Sub-second vehicle trajectory reconstruction method based on high-frequency satellite positioning data

Abstract

This application belongs to the field of transportation science and big data technology, and discloses a sub-second vehicle trajectory reconstruction method based on high-frequency satellite positioning data. It uses the self-similarity characteristics of vehicle trajectory signals for encryption, can well capture the self-similarity and local details of the trajectory, has low computational complexity, and reduces the need for prior knowledge. Its parameter selection takes into account satellite positioning system errors, vehicle motion consistency and physical consistency constraints, has strong adaptability, and does not require a large amount of training data and multi-source perception data for correction to achieve reliable performance. Therefore, this application is an economical, efficient, accurate and reliable data encryption method for solving large-scale temporal and spatial trajectories at a high-frequency sampling rate.

Description

Technical Field

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

[0002] In recent years, vehicle trajectory information has shown tremendous potential and broad prospects for a wide range of applications. Vehicle trajectories provide critical information for a variety of transportation applications, including high-precision digital map construction, traffic safety analysis, and mobility-related applications. With the advancement of satellite positioning accuracy, frequency, and ease of acquisition, mobile sensor trajectory data has become more reliable and can cover any desired temporal and spatial range. However, the quality of mobile sensor data should be a primary consideration, as 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 significantly improved their positioning accuracy and frequency, such as GPS trajectory data with a 1Hz sampling rate, which is already widely collected and utilized, the distance between adjacent trajectory points is approximately 20-30 meters, which is too far for many trajectory-based road and traffic flow safety analyses. Road management departments and highway management companies currently collect large amounts 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] Trajectory data collected by GNSS still contains some signal noise, such as satellite and receiver clock errors and orbit errors. This noise is random in nature, so algorithms must simultaneously remove it while improving trajectory data resolution. Furthermore, reconstruction algorithms must consider economic costs. Collecting the necessary amount of labeled training or utilizing multi-source sensing devices is prohibitively expensive for big data. Developing successful artificial intelligence or trajectory models requires access to vast amounts of data, so developing cost-effective methods to improve data resolution and accuracy is essential. Summary of the Invention

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

[0006] In order to solve the technical problem, the technical solution of this application is: a vehicle trajectory sub-second reconstruction method based on high-frequency satellite positioning data, comprising the following steps:

[0007] Step 1: Acquisition of electronic map data;

[0008] Step 2: Acquire large-scale satellite-based vehicle trajectories and process them;

[0009] Step 2-1: vehicle trajectory grouping;

[0010] Step 2-2: Vehicle trajectory format adjustment;

[0011] Step 2-3: Remove abnormal points in vehicle trajectories;

[0012] Step 3: Match the processed vehicle trajectory with geographic information;

[0013] Step 3-1: Projection transformation, converting the latitude and longitude coordinates of the vehicle trajectory into a projected coordinate system;

[0014] Step 3-2: Map matching, matching the vehicle trajectory in the projected coordinate system with the electronic map data obtained in step 1;

[0015] Step 3-3: Frenet coordinate conversion, based on the electronic map data matching, obtain the longitudinal position S and lateral position D coordinates of the vehicle trajectory in Frenet coordinates;

[0016] Step 4: Sub-second reconstruction of vehicle trajectory;

[0017] Step 4-1: Trajectory segmentation based on Hurst exponent The statistics divide the vehicle trajectory processed in step 3 into multiple sub-trajectories;

[0018] Step 4-2: Fractal interpolation encrypts the trajectory, encrypting multiple sub-trajectories through fractal interpolation, and inserting interpolation points between the original trajectory points of the vehicle trajectory processed in step 3;

[0019] Step 4-3: Denoise and smooth the interpolation points;

[0020] Step 4-4: Align the interpolation points with the original trajectory points and align the interpolation points at equal distances;

[0021] Step 4-5: Repeat steps 4-1 to 4-4 to obtain the reconstructed satellite positioning trajectory;

[0022] Step 5: Reverse-convert the reconstructed satellite positioning trajectory into the Cartesian coordinate system, re-match the electronic map data, and calculate the vehicle motion characteristics.

[0023] Preferably, the vehicle trajectory grouping in step 2-1 is specifically: grouping the large-scale satellite positioning vehicle trajectories by vehicle ID, and sorting each group by timestamp.

[0024] Preferably, the removal of vehicle trajectory abnormal points in step 2-3 is specifically as follows:

[0025] The vehicle trajectory anomalies include position jump anomalies, time interval anomalies, and trajectory deviation anomalies. First, the position jump anomalies and time interval anomalies are removed, and then the trajectory deviation anomalies are removed using the abnormal outlier factor algorithm. Finally, each group is saved as a separate data file.

[0026] The specific process of the outlier factor algorithm to remove trajectory deviation anomalies is as follows: first, for each original trajectory point of the vehicle trajectory, its nearest k neighbors are found, and the density between the original trajectory point and its neighbors is calculated. If the density of an original trajectory point is significantly lower than that of its surrounding neighbors, it will be marked as an outlier, and trajectory deviation anomalies that significantly deviate from the normal trajectory are screened out.

[0027] Preferably, the step 3-1 specifically comprises: converting the latitude and longitude coordinates of the vehicle trajectory into a projection coordinate system using the pyproj library according to the EPSG code of the data coordinate system;

[0028] Step 3-2 specifically includes: performing map matching, constructing a binary tree of the coordinates of the road centerline points in the electronic map data obtained in step 1 using a KD-tree algorithm to accelerate the query of the nearest neighbor road coordinates;

[0029] Step 3-3 specifically includes: traversing the vehicle trajectory to query the nearest neighbor road coordinates of the original trajectory point, thereby obtaining the midline point of the two nearest neighbor road coordinates corresponding to the original trajectory point; based on the coordinates of the midline point, calculating the longitudinal position S and lateral position D coordinates of the original trajectory point in Frenet coordinates.

[0030] Preferably, the step 3-3 is specifically as follows:

[0031] Each original trajectory point of the vehicle trajectory set Node pairs matched to nearest neighbor road coordinates and , establish the node vector , using the node vector Calculate the original trajectory points Perpendicular distance to the local sub-segment ; For each current subset, define the original trajectory point To node pair Vector , then calculate the vertical distance and longitudinal incremental distance , according to the electronic map data in step 1, obtain the road boundary stake number , the longitudinal position S and lateral position D coordinates of the original trajectory point in Frenet coordinates are obtained:

[0032] ;

[0033] ;

[0034] Where:

[0035] The road boundary station number.

[0036] Preferably, the step 4-1 is specifically as follows: selecting a minimum time window for sliding, and identifying the Extreme point sequence of statistics As the segmentation candidate point, set a threshold to judge the extreme point less than the threshold, exclude the extreme point less than the threshold from the segmentation candidate point, obtain the final segmentation candidate point, and then obtain multiple sub-trajectories, and use the list index to mark the original point position of the segmented sub-trajectory;

[0037] described The statistical calculation formula is as follows:

[0038] ;

[0039] In the above formula and The calculation formula is:

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] ;

[0045] Where:

[0046] is the length of the sub-trajectory, i.e., the time span;

[0047] is the mean-adjusted series, representing the original value Deviation from the mean m;

[0048] is the original value, the observation value at the i-th moment in the original trajectory point;

[0049] For time series The arithmetic mean of the time series for A collection of

[0050] n is the time series The total length of

[0051] Preferably, in step 4-2, multiple sub-trajectories are encrypted by fractal interpolation, and interpolation points are inserted between original trajectory points as follows:

[0052] Let the interpolation point be represented by {S, D} = , the point set is linearly sorted by its horizontal coordinate, , the two-dimensional plane fractal interpolation function is:

[0053] ;

[0054] Solving the above equations yields some parameters:

[0055] ;

[0056] ;

[0057] These mappings satisfy the following conditions:

[0058] ;

[0059] Where:

[0060] Real numbers Completely determined by the interpolation points;

[0061] Each interval The vertical scaling factor of .

[0062] Preferably, the denoising and smoothing of the interpolation points in step 4-3 are specifically as follows:

[0063] According to the fractal signal of the vehicle trajectory in step 4-2, the Butterworth filter is used to remove the deterministic signal, colored noise and Gaussian white noise in the satellite positioning signal, and the interpolation point obtained in step 4-2 is Denoising is done by the following equation to obtain 、 :

[0064] ;

[0065] ;

[0066] ;

[0067] Where:

[0068] is the signal frequency, Hz;

[0069] is the filter cutoff frequency, Hz;

[0070] is the order of the filter;

[0071] Represents the convolution operation;

[0072] Use SG filter to smooth the trajectory so that it conforms to reality. The form of SG filter is shown in the following equation:

[0073] ;

[0074] ;

[0075] Where:

[0076] 、 is the smoothed value;

[0077] 、 is the denoised value;

[0078] It is filter coefficients, the order is Polynomial calculation; if the length of the vehicle trajectory is expressed as 2m+1, then The value range of is [-m,m];

[0079] is half the filter length.

[0080] Preferably, the vertical scaling factor in step 4-2 is It is determined based on the motion consistency of the sub-trajectories and the vehicle dynamics constraints.

[0081] Preferably, step 4-4 is specifically as follows: combining the segmentation candidate points before segmentation, aligning interpolation points between adjacent segmentation candidate points at intervals of 0.1 seconds, and obtaining a sub-second reconstructed satellite positioning trajectory.

[0082] Compared with the prior art, the advantages of this application are:

[0083] (1) This application proposes a sub-second vehicle trajectory reconstruction method based on high-frequency satellite positioning data. The method utilizes the self-similarity characteristics of vehicle trajectory signals for encryption, which can well capture the self-similarity and local details of the trajectory. The computational complexity is low, and the need for prior knowledge is reduced. The parameter selection takes into account the satellite positioning system error, vehicle motion consistency, and physical consistency constraints. The method has strong adaptability and does not require a large amount of training data and multi-source perception data for correction to achieve reliable performance. Therefore, this application is an economical, efficient, accurate and reliable data encryption method for solving large-scale temporal and spatial trajectories at a high sampling rate.

[0084] (2) This application aligns interpolation points between adjacent segmented candidate points at intervals of 0.1 seconds to obtain sub-second reconstructed satellite positioning trajectories. Therefore, the intervals between adjacent trajectory points can be refined from the original average of 20-30 meters to within 1 meter. This method improves the accuracy of GPS vehicle trajectory matching maps 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.

[0085] (3) This application uses a Butterworth filter for denoising. The denoising process considers retaining the overall smooth trajectory while removing high-frequency and low-frequency noise, retaining motion details and improving the quality of vehicle trajectory reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 Flowchart of the sub-second vehicle trajectory reconstruction method based on high-frequency satellite positioning data;

[0087] Figure 2 Matching GPS vehicle trajectory electronic map with Frenet coordinate conversion map;

[0088] Figure 3 is the vehicle trajectory segmentation map;

[0089] Figure 4 Reconstruct the trajectory fractal;

[0090] Figure 5 Denoising and smoothing graph of GPS vehicle trajectory signal;

[0091] Figure 6 Comparison chart of the original vehicle trajectory and the sub-second reconstruction of the trajectory. DETAILED DESCRIPTION

[0092] The present application is described in detail below with reference to the accompanying drawings and specific examples, but the present application is not limited to these examples. This application covers any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this application. To provide a thorough understanding of this application, specific details are described in detail in the following examples of this application, but those skilled in the art can fully understand this application without these detailed descriptions.

[0093] like Figure 1 FIG. 1 is a flowchart of a method for reconstructing a vehicle trajectory in sub-seconds based on high-frequency satellite positioning data of the present application, which discloses a method for reconstructing a vehicle trajectory in sub-seconds based on high-frequency satellite positioning data, comprising the following steps:

[0094] Step 1: Acquisition of electronic map data;

[0095] Step 2: Acquire large-scale satellite-based vehicle trajectories and process them;

[0096] Step 2-1: vehicle trajectory grouping;

[0097] Step 2-2: Vehicle trajectory format adjustment;

[0098] Step 2-3: Remove abnormal points in vehicle trajectories;

[0099] Step 3: Match the processed vehicle trajectory with geographic information;

[0100] Step 3-1: Projection transformation, converting the latitude and longitude coordinates of the vehicle trajectory into a projected coordinate system;

[0101] Step 3-2: Map matching, matching the vehicle trajectory in the projected coordinate system with the electronic map data obtained in step 1;

[0102] Step 3-3: Frenet coordinate conversion, based on the electronic map data matching, obtain the longitudinal position S and lateral position D coordinates of the vehicle trajectory in Frenet coordinates;

[0103] Step 4: Sub-second reconstruction of vehicle trajectory;

[0104] Step 4-1: Trajectory segmentation based on Hurst exponent The statistics divide the vehicle trajectory processed in step 3 into multiple sub-trajectories;

[0105] Step 4-2: Fractal interpolation encrypts the trajectory, encrypting multiple sub-trajectories through fractal interpolation, and inserting interpolation points between the original trajectory points of the vehicle trajectory processed in step 3;

[0106] Step 4-3: Denoise and smooth the interpolation points;

[0107] Step 4-4: Align the interpolation points with the original trajectory points and align the interpolation points at equal distances;

[0108] Step 4-5: Repeat steps 4-1 to 4-4 to obtain the reconstructed satellite positioning trajectory;

[0109] Step 5: Reverse-convert the reconstructed satellite positioning trajectory into the Cartesian coordinate system, re-match the electronic map data, and calculate the vehicle motion characteristics.

[0110] Preferably, the vehicle trajectory grouping in step 2-1 is specifically: grouping the large-scale satellite positioning (GPS) vehicle trajectories by vehicle ID, and sorting each group by timestamp.

[0111] Preferably, the removal of vehicle trajectory abnormal points in step 2-3 is specifically as follows:

[0112] The vehicle trajectory anomalies include position jump anomalies, time interval anomalies, and trajectory deviation anomalies. First, the position jump anomalies and time interval anomalies are removed, and then the trajectory deviation anomalies are removed using the abnormal outlier factor algorithm. Finally, each group is saved as a separate data file.

[0113] The specific process of the outlier factor algorithm to remove trajectory deviation anomalies is as follows: first, for each original trajectory point of the vehicle trajectory, its nearest k neighbors are found, and the density between the original trajectory point and its neighbors is calculated. If the density of an original trajectory point is significantly lower than that of its surrounding neighbors, it will be marked as an outlier, and trajectory deviation anomalies that significantly deviate from the normal trajectory are screened out.

[0114] The outlier factor algorithm (LOF algorithm) sets the LOF threshold lateral error to 5 meters to screen out abnormal points that deviate significantly from the normal trajectory.

[0115] Preferably, the step 3-1 specifically comprises: converting the latitude and longitude coordinates of the vehicle trajectory into a projection coordinate system using the pyproj library according to the EPSG code of the data coordinate system;

[0116] Step 3-2 specifically includes: performing map matching, constructing a binary tree of the coordinates of the road centerline points in the electronic map data obtained in step 1 using a KD-tree algorithm to accelerate the query of the nearest neighbor road coordinates;

[0117] Step 3-3 specifically includes: traversing the vehicle trajectory to query the nearest neighbor road coordinates of the original trajectory point, thereby obtaining the midline point of the two nearest neighbor road coordinates corresponding to the original trajectory point; based on the coordinates of the midline point, calculating the longitudinal position S and lateral position D coordinates of the original trajectory point in Frenet coordinates.

[0118] Preferably, the step 3-3 is specifically as follows:

[0119] Each original trajectory point of the vehicle trajectory set Node pairs matched to nearest neighbor road coordinates and , establish the node vector , using the node vector Calculate the original trajectory points Perpendicular distance to the local sub-segment ; For each current subset, define the original trajectory point To node pair Vector , then calculate the vertical distance and longitudinal incremental distance , according to the electronic map data in step 1, obtain the road boundary stake number , the longitudinal position S and lateral position D coordinates of the original trajectory point in Frenet coordinates are obtained:

[0120] ;

[0121] ;

[0122] Where:

[0123] The road boundary station number.

[0124] Preferably, the step 4-1 is specifically as follows: selecting a minimum time window for sliding, and identifying the Extreme point sequence of statistics As the segmentation candidate point, set a threshold to judge the extreme point less than the threshold, exclude the extreme point less than the threshold from the segmentation candidate point, obtain the final segmentation candidate point, and then obtain multiple sub-trajectories, and use the list index to mark the original point position of the segmented sub-trajectory;

[0125] described The statistical calculation formula is as follows:

[0126] ;

[0127] In the above formula and The calculation formula is:

[0128] ;

[0129] ;

[0130] ;

[0131] ;

[0132] ;

[0133] Where:

[0134] is the length of the sub-trajectory, i.e., the time span;

[0135] is the mean-adjusted series, representing the original value Deviation from the mean m;

[0136] is the original value, the observation value at the i-th moment in the original trajectory point;

[0137] For time series The arithmetic mean of the time series for A collection of

[0138] n is the time series The total length of

[0139] Preferably, in step 4-2, multiple sub-trajectories are encrypted by fractal interpolation, and interpolation points are inserted between original trajectory points as follows:

[0140] Let the interpolation point be represented by {S, D} = , the point set is linearly sorted by its horizontal coordinate, , the two-dimensional plane fractal interpolation function is:

[0141] ;

[0142] Solving the above equations yields some parameters:

[0143] ;

[0144] ;

[0145] These mappings satisfy the following conditions:

[0146] ;

[0147] Where:

[0148] Real numbers Completely determined by the interpolation points;

[0149] Each interval The vertical scaling factor of .

[0150] Preferably, the denoising and smoothing of the interpolation points in step 4-3 are specifically as follows:

[0151] According to the fractal signal of the vehicle trajectory in step 4-2, the Butterworth filter is used to remove the deterministic signal, colored noise and Gaussian white noise in the satellite positioning signal, and the interpolation point obtained in step 4-2 is Denoising is done by the following equation to obtain 、 :

[0152] ;

[0153] ;

[0154] ;

[0155] Where:

[0156] is the signal frequency, Hz;

[0157] is the filter cutoff frequency, Hz;

[0158] is the order of the filter;

[0159] Represents the convolution operation;

[0160] Use SG filter to smooth the trajectory so that it conforms to reality. The form of SG filter is shown in the following equation:

[0161] ;

[0162] ;

[0163] Where:

[0164] 、 is the smoothed value;

[0165] 、 is the denoised value;

[0166] It is filter coefficients, the order is Polynomial calculation; if the length of the vehicle trajectory is expressed as 2m+1, then The value range of is [-m,m];

[0167] is half the filter length.

[0168] Preferably, the vertical scaling factor in step 4-2 is It is determined based on the motion consistency of the sub-trajectories and the vehicle dynamics constraints.

[0169] Preferably, step 4-4 is specifically as follows: combining the segmentation candidate points before segmentation, aligning interpolation points between adjacent segmentation candidate points at intervals of 0.1 seconds, and obtaining a sub-second reconstructed satellite positioning trajectory.

[0170] The selection of the SG filter smoothing order and the selection of the Butterworth filter parameters are based on the trajectory of the drone of the same vehicle as the real trajectory to train the parameters. The objective function is to minimize the cost of the reconstructed trajectory from the fractal state to the real trajectory state. The cost is defined as the RMSE of the reconstructed trajectory and the measured trajectory. The objective function can be expressed by the formula:

[0171] ;

[0172] in, is the cost of reconstructing the trajectory; The vehicle at time GPS location coordinates; is the control vector of the vehicle at time t after reconstruction, is the initial time of the measurement trajectory, in seconds, is the final time of the measurement trajectory in seconds, and the Euclidean distance is used as the objective function.

[0173] Example 1

[0174] The following uses the GPS vehicle trajectory of a 1km circular curve section of a highway in Guilin as an example to illustrate the present application method. The specific process is as follows:

[0175] (1) A large number of GPS vehicle trajectories along a 1 km section of Guilin Expressway were selected and grouped. The outlier factor algorithm (LOF algorithm) was used to remove outliers from the GPS vehicle trajectories, with the threshold set to 2 m.

[0176] The pyproj library was used to convert the coordinates to the projected coordinate system CGCS2000 / 3-degree Gauss-Kruger CM 111E (epsg:4546) using the code: transform(Proj(init='epsg:4490'), Proj(init='epsg:4549'), longitude, latitude). The road centerline was then crawled and divided into coordinates with 1-meter intervals. The nearest neighbor algorithm was used to match the vehicle trajectory to the centerline points of the two nearest neighbor road coordinates. The coordinates were then converted to the Frenet coordinate system, as shown in Table 1:

[0177] Table 1 Original vehicle trajectory projection transformation and Frenet coordinate system transformation (partial)

[0178]

[0179] like Figure 2 The figure shows the GPS vehicle trajectory electronic map matching and Frenet coordinate conversion diagram. (a) in the figure is the GPS vehicle trajectory electronic map matching, and its coordinate system is CGJ-02 (epsg:4490). (b) in the figure is the conversion of the Cartesian coordinate system into the Frenet coordinate system, which includes the original trajectory points and the original trajectory lines.

[0180] (2) Select the minimum sliding window unit length of the sub-trajectory to be 3 seconds. If The statistic continues to increase over time, incorporating the self-similarity of longer sequence enhancer trajectories. After a certain point in time, The statistic suddenly drops (extreme point), and this point is used as the candidate point for segmentation. Finally, the extreme point threshold is set to 0.05, and the candidate points for segmentation that are less than the threshold are merged to obtain the segmented sub-tracks.

[0181] like Figure 3 As shown in the figure, it is a vehicle trajectory segmentation map, where (a) is the extreme point identified by the V statistic, and (b) is the trajectory segmentation map.

[0182] (3) All the real points of each sub-trajectory are used as interpolation points. Interpolation points are sequentially inserted between any two adjacent points in this segment to generate fractal points. The first and last points of the fractal points are then set as the starting and ending points of the adjacent points. Therefore, the number of points in the adjacent point iteration is equal to the number of real points selected in the initial segment. The second iteration is to use the newly generated points in the first iteration as interpolation points and iterate. The first iteration generates 5 points between adjacent points. The second iteration uses all the points in the first iteration to generate 25 points. Two iterations are used to fill in the noise and motion details of the original GPS vehicle trajectory information.

[0183] like Figure 4 As shown in the figure, it is a trajectory fractal reconstruction diagram, (a) is a trajectory fractal iteration process diagram, and (b) is a trajectory fractal interpolation diagram.

[0184] (4) The order of the Butterworth filter is selected as 6; the denoising considers retaining the overall smooth trajectory while removing these high-frequency and low-frequency noises, while retaining the motion details, and the cutoff frequency is selected as 1Hz. Then the trajectory shot by the drone of the same car is used as the real trajectory to train the SG filter parameters, and the order is =3 and half filter length =10 minimizes the MSE of the GPS and drone trajectories and obtains a smooth motion trajectory.

[0185] like Figure 5 As shown in Figure 2, (a) is the trajectory denoising map, and (b) is the trajectory smoothing map.

[0186] (5) Combined with the candidate points before segmentation, the interpolation points between adjacent candidate points are aligned at intervals of 0.1 seconds to obtain the sub-second reconstructed satellite positioning trajectory; the coordinates are then inversely calculated into the XY coordinate system, and finally the sub-second reconstructed trajectory is re-matched to the road according to step 3, as shown in Table 2:

[0187] Table 2 Time calculation and field heap area (partial)

[0188]

[0189] like Figure 6 The following figure shows the comparison between the original vehicle trajectory and the sub-second reconstruction of the trajectory. Figure 6 (a) is the original vehicle trajectory diagram. Figure 6 (b) is the sub-second reconstruction of the trajectory.

[0190] This application works as follows:

[0191] This application proposes a sub-second vehicle trajectory reconstruction method based on high-frequency satellite positioning data. It is suitable for high-frequency data. First, large-scale satellite positioning vehicle trajectories are obtained and processed to remove vehicle trajectory anomalies. The vehicle trajectory is then projected and transformed and matched to the road information of the electronic map data using the nearest neighbor algorithm to obtain the Frenet coordinate system information of the vehicle trajectory. The trajectory is then segmented based on the V statistic of the Hurst exponent, and the fractal interpolation method is used to improve the resolution of the vehicle trajectory signal. The vehicle trajectory is then denoised and smoothed. Finally, the data is aligned and the motion characteristics are inferred. This application improves the resolution of vehicle trajectory data obtained by satellite positioning systems and the accuracy of vehicle trajectory matching maps, promoting the development of fields such as traffic prediction and road safety analysis.

[0192] This application proposes a sub-second vehicle trajectory reconstruction method based on high-frequency satellite positioning data. It uses the self-similarity characteristics of vehicle trajectory signals for encryption, can well capture the self-similarity and local details of the trajectory, has low computational complexity, and reduces the need for prior knowledge. Its parameter selection takes into account satellite positioning system errors, vehicle motion consistency and physical consistency constraints. It has strong adaptability and does not require a large amount of training data and multi-source perception data for correction to achieve reliable performance. Therefore, this application is an economical, efficient, accurate and reliable data encryption method for solving large-scale temporal and spatial trajectories at high-frequency sampling rates.

[0193] This application aligns interpolation points between adjacent segmented candidate points at intervals of 0.1 seconds to obtain sub-second reconstructed satellite positioning trajectories. Therefore, the intervals between adjacent trajectory points can be refined from the original average of 20-30 meters to within 1 meter. This method improves the accuracy of GPS vehicle trajectory matching maps 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.

[0194] This application uses a Butterworth filter for denoising. The denoising process considers retaining the overall smooth trajectory while removing high-frequency and low-frequency noise, retaining motion details and improving the quality of vehicle trajectory reconstruction.

[0195] The preferred embodiments of the present application have been described in detail above, but the present application is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in this field without departing from the purpose of the present application.

[0196] 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 the specific embodiments, and the scope of the present application is defined by the appended claims.

Claims

1. A sub-second vehicle trajectory reconstruction method based on high-frequency satellite positioning data, characterized by: The following steps are involved: Step 1: Acquisition of electronic map data; Step 2: Acquire large-scale satellite-based vehicle trajectories and process them; Step 2-1: vehicle trajectory grouping; Step 2-2: Vehicle trajectory format adjustment; Step 2-3: Remove abnormal points in vehicle trajectories; Step 3: Match the processed vehicle trajectory with geographic information; Step 3-1: Projection transformation, converting the latitude and longitude coordinates of the vehicle trajectory into a projected coordinate system; Step 3-2: Map matching, matching the vehicle trajectory in the projected coordinate system with the electronic map data obtained in step 1; Step 3-3: Frenet coordinate conversion, based on the electronic map data matching, obtain the longitudinal position S and lateral position D coordinates of the vehicle trajectory in Frenet coordinates; Step 4: Sub-second reconstruction of vehicle trajectory; Step 4-1: Trajectory segmentation based on Hurst exponent The statistics divide the vehicle trajectory processed in step 3 into multiple sub-trajectories; Step 4-2: Fractal interpolation encrypts the trajectory, encrypting multiple sub-trajectories through fractal interpolation, and inserting 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 the interpolation points with the original trajectory points and align the interpolation points at equal distances; Step 4-5: Repeat steps 4-1 to 4-4 to obtain the reconstructed satellite positioning trajectory; Step 5: Reverse-convert the reconstructed satellite positioning trajectory into the Cartesian coordinate system, re-match the electronic map data, and calculate the vehicle motion characteristics.

2. The vehicle trajectory sub-second reconstruction method based on high-frequency satellite positioning data according to claim 1 is characterized in that: The vehicle trajectory grouping in step 2-1 is specifically as follows: grouping the large-scale satellite positioning vehicle trajectories by vehicle ID, and sorting each group by timestamp.

3. The vehicle trajectory sub-second reconstruction method based on high-frequency satellite positioning data according to claim 2 is characterized in that: The specific removal of vehicle trajectory abnormal points in step 2-3 is: The vehicle trajectory anomalies include position jump anomalies, time interval anomalies, and trajectory deviation anomalies. First, the position jump anomalies and time interval anomalies are removed, and then the trajectory deviation anomalies are removed using the abnormal outlier factor algorithm. Finally, each group is saved as a separate data file. The specific process of the outlier factor algorithm to remove trajectory deviation anomalies is as follows: first, for each original trajectory point of the vehicle trajectory, its nearest k neighbors are found, and the density between the original trajectory point and its neighbors is calculated. If the density of an original trajectory point is significantly lower than that of its surrounding neighbors, it will be marked as an outlier, and trajectory deviation anomalies that significantly deviate from the normal trajectory are screened out.

4. The vehicle trajectory sub-second reconstruction method based on high-frequency satellite positioning data according to claim 3 is characterized in that: The step 3-1 is specifically as follows: using the pyproj library to convert the latitude and longitude coordinates of the vehicle trajectory into a projection coordinate system according to the EPSG code of the data coordinate system; Step 3-2 specifically includes: performing map matching, constructing a binary tree of the coordinates of the road centerline points in the electronic map data obtained in step 1 using a KD-tree algorithm to accelerate the query of the nearest neighbor road coordinates; Step 3-3 specifically includes: traversing the vehicle trajectory to query the nearest neighbor road coordinates of the original trajectory point, thereby obtaining the midline point of the two nearest neighbor road coordinates corresponding to the original trajectory point; based on the coordinates of the midline point, calculating the longitudinal position S and lateral position D coordinates of the original trajectory point in Frenet coordinates.

5. The vehicle trajectory sub-second reconstruction method based on high-frequency satellite positioning data according to claim 4 is characterized in that: The step 3-3 is specifically as follows: Each original trajectory point of the vehicle trajectory set Node pairs matched to nearest neighbor road coordinates and , establish the node vector , using the node vector Calculate the original trajectory points Perpendicular distance to the local sub-segment ; For each current subset, define the original trajectory point To node pair Vector , then calculate the vertical distance and longitudinal incremental distance , according to the electronic map data in step 1, obtain the road boundary stake number , the longitudinal position S and lateral position D coordinates of the original trajectory point in Frenet coordinates are obtained: ； ； Where: The road boundary station number.

6. The vehicle trajectory sub-second reconstruction method based on high-frequency satellite positioning data according to claim 1 is characterized in that: The step 4-1 is specifically as follows: selecting the minimum time window for sliding, and identifying the Extreme point sequence of statistics As the segmentation candidate point, set a threshold to judge the extreme point less than the threshold, exclude the extreme point less than the threshold from the segmentation candidate point, obtain the final segmentation candidate point, and then obtain multiple sub-trajectories, and use the list index to mark the original point position of the segmented sub-trajectory; described The statistical calculation formula is as follows: ； In the above formula and The calculation formula is: ； ； ； ； ； Where: is the length of the sub-trajectory, i.e., the time span; is the mean-adjusted series, representing the original value Deviation from the mean m; is the original value, the observation value at the i-th moment in the original trajectory point; For time series The arithmetic mean of the time series for A collection of n is the time series The total length of 7. The vehicle trajectory sub-second reconstruction method based on high-frequency satellite positioning data according to claim 6 is characterized in that: In step 4-2, multiple sub-trajectories are encrypted by fractal interpolation, and interpolation points are inserted between the original trajectory points as follows: Let the interpolation point be represented by {S, D} = , the point set is linearly sorted by its horizontal coordinate, , the two-dimensional plane fractal interpolation function is: ； Solving the above equations yields some parameters: ； ； These mappings satisfy the following conditions: ； Where: Real numbers Completely determined by the interpolation points; Each interval The vertical scaling factor of .

8. The vehicle trajectory sub-second reconstruction method based on high-frequency satellite positioning data according to claim 7 is characterized in that: The denoising and smoothing of the interpolation points in step 4-3 are specifically as follows: According to the fractal signal of the vehicle trajectory in step 4-2, the Butterworth filter is used to remove the deterministic signal, colored noise and Gaussian white noise in the satellite positioning signal, and the interpolation point obtained in step 4-2 is Denoising is done by the following equation to obtain 、 : ； ； ； Where: is the signal frequency, Hz; is the filter cutoff frequency, Hz; is the order of the filter; Represents the convolution operation; Use SG filter to smooth the trajectory so that it conforms to reality. The form of SG filter is shown in the following equation: ； ； Where: 、 is the smoothed value; 、 is the denoised value; It is filter coefficients, the order is Polynomial calculation; if the length of the vehicle trajectory is expressed as 2m+1, then The value range of is [-m,m]; is half the 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 It is determined based on the motion consistency of the sub-trajectories and the vehicle dynamics constraints.

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

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