WO2023201938A1

WO2023201938A1 - Missing trajectory filling method and system

Info

Publication number: WO2023201938A1
Application number: PCT/CN2022/112691
Authority: WO
Inventors: 亓晋; 陈湘婷; 谭雨恬; 陈欣冉; 孙雁飞; 许斌; 陆音
Original assignee: 南京邮电大学
Priority date: 2022-04-22
Filing date: 2022-08-16
Publication date: 2023-10-26
Also published as: CN114860700A

Abstract

A missing trajectory filling method, comprising: acquiring an original trajectory; dividing the original trajectory into a plurality of sub-trajectories; calculating a time distance, a space distance and a velocity distance between the sub-trajectories; calculating weights of the time distance, the space distance and the velocity distance; acquiring a comprehensive distance between the sub-trajectories according to the weights of the time distance, the space distance and the velocity distance; and according to the comprehensive distance, filling a missing trajectory by means of clustering. By using a clustering method based on a fuzzy logic, flexible fuzzy division is performed on trajectory data, such that the degree of similarity between different sub-trajectories can be measured more truly and effectively according to different application scenarios, thereby improving the accuracy of trajectory data filling.

Description

Missing trajectory filling method and system

Technical field

The invention belongs to the technical field of trajectory data processing, and in particular relates to a method and system for filling missing trajectories.

Background technique

With the development of society and the advancement of science and technology, as well as the development of satellite networks, wireless networks, and positioning equipment, the trajectory data of a large number of moving objects is showing a rapid growth trend. The study of trajectory data can obtain unknown knowledge about the movement of objects. It is called future research hotspot and application growth point. There are four common trajectories, namely human trajectories and vehicle trajectories. Animal tracks and natural phenomenon tracks. For example, vehicle trajectory data can be used to improve transportation networks, such as using trajectory data to generate road information. Vehicle trajectory data can also be used for resource allocation, such as predicting vehicle demand in a certain area, so that platforms like Didi can schedule idle vehicles in advance. Vehicle trajectory data can also be used for traffic analysis, such as using trajectory data to discover congested road sections or detect damaged road sections.

The GPS (Global Positioning System) receiving module is a common way to obtain trajectory data. In the intelligent vehicle-road collaboration system, in theory, any vehicle trajectory can be obtained. In practice, due to many reasons such as failures of on-board equipment and roadside units, loss of wireless transmission, etc., the vehicle trajectory data obtained by the base station and upper-layer data management center may be incomplete, and these incomplete trajectory data are processed directly. It will inevitably affect the accuracy of results and the reliability of decision-making. Therefore, post-stage data processing and knowledge discovery are crucial to recover missing trajectory data.

Contents of the invention

In order to solve the problems existing in the existing technology, the present invention provides a missing trajectory filling method and system, which can complete the missing trajectory data.

The technical problems to be solved by the present invention are achieved through the following technical solutions:

The first aspect provides a missing trajectory filling method, including:

Get the original trajectory;

Divide the original trajectory into several sub-trajectories;

Calculate the time distance, space distance and speed distance between each sub-trajectory;

Calculate the weight of time distance, space distance and speed distance;

Obtain the comprehensive distance between each sub-trajectory based on the weight of time distance, space distance and speed distance;

Clustering is used to fill in the missing trajectories based on the comprehensive distance.

Combined with the first aspect, further, dividing the original trajectory into several sub-trajectories includes:

2-1) Scan each recording point in the original trajectory one by one to generate the original trajectory set T={P ₀ ,...P _i ,...,P _n }, where P _i =(xi _, y _i ,v _i ,t _i ), x _i , y _i , vi _, and t _i are respectively the abscissa, ordinate, speed, and recording time of _the i-th recording point Pi in the trajectory set. Let the starting point P of the sub-trajectory be _start =P ₀ , current recording point P _now =P ₁ ;

2-2) Let the sub-trajectory set be STC, STC={st ₀ ,...st _i ,...,st _n }, st _i ={P _i0 ,...,P _ij ,...,P _in }, P _ij = {x _ij ,y _ij ,v _ij ,t _ij }, i=0...n, and initialize all elements in STC, st _i and P _ij to 0, where st _i is the i-th For the sub-trajectory, P _i0 and P _in are respectively the starting point and the end point of the sub-trajectory st _i . x _ij , y _ij , v _ij and t _ij are respectively the abscissa and ordinate coordinates of the j-th recording point P _ij of the i-th sub-trajectory. , speed and recording time;

1-3) Define the direction change amount of the current recording point as Δd, and the cumulative direction change amount of the sub-track as Δd ₊ . Set their initial values to 0, d _now and d _start are the direction and sub-direction of the current recording point respectively. The direction of the trajectory starting point;

2-4) Define the average rate change of the current recording point as

The initial value is set to 0;

2-5) If P _start ≠P _n , calculate the absolute value of the direction change Δd, |Δd|=|d _now -d _start |, otherwise end the feature point determination;

2-6) Calculate the absolute value of the cumulative change in direction Δd ₊ of the current recording point, |Δd ₊ | = |Δd + Δd _{+ (old)} |, Δd _{+ (old)} is the cumulative change in direction of the previous recording point;

2-7) Calculate the average rate change

2-8) If the obtained absolute value |Δd| of the direction change of the current recording point or the absolute value of the cumulative direction change |Δd ₊ | is greater than the set direction threshold d, the current recording point will be identified as a candidate Feature points, let P _end =P _now , and add the sub-trajectory st _i ={P _start ,...P _end } to the sub-trajectory set STC, add Δd, Δd ₊ ,

Reassign the value to 0, then set P _start = P _end , jump to step 2-5) to continue the determination of the next point, P _end is the end point of the current sub-trajectory;

If the obtained absolute value of direction change |Δd| and the absolute value of cumulative direction change |Δd ₊ | are less than or equal to the set direction threshold value d, then compare the calculated average velocity change

and the speed threshold value v, if

exceeds the speed threshold v, then the record point is considered a candidate feature point, let P _end =P _now , and add the sub-trajectory st _i ={P _start ,...,P _end } to the sub-trajectory set STC , jump to step 2-5) to continue judging the next recording point;

If the obtained absolute value of direction change |Δd| and the absolute value of cumulative direction change |Δd ₊ | are less than or equal to the set direction threshold value d, and the average velocity change

If it is less than the speed threshold value v, let P _now = P _{now + 1} and jump to step 2-5) to continue judging the next recording point.

Combined with the first aspect, further, calculating the time distance, space distance and speed distance between each sub-trajectory includes:

Calculate the time distance between two sub-trajectories according to equation (1)

dist _t (st _i ,st _j )=|t _i -t _j | (1);

Among them, t _i represents the intermediate time of the i-th sub-trajectory st _i , and t _j represents the intermediate time of the j-th sub-trajectory st _j ;

Calculate the spatial distance between two sub-trajectories according to equation (2)

in,

is the spatial distance from sub-trajectory st _i to sub-trajectory st _j ,

is the spatial distance from sub-trajectory st _j to sub-trajectory st _i ;

Calculate the speed distance between the two sub-trajectories according to equation (3)

in,

is the average speed of sub-trajectory st _i ,

is the average speed of sub-trajectory st _j .

Combined with the first aspect, further, the calculation of the weights of time distance, space distance and speed distance includes:

The time distance, spatial distance and velocity distance between each sub-trajectory and other sub-trajectories are used as samples to perform comprehensive weighting calculations, including the following steps:

Assume that there are u data objects x ₁ , x ₂ ,...x _i ,...x _u in the sample space. According to the following formula, the difference coefficient S _k of the k-th data object in the entire sample space containing u data objects is obtained;

in,

is the average value of the kth data object in the entire sample space;

According to equation (6), the uncorrelated coefficient R _k of the k-th data object in the entire sample space containing u data objects is obtained

Among them, r _ik is the correlation coefficient between the i-th data object and the k-th data object;

According to equations (7) and (8), the information entropy E _k of the k-th data object in the entire sample space containing u data objects is obtained

Among them, P _k is the proportion of the indicator value of the k-th data object;

According to equation (9), the weight ω _k of the k-th data object in the entire sample space containing u data objects is obtained

Combined with the first aspect, further obtaining the comprehensive distance between each sub-trajectory includes:

The comprehensive distance between each sub-trajectory is obtained through Equation (10)

dist (st _i ,st _j )=α×dist _t (st _i ,st _j )+β×dist _s (st _i ,st _j )+γ×dist _v (st _i ,st _j ) (10)

Among them, α, β, and γ are the weight values of time distance, space distance, and speed distance respectively. When the k-th data object is time distance, ω _k and α correspond to each other. When the k-th data object is space distance, ω _k and β corresponds to ω _k and γ when the k-th data object is a spatial distance.

Combined with the first aspect, further, using clustering according to the comprehensive distance to fill the missing trajectories includes:

5-1) Initialize the membership matrix, initialize the membership matrix U with a random number within the value range [0,1], and make the sum of all elements in the matrix equal to 1. The membership matrix represents the membership of each sub-trajectory to the extent of each cluster;

5-2) Select the core trajectory for each cluster, that is, calculate the cluster center c _i of fuzzy C-means clustering according to Equation (11), i=1,...,c;

Among them, c is the number of cluster centers, n is the number of sub-trajectories, u _ij is the membership degree of the j-th sub-trajectory to the i-th sub-trajectory, st _i represents the i-th sub-trajectory;

5-3) Update the membership matrix, that is, recalculate the membership degree of the j-th sub-trajectory to the i-th sub-trajectory according to equation (12);

Among them, d _ij is the distance between the i-th sub-trajectory and the j-th sub-trajectory;

5-4) Calculate the value of the cost function, that is, calculate the value J of the cost function according to equation (13);

If J is less than the cost threshold or the change relative to the last calculated cost function J is less than the change threshold, end the calculation, otherwise return to step 5-2);

5-5) Trajectory filling, that is, using the membership matrix as a weight to multiply the cluster center of each cluster to obtain the final filled trajectory.

The second aspect provides a missing trajectory filling system, including:

Data acquisition module, used to obtain original trajectories;

The trajectory division module is used to divide the original trajectory into several sub-trajectories;

Comprehensive distance calculation module, used to calculate the time distance, space distance and speed distance between each sub-trajectory;

Calculate the weight of time distance, space distance and speed distance;

The trajectory filling module is used to fill in missing trajectories using clustering based on comprehensive distance.

Beneficial effects of the present invention: 1. The present invention considers that in the concept of space and time, two trajectories passing through the same position at different speeds at the same time should be different, so the Euclidean distance cannot be simply used to measure similarity. New The inter-trajectory distance measurement method provides a processing process for the three dimensions of trajectory data: time, space and speed, which improves the accuracy of the final result. It introduces weight parameters to coordinate the influence of each component on the clustering result, making it more accurate.

2. The present invention comprehensively considers the correlation, difference, discreteness and other properties of data, and creates a method of automatically adjusting weight parameters, which solves the problem of low efficiency of manual adjustment of weight parameters, and at the same time makes the calculation of weight parameters more efficient. Scientifically valid.

3. This invention takes into account the uncertainty that a sub-trajectory may belong to multiple trajectory clusters, and uses a fuzzy logic-based clustering method to perform flexible fuzzy division of trajectory data. This method can more realistically and effectively measure the trajectory data according to different application scenarios. The degree of similarity between different sub-trajectories, thereby improving the accuracy of trajectory data filling.

Description of the drawings

Figure 1 is a flow chart of the present invention;

Figure 2 is a flow chart of the original trajectory in the present invention;

Figure 3 is a schematic diagram of sub-trajectory segments after the original trajectory is divided according to the present invention;

Figure 4 is a schematic diagram of the time distance of neutron trajectories in the case of time separation according to the present invention;

Figure 5 is a schematic diagram of the time distance of neutron trajectories in the case of time intersection according to the present invention;

Figure 6a is a schematic diagram of the spatial distance from neutron trajectory st _i to st _j in the present invention;

Figure 6b is a schematic diagram of the spatial distance from neutron trajectory st _j to st _i in the present invention;

Figure 7 is a schematic diagram of the weights of time, space and speed distance in the process of calculating the comprehensive distance of the sub-trajectory in the present invention.

Detailed ways

In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. Embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

In order to better understand the present invention, the relevant technologies in the technical solution of the present invention will be described below.

Example 1

As shown in Figures 1-7, the present invention discloses a missing trajectory filling method, which includes the following steps:

Step 1. Obtain the original trajectory

Get the original trajectory of the original car motion containing all recorded points.

Step 2: Divide sub-trajectories

2-1) First, scan each recording point in the original trajectory one by one to obtain the original trajectory set T={P ₀ ,...P _i ,...,P _n }, where P _i =(xi _, y _i , vi _, t _i ), x _i , y _i , vi _, and t _i are respectively the abscissa, ordinate, speed, and recording time of the i-th recording point P _i in the trajectory set. Let the starting point of the sub-trajectory be Starting point P _start =P ₀ , current recording point P _now =P ₁ ;

2-2) Let the sub-trajectory set be STC, STC={st ₀ ,...st _i ,...,st _n }, st _i ={P _i0 ,...,P _ij ,...,P _in }, P _ij = {x _ij ,y _ij ,v _ij ,t _ij }, i=0...n, and initialize all elements in STC, st _i and P _ij to 0, where st _i is the i-th For the sub-trajectory, _P _i0 and P _in are _respectively the _starting point and the end point of the sub-trajectory _st _i _. , speed and recording time;

2-3) Define the direction change amount of the current recording point as Δd, and the cumulative direction change amount of the sub-track as Δd ₊ . Set their initial values to 0. d _now and d _start respectively represent the direction and sub-track of the current recording point. The direction of the trajectory starting point;

2-4) Define the average rate change of the current recording point as

The initial value is set to 0;

2-7) Calculate the average rate change

2-8) If the obtained absolute value |Δd| of the direction change of the current recording point or the absolute value of the cumulative direction change |Δd ₊ | is greater than the set direction threshold d (the threshold is determined through empirical values ), the current recording point is identified as a candidate feature point, let P _end =P _now , and the sub-trajectory st _i ={P _start ,...P _end } is added to the sub-trajectory set STC, and Δd, Δd ₊ ,

and the speed threshold value v, if

If the obtained absolute value of direction change |Δd| and the absolute value of cumulative direction change |Δd ₊ | are less than or equal to the set direction threshold d (set based on empirical values), and the average velocity change

is less than the speed threshold value v, then let P _now =P _now+1 , and then jump to step 2-5) to continue judging the next recording point.

Finding the sub-trajectory is mainly to find the starting point and the ending point of the sub-trajectory. These two points are both characteristic points. Once these two are determined, the sub-trajectory is determined. You only need to add the starting point and the ending point and the distance between them. The complete sub-trajectory can be obtained by connecting the common recording points in series.

Step 3: Calculate the time distance, space distance and speed distance between sub-trajectories

After obtaining the sub-trajectories, we need to calculate the time, space and speed distances between the sub-trajectories respectively, which will be used in subsequent steps to comprehensively consider all relevant attribute dimensions in the trajectory data.

The calculation process of the three distances mainly includes the following steps:

First, let's find the time distance, take two sub-trajectories st _i and st _j , the start time of the two sub-trajectories are t _si and t _sj respectively, the end time of the two sub-trajectories are t _ei and t _ej respectively, the middle of the sub-trajectory The absolute value of the difference in time points is taken as the time distance between subtrajectories.

Find the time distance between two sub-trajectories by the following formula

dist _t (st _i ,st _j )=|t _i -t _j | (1);

Next, we find the spatial distance, sub-trajectory st _i ={P _i0 ,P _i1 ,...,P _iq }, sub-trajectory st _j ={P _j0 ,P _j1 ,...,P _jw }

Among them, each element in st _i and st _j is the recording point of the sub-track. At the same time, the first element and the last element are also the feature points selected in step 2. The feature points are first the recording points, and q is the recording point of st _i . The number of , w is the number of recording points in st _j , and the minimum distance from any recording point in sub-track st _i to sub-track st _j is taken as the distance from the recording point to st _j . The minimum distance from any recording point in sub-track st _j to sub-track st _i is taken as the distance from the recording point to st _i .

Calculate the spatial distance between sub-trajectories based on two-way trajectory matching, as shown in Equation (2)

in,

is the spatial distance from sub-trajectory st _i to sub-trajectory st _j ,

is the spatial distance from sub-trajectory st _j to sub-trajectory st _i ;

Finally find the speed distance

The average speed of all recording points in the sub-trajectory is taken as the speed of the sub-trajectory segment, and the absolute value of the speed difference between the sub-trajectory segments to be compared is taken as the speed distance between the sub-trajectories, as shown in Equation (3),

in,

is the average speed of sub-trajectory st _i ,

is the average speed of sub-trajectory st _j .

Step 4: Find the weights of various distances

Use the three distances calculated in the three steps as parameters to generate a new set N _i as sample input

N _i ={{dist _t (st _i ,st ₀ ),dist _s (st _i ,st ₀ ),dist _v (st _i ,st ₀ )},...,

{dist _t (st _i ,st _j ),dist _s (st _i ,st _j ),dist _v (st _i ,st _j )},...,{dist _t (st _i ,st _n ),dist _s ( st _i ,st _n ),dist _v (st _i ,st _n )}}

The improved CRITIC algorithm and entropy weight method are used to perform comprehensive weighting calculations on the position, time, and velocity components of each sub-trajectory data sample. Assume that there are u data objects x ₁ , x ₂ ,...x _i ,...x _u in the sample space. According to formulas (4) and (5), the k-th data object in the entire sample space containing u data objects is obtained. Difference coefficient _Sk

in,

is the average value of the kth data object in the entire sample space;

Use the improved CRITIC algorithm to obtain the uncorrelated coefficient R _k of the k-th data object in the entire sample space containing u data objects, as shown in Equation (6)

Use the entropy weight method to obtain the information entropy E _k of the k-th data object in the entire sample space containing u data objects according to equations (7) and (8).

Combining the CRITIC method and the entropy weight method, the weight ω _k of the k-th data object in the entire sample space containing u data objects is obtained according to Equation (9)

Step 5: Find the comprehensive distance

The traditional similarity measurement method between trajectories does not take into account the impact of multiple attribute dimensions of trajectory data on trajectory data quantification at the same time. The present invention comprehensively considers the time distance, rate distance and spatial distance in trajectory data to calculate the comprehensive distance, as shown in Eq. As shown in (10), dist(st _i ,st _j )=α×dist _t (st _i ,st _j )+β×dist _s (st _i ,st _j )+γ×dist _v (st _i ,st _j ) (10)

Step 6: Fill in missing tracks

6-1) Initialize the membership matrix. The membership matrix represents the degree to which each sub-trajectory belongs to each cluster. Initialize the membership matrix U with a random number in the range [0,1], and make the matrix The sum of all elements is equal to 1, and the membership matrix represents the degree to which each sub-trajectory belongs to each cluster;

6-2) Select the core trajectory for each cluster, that is, calculate the cluster center c _i of fuzzy C-means clustering according to Equation (11), i=1,...,c;

6-3) Update the membership matrix, that is, recalculate the membership degree of the j-th sub-trajectory to the i-th sub-trajectory according to equation (12);

6-4) Calculate the value of the cost function. The distance between trajectories determines the degree to which a trajectory belongs to a certain cluster. Calculate the value J of the cost function according to Equation (13);

If J is less than a certain cost threshold ((for example: e ^-6 )) or the change relative to the last calculated cost function J is less than the change threshold (for example: e ^-6 ), the algorithm ends, otherwise Return to step 6-2);

6-5) Track filling. After clustering is completed, the membership matrix of each cluster is obtained. This matrix is used as a weight to multiply the parameters of the core trajectory of each cluster to obtain the final filled trajectory data.

Example 2

The present invention also provides a missing trajectory filling system, including:

Data acquisition module, used to obtain original trajectories;

Calculate the weight of time distance, space distance and speed distance;

Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment that combines software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.

The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each process and/or block in the flowchart illustrations and/or block diagrams, and combinations of processes and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions executed by the processor of the computer or other programmable data processing device produce a use A device for realizing the functions specified in one process or multiple processes of the flowchart and/or one block or multiple blocks of the block diagram.

These computer program instructions may also be stored in a computer-readable memory that causes a computer or other programmable data processing apparatus to operate in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including the instruction means, the instructions The device implements the functions specified in a process or processes of the flowchart and/or a block or blocks of the block diagram.

These computer program instructions may also be loaded onto a computer or other programmable data processing device, causing a series of operating steps to be performed on the computer or other programmable device to produce computer-implemented processing, thereby executing on the computer or other programmable device. Instructions provide steps for implementing the functions specified in a process or processes of a flowchart diagram and/or a block or blocks of a block diagram.

Claims

A missing trajectory filling method, which is characterized by including:

Get the original trajectory;

Divide the original trajectory into several sub-trajectories;

Calculate the time distance, space distance and speed distance between each sub-trajectory;

Calculate the weight of time distance, space distance and speed distance;

Obtain the comprehensive distance between each sub-trajectory based on the weight of time distance, space distance and speed distance;

Clustering is used to fill in the missing trajectories based on the comprehensive distance.
A missing trajectory filling method according to claim 1, characterized in that dividing the original trajectory into several sub-trajectories includes:

2-1) Scan each recording point in the original trajectory one by one to generate the original trajectory set T={P 0 ,...P i ,...,P n }, where P i =(xi , y i ,v i ,t i ), x i , y i , vi , and t i are respectively the abscissa, ordinate, speed, and recording time of the i-th recording point Pi in the trajectory set. Let the starting point P of the sub-trajectory be start =P 0 , current recording point P now =P 1 ;

2-2) Let the sub-trajectory set be STC, STC={st 0 ,...st i ,...,st n }, st i ={P i0 ,...,P ij ,...,P in }, P ij = {x ij ,y ij ,v ij ,t ij }, i=0...n, and initialize all elements in STC, st i and P ij to 0, where st i is the i-th For the sub-trajectory, P i0 and P in are respectively the starting point and the end point of the sub-trajectory st i . x ij , y ij , v ij and t ij are respectively the abscissa and ordinate coordinates of the j-th recording point P ij of the i-th sub-trajectory. , speed and recording time;

2-3) Define the direction change amount of the current recording point as Δd, and the cumulative direction change amount of the sub-track as Δd + . Set their initial values to 0, d now and d start are the direction and sub-direction of the current recording point respectively. The direction of the trajectory starting point;

2-4) Define the average rate change of the current recording point as
The initial value is set to 0;

2-5) If P start ≠P n , calculate the absolute value of the direction change Δd, |Δd|=|d now -d start |, otherwise end the feature point determination;

2-6) Calculate the absolute value of the cumulative change in direction Δd + of the current recording point, |Δd + | = |Δd + Δd + (old) |, Δd + (old) is the cumulative change in direction of the previous recording point;

2-7) Calculate the average rate change

2-8) If the obtained absolute value |Δd| of the direction change of the current recording point or the absolute value of the cumulative direction change |Δd + | is greater than the set direction threshold d, the current recording point will be identified as a candidate. Feature points, let P end =P now , and add the sub-trajectory st i ={P start ,...P end } to the sub-trajectory set STC, add Δd, Δd + ,
Reassign the value to 0, then set P start = P end , jump to step 2-5) to continue the determination of the next point, P end is the end point of the current sub-trajectory;

If the obtained absolute value of direction change |Δd| and the absolute value of cumulative direction change |Δd + | are less than or equal to the set direction threshold value d, then compare the calculated average velocity change
and the speed threshold value v, if
exceeds the speed threshold v, then the record point is considered a candidate feature point, let P end =P now , and add the sub-trajectory st i ={P start ,...,P end } to the sub-trajectory set STC , jump to step 2-5) to continue judging the next recording point;

If the obtained absolute value of direction change |Δd| and the absolute value of cumulative direction change |Δd + | are less than or equal to the set direction threshold value d, and the average velocity change
If it is less than the speed threshold value v, let P now = P now + 1 and jump to step 2-5) to continue judging the next recording point.
A missing trajectory filling method according to claim 1, characterized in that the calculation of the time distance, spatial distance and speed distance between each sub-trajectory includes:

Calculate the time distance between two sub-trajectories according to equation (1)

dist t (st i ,st j )=|t i -t j | (1);

Among them, t i represents the intermediate time of the i-th sub-trajectory st i , and t j represents the intermediate time of the j-th sub-trajectory st j ;

Calculate the spatial distance between two sub-trajectories according to equation (2)

in,
is the spatial distance from sub-trajectory st i to sub-trajectory st j ,
is the spatial distance from sub-trajectory st j to sub-trajectory st i ;

Calculate the speed distance between the two sub-trajectories according to equation (3)

in,
is the average speed of sub-trajectory st i ,
is the average speed of sub-trajectory st j .
A missing trajectory filling method according to claim 3, characterized in that the calculation of the weights of time distance, space distance and speed distance includes:

The time distance, spatial distance and velocity distance between each sub-trajectory and other sub-trajectories are used as samples to perform comprehensive weighting calculations, including the following steps:

Assume that there are u data objects x 1 , x 2 ,...x i ,...x u in the sample space. According to the following formula, the difference coefficient S k of the k-th data object in the entire sample space containing u data objects is obtained;

in,
is the average value of the kth data object in the entire sample space;

According to equation (6), the uncorrelated coefficient R k of the k-th data object in the entire sample space containing u data objects is obtained

Among them, r ik is the correlation coefficient between the i-th data object and the k-th data object;

According to equations (7) and (8), the information entropy E k of the k-th data object in the entire sample space containing u data objects is obtained

Among them, P k is the proportion of the indicator value of the k-th data object;

According to equation (9), the weight ω k of the k-th data object in the entire sample space containing u data objects is obtained
A missing trajectory filling method according to claim 4, characterized in that obtaining the comprehensive distance between each sub-trajectory includes:

The comprehensive distance between each sub-trajectory is obtained through Equation (10)

dist (st i ,st j )=α×dist t (st i ,st j )+β×dist s (st i ,st j )+γ×dist v (st i ,st j ) (10)

Among them, α, β, and γ are the weight values of time distance, space distance, and speed distance respectively. When the k-th data object is time distance, ω k and α correspond to each other. When the k-th data object is space distance, ω k and β corresponds to ω k and γ when the k-th data object is a spatial distance.
A missing trajectory filling method according to claim 1, characterized in that the filling of missing trajectories by clustering based on comprehensive distance includes:

5-1) Initialize the membership matrix, initialize the membership matrix U with a random number within the value range [0,1], and make the sum of all elements in the matrix equal to 1. The membership matrix represents the membership of each sub-trajectory to the extent of each cluster;

5-2) Select the core trajectory for each cluster, that is, calculate the cluster center c i of fuzzy C-means clustering according to Equation (11), i=1,...,c;

Among them, c is the number of cluster centers, n is the number of sub-trajectories, u ij is the membership degree of the j-th sub-trajectory to the i-th sub-trajectory, st i represents the i-th sub-trajectory;

5-3) Update the membership matrix, that is, recalculate the membership degree of the j-th sub-trajectory to the i-th sub-trajectory according to equation (12);

Among them, d ij is the distance between the i-th sub-trajectory and the j-th sub-trajectory;

5-4) Calculate the value of the cost function, that is, calculate the value J of the cost function according to equation (13);

If J is less than the cost threshold or the change relative to the last calculated cost function J is less than the change threshold, end the calculation, otherwise return to step 5-2);

5-5) Trajectory filling, that is, using the membership matrix as a weight to multiply the cluster center of each cluster to obtain the final filled trajectory.
A missing track filling system, which is characterized by including:

Data acquisition module, used to obtain original trajectories;

The trajectory division module is used to divide the original trajectory into several sub-trajectories;

Comprehensive distance calculation module, used to calculate the time distance, space distance and speed distance between each sub-trajectory;

Calculate the weight of time distance, space distance and speed distance;

Obtain the comprehensive distance between each sub-trajectory based on the weight of time distance, space distance and speed distance;

The trajectory filling module is used to fill in missing trajectories using clustering based on comprehensive distance.