Trajectory reconstruction method based on satellite positioning data of floating vehicles

Abstract

The present invention relates to a trajectory reconstruction method based on satellite positioning data of a floating vehicle, comprising the following steps: processing input satellite positioning data containing errors and faults; accurately matching the floating vehicle satellite positioning data to the road centerline based on a hidden Markov model; processing the floating vehicle satellite positioning data according to a map matching method to obtain discrete floating vehicle trajectory data; and combining an interpolation algorithm and consistency constraints to propose a smooth reconstruction of the discrete matched satellite positioning data. This invention enables the effective utilization of satellite positioning data obtained by a satellite positioning system, promoting development in fields such as traffic status prediction and traffic management and control.

Description

Technical Field

[0001] The invention relates to a trajectory reconstruction method based on floating vehicle satellite positioning data, and belongs to the field of traffic engineering. Background Art

[0002] Smart transportation has been developing rapidly in recent years. Its intertwined development with fields like communications and computer science has generated a vast amount of traffic trajectory data. Floating car technology, due to its low cost, has become a primary method for collecting trajectory data. This technology utilizes onboard GPS (Global Positioning System) devices to obtain vehicle location, speed, and acceleration information, making global satellite positioning data a crucial source of vehicle trajectory data.

[0003] GPS trajectory data inevitably contains errors due to factors such as the vehicle's surrounding environment, obstructions from urban buildings, and communication signal interference. Furthermore, due to economic and technical limitations, only discrete vehicle location information can be obtained. This results in low GPS data accuracy and low sampling rate, which in turn prevents the effective utilization of a large amount of GPS trajectory data.

[0004] Although the low precision and low sampling rate of GPS data make the trajectory data collected by floating vehicles inferior to the current state-of-the-art trajectory data collection technologies, trajectory reconstruction research using data collected by floating vehicles still has its application value and necessity. Therefore, it is very meaningful and necessary to design a method to address the low precision and low sampling rate of GPS data, so as to fully and scientifically utilize GPS vehicle trajectory data collected by floating vehicles. Summary of the Invention

[0005] The present invention provides a trajectory reconstruction method based on satellite positioning data of a floating vehicle, which processes input satellite positioning data with errors and faults; accurately matches the floating vehicle satellite positioning data to the road centerline based on a hidden Markov model; processes the floating vehicle satellite positioning data according to a map matching method to obtain discrete floating vehicle trajectory data; and proposes smooth reconstruction of discrete matched satellite positioning data by combining an interpolation algorithm and consistency constraints. The method enables the satellite positioning data obtained by the satellite positioning system to be effectively utilized, improves the accuracy of trajectory reconstruction of the floating vehicle satellite positioning data, obtains continuous and smooth reconstructed trajectory data, and promotes the development of fields such as traffic state prediction and traffic management and control.

[0006] The technical solution adopted by the present invention to solve its technical problem is:

[0007] A method for reconstructing a trajectory of a floating vehicle based on satellite positioning data comprises the following steps:

[0008] S1. Data processing, including electronic map acquisition and floating vehicle satellite positioning data processing.

[0009] S2, vertically project the satellite positioning point data to the distance d from the satellite positioning point k On the road sections within the range, multiple projection points on the road centerline are obtained;

[0010] S3. Calculate each projection point based on the hidden Markov model By the corresponding satellite positioning point z i The output observation probability emitted and each projection point The state transition probability of switching between

[0011] S4. Establish the shortest path problem based on the output observation probability and state transition probability of each state, and construct a shortest path problem search graph model;

[0012] S5. Solve the shortest path from the source point to the end point in the constructed search graph, output the shortest path node, and obtain a map matching sequence;

[0013] S6. Using a map matching algorithm, the satellite positioning data of the floating vehicle on the road section is matched to the road section, the matched floating vehicle trajectory data is obtained, and the distance between the projection point and the starting point of the road section is calculated;

[0014] S7. Reconstruct the vehicle trajectory using a trajectory reconstruction algorithm to obtain continuous and smooth vehicle trajectory data based on the floating vehicle satellite positioning data.

[0015] Furthermore, in S1, the electronic map includes road location information, road topology information, and road grade information.

[0016] Furthermore, in S2, the two electronic map positioning points are taken as road sections, and the floating vehicle satellite positioning data is projected to a point where the distance from both end points of the electronic map is less than the distance d. k The projection point must fall on the road segment. The projection result that falls on the extension line of the line segment where the road segment is located will not be selected as the projection point.

[0017] Furthermore, in S3, the present invention changes the traditional output observation probability and state transition probability calculation model from Gaussian distribution and complex probability density function model to the following simplified model:

[0018] The output observation probability model for calculating the projection point is:

[0019]

[0020] Among them, σ z is the variance of the satellite positioning system error that follows Gaussian distribution, is the trajectory point z i With the projection point The distance of the Earth's great circle;

[0021] The state transition probability model for calculating the projection point is:

[0022]

[0023] In formula (2) The calculation method is:

[0024]

[0025] The calculation method of β in formula (2) is:

[0026]

[0027] in Represents the projection point To the projection point The shortest distance, δ(z i-1 ,z i ) represents the floating vehicle satellite positioning point z i-1 To the next positioning point z i The earth circle distance, α is a value between 0 and 1, which is used to control the weight between node cost and edge cost, d represents the upper bound of the earth circle distance from the floating vehicle satellite positioning point to the corresponding projection point, and t represents the acceptable critical value of the ratio of the shortest distance between the projection points to the earth circle distance between the floating vehicle satellite positioning points.

[0028] Furthermore, in S4, the nodes of the search graph are composed of projection points, the edges of the search graph are composed of paths between projection points, the node cost of the search graph is the output observation probability value of the projection point, and the edge cost of the search graph is the state transition probability value of the projection point.

[0029] Furthermore, in S5, the solution algorithm for the hidden Markov model is improved from the Viterbi algorithm to the bidirectional Dijkstra algorithm, further accelerating the solution of the single-source shortest path problem. The source point is the set of all potential projection points of the first floating vehicle's satellite positioning point, and the destination point is the set of all potential projection points of the last floating vehicle's positioning point. The sequence of projection points with the minimum distance obtained by the bidirectional Dijkstra algorithm is the matching sequence of the satellite positioning point to the road centerline. The algorithm objective function is:

[0030]

[0031] Ultimately, each satellite positioning point has one and only one corresponding projection point, including the source point and the end point.

[0032] Furthermore, in S7, based on the basic two-point cubic Hermite interpolation reconstruction algorithm, a segmented Hermite interpolation method is proposed for trajectory reconstruction. Based on the idea of ​​local weighted polynomial regression, a local polynomial regression interpolation reconstruction algorithm is proposed.

[0033] The two-point cubic Hermite interpolation function is:

[0034] H3(t)=y0α0(t)+y1α1(t)+m0β0(t)+m1β1(t) (6)

[0035] Where y0 and y1 are the function values ​​at points x0 and x1, m0 and m1 are the first-order derivative values ​​at points x0 and x1, α0(t), α1(t), β0(t) and β1(t) are the basis functions used to construct the interpolation function. The basis functions are as follows:

[0036]

[0037]

[0038]

[0039]

[0040] Where t0 and t1 in equations (7), (8), (9), and (10) represent the recording time of the projection points x0 and x1 of the floating vehicle satellite positioning point.

[0041] The piecewise Hermite interpolation function uses the calculation results of the G function to replace m0 and m1 in formula (6). The form of the G function is:

[0042]

[0043] Δ i-1 The calculation method is:

[0044]

[0045] The calculation method of α is:

[0046]

[0047] h i The calculation method is:

[0048]

[0049] where t i is the time recorded by the floating vehicle satellite positioning point, x i It is the path distance from the satellite positioning projection point of the floating vehicle to the starting point of the road section.

[0050] The interpolation function of the piecewise Hermite interpolation reconstruction algorithm is:

[0051]

[0052] The processing of boundary points is as follows:

[0053]

[0054]

[0055] The objective function of the local polynomial regression interpolation algorithm is:

[0056]

[0057] where β i The interpolation function is defined as the coefficient of each order, and d represents the highest order of the interpolation function. The local polynomial regression interpolation algorithm introduces the sliding window parameter w and the highest order parameter d. The basic selection strategy for the sliding window size and the highest order parameter is to combine the greedy approach and select a combination of the sliding window size and the highest order parameter for each regression. For each selection, the mean absolute error is calculated using the formula:

[0058]

[0059] Each time, the sliding window with the smallest MAE value and the highest order combination are selected. When there are multiple equal MAE values, the combination with the highest order among all combinations corresponding to the minimum MAE values ​​is selected.

[0060] Through the above technical solution, compared with the existing technology, the present invention has the following beneficial effects:

[0061] The trajectory reconstruction method based on floating vehicle satellite positioning data provided by the present invention comprehensively considers the impact of satellite positioning system errors, driver's wrong-way driving behavior, and multi-noise input data on map matching. It also comprehensively considers the impact of physical consistency constraints, different driver driving behaviors, and trajectory monotonicity constraints on trajectory reconstruction. These factors are then integrated into the two major algorithms of map matching and trajectory interpolation. A trajectory reconstruction method is proposed by combining map matching and trajectory interpolation algorithms. The provided reconstruction method is adaptable to multi-noise, complex, and changeable application scenarios, improves the efficiency of the trajectory reconstruction algorithm and the rationality of the trajectory reconstruction results, and provides a large amount of effective analysis data for traffic management and control, and traffic status prediction and analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] The present invention will be further described below with reference to the accompanying drawings and examples.

[0063] Figure 1This is a flow chart of the trajectory reconstruction method based on floating vehicle satellite positioning data provided by the present invention;

[0064] Figure 2 This is a flow chart of data processing of floating vehicle trajectory data provided by the present invention;

[0065] Figure 3 This is a flow chart of the local polynomial regression interpolation reconstruction algorithm provided by the present invention. DETAILED DESCRIPTION

[0066] The present invention will now be described in further detail with reference to the accompanying drawings, which are simplified schematic diagrams that illustrate the basic structure of the present invention in a schematic manner.

[0067] like Figure 1 As shown in Figure 1, the trajectory reconstruction method based on the floating vehicle satellite positioning data is divided into the following seven steps. The specific implementation plan is described below in combination with a specific case:

[0068] The first step is data processing, which involves acquiring electronic maps and processing floating vehicle satellite positioning data. Electronic maps contain other information, including road location information, road topology, and road grades. The electronic map described in this case study is based on electronic map data from the OpenStreetMap open source map project. The Overpass tool provided by OSM was used to obtain basic road information, including road grades, for a portion of Shenzhen's urban road network. GIS tools were then used to extract the road network coordinate and topology information, generating three files: a road segment coordinate point information file, a road network shortest path matrix file, and a road network coordinate point index file.

[0069] The steps for processing floating vehicle satellite positioning data are as follows:

[0070] Step 1: Use the license plate number field to extract raw data by vehicle, and generate a timestamp field based on the year, month, day, hour, minute, and second data;

[0071] Step 2: Arrange the trajectory data of each vehicle in ascending order according to the timestamp field. Segment the data where the time span between adjacent trajectory points is greater than 200 seconds;

[0072] Step 3: Finally, since there is a certain amount of duplicate data in the trajectory data, the repeated fields of these duplicate data are different and can be mainly divided into two categories. One category is data with the same timestamp, longitude, and latitude fields, and the other category is data with only the same longitude and latitude fields. The first category of duplicate data is processed by extracting unique data, while the second category is not processed;

[0073] Step 4: The present invention processes the collected floating vehicle satellite positioning data using resampling technology. The processing method is to calculate the actual distance between two adjacent floating vehicle satellite positioning points. When the Earth's great circle distance between the two points is less than a threshold of 15 meters, the latter data is discarded. Until a trajectory point is found with a distance greater than the threshold, this trajectory point is used as the resampling point, and the above process is repeated using it as the benchmark.

[0074] The data structure after the above processing is shown in Table 1:

[0075] Table 1

[0076]

[0077] The second step is to project the satellite positioning point data vertically to the distance d from the satellite positioning point. k = 300m, obtain multiple projection points on the road centerline. Based on the line segment formed by the road centerline positioning points of the two electronic maps, search whether the trajectory point to be projected can be projected onto the line segment. The steps are as follows:

[0078] Step 1: Search for a road section in the electronic map where the distance between both endpoints and the trajectory point to be projected is less than 300m;

[0079] Step 2: Project the trajectory point to be projected vertically onto the straight line where the searched road section is located, and determine whether the projected point is on the road section;

[0080] Step 3: If the projection point is on the road section and the distance between the projection point and the road section is less than 50m, it is considered a reasonable projection point, otherwise the projection result is invalid.

[0081] The third step is to calculate each projection point based on the hidden Markov model. By the corresponding satellite positioning point z i The output observation probability emitted and each projection point The state transition probability of switching between The specific method is as follows:

[0082] Step 1: For each candidate projection point According to formula (1), we have Position sends GPS track point z i The output observation probability of

[0083] Step 2: For GPS location z i Each candidate projection point According to formula (2), it is calculated to transfer to the next GPS position z i+1 All candidate projection points of The state transition probability.

[0084] The fourth step is to establish the shortest path problem based on the output observation probability and state transition probability of each state, and construct a search graph model for the shortest path problem. The nodes of the search graph are composed of projection points, and the edges of the search graph are composed of paths between projection points. The node cost of the search graph is the output observation probability value of the projection point, and the edge cost of the search graph is the state transition probability value of the projection point.

[0085] The fifth step is to find the shortest path from the source to the end point in the constructed search graph, output the shortest path node, and obtain the map matching sequence. The bidirectional Dijkstra algorithm is an improvement based on the Dijkstra algorithm. The specific method of the bidirectional Dijkstra algorithm is described as follows:

[0086] Step 1: Declare a set s to store the source point and the vertices for which the shortest path has been determined. For any vertex V not included in the graph, update the distance and path from the source point to the vertex;

[0087] Step 2: The path only passes through the vertices stored in set s until all vertices enter set s;

[0088] Step 3: Treat the end point as a source point and perform steps 1 and 2 on it;

[0089] Step 4: When two directions meet for the first time, obtain a candidate shortest path and continue to expand the vertices until all candidate paths are found.

[0090] Step 5: Select the shortest path among all candidate paths and the algorithm ends.

[0091] The sixth step is to use the map matching algorithm to match the satellite positioning data of the floating vehicle on the road section to the road section, obtain the matched floating vehicle trajectory data, and calculate the distance between the projection point and the starting point of the road section. The specific processing steps are as follows:

[0092] Step 1: Obtain a trajectory dataset corresponding to the experimental road network. This was done using QGIS software, using the Extract by Range feature in the Geographic Information Processing Toolbox, to extract floating vehicle trajectory data within 50 meters of the experimental road section. A total of 32,337 floating vehicle trajectory data were obtained.

[0093] Step 2: Perform noise reduction on the floating vehicle trajectory data near the test section using the same method used for clustered trajectory data in Step 1. Then, group the data by license plate number and select datasets with more than 20 samples, resulting in 157 vehicle trajectory datasets.

[0094] Step 3: Further partition the vehicle trajectory dataset. After sorting by timestamp in ascending order, split the vehicle trajectory data with a time interval greater than 200 seconds into two trajectory datasets. Filter out samples with more than 10 trajectories. This results in 174 partitioned datasets.

[0095] Step 4: Use a map matching algorithm based on a hidden Markov model to project the 174 partitioned datasets onto the experimental road segment. A total of 122 datasets were obtained (some datasets were deleted because they had U-turns on the road segment, making it impossible to obtain a reasonable projection sequence).

[0096] Step 5: Extract trajectory point data by direction and calculate the distance from the projection point to the starting point of the road section direction, thereby converting the two-dimensional vehicle trajectory position information into one-dimensional position information. Datasets with sample sizes greater than 10 were screened, resulting in 31 single-direction datasets. (Some datasets were deleted due to track points being removed due to wrong-way driving on the road section, resulting in a sample size of less than 10 and were therefore removed.)

[0097] After the above five steps, the original input data of the smooth reconstruction of the spatiotemporal trajectory of traffic flow is finally obtained. The data is shown in Table 1:

[0098] Table 2

[0099]

[0100]

[0101] In the seventh step, the vehicle trajectory is reconstructed using the trajectory reconstruction algorithm to obtain continuous and smooth vehicle trajectory data based on the floating vehicle satellite positioning data.

[0102] The two-point cubic Hermite interpolation reconstruction method uses equations (6)(7)(8)(9)(10) to reconstruct and interpolate between two adjacent satellite positioning data at an interval of 1s. After the interpolation of two adjacent positioning points is completed, the interpolation of the next interval is performed.

[0103] The piecewise Hermite interpolation reconstruction method first calculates the first-order derivative of each floating vehicle satellite positioning point using equations (15), (16) and (17), and then reconstructs the trajectory according to the two-point cubic Hermite interpolation reconstruction method.

[0104] The steps of the local polynomial regression interpolation reconstruction algorithm are as follows: Figure 3 As shown, the specific description is:

[0105] Step 1: Select candidate regression order d and then select sliding window size w to form a combination. The regression order set is {1, 2, 3}, and the sliding window size set is {2, 3, 4, 5, 6, 7, 8, 9};

[0106] Step 2: Use the selected parameters to perform regression and calculate the MAE value of the regression results;

[0107] Step 3: If all window sizes in the sliding window size are selected, select the next order in the regression order set and repeat step 2 until the regression order set is also traversed;

[0108] Step 4: Select the combination with the smallest MAE value from all combinations;

[0109] Step 5: Interpolate according to the minimum MAE combination with an interpolation interval of 1s.

[0110] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art to which this application belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art and, unless defined as such herein, will not be interpreted in an idealized or overly formal sense.

[0111] The meaning of "and / or" in this application means that both situations where each exists alone or both exist at the same time are included.

[0112] The term “connection” as used in this application may mean a direct connection between components or an indirect connection between components via other components.

[0113] With the above-described preferred embodiments of the present invention as a guide, and with reference to the above description, relevant personnel are fully capable of making various changes and modifications without departing from the technical scope of this invention. The technical scope of this invention is not limited to the contents of the specification and must be determined according to the scope of the claims.

Claims

1. A trajectory reconstruction method based on floating vehicle satellite positioning data, characterized by: The following steps are involved: S1. Data processing, including electronic map acquisition and floating vehicle satellite positioning data processing; S2, vertically project the satellite positioning point data to the distance d from the satellite positioning point k On the road sections within the range, multiple projection points on the road centerline are obtained; S3. Calculate each projection point based on the hidden Markov model By the corresponding satellite positioning point z i The output observation probability emitted and each projection point The state transition probability of switching between In S3, the output observation probability model of the projection point is calculated as: Among them, σ z is the variance of the satellite positioning system error that follows Gaussian distribution, is the trajectory point z i With the projection point The distance of the Earth's great circle; The state transition probability model for calculating the projection point is: In formula (2) The calculation method is: The calculation method of β in formula (2) is: in Represents the projection point To the projection point The shortest distance, δ(z i-1 ,z i ) represents the floating vehicle satellite positioning point z i-1 To the next positioning point z i The earth circle distance, α is a value between 0 and 1, which is used to control the weight between node cost and edge cost, d represents the upper bound of the earth circle distance from the floating vehicle satellite positioning point to the corresponding projection point, and t represents the acceptable critical value of the ratio of the shortest distance between the projection points to the earth circle distance between the floating vehicle satellite positioning points; S4. Establish the shortest path problem based on the output observation probability and state transition probability of each state, and construct a shortest path problem search graph model; S5. Solve the shortest path from the source point to the end point in the constructed search graph, output the shortest path node, and obtain a map matching sequence; S6. Using a map matching algorithm, the satellite positioning data of the floating vehicle on the road section is matched to the road section, the matched floating vehicle trajectory data is obtained, and the distance between the projection point and the starting point of the road section is calculated; S7. Reconstruct the vehicle trajectory using a trajectory reconstruction algorithm to obtain continuous and smooth vehicle trajectory data based on the floating vehicle satellite positioning data.

2. The trajectory reconstruction method based on floating vehicle satellite positioning data according to claim 1 is characterized in that: In S1, the electronic map includes road position information, road topology information and road grade information.

3. The trajectory reconstruction method based on floating vehicle satellite positioning data according to claim 1 is characterized in that: In S2, the two electronic map positioning points are used as road segments, and the floating vehicle satellite positioning data is projected to a point where the distance from both end points of the electronic map is less than the distance d. k On the road section.

4. The trajectory reconstruction method based on floating vehicle satellite positioning data according to claim 1 is characterized in that: In S4, the nodes of the search graph are composed of projection points, the edges of the search graph are composed of paths between projection points, the node cost of the search graph is the output observation probability value of the projection point, and the edge cost of the search graph is the state transition probability value of the projection point.

5. The trajectory reconstruction method based on floating vehicle satellite positioning data according to claim 1 is characterized in that: In S5, the source point is the set of all potential projection points of the first floating vehicle satellite positioning point, and the destination point is the set of all potential projection points of the last floating vehicle positioning point. The sequence of projection points with the minimum distance obtained by the bidirectional Dijkstra algorithm is the matching sequence of the satellite positioning point to the road centerline. The algorithm objective function is: Ultimately, each satellite positioning point has one and only one corresponding projection point, including the source point and the end point.

6. The trajectory reconstruction method based on floating vehicle satellite positioning data according to claim 1 is characterized in that: In S7, the trajectory reconstruction method includes three different algorithms, namely the two-point cubic Hermite interpolation reconstruction algorithm, the local polynomial regression interpolation reconstruction algorithm, and the segmented Hermite interpolation reconstruction algorithm.

7. The trajectory reconstruction method based on floating vehicle satellite positioning data according to claim 6 is characterized in that: The two-point cubic Hermite interpolation function is: H3(t)=y0α0(t)+y1α1(t)+m0β0(t)+m1β1(t) (6) Where y0 and y1 are the function values ​​at points x0 and x1, m0 and m1 are the first-order derivative values ​​at points x0 and x1, α0(t), α1(t), β0(t) and β1(t) are the basis functions used to construct the interpolation function. The basis functions are as follows: Where t0 and t1 in equations (7), (8), (9), and (10) represent the recording time of the projection points x0 and x1 of the floating vehicle satellite positioning point.

8. The trajectory reconstruction method based on floating vehicle satellite positioning data according to claim 7 is characterized in that: The piecewise Hermite interpolation function uses the calculation results of the G function to replace m0 and m1 in formula (6). The form of the G function is: Δ i-1 The calculation method is: The calculation method of α is: h i The calculation method is: where t i is the time recorded by the floating vehicle satellite positioning point, x i is the path distance from the floating vehicle satellite positioning projection point to the starting point of the road section; The interpolation function of the piecewise Hermite interpolation reconstruction algorithm is: The objective function of the local polynomial regression interpolation algorithm is: where β i are the coefficients of each order of the interpolation function, and d represents the highest order of the interpolation function.

9. The trajectory reconstruction method based on floating vehicle satellite positioning data according to claim 8, characterized in that: The local polynomial regression interpolation algorithm introduces the sliding window parameter w and the highest order parameter d. The basic selection strategy for the sliding window size and the highest order parameter is to combine the greedy idea and select a combination of the sliding window size and the highest order parameter for each regression. For each selection, the mean absolute error is calculated using the following formula: Each time, the sliding window with the smallest MAE value and the highest order combination are selected. When there are multiple equal MAE values, the combination with the highest order among all combinations corresponding to the minimum MAE values ​​is selected.

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