Fast Clustering Method for Track Association Based on Improved OSPA Distance Metric

Abstract

The present invention discloses a fast clustering method based on an improved OSPA distance metric to solve the problem of ship track association in a scenario where three sensors in the VTS system of the maritime supervision department monitor multiple ships. The traditional OSPA distance metric uses the Hungarian algorithm to find the optimal match. In the present invention, the time unidirectionality is utilized to reduce the time complexity of the OSPA distance metric to find the optimal match to reach the linear level of the track length. In one embodiment, for this fast clustering algorithm, all the tracks to be associated are added to a queue, and then the track at the head of the queue is taken to calculate the OSPA distance metric with the remaining tracks. If its value is greater than the cut-off distance c, it is determined that these two tracks are not the tracks of the same ship. Otherwise, they are the monitoring tracks of the same ship. Compared with other clustering algorithms, this algorithm not only has high accuracy but also does not need to calculate the OSPA distance between every two tracks in advance, reducing the computational complexity.

Description

Technical Field

[0001] The present invention belongs to the technical field of ship traffic supervision, and particularly relates to a track association clustering method based on an improved OSPA distance index, which solves the problem of track association before fusing multi-source sensor tracks, that is, finding track data monitored by different sensors from the same ship. Background Art

[0002] To enhance the navigation safety of water transportation ships and improve shipping efficiency, the VTS systems of maritime supervision departments usually use devices such as AIS / VDES, radar, and CCTV high-definition / ultra-high-definition cameras to collect ship traffic information in the navigation area. Fully mining the information collected by these devices can effectively supervise and manage ships in navigation. The position information provided by AIS devices is relatively accurate, but the update frequency is slow, generally updated once every 8 - 12 s or even longer. Radar devices update information every 2 - 4 s, while CCTV devices can continuously and real-timely monitor a water area. Therefore, a practical approach is to combine the advantages and disadvantages of the three data sources and fuse them into a track with rich information. This task can be modeled as multi-source sensor data fusion.

[0003] Since the three devices supervise ships from different perspectives and are sent to the maritime supervision department separately, it is necessary to associate different track data from the same ship before fusing multiple data. This process can be called track-to-track association (TTTA). The solution methods for the TTTA problem can generally be divided into two categories, one is the method based on fuzzy mathematics, and the other is the method based on statistics.

[0004] In the method based on statistics, the field of machine learning has developed rapidly and has shown remarkable application effects in many fields. And some researchers have applied machine learning algorithms to the TTTA problem. The most concerned algorithm among them is the application of clustering algorithms in the TTTA problem: by calculating the correlation metric criteria between tracks, such as distance, and then using the relevant clustering algorithm to cluster several tracks from the same ship into one category.

[0005] However, there are many problems in the existing methods. The k-means clustering method needs to set the number of clusters in advance, and the AGNES algorithm needs to calculate the distance between each pair before clustering, and the time complexity is usually of the order of the square of the track length.

[0006] The present invention assumes that complete track information has been obtained from the three data sources and uses a new fast clustering algorithm to solve the problem of track association. Summary of the Invention

[0007] Technical Problem:

[0008] In the vessel traffic service (VTS) system, in the scenario where three sensors monitor multiple vessels, considering the different characteristics of the three sensors, data fusion technology is used to combine their advantages and disadvantages. However, before fusing the tracks, it is necessary to associate the tracks from the same vessel. Existing clustering technologies have the problem of high computational complexity. Therefore, the fast clustering algorithm based on the improved OSPA distance metric proposed in this invention has the advantage of low computational complexity and can enhance the practical characteristics of the algorithm in the big data era. In addition, the traditional OSPA algorithm is improved by utilizing the unidirectional increase of time to reduce its computational complexity, further increasing its practical characteristics.

[0009] Technical solution:

[0010] This invention proposes a track association and clustering method based on the improved OSPA distance metric. This clustering method uses the improved OSPA metric to calculate the distance between two tracks. Its features are as follows:

[0011] Step 1: Add the tracks of T targets obtained by all S sensors to a queue Q.

[0012]

[0013] Step 2: Take out the track at the head of the queue Q Then take out any track in the queue Q Utilize the unidirectionality of time in the track to reduce the high complexity of the original OSPA distance calculation method from cubic level to linear level.

[0014] Step 3: Determine whether the OSPA distance exceeds the cut-off distance c. If it is greater than or equal to the cut-off distance c, it is considered unassociated and added back to the queue Q. If it is less than the cut-off distance c, then it is considered associated with and not put back into the queue Q. If does not match any of the remaining in the queue, then is clustered into a separate class.

[0015] Step 4: Repeat steps 2 - 3 until the queue Q is empty.

[0016] Furthermore, the calculation method of the OSPA metric distance in step 2 includes the following steps:

[0017] Step 2.1: Take and the shorter track in the tracks and match the i-th track state vector of the shorter track in ascending order of time with the second track Calculate the absolute value of the numerical difference in the time components of the two using the track state vectors in it. If it is the smallest among the absolute values of the numerical differences in the time components of the j-th track state vector in the track , that is: And Then it is regarded as matching the j-th track state vector of the second track ; where represents the time component of the i-th track state vector in the track , represents the time component of the j-th track state vector in

[0018] Step 2.2: Then continue to take the unmatched track state vectors in the track and calculate the absolute value of the numerical difference in their time components starting from the next point of the most recently matched track state vector in the track , and judge whether they match according to the judgment conditions in Step 2.1;

[0019] Step 2.3: Repeat Step 2.2 until all the tracks are completely matched.

[0020] Furthermore, the calculation formula of the cut-off distance c in Step 2 is shown in Formula (1), where is the weighted modulus of the track state vector and the track state vector , where represents the q-th track state vector in the track, x q , y q represent longitude and latitude respectively, v q represents the speed of the ship, θ q represents the direction angle of the ship, time q represents the time of the ship, Similarly, the specific calculation process is as shown in Formula (2), where a, b, c, d, e are weighted coefficients, and a = b = c = d = 1, e = 0;

[0021]

[0022] The cut-off distance c is set to the average error of the monitoring device with the largest error, and it should depend on the error of the actual radar used.

[0023] Furthermore, the empirical value p is set to 2.

[0024] Furthermore, when the length u of is greater than the length v of

[0025] Beneficial effects: Only the spatial position and time information monitored by each sensor are required to associate different tracks from the same ship, and the high time complexity of the OSPA distance metric is improved. The proposed clustering method has better computational efficiency compared with common clustering algorithms. Description of the Drawings

[0026] Figure 1 is the overall flowchart of a fast clustering algorithm for track association based on an improved OSPA distance metric according to the present invention;

[0027] Figure 2 is a schematic diagram of an improved method for finding the optimal match calculation in the OSPA distance metric of the present invention;

[0028] Figure 3 is a schematic diagram of 15 tracks of 5 targets and 3 sensors generated using simulation data;

[0029] Figure 4 is a result diagram of track association for 5 ships using the method of the present invention. Detailed Implementation Manner

[0030] Step 1: Add the tracks of T targets obtained by all S sensors to a queue Q.

[0031] Consider a multi-sensor multi-target scenario,

[0032]

[0033]

[0034] Formula (1) is the state equation of the ship track. represents the (n + 1)-th track state vector of the t-th target, which includes five states: planar coordinate x, planar coordinate y, speed magnitude v, navigation direction angle θ, and UTC time time, that is is the state transition matrix, is the noise in the transition process, which generally follows a normal distribution.

[0035] Formula (2) is the observation equation of the ship track. is the observation matrix of the ship track, is the observation noise of the ship track, which generally follows a normal distribution. is the observation value of the (n + 1)-th track state vector of the t-th target by the s-th sensor, which is the finally obtained track data.

[0036] Therefore, the track of the t-th target observed by the s-th sensor can be expressed as Define the number of track state vectors as the length of the track. Here is a general representation, denoted as length \(n\). s .

[0037] Finally, add the observation data of all sensors to the queue \(Q\) (the order can be random, depending on the actual situation. Here, sequential arrangement is adopted for convenient reading).

[0038] Step 2: Take out the track at the head of the queue \(Q\). Then take out any track in the queue \(Q\). Calculate the OSPA metric distance.

[0039] Step 2.1: Optimize the OSPA distance calculation method.

[0040] The OSPA metric distance is calculated as shown in formula (3). Assume that the length of track is \(u\), and the length of track is \(v\), and assume \(u\leq v\). In formula (3), takes the minimum, indicating that when calculating the OSPA distance metric between track and track , it is necessary to perform an optimal matching of the track state vectors in the two tracks. Here, the Hungarian algorithm is used for the matching of track state vectors. However, the time complexity of its algorithm is \(O(\max(u, v) 3 ), so it cannot meet the real-time calculation scenario.

[0041]

[0042] The present invention uses the time unidirectionality in the ship's track to reduce the time complexity of this calculation process. Its implementation is as Figure 2 shown. The lengths of track and track are \(u\) and \(v\) respectively. The time dimension of the vector is listed beside the track state vector point, and the time component is used to find the optimal matching of the track state vectors. The process is as follows:

[0043] Step 2.1.1: Take the \(i\)-th track state vector of the shorter track in ascending order of time and calculate the absolute value of the difference in the time component values between it and the track state vectors in the second track . If the absolute value of the difference in the time component values with the \(j\)-th track state vector in the track is the smallest, that is: And Then it is regarded as matching the \(j\)-th track state vector of the second track .

[0044] Step 2.1.2: Then continue to obtain the track The unmatched track state vectors in it are used to calculate the absolute value of the difference in the time component values between the next point of the track state vector that was most recently matched in track and the current track state vector, and then judge whether they match according to the judgment conditions in Step 1.

[0045] Step 2.1.3: Repeat Step 2.1.2 until all tracks are completely matched.

[0046] As can be seen from the above steps, due to the unidirectional increase of time, it is not necessary to traverse and match from the first track state vector of each track every time during the matching process. Therefore, the time complexity is reduced to the linear level of Ο(u + v).

[0047] Step 2.2: Set a reasonable value for the cut-off distance c;

[0048] The calculation formula for the cut-off distance is shown in Formula (4), where is the weighted modulus of the track state vector and the track state vector . The specific calculation process is shown in Formula (5). Since the coefficient of the fifth term is usually set to 0, it is not written in the formula. Generally, a = b = c = d = 1 and e = 0 are set. It can be seen from the calculation formula that the OSPA distance between two tracks will not exceed the cut-off distance c. Therefore, it needs to be set correctly.

[0049]

[0050] In the maritime supervision center, three monitoring devices are used to monitor ships, namely the AIS system, the radar monitoring system, and the high-definition camera monitoring system. The errors of the three devices are different. The AIS system has the highest measurement accuracy of position information, followed by the high-definition camera monitoring system, and the radar monitoring system has the largest error. In order to associate the tracks from the same ship using the OSPA distance, the cut-off distance c should be set to the average error of the monitoring device with the largest error. Therefore, the cut-off distance is an empirical value setting and should depend on the actual error of the radar used.

[0051] Step 2.3: Set a reasonable order p;

[0052] As the value of the order p increases, when the distance between track state vectors in two tracks exceeds the cut-off distance c, the contribution to the overall ospa distance value becomes greater. That is

[0053]

[0054] According to the empirical value, p is generally set to 2.

[0055] Step 2.4: For with a length greater than Handling of the length situation.

[0056] According to the symmetry of the OSPA distance metric, when the length u of is greater than the length v of

[0057]

[0058] Step 3: Determine whether the OSPA distance exceeds the cut-off distance c. If it is greater than or equal to the cut-off distance c, it is regarded as uncorrelated and re-added to the queue Q. If it is less than the cut-off distance c, then it is regarded as correlated with and not put back into the queue Q. If does not match any of the remaining in the queue, then is clustered into a separate class.

[0059] Step 4: Repeat Steps 2 - 3 until the queue Q is empty.

[0060] Use a computer simulation program to simulate and verify a track association clustering algorithm based on an improved OSPA distance metric mentioned in the present invention. Use the program to simulate and generate tracks as shown in Figure 3 . Only the planar coordinates (x, y) are shown in the figure. Add noise to the x and y coordinates of each real track using Gaussian noise, and set the sampling rate according to the real sensor update frequency. Here, simulate the data sources of AIS, radar, and high-definition video monitoring equipment cctv in the maritime supervision center. The average error of the AIS monitoring equipment is about 5m, and it is generally updated once every 8 - 12s; the average error of the radar monitoring equipment is about 30m, and it is generally updated once every 2 - 5s; the cctv monitoring equipment is a continuous monitoring equipment, and its method of measuring the ship position usually uses AIS data for calibration, so the error is slightly larger than that of AIS. The detailed reference data of each track is shown in Table 1. Since it is simulation data, the starting position is set from the coordinate origin, and the starting time starts from 0s.

[0061] Table 1: Simulation parameter settings for the tracks of 5 ships

[0062]

[0063]

[0064] Here, the tracks of five ships are simulated, including overlapping tracks and crossing tracks. Using this method can effectively associate the tracks. Here, it is assumed that each ship is monitored by three sensors at the same time, so there are a total of 15 tracks. AsFigure 3 As shown, the same digital sequence prefix is used to represent the tracks from the same ship, and the name of the sensor is used to distinguish the tracks. For example, 000001ais, where 000001 represents Ship No. 1 and ais represents the track monitored by ais. Figure 3 It can be seen that except for Ship No. 000004, there are track intersections and overlaps in the tracks of the other four ships.

[0065] Set the cut-off distance in the ospa distance calculation to 15m and the order to 2. Finally Figure 4 For the matching result graph, when storing the matching results, the labels of the tracks clustered into the same ship (for example: 000001ais) are concatenated into a string. As shown in the first row of the figure: 000001ais000001radar000001cctv. This result indicates that the three tracks of Ship No. 1 have been associated. Similarly, the results of other ships can be obtained. Therefore, from the overall results, even in the case of track intersections and overlaps, the track association algorithm of the present invention can well associate the ship tracks.

[0066] The above content is a further detailed description of the present invention in combination with specific preferred embodiments. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention belongs, without departing from the concept of the present invention, several deductions or substitutions can still be made, which should all be regarded as belonging to the protection scope of the present invention.

Claims

1. A fast clustering method for track association based on improved OSPA distance metric, Characterized in that, Specifically includes the following steps: Step 1: Add the tracks of T targets obtained by all S sensors into a queue Q. Step 2: Take out the track at the head of the queue Q Then take out any track in the queue Q Utilize the time unidirectionality in the track to reduce the high time complexity of the original OSPA distance calculation method from the cubic level complexity of the original calculation method to the linear level; and set a reasonable cut-off distance c and order p; Step 3: Determine whether the OSPA distance exceeds the cut-off distance c. If it is greater than or equal to the cut-off distance c, it is regarded as unassociated and re-added to the queue Q. If it is less than the cut-off distance c, then it is regarded as associated with and not put back into the queue Q; Step 4: Repeat steps 2 - 3 until the queue Q is empty; The calculation method of the OSPA distance in step 2 includes the following steps: Step 2.1: Take and the track with a shorter length in the track The i-th track state vector of which is in ascending order of time and the second track Calculate the absolute value of the numerical difference of the time components of the two track state vectors. If the absolute value of the numerical difference with the time component of the j-th track state vector in the track is the smallest, that is: and then it is regarded as matching the j-th track state vector of the second track ; where represents the time component of the i-th track state vector in the track , represents the time component of the j-th track state vector in Step 2.2: Then continue to obtain the track The unmatched track state vectors in are calculated from the next point of the track state vector that was most recently matched in track the absolute value of the difference in the time components of the two is calculated, and it is determined whether they match according to the judgment conditions in Step 2.1; Step 2.3: Repeat Step 2.2 until the track is fully matched; The calculation formula for the cut-off distance c in step 2 is shown in formula (1), where is the track state vector and the track state vector of the weighted modulus, where means the q-th track state vector in the track, x q , y q represent the longitude and latitude respectively, v q represents the speed of the ship, θ q represents the direction angle of the ship, time q represents the time of the ship, Similarly, the specific calculation process is as formula (2), where a, b, c, d, e are weighting coefficients, and a = b = c = d = 1, e = 0; The cut-off distance c is set to the average error of the monitoring device with the largest error, depending on the error of the radar actually used; The empirical value p is set to 2.

2. A fast clustering method for track association based on improved OSPA distance metric according to claim 1, Characterized in that, When the length u of is greater than the length v of

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