A method for target trajectory similarity analysis

Abstract

The present invention proposes a target trajectory similarity analysis method, formulates target trajectory similarity measurement criteria, including: trajectory point spatial position feature similarity measurement criteria, trajectory curve shape feature similarity measurement criteria, trajectory curve point real-time following feature similarity measurement criteria; calculates the metric distance between the reference trajectory and other trajectories under the three similarity measurement criteria, converts the metric distance into a similarity value through the similarity measurement standard, and uses a value of 0-1 to characterize the similarity between the two trajectories. The present invention defines the similarity of two trajectories through the characteristics of trajectory similarity spatial position, shape, and real-time following, and provides researchers with a criterion for measuring the similarity of two target trajectories.

Description

Technical Field

[0001] The invention relates to the field of geographic information, and in particular to a target trajectory similarity analysis method. Background Art

[0002] There are many means of monitoring target trajectory data and a wide range of data sources, resulting in a large amount of data and high complexity. The trajectory data contains the target state data at the same time monitored by different means, including three-dimensional coordinates in geographic space, target movement speed, etc. Although visualization tools such as three-dimensional digital earth can effectively display multi-dimensional space-time target trajectory data and intuitively display the target's movement trajectory, it is impossible to obtain the target's movement rules and the relationship between each target's movement. The existing processing of target trajectory data generally focuses on data denoising and outlier removal, and studying the data rules of a single target trajectory. It is impossible to analyze and process the trajectory data of multiple targets, and it is impossible to obtain the behavioral relationship between each target through the trajectory data of each target. In order to reveal the action rules between the trajectory data of each target, so as to analyze the historical status of the target, explore the tracking changes of each target, and analyze the collaborative relationship of each target, it is necessary to jointly analyze and process the trajectory data of multiple targets to form a trajectory similarity analysis method for the target. Summary of the invention

[0003] The purpose of the present invention is to provide a target trajectory similarity analysis method.

[0004] The technical solution to achieve the purpose of the present invention is: a target trajectory similarity analysis method, comprising the following steps:

[0005] Step 1: Formulate target trajectory similarity measurement criteria, including: trajectory point spatial position feature similarity measurement criteria, trajectory curve shape feature similarity measurement criteria, trajectory curve point real-time following feature similarity measurement criteria, where:

[0006] The similarity measurement criterion of the spatial position feature of trajectory points uses the shortest distance between two trajectories in space as the measurement of spatial position features, and describes the characteristics of the two targets appearing in space through the shortest distance;

[0007] The similarity measurement criterion of trajectory curve shape features uses the projection of the vector formed by the matching trajectory in space on the target trajectory as the measurement of shape features, and reflects the parallel and cross characteristics of the target trajectory path in space through the vector projection;

[0008] The similarity measurement criterion of the real-time following feature of the trajectory curve point adopts the distance between the two trajectories at the same time in space as the real-time following feature measurement. The distance at the same time reflects the following distance and the following duration of the two targets, thereby determining the motion relationship between the two targets.

[0009] Step 2: Calculate the metric distance between the reference trajectory and other trajectories under the three similarity measurement criteria, convert the metric distance into a similarity value through the similarity measurement standard, and use a value of 0-1 to characterize the similarity between the two trajectories.

[0010] Furthermore, based on the similarity measurement criterion of the spatial position features of the trajectory points, the metric distance between the two trajectories in the spatial position features is calculated. The specific calculation method is:

[0011] S1, select the longitude, latitude and altitude data of the two target trajectory data, and perform maximum and minimum normalization on the data. The specific calculation method is as follows:

[0012] 1) Take the longitude, latitude and altitude data of the two target trajectories to form a data set Where trajectory 1 has n 1 data points, trajectory 2 has n 2 Data points:

[0013]

[0014] 2) Normalize the longitude, latitude, and altitude data using maximum and minimum normalization. The method is as follows:

[0015]

[0016] Among them: (long*,lat*,alt*) is the data set The original data of a certain point in the data, the maximum and minimum values ​​of longitude, latitude, and altitude are:

[0017]

[0018] S2, two target trajectory data The similarity measurement criteria of spatial location features are: As a benchmark, calculate Each point to the trajectory The distance between the closest points and;

[0019] 1) Calculate using normalized data Each point to the trajectory The distance matrix of each point for:

[0020]

[0021] The distance calculation method is Euclidean distance. The Euclidean distance d between any two points p and q p,q for:

[0022]

[0023] 2) As a benchmark, and Metric distance of spatial location features is the distance matrix The sum of the minimum values ​​in each row is calculated as follows:

[0024]

[0025] Furthermore, based on the trajectory curve shape feature similarity measurement criterion, the metric distance between the two trajectories in the curve shape feature is calculated. The specific calculation method is:

[0026] S1, take the velocity magnitude and velocity direction data of the two target trajectories to form a data set Where trajectory 1 has n 1 data points, trajectory 2 has n 2 Data points:

[0027]

[0028] S2, two target trajectory data The similarity measurement criterion of curve shape features is: As a benchmark, calculate Each vector in the trajectory The projection on and;

[0029] 1) Calculation Each vector in the trajectory The projection matrix on for:

[0030]

[0031] Each element of the matrix pr p,q for The point p is The projection calculation method on point q is:

[0032] pr p,q =v p2 cos(vθ q1 -vθ p2 ) (8)

[0033] 2) As a benchmark, and Metric distance of curve shape features is the sum of the projection matrix elements, calculated as follows:

[0034]

[0035] Furthermore, based on the similarity measurement criterion of the real-time following feature of the trajectory curve point, the metric distance between the two trajectories on the real-time following feature is calculated. The specific calculation method is:

[0036] S1, take the moment data of the two target trajectories to form a data set Where trajectory 1 has n 1 data points, trajectory 2 has n 2 data points;

[0037]

[0038] For time period Set the sampling rate to f and the acquisition time interval to t f =1 / f, generating a set of equally spaced time points as the overlapping time period S t :

[0039] S t ={(T 1 ,T 1 +t f ,…,T 1 +k*t f ,…,min(T 2 ,T 1 +K*t f )), k=0,1,2,…,K} (11)

[0040] S2, based on the cubic spline curve interpolation algorithm, combined with the given overlap time period S t The trajectory data S of the two targets in the overlapping time period are reconstructed by the sampling rate f data 1 S 2 , so that the trajectory data of the two targets are at the same time, and the dataset after trajectory data reconstruction is:

[0041]

[0042] S3, the trajectory data S of the coincident time period of two targets at the same time 1 S 2 The similarity measurement calculation of the real-time following feature of the trajectory curve point is performed as follows:

[0043] 1) Calculate the three-dimensional spherical distance between two points at the same time:

[0044] At a certain time t i The coordinates (time, longitude, latitude, altitude) of the next two target trajectory points are S1pointi=(t i ,long1 i ,lat1 i ,alt1 i ) and S2pointi=(t i,long2 i ,lat2 i ,alt2 i ), first use the Haversine formula to calculate the distance between the two points on the horizontal plane, and then consider the height difference between the two points to calculate the distance between the two points on the three-dimensional sphere. The distance between the two points on the horizontal plane is calculated to be

[0045]

[0046] Where: haversin(θ) = sin 2 (θ / 2) = (1-cos(θ)) / 2, R is the radius of the earth, which is 6371 km;

[0047] Calculate the distance between two points on the three-dimensional sphere as d12 i , the calculation formula is as follows:

[0048]

[0049] 2) Calculate the velocity vector projection of two points at the same time:

[0050] At a certain time t i The velocity vector coordinates (time, velocity magnitude, velocity direction) of the next two target trajectory points are S1pointi=(t i ,v1 i ,vθ1 i ) and S2pointi=(t i ,v2 i ,vθ2 i ), taking S1 as the reference target trajectory, calculate the projection of S2pointi on S1pointi as pr S1pointi,S2pointi , the formula is as follows:

[0051] pr S1pointi，S2pointi =v2 i cos(vθ2 i -vθ1 i ) (15)

[0052] 3) S 1 S 2 The metric distance of the real-time following feature of the trajectory curve point is the position distance d12 of the simultaneous points and the velocity vector distance pr12 of the simultaneous points in the overlapping time period. The calculation formula is as follows:

[0053]

[0054] Where K represents the number of sampling points in the overlapping time period.

[0055] Furthermore, the metric distance between the benchmark trajectory and other trajectories under the three feature similarity measurement criteria is calculated. The metric distance can be converted into a similarity value through the similarity measurement standard, and a value of 0-1 is used to characterize the similarity between the two trajectories. The specific method is as follows:

[0056]

[0057] in is the metric distance between the jth trajectory and the reference trajectory data in the feature dimension q, k is the input cutoff ratio, Represents the metric distance between the reference trajectory and the noisy trajectory of the reference trajectory in the feature dimension q.

[0058] A target trajectory similarity analysis system realizes target trajectory similarity analysis based on the target trajectory similarity analysis method.

[0059] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, target trajectory similarity analysis is implemented based on the target trajectory similarity analysis method.

[0060] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, target trajectory similarity analysis is implemented based on the target trajectory similarity analysis method.

[0061] Compared with the prior art, the present invention has the following significant advantages: the similarity of two trajectories is defined by the spatial position, shape and real-time following characteristics of the trajectory similarity, providing researchers with a criterion for measuring the similarity of two target trajectories. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a framework diagram of target trajectory data similarity analysis.

[0063] Figure 2 It is a two-target trajectory similarity measurement criterion graph of trajectory features.

[0064] Figure 3 It is a flow chart of the target trajectory similarity calculation method. DETAILED DESCRIPTION

[0065] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0066] The target trajectory similarity calculation method of the present invention mainly solves the following problems, including:

[0067] (1) Target trajectory similarity metric problem:

[0068] The target trajectory data is a time series of position coordinates and motion vectors. In order to ensure the accuracy of data collection, different acquisition equipment is often used to collect data at different sampling frequencies, resulting in the target trajectory data set being a multi-frequency, discontinuous time series of position coordinates and motion vectors. Therefore, it is impossible to measure the similarity of two target trajectories based solely on the sampling point information. Therefore, it is necessary to propose a criterion for measuring the similarity of two target trajectories, and convert the data obtained by different acquisition methods into data under the same criterion according to the criterion, so as to facilitate the similarity calculation.

[0069] (2) Problems with target trajectory similarity calculation methods:

[0070] After the target trajectory data obtained by different acquisition methods are converted into data under the same criterion according to the similarity measurement criterion, it is necessary to use a numerical value to objectively reflect the similarity between the multi-trajectory data, that is, to measure the similarity between the target trajectory and other trajectories in the trajectory set, and obtain the similarity value (0-1) between the target trajectory and other trajectories. According to the similarity value, the similarity of each target motion behavior can be determined.

[0071] Accordingly, a target trajectory similarity calculation method of the present invention includes two stages: Stage 1 is to define the target trajectory similarity, mainly from the three feature dimensions of trajectory point spatial position, spatial shape and real-time following; Stage 2 is a calculation method for measuring the similarity of two trajectory similarities based on trajectory data by considering the three feature dimensions respectively. Among them, stage 1 is a two-target trajectory similarity measurement criterion based on trajectory features, including step 1 trajectory point spatial position feature similarity measurement criterion, step 2 trajectory curve shape feature similarity measurement criterion and step 3 trajectory curve point real-time following feature similarity measurement criterion, and the trajectory data is judged similarly from the similarity measurement criteria of these three feature dimensions; stage 2 is a target trajectory similarity calculation method based on trajectory features, mainly including step 1 generation of a perturbed trajectory with 100% similarity to the original target, step 2 method of converting the mathematical distance of the feature trajectory similarity measurement criterion into similarity, and step 3 multi-target trajectory similarity analysis output. The specific implementation steps are as follows:

[0072] 1. The process of measuring the similarity of two target trajectories of target trajectory features in stage 1 is as follows:

[0073] The high-quality trajectory reconstruction data in stage 1 can display the target motion trajectory on the three-dimensional digital earth. In the business, it is necessary to judge the similarity of the trajectory of each target to determine the relationship between the targets displayed on the digital earth. This method judges the relationship between two targets from the following three dimensions.

[0074] Step 1: Trajectory point spatial position feature similarity measurement criteria

[0075] Step 1.1: For the two known target trajectories, the spatial position characteristics of the two trajectories can reflect the relationship between the targets in the position dimension. Select the longitude, latitude and altitude data of the two target trajectory data, and perform maximum and minimum normalization on the data. The specific calculation method is as follows:

[0076] 1) Take the longitude, latitude and altitude data of the two target trajectories to form a data set Where trajectory 1 has n 1 data points, trajectory 2 has n 2 Data points:

[0077]

[0078] 2) Normalize the longitude, latitude, and altitude data using maximum and minimum normalization. The method is as follows:

[0079]

[0080] Among them: (long*,lat*,alt*) is the data set At a certain point in the data, the original data, the maximum and minimum values ​​of longitude, latitude, and altitude are:

[0081]

[0082] Step 1.2: Two target trajectory data The similarity measurement criteria of spatial location features are: As a benchmark, arrive The spatial location similarity measurement criterion is Each point to the trajectory The distance between the closest points and;

[0083] 1) Calculate using normalized data Each point to the trajectory The distance matrix of each point for:

[0084]

[0085] The distance calculation method is Euclidean distance. The Euclidean distance d between any two points p and q p,q for:

[0086]

[0087] 2) As a benchmark, arrive Spatial location similarity measure is the distance matrix The sum of the minimum values ​​in each row is calculated as follows:

[0088]

[0089] Step 2: Trajectory curve shape feature similarity measurement criteria

[0090] Step 2.1: Take the velocity magnitude and velocity direction data of the two target trajectories to form a data set Where trajectory 1 has n 1 data points, trajectory 2 has n 2 Data points:

[0091]

[0092] Step 2.2: Two target trajectory data The similarity measurement criterion of curve shape features is: As a benchmark, arrive The curve shape similarity criterion is Each vector in the trajectory The projection on and;

[0093] 1) Calculation Each vector in the trajectory The projection matrix on for:

[0094]

[0095] Each element of the matrix is Point p(p=1,2,…,n 1 ) Point q (q=1,2,…,n 2 ) on the projection pr p,q The calculation method is:

[0096] pr p,q =v p2 cos(vθ q1 -vθ p2 ) (8)

[0097] 2) As a benchmark, arrive Curve shape similarity measure is the sum of the projection matrix elements, calculated as follows:

[0098]

[0099] Step 3: Real-time tracking of feature similarity measurement criteria for trajectory curve points

[0100] For two known target trajectories, the spatial positions and shape characteristics of the two targets at the same time can reflect the real-time relationship of the targets on the actual running curve. The specific calculation method is as follows:

[0101] Step 3.1: Take the moment data of the two target trajectories to form a data set Where trajectory 1 has n 1 data points, trajectory 2 has n 2 Data points:

[0102]

[0103] For time period Set the sampling rate f (algorithm input parameter, the default is 1, that is, one time point per second), and let the collection time interval t f =1 / f, generating a set of equally spaced time points as the overlapping time period S t :

[0104] S t ={(T 1 ,T 1 +t f ,…,T 1 +k*t f ,…,min(T 2 ,T 1 +K*t f )), k=0,1,2,…,K} (11)

[0105] Step 3.2: Based on the cubic spline curve interpolation algorithm, combined with the given overlap time period S t The trajectory data S of the two targets in the overlapping time period are reconstructed by the sampling rate f data 1 S 2 , so that the trajectory data of the two targets are at the same time, and the dataset after trajectory data reconstruction is:

[0106]

[0107] Step 3.3: For the trajectory data S of the two targets with the same time period 1 S 2 The similarity measurement calculation of the real-time following feature of the trajectory curve point is performed as follows:

[0108] 1) Calculate the three-dimensional spherical distance between two points at the same time:

[0109] At a certain time t i The coordinates (longitude, latitude and altitude) of the next two target trajectory points are S1pointi=(t i,long1 i ,lat1 i ,alt1 i ) and S2pointi=(t i ,long2 i ,lat2 i ,alt2 i ), first use the Haversine formula to calculate the distance between the two points on the horizontal plane, then consider the height difference between the two points to calculate the distance between the two points on the three-dimensional sphere, and the calculated distance between the two points on the horizontal plane is

[0110]

[0111] Where: haversin(θ) = sin 2 (θ / 2) = (1-cos(θ)) / 2, R is the radius of the earth, which is 6371 km; the distance between the two points on the three-dimensional sphere is d12 i , the calculation formula is as follows:

[0112]

[0113] 2) Calculate the velocity vector projection of two points at the same time:

[0114] At a certain time t i The velocity vector coordinates (speed magnitude and direction) of the next two target trajectory points, S1 is the reference target trajectory, S1pointi=(t i ,v1 i ,vθ1 i ) and S2pointi=(t i ,v2 i ,vθ2 i ), the projection of S2pointi on S1pointi is pr S1pointi,S2pointi , the calculation formula is as follows:

[0115] pr S1pointi，S2pointi =v2 i cos(vθ2 i -vθ1 i ) (15)

[0116] 3) S 1 S 2 The similarity measurement of the real-time following feature of the trajectory curve point is the position distance d12 of the same moment point and the velocity vector distance pr12 of the same moment point in the unit acquisition time. The calculation formula is as follows:

[0117]

[0118] 2. The target trajectory similarity calculation method of the target trajectory features in stage 2 is as follows:

[0119] The flow chart of the method for calculating the similarity of two target trajectories based on trajectory features is as follows: Figure 3 As shown, it mainly includes step 1, generating a perturbed trajectory with 100% similarity to the original target, step 2, converting the mathematical distance of the trajectory similarity measurement criterion of the feature into a similarity method, and step 3, outputting the multi-target trajectory similarity analysis.

[0120] Step 1: Generate a perturbation trajectory with 100% similarity to the original target

[0121] In actual engineering practice, all target trajectory data are usually temporarily stored on the three-dimensional digital earth, and the trajectory of a certain target is selected as the reference trajectory. The similarity between other target trajectories and the selected target trajectory is checked, and the value of the similarity metric is given. Based on this usage scenario, this method considers the data error caused by observation, and defines the similarity between the trajectory of the random fluctuation of the reference trajectory within a certain range and the reference trajectory as 100%. For a certain reference trajectory D = {(t i ,long i ,lat i ,alt i ,v i ,vθ i ),i=1,2,…n} The specific implementation method is as follows:

[0122] 1)Measure the time delay of data

[0123] Randomly select nt (nt = pt*n, the time delay error rate of pt input is generally 0.1) points from n points, and delay each point by time, t i · =t i +rand(0,1) / f (rand(0,1) is a random number generated from 0 to 1, and f is the sampling rate of the trajectory resampling). For the data at this point, use t i · Instead of i , complete the time delay processing of the measurement data.

[0124] 2) Random fluctuations in the spatial position of the measurement point

[0125] Randomly select np (nt = pp * n, pp input position fluctuation error rate, generally 0.1) points from n points, and perform spatial position fluctuation on each point:

[0126]

[0127] (rand(-1,1) is used to generate a random number between -1 and 1). Replace x i , complete the fluctuation processing of the measured data in the spatial position, and after the above two steps, the disturbance data set of the reference trajectory is obtained as D 0 The dataset is denoted as D 0 ={(t i ,long i ,lat i ,alt i ,v i ,vθ i ),i=1,2,…n}.

[0128] Step 2: Method for converting mathematical distance of feature trajectory similarity measurement criteria into similarity

[0129] Step 2.1: Mathematical distance representation of feature trajectory similarity metric

[0130] According to stage 2, the mathematical distance between any two target trajectories under the feature similarity measurement criterion can be calculated. In actual practice, it is necessary to obtain the mathematical distance between the baseline trajectory and other trajectories under the similarity measurement criterion on three features.

[0131] 1) Trajectory data set: one baseline trajectory data, one baseline trajectory perturbation data, and l (number of target trajectory data sets) trajectory data {D, D 0 ,D 1 ,D 2 ,…,D l}, which means the following:

[0132]

[0133] 2) The mathematical distance between the reference trajectory data D and other trajectory data under the trajectory point spatial position feature similarity measurement criterion is: (For calculation method, see Phase 2, Step 1);

[0134] 3) The mathematical distance between the reference trajectory data D and other trajectory data under the trajectory curve shape feature similarity measurement criterion is: (For calculation method, see Phase 2, Step 2);

[0135] 4) The mathematical distance between the reference trajectory data D and other trajectory data under the similarity measurement criterion of real-time following characteristics of trajectory curve points is:

[0136] (For calculation method, see Phase 2, Step 3);

[0137] Step 2.2: Method for converting mathematical distance into similarity

[0138] In actual practice, it is necessary to obtain the similarity between the baseline trajectory and other trajectories in three features. The similarity value (0-1) given to the two target trajectories needs to well reflect the similarity of the two target trajectories in this feature. According to the results of step 2.1 of this stage, the similarity definition function of each feature dimension is determined by the mathematical distance of the feature. The calculation formula for converting mathematical distance to similarity is as follows:

[0139]

[0140] in (It is advisable or ) is the mathematical distance between the jth trajectory and the benchmark trajectory data in the feature dimension q, k is the input cutoff ratio, and it is artificially set that when the distance between a certain trajectory and the benchmark trajectory is greater than k times the distance between the perturbation trajectory and the benchmark trajectory, the similarity between the trajectory and the benchmark trajectory is 0. The similarity between the lth trajectory data and the benchmark trajectory data under the three feature dimensions is calculated as or

[0141] The present invention also proposes a target trajectory similarity analysis system, which implements target trajectory similarity analysis based on the target trajectory similarity analysis method.

[0142] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, target trajectory similarity analysis is implemented based on the target trajectory similarity analysis method.

[0143] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, target trajectory similarity analysis is implemented based on the target trajectory similarity analysis method.

[0144] In summary, for multi-trajectory similarity analysis, the method of the present invention can determine the trajectory similarity of each target trajectory in a certain feature dimension. The present invention can perform similarity judgment on multi-target trajectories on multiple features and quickly find similar targets of a specified target under the similarity measurement criterion in the target trajectory data set.

[0145] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0146] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A target trajectory similarity analysis method, characterized in that: The steps include: Step 1: Formulate target trajectory similarity measurement criteria, including: trajectory point spatial position feature similarity measurement criteria, trajectory curve shape feature similarity measurement criteria, trajectory curve point real-time following feature similarity measurement criteria, where: The similarity measurement criterion of the spatial position feature of trajectory points uses the shortest distance between two trajectories in space as the measurement of spatial position features, and describes the characteristics of the two targets appearing in space through the shortest distance; The similarity measurement criterion of trajectory curve shape features uses the projection of the vector formed by the matching trajectory in space on the target trajectory as the measurement of shape features, and reflects the parallel and cross characteristics of the target trajectory path in space through the vector projection; The similarity measurement criterion of the real-time following feature of the trajectory curve point uses the distance between the two trajectories at the same time in space as the real-time following feature measurement. The distance at the same time reflects the following distance and the following duration of the two targets, thereby determining the motion relationship between the two targets. Step 2: Calculate the distance between the reference trajectory and other trajectories under the three similarity measurement criteria, convert the distance into a similarity value through the similarity measurement standard, and use a value of 0-1 to describe the similarity between the two trajectories; In step 1, based on the similarity measurement criterion of the real-time following feature of the trajectory curve point, the metric distance between the two trajectories on the real-time following feature is calculated. The specific calculation method is: S1, take the moment data of the two target trajectories to form a data set Among them, trajectory 1 has n1 data points, and trajectory 2 has n2 data points; For time period Set the sampling rate to f and the acquisition time interval to t f =1 / f, generating a set of equally spaced time points as the overlapping time period S t : S t ={(T1,T1+t f ,…,T1+k*t f ,…,min(T2,T1+K*t f )),k=0,1,2,…,K} (11) S2, based on the cubic spline interpolation algorithm, combined with the given overlap time period S t The trajectory data S1 and S2 of the two targets in the overlapping time period are reconstructed with the sampling rate f data, so that the trajectory data of the two targets are at the same time. The trajectory data after reconstruction is: S3, the trajectory data S1 and S2 of the two targets with the same time period are used to calculate the similarity measurement of the real-time following characteristics of the trajectory curve points. The calculation method is as follows: 1) Calculate the three-dimensional spherical distance between two points at the same time: At a known time t i The coordinates of the next two target trajectory points are S1pointi=(t i ,long1 i ,lat1 i ,alt1 i ) and S2pointi=(t i ,long2 i ,lat2 i ,alt2 i ), first use the Haversine formula to calculate the distance between the two points on the horizontal plane, and then consider the height difference between the two points to calculate the distance between the two points on the three-dimensional sphere. The distance between the two points on the horizontal plane is calculated to be Where: haversin(θ) = sin 2 (θ / 2) = (1-cos(θ)) / 2, R is the radius of the earth, which is 6371 km; Calculate the distance between two points on the three-dimensional sphere as d12 i , the calculation formula is as follows: 2) Calculate the velocity vector projection of two points at the same time: At a known time t i The velocity vector coordinates of the next two target trajectory points are S1pointi=(t i ,v1 i ,vθ1 i ) and S2pointi=(t i ,v2 i ,vθ2 i ), taking S1 as the reference target trajectory, calculate the projection of S2pointi on S1pointi as pr S1pointi,S2pointi , the formula is as follows: pr S1pointi，S2pointi =v2 i cos(vθ2 i -vθ1 i ) (15) 3) The metric distance of the real-time following feature of the S1 and S2 trajectory curve points is the simultaneous point position distance d12 and the simultaneous point velocity vector distance pr12 in the overlapping time period. The calculation formula is as follows: Where K represents the number of sampling points in the overlapping time period.

2. The target trajectory similarity analysis method according to claim 1, characterized in that: In step 1, based on the similarity measurement criterion of the spatial position features of the trajectory points, the metric distance between the two trajectories in the spatial position features is calculated. The specific calculation method is: S1, select the longitude, latitude and altitude data of the two target trajectory data, and perform maximum and minimum normalization on the data. The specific calculation method is as follows: 1) Take the longitude, latitude and altitude data of the two target trajectories to form a data set Where track 1 has n1 data points and track 2 has n2 data points: 2) Normalize the longitude, latitude, and altitude data using maximum and minimum normalization. The method is as follows: Among them: (long*,lat*,alt*) is the data set The original data of a certain point in the data, the maximum and minimum values ​​of longitude, latitude, and altitude are: S2, two target trajectory data The similarity measurement criteria of spatial location features are: As a benchmark, calculate Each point to the trajectory The distance between the closest points and; 1) Calculate using normalized data Each point to the trajectory The distance matrix of each point for: The distance calculation method is Euclidean distance. The Euclidean distance d between any two points p and q p,q for: 2) As a benchmark, and Metric distance of spatial location features is the distance matrix The sum of the minimum values ​​in each row is calculated as follows:

3. The target trajectory similarity analysis method according to claim 1, characterized in that: In step 1, based on the trajectory curve shape feature similarity measurement criterion, the metric distance between the two trajectories on the curve shape feature is calculated. The specific calculation method is: S1, take the velocity magnitude and velocity direction data of the two target trajectories to form a data set Where track 1 has n1 data points and track 2 has n2 data points: S2, two target trajectory data The similarity measurement criterion of curve shape features is: As a benchmark, calculate Each vector in the trajectory The projection on and; 1) Calculation Each vector in the trajectory The projection matrix on for: Each element of the matrix pr p,q for The point p is The projection calculation method on point q is: pr p,q =v p2 cos(vθ q1 -vθ p2 ) (8) 2) As a benchmark, and Metric distance of curve shape features is the sum of the projection matrix elements, calculated as follows: 。 4. The target trajectory similarity analysis method according to claim 1, characterized in that: In step 2, the metric distance between the reference trajectory and other trajectories under the three feature similarity measurement criteria is calculated. The metric distance can be converted into a similarity value through the similarity measurement standard, and a value of 0-1 is used to characterize the similarity between the two trajectories. The specific method is: in is the metric distance between the jth trajectory and the reference trajectory data in the feature dimension q, k is the input cutoff ratio, Represents the metric distance between the reference trajectory and the noisy trajectory of the reference trajectory in the feature dimension q.

5. A target trajectory similarity analysis system, characterized in that: Based on the target trajectory similarity analysis method described in any one of claims 1 to 4, target trajectory similarity analysis is implemented.

6. A computer device, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, wherein when the processor executes the computer program, target trajectory similarity analysis is implemented based on the target trajectory similarity analysis method according to any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, target trajectory similarity analysis is implemented based on the target trajectory similarity analysis method according to any one of claims 1 to 4.

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