscissa, , the two-dimensional plane fractal interpolation function is: ; Solving the above equation to obtain some parameters: ; ; These mappings satisfy the following conditions: ; In the formula: Real number Is completely determined by the interpolation points; Is the vertical scaling factor of each interval , and the value range is ;

[0013] Preferably, in step 4-3, denoising and smoothing of the interpolation points are specifically: Using the signal after fractalizing the vehicle trajectory in step 4-2, a Butterworth filter is used for denoising to eliminate the deterministic signal, colored noise, and Gaussian white noise in the satellite positioning signal, and the interpolation points obtained in step 4-2 are denoised through the following equations to obtain 、 : ; ; ; In the formula: is the signal frequency, Hz; is the cut-off frequency of the filter, Hz; is the order of the filter; represents the convolution operation; The SG filter is used for smoothing to make the trajectory conform to the reality. The form of the SG filter is shown in the following equation: ; ; In the formula: 、 are the smoothed values; 、 are the denoised values; is the th filtering coefficient, calculated through a polynomial of order ; if the length of the vehicle trajectory is expressed as 2m + 1, then ranges from [-m, m]; is the half-filtering length.

[0014] Preferably, the vertical scaling factor in step 4-2 is determined according to the motion consistency of the sub-trajectory and the vehicle dynamics constraints.

[0015] Preferably, step 4-4 is specifically: combining the segmented candidate points before segmentation, aligning the interpolation points at intervals of 0.1 second between adjacent segmented candidate points to obtain a sub-second reconstructed satellite positioning trajectory.

[0016] Compared with the prior art, the advantages of this application are: (1) This application proposes a method for sub - second reconstruction of vehicle trajectories based on high - frequency satellite positioning data. By using the self - similarity feature of vehicle trajectory signals for encryption, it can well capture the self - similarity and local details of the trajectory, with low computational complexity, reducing the need for prior knowledge. Its parameter selection takes into account satellite positioning system errors, vehicle motion consistency, and physical consistency constraints, with strong adaptability. Moreover, it can achieve reliable performance without the need for a large amount of training data and multi - source perception data for calibration. Therefore, this application is an economical, efficient, accurate, and reliable data encryption method for solving spatio - temporal large - range trajectories at high - frequency sampling rates; (2) This application aligns interpolation points at intervals of 0.1 seconds between adjacent segmented candidate points to obtain a sub - second reconstructed satellite positioning trajectory. Therefore, the interval between adjacent trajectory points can be refined from the original average of 20 - 30m to within 1m. The method of this application improves the accuracy of GPS vehicle trajectory matching with the map and the resolution of vehicle trajectory feature analysis, providing a large amount of effective high - quality and high - resolution data for various vehicle trajectory applications; (3) This application uses a Butterworth filter for denoising. During the denoising process, it considers removing high - frequency and low - frequency noise while retaining the overall smooth trajectory, preserving the motion details and improving the quality of vehicle trajectory reconstruction. Description of the Drawings

[0017] Figure 1 is a flowchart of the method for sub - second reconstruction of vehicle trajectories based on high - frequency satellite positioning data; Figure 2 is a GPS vehicle trajectory electronic map matching and Frenet coordinate conversion diagram; Figure 3 is a vehicle trajectory segmentation diagram; Figure 4 is a trajectory fractal reconstruction diagram; Figure 5 is a GPS vehicle trajectory signal denoising and smoothing diagram; Figure 6 is a comparison diagram between the original vehicle trajectory and the sub - second reconstructed trajectory diagram. Detailed Embodiments

[0018] The following describes this application in detail with reference to the drawings and specific embodiments, but this application is not limited to these embodiments. This application covers any alternatives, modifications, equivalent methods, and solutions made within the essence and scope of this application. For the public to have a thorough understanding of this application, specific details are described in detail in the following embodiments of this application, but those skilled in the art can fully understand this application without these detailed descriptions.

[0019] Such as Figure 1As shown in the figure, it is a flowchart of the vehicle trajectory sub-second reconstruction method based on high-frequency satellite positioning data in this application. A vehicle trajectory sub-second reconstruction method based on high-frequency satellite positioning data is disclosed, including the following steps: Step 1: Obtain electronic map data; Step 2: Obtain large-scale satellite positioning vehicle trajectories and process the large-scale satellite positioning vehicle trajectories; Step 2-1: Group vehicle trajectories; Step 2-2: Adjust the format of vehicle trajectories; Step 2-3: Remove abnormal points from vehicle trajectories; Step 3: Match the processed vehicle trajectories with geographical information; Step 3-1: Projection transformation, convert the longitude and latitude coordinates of the vehicle trajectory into a projected coordinate system; Step 3-2: Map matching, match the vehicle trajectory in the projected coordinate system with the electronic map data obtained in Step 1; Step 3-3: Frenet coordinate transformation, based on the electronic map data matching, obtain the longitudinal position S and transverse position D coordinates of the vehicle trajectory in the Frenet coordinates; Step 4: Sub-second reconstruction of vehicle trajectories; Step 4-1: Trajectory segmentation, based on the statistic of the Hurst exponent, segment the vehicle trajectory processed in Step 3 to obtain multiple sub-trajectories; Step 4-2: Fractal interpolation to encrypt the trajectory, encrypt multiple sub-trajectories through fractal interpolation, and insert interpolation points between the original trajectory points of the vehicle trajectory processed in Step 3; Step 4-3: Denoise and smooth the interpolation points; Step 4-4: Align and interpolate the interpolation points with the original trajectory points, and align the interpolation points at equal intervals; Step 4-5: Repeat Steps 4-1 to 4-4 to obtain the reconstructed satellite positioning trajectory; Step 5: Reverse-transform the reconstructed satellite positioning trajectory to the Cartesian coordinate system, re-match the electronic map data, and calculate the vehicle motion characteristics.

[0020] Preferably, in Step 2-1, the vehicle trajectory grouping is specifically as follows: Group the large-scale satellite positioning (GPS) vehicle trajectories by vehicle ID, and sort each group by timestamp.

[0021] Preferably, in Step 2-3, the removal of abnormal points from vehicle trajectories is specifically as follows: The abnormal vehicle trajectory points include position jump abnormal points, time interval abnormal points, and trajectory deviation abnormal points. First, remove the position jump abnormal points and time interval abnormal points, then use the outlier factor algorithm to remove the trajectory deviation abnormal points, and finally save each group as a data file separately; The specific process of removing the trajectory deviation abnormal points by the outlier factor algorithm is as follows: First, find the k nearest neighbors for each original trajectory point of the vehicle trajectory, calculate the density between the original trajectory point and its neighbors. If the density of a certain original trajectory point is significantly lower than that of the surrounding neighbors, it will be marked as an abnormal point, and the trajectory deviation abnormal points that deviate significantly from the normal trajectory are screened out.

[0022] In the outlier factor algorithm (LOF algorithm), set the LOF threshold for lateral error to 5 meters, and screen out the abnormal points that deviate significantly from the normal trajectory.

[0023] Preferably, the specific step 3-1 is: Use the pyproj library to convert the longitude and latitude coordinates of the vehicle trajectory into a projected coordinate system according to the EPSG code of the data coordinate system; The specific step 3-2 is: Perform map matching. Use the KD-tree algorithm to construct a binary tree from the road centerline point coordinates in the electronic map data obtained in step 1 for accelerating the query of the nearest neighbor road coordinates; The specific step 3-3 is: Traverse the vehicle trajectory to query the nearest neighbor road coordinates of the original trajectory points, so as to obtain the midpoint coordinates of the two nearest neighbor road coordinates corresponding to the original trajectory points; Based on the midpoint coordinates, calculate the longitudinal position S and lateral position D coordinates of the original trajectory points in the Frenet coordinate system.

[0024] Preferably, the specific step 3-3 is: For each original trajectory point in the vehicle trajectory set Match the node pairs of the nearest neighbor road coordinates and , establish a node vector , use the node vector to calculate the perpendicular distance from the original trajectory point to the local sub-segment; For each current sub-set, define the vector from the original trajectory point to the node pair , then calculate the perpendicular distance and the longitudinal incremental distance , obtain the road boundary stake numbers according to the electronic map data in step 1 , and obtain the longitudinal position S and lateral position D coordinates of the original trajectory points in the Frenet coordinate system: ; ; In the formula: is the road boundary stake number.

[0025] Preferably, the specific step 4-1 is: select the smallest time window for sliding, and identify the extreme point sequence of the statistic as the segmentation candidate points, set a threshold to judge the extreme points less than the threshold, exclude the extreme points less than the threshold from the segmentation candidate points, obtain the final segmentation candidate points, and then obtain multiple sub-trajectories, and use the list index to mark the original point positions of the sub-trajectories after segmentation; The statistic calculation formula is as follows: ; In the above formula and The calculation formulas are: ; ; ; ; ; In the formula: is the length of the sub-trajectory, that is, the time span; is the mean adjustment sequence, representing the deviation between the original value and the mean m; is the original value, the observed value at the i-th moment in the original trajectory points; is the time series The arithmetic mean of, the time series is The set of; n is the total length of the time series ;

[0026] Preferably, in step 4-2, multiple sub-trajectories are encrypted by fractal interpolation, and the specific method of inserting interpolation points between the original trajectory points is: Let the interpolation points be expressed as {S, D} = , the point set is linearly sorted according to its abscissa, , the two-dimensional plane fractal interpolation function is: ; Solve the above equation to obtain some parameters: ; ; These mappings satisfy the following conditions: ; In the formula: real number is completely determined by the interpolation points; is the vertical scaling factor for each interval with a value range of .

[0027] Preferably, the denoising and smoothing of the interpolation points in step 4-3 are specifically as follows: Based on the signal after fractalizing the vehicle trajectory in step 4-2, use a Butterworth filter for denoising to eliminate the deterministic signal, colored noise, and Gaussian white noise in the satellite positioning signal, and denoise the interpolation points obtained in step 4-2 through the following equation to obtain , : ; ; ; In the formula: is the signal frequency, Hz; is the cut-off frequency of the filter, Hz; is the order of the filter; represents the convolution operation; Use an SG filter for smoothing to make the trajectory conform to reality. The form of the SG filter is shown in the following equation: ; ; In the formula: , are the smoothed values; , are the denoised values; is the th filtering coefficient, calculated by a polynomial of order ; if the length of the vehicle trajectory is expressed as 2m + 1, then ranges from [-m, m]; is the half-filtering length.

[0028] Preferably, the vertical scaling factor in step 4-2 is determined according to the motion consistency of the sub-trajectory and vehicle dynamics constraints.

[0029] Preferably, step 4-4 is specifically: combining the segmented candidate points before segmentation, aligning the interpolation points at intervals of 0.1 second between adjacent segmented candidate points, to obtain a sub-second reconstructed satellite positioning trajectory.

[0030] The selection of the SG filtering smoothing order and the selection of Butterworth filter parameters are based on the UAV trajectory of the same vehicle as the true trajectory to train the parameters. The objective function is to minimize the cost of the reconstructed trajectory from the fractal state to the true trajectory state, and this cost is defined as the RMSE between the reconstructed trajectory and the measured trajectory. The objective function can be expressed by the formula: ; where is the cost of the reconstructed trajectory; is the GPS position coordinate of the vehicle at time ; is the control vector of the vehicle at the reconstructed time t, is the initial time of the measured trajectory, in seconds, is the end time of the measured trajectory, in seconds, and the Euclidean distance is used as the objective function.

[0031] Embodiment 1 Taking the GPS vehicle trajectory of a 1-km long circular curve section of a certain expressway in Guilin City as an example, the method of this application is described as follows. The specific process is as follows: (1) Select a large number of GPS vehicle trajectories of a 1-km long section of the expressway in Guilin City, group the large number of GPS vehicle trajectories, and use the Local Outlier Factor (LOF) algorithm to remove the outliers of the GPS vehicle trajectories, with the threshold set to 2 m.

[0032] Use the pyproj library to convert it using the code: transform(Proj(init='epsg:4490'), Proj(init='epsg:4549'), longitude, latitude) to the projection coordinate system CGCS2000 / 3-degree Gauss-Kruger CM 111E (epsg:4546). Then crawl the road centerline and divide it into coordinates at 1-m intervals, use the nearest neighbor algorithm to match the vehicle trajectory to the midpoint of the two nearest neighbor road coordinates, and then convert it to the Frenet coordinate system, as shown in Table 1: Table 1 Projection transformation of the original vehicle trajectory and conversion to the Frenet coordinate system (partial) As shown Figure 2 in the figure, it is a GPS vehicle trajectory electronic map matching and Frenet coordinate conversion diagram. In the figure, (a) is the GPS vehicle trajectory electronic map matching, and its coordinate system is CGJ-02 (epsg:4490). In the figure, (b) is the conversion of the Cartesian coordinate system into the Frenet coordinate system, and the figure includes the original trajectory points and the original trajectory line.

[0033] (2) Select the minimum sliding window unit length of the sub-trajectory to be 3 seconds. If the statistic continues to increase with the time series, a longer sequence is incorporated to enhance the self-similarity of the sub-trajectory. After a certain time point the statistic suddenly drops (extreme point), and this point is used as the segmentation candidate point. Finally, set the extreme point threshold to 0.05, and merge the segmentation candidate points smaller than the threshold to obtain the segmented sub-trajectories.

[0034] As shown Figure 3 in the figure, it is a vehicle trajectory segmentation diagram. In the figure, (a) is the extreme point identified by the V statistic, and in the figure, (b) is the trajectory segmentation diagram.

[0035] (3) Take all the real points of each sub-trajectory as interpolation points, and substitute the interpolation points between any two adjacent points in this section in turn to interpolate and generate fractal points. Then set the first and last points of the fractal points as the start and end points of the adjacent points. Therefore, the number of points iterated by the adjacent points is equal to the number of real points selected at the beginning. The second iteration is to use the points newly generated in the first iteration as interpolation points for iteration. 5 points are iterated between the first adjacent points, and 25 points are iterated by substituting all the points iterated in the first iteration for the second time. The two iterations are used respectively to fill the noise and motion details of the original GPS vehicle trajectory information.

[0036] As shown Figure 4 in the figure, it is a trajectory fractal reconstruction diagram. In the figure, (a) is the trajectory fractal iteration process diagram, and in the figure, (b) is the trajectory fractal interpolation diagram.

[0037] (4) Select the order of the Butterworth filter to be 6; for denoising, consider removing these high-frequency and low-frequency noises while retaining the overall smooth trajectory and also retaining the motion details, and select the cut-off frequency to be 1Hz. Then use the trajectory taken by the drone of the same vehicle as the real trajectory to train the SG filter parameters. The order = 3 and the half filter length = 10 minimize the MSE between the GPS and the drone trajectories to obtain a smooth motion trajectory.

[0038] As shown Figure 5 in the figure, in the figure, (a) is the trajectory denoising diagram, and in the figure, (b) is the trajectory smoothing diagram.

[0039] (5) Combine the segment candidate points before segmentation, align the interpolation points at intervals of 0.1 seconds between adjacent segment candidate points to obtain a sub - second - level reconstructed satellite positioning trajectory; then perform coordinate back - calculation into the XY coordinate system, and finally re - match the sub - second - level reconstructed trajectory to the road according to step 3, as shown in Table 2: Table 2 Time Deduction and Field Heap Area (Partial) As Figure 6 shown, it is a comparison diagram between the original vehicle trajectory and the sub - second - level reconstructed trajectory diagram. Figure 6 In it, (a) is the original vehicle trajectory diagram. Figure 6 In it, (b) is the sub - second - level reconstructed trajectory diagram.

[0040] The working principle of this application is as follows: This application proposes a method for sub - second - level reconstruction of vehicle trajectories based on high - frequency satellite positioning data, which is applicable to data with a high sampling rate. First, obtain a large - scale satellite - positioned vehicle trajectory, process the large - scale satellite - positioned vehicle trajectory, and remove abnormal points of the vehicle trajectory; then project and transform the vehicle trajectory and use the nearest - neighbor algorithm to match the road information of the electronic map data to obtain the Frenet coordinate system information of the vehicle trajectory; then perform trajectory segmentation based on the V - statistic of the Hurst index, use the fractal interpolation method to improve the resolution of the vehicle trajectory signal, and denoise and smooth the vehicle trajectory; finally, align the data and deduce the motion characteristics. This application improves the resolution of the vehicle trajectory data obtained by the satellite positioning system and the accuracy of the vehicle trajectory matching the map, and promotes the development of fields such as traffic prediction and road safety analysis.

[0041] This application proposes a method for sub - second - level reconstruction of vehicle trajectories based on high - frequency satellite positioning data. It encrypts using the self - similarity characteristics of the vehicle trajectory signal, can well capture the self - similarity and local details of the trajectory, has a low computational complexity, reduces the need for prior knowledge, and its parameter selection takes into account the satellite positioning system error, vehicle motion consistency, and physical consistency constraints, with strong self - adaptability. And it can achieve reliable performance without the need for a large amount of training data and multi - source perception data for calibration. Therefore, this application is an economical, efficient, accurate, and reliable data encryption method for solving spatio - temporal large - range trajectories at a high sampling rate.

[0042] This application aligns the interpolation points at intervals of 0.1 seconds between adjacent segment candidate points to obtain a sub - second - level reconstructed satellite positioning trajectory. Therefore, the interval between adjacent trajectory points can be refined from the original average of 20 - 30 m to within 1 m. The method of this application improves the accuracy of GPS vehicle trajectory matching the map and the resolution of vehicle trajectory feature analysis, providing a large amount of effective high - quality and high - resolution data for various vehicle trajectory applications.

[0043] In this application, a Butterworth filter is used for denoising. During the denoising process, while considering retaining the overall smooth trajectory, high-frequency and low-frequency noises are removed, the motion details are retained, and the quality of vehicle trajectory reconstruction is improved.

[0044] The preferred embodiments of the present application are described in detail above. However, the present application is not limited to the above embodiments, and various changes can be made without departing from the gist of the present application within the knowledge scope of those of ordinary skill in the art.

[0045] Many other changes and modifications can be made without departing from the concept and scope of the present application. It should be understood that the present application is not limited to specific embodiments, and the scope of the present application is defined by the appended claims.

Claims

1. A method for sub - second reconstruction of vehicle trajectories based on high - frequency satellite positioning data, characterized in that, It includes the following steps: Step 1: Obtain electronic map data; Step 2: Obtain large-scale satellite positioning vehicle trajectories and process the large-scale satellite positioning vehicle trajectories; Step 2-1: Group vehicle trajectories; Step 2-2: Adjust the format of vehicle trajectories; Step 2-3: Remove abnormal points from vehicle trajectories; Step 3: Match the processed vehicle trajectories with geographical information; Step 3-1: Projection transformation to convert the longitude and latitude coordinates of vehicle trajectories into a projected coordinate system; Step 3-2: Map matching to match the vehicle trajectories in the projected coordinate system with the electronic map data obtained in Step 1; Step 3-3: Frenet coordinate transformation to obtain the longitudinal position S and lateral position D coordinates of the vehicle trajectories in the Frenet coordinates based on the matching of electronic map data; Step 4: Reconstruct vehicle trajectories at sub-second level; Step 4-1: Trajectory segmentation. Based on the statistic of the Hurst exponent, segment the vehicle trajectory processed in Step 3 to obtain multiple sub-trajectories; Step 4-2: Interpolate and encrypt trajectories by fractal interpolation, insert interpolation points between the original trajectory points of the vehicle trajectories processed in Step 3; Step 4-3: Denoise and smooth the interpolation points; Step 4-4: Align and interpolate the interpolation points with the original trajectory points, and align the interpolation points at equal intervals; Step 4-5: Repeat Steps 4-1 to 4-4 to obtain the reconstructed satellite positioning trajectories; Step 5: Reverse-transform the reconstructed satellite positioning trajectories to the Cartesian coordinate system, rematch the electronic map data, and calculate vehicle motion characteristics.

2. The vehicle trajectory sub-second reconstruction method based on high-frequency satellite positioning data according to claim 1, wherein, In the vehicle trajectory grouping in Step 2-1, specifically: group the large-scale satellite positioning vehicle trajectories by vehicle ID, and sort each group by timestamp.

3. The vehicle trajectory sub - second - level reconstruction method based on high - frequency satellite positioning data according to claim 2, wherein, In the removal of abnormal points from vehicle trajectories in Step 2-3, specifically: The abnormal points of vehicle trajectories include position jump abnormal points, time interval abnormal points, and trajectory deviation abnormal points. First, remove the position jump abnormal points and time interval abnormal points, then use the outlier factor algorithm to remove the trajectory deviation abnormal points, and finally save each group as a data file separately; The specific process of removing trajectory deviation abnormal points by the outlier factor algorithm is: first find the nearest k neighbors for each original trajectory point of the vehicle trajectory, calculate the density between the original trajectory point and the neighbors. If the density of a certain original trajectory point is significantly lower than that of the surrounding neighbors, it will be marked as an abnormal point, and filter out the trajectory deviation abnormal points that deviate significantly from the normal trajectory.

4. The vehicle trajectory sub - second - level reconstruction method based on high - frequency satellite positioning data according to claim 3, wherein, In Step 3-1, specifically: use the pyproj library to convert the longitude and latitude coordinates of vehicle trajectories into a projected coordinate system according to the EPSG code of the data coordinate system; In Step 3-2, specifically: perform map matching, and construct a binary tree from the road centerline point coordinates in the electronic map data obtained in Step 1 through the KD-tree algorithm to accelerate the query of the nearest neighbor road coordinates; In Step 3-3, specifically: traverse the vehicle trajectory to query the nearest neighbor road coordinates of the original trajectory points, so as to obtain the midpoint of the two nearest neighbor road coordinates corresponding to the original trajectory points; based on the midpoint coordinates, calculate the longitudinal position S and lateral position D coordinates of the original trajectory points in the Frenet coordinates.

5. The vehicle trajectory sub-second reconstruction method based on high-frequency satellite positioning data according to claim 4, wherein In Step 3-3, specifically: Each original trajectory point of the vehicle trajectory set Node pairs that match to the nearest neighbor road coordinates and , establish a node vector , use the node vector to calculate the original trajectory point to the perpendicular distance of the local sub-segment ; for each current subset, define the vector from the original trajectory point to the node pair , then calculate the perpendicular distance and the longitudinal incremental distance , obtain the road boundary stake numbers according to the electronic map data in step 1 , and obtain the longitudinal position S and lateral position D coordinates of the original trajectory point in the Frenet coordinate:​ ； ； In the formula: It is the road boundary stake number.

6. The vehicle trajectory sub-second reconstruction method based on high-frequency satellite positioning data according to claim 1, wherein The specific content of step 4-1 is as follows: Select the smallest time window for sliding, and identify the extreme point sequence of the statistic as the candidate points for segmentation. Set a threshold to judge the extreme points smaller than the threshold, exclude the extreme points smaller than the threshold from the candidate points for segmentation, obtain the final candidate points for segmentation, and then obtain multiple sub-trajectories, and use the list index to mark the original point positions of the sub-trajectories after segmentation; The statistic calculation formula is as follows: ； In the above formula and The calculation formula is as follows: ； ； ； ； ； In the formula: is the length of the sub-trajectory, i.e., the time span; is the mean-adjusted sequence, representing the original value is the deviation from the mean m; is the original value and the observed value at the i-th moment in the original trajectory point; is the arithmetic mean of the time series and the time series is a set of; n is the total length of the time series .

7. The vehicle trajectory sub-second reconstruction method based on high-frequency satellite positioning data according to claim 6, wherein In step 4-2, multiple sub-trajectories are encrypted by fractal interpolation. Specifically, the interpolation points are inserted between the original trajectory points as follows: Let the interpolation points be represented as {S, D} = , the point set is linearly sorted by its abscissa, , and the two-dimensional plane fractal interpolation function is: ； Solve the above equations to obtain some parameters: ； ； These mappings satisfy the following conditions: ； In the formula: Real number Completely determined by the interpolation points; is the vertical scaling factor for each interval with a value range of .

8. The vehicle trajectory sub-second reconstruction method based on high-frequency satellite positioning data according to claim 7, characterized in that In step 4-3, the interpolation points are denoised and smoothed specifically as follows: According to the signal after fractalizing the vehicle trajectory in Step 4-2, use a Butterworth filter to denoise, eliminate the deterministic signal, colored noise, and Gaussian white noise in the satellite positioning signal, and use the interpolation points obtained in Step 4-2 Denoise through the following equation to obtain , : ； ； ； In the formula: is the signal frequency, Hz; is the cut-off frequency of the filter, Hz; is the order of the filter; Denotes a convolution operation; Use the SG filter for smoothing to make the trajectory conform to the reality. The form of the SG filter is shown in the following equation: ； ； In the formula: , is the smoothed value; , is the value after denoising; is the th filter coefficient, calculated by a polynomial of order ; if the length of the vehicle trajectory is expressed as 2m + 1, then ranges from [-m, m]; is the half filter length.

9. The vehicle trajectory sub - second reconstruction method based on high - frequency satellite positioning data according to claim 7, characterized in that, The vertical scaling factor in step 4-2 is determined according to the motion consistency of the sub-trajectory and vehicle dynamics constraints.

10. The vehicle trajectory sub - second level reconstruction method based on high - frequency satellite positioning data according to claim 7, characterized in that, Step 4-4 is specifically as follows: Combine the segmented candidate points before segmentation, align the interpolation points at intervals of 0.1 second between adjacent segmented candidate points, and obtain a sub-second reconstructed satellite positioning trajectory.

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