An Efficient Trajectory Negotiation and Verification Method Based on Spatiotemporal Pattern Mining

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Introduction
With the continuous and rapid growth of the global air transport industry, the number of civil aviation aircraft continues to rise, and the traffic flow and flight safety issues caused by flight delays and air traffic jams are becoming more and more frequent [1].
To cope with the continuous and rapid growth of traffic flow, improve the safety level of flight operation, and reduce flight delay, in 2004, Europe proposed the Single European Sky ATM Research (SESAR) [2]; in 2005, the United States proposed the Next Generation Air Transportation System (NextGen) plan [3]; and in 2012, the International Civil Aviation Organization (ICAO), with the vision of the Global Air Traffic Management Operational Concept (GATMOC), proposed the long-awaited Aviation System Block Upgrade (ASBU) plan [4].However, whether it is the United States' NextGen, Europe's SESAR development plan, or the ICAO's ASBU plan, trajectory-based operations will be the core technology of air traffic management in the future.
In trajectory-based operations, trajectory negotiation and verification are key components [5], which assist users in improving flight efficiency and reducing flight conflicts.Therefore, the trajectory negotiation and verification architecture for air traffic management systems and airspace users were studied.Gardi et al. [6] introduced the conceptual design of a novel four-dimensional trajectory planning, negotiation, and verification (4-PNV) system capable of automatically negotiating and verifying the trajectory in complex air traffic situations and adopting adequate separation and avoiding criteria to resolve traffic conflicts.Lunlong and Jiongpo [7] analyze the functional requirements and architecture of the new generation of flight management system (FMS); the new generation of FMS system is required to be interoperable with the future ground-based fourdimensional trajectory planning, negotiation, and verification (4-PNV) system to achieve trajectory-based operations.In order to deal with uncertainty and improve the efficiency of trajectory negotiation, Hunter et al. [8] proposed a cloudbased automatic trajectory negotiation service (ATNS) system, which is independent of the traditional national airspace system (NAS) architecture and has the capability of rapid deployment, increasing the flexibility of airspace users in uncertain situations.In order to reduce the negotiation time, Idris et al. [9] analyzed the cooperation scheme and automation system used by the flight crew and dispatcher for route change requests, which improves the accuracy and flexibility of route change and avoids increasing the controller's workload.Trajectory negotiation is helpful to reduce flight conflicts; as an important indicator, researchers have paid attention to flight safety during trajectory negotiation.Park and Menon [10] proposed a new trajectory negotiation mechanism to distribute the benefits of trajectory-based operations fairly among all stakeholders, while minimizing the cost of deviation from the desired trajectory of each aircraft, in order to ensure fairness and prevent flight conflicts.To improve the real-time performance of conflict detection at low altitude, Miao et al. [11] proposed a flight conflict detection algorithm based on the multilevel grid spatiotemporal index, which transformed the traditional trajectorytraversing multivariate conflict computation into a grid conflict state query of distributed grid databases.
Although trajectory negotiation has attracted the attention of researchers around the world, the current methods make it challenging to explore the potential information from trajectories proposed by users.With the advancement of computer technology in recent years, data mining and machine learning techniques have become increasingly popular.In order to analyze potential risks from a large quantity of historical trajectory data, Zhang et al. [12] proposed an end-to-end framework based on the depth automatic encoder network that can effectively identify typical spatial anomalies in a timely manner.Olive and Basora [13] proposed a framework based on automatically encoded artificial neural networks for detecting and identifying anomalies.The experimental results can improve safety models and support stakeholders such as airlines and airports to optimize their operating models.To overcome the shortcomings of converting the flight trajectory into a time series of equal length, Liu et al. [14] proposed a trajectory three-channel image representation method, which maps trajectory information to a three-dimensional matrix; the results indicate that this method can analyze the similarity between different trajectories and detect anomaly trajectories.In order to improve the efficiency of conflict resolution in the process of trajectory negotiation, Kim et al. [15] proposed a datadriven conflict resolution generator that uses machine learning technology to automatically generate conflict resolution strategies based on information extracted from flight data.To reduce flight conflicts and ensure flight safety, changing the flight route through trajectory negotiation has become a research hotspot.Evans et al. [16] developed a method for calculating the acceptability of aircraft rerouting using data mining techniques, so as to reduce the workload during the rerouting procedure.However, few studies have been conducted in the preflight and in-flight stages to mine and analyze flight trajectories proposed by users for detecting flight conflicts and identifying flight combinations with close flight intervals and long flight delays in congested airspace; thus, it is of great significance to conduct research on trajectory negotiation and verification methods based on spatiotemporal weighted data mining algorithms.
In light of the challenges associated with the negotiation and verification of four-dimensional trajectory, this paper seeks to ensure the safety of airspace operations while increasing the flight efficiency of users.Therefore, this paper develops a system architecture for air-ground trajectory negotiation and verification in trajectory-based operations.First, the system enables the air traffic management system and users to initiate flexible trajectory negotiation requests based on the airspace traffic environment and flight preferences of aircrafts.Second, a spatiotemporal weighted pattern mining algorithm is proposed, which takes flight delay time as weight information and analyzes flight trajectory information proposed by users by setting horizontal and vertical flight interval constraints and weight constraint.Finally, the experimental results demonstrate that the algorithm accurately identifies potential conflicts and flight combinations with close flight intervals and long flight delays in the airspace, thereby enabling ATM and users to collaboratively adjust the flight trajectory, reduce flight delay, and ensure the airspace operation safety.The highlights of our proposed method are shown as follows: (1) In trajectory-based operations, a framework for trajectory negotiation and verification is developed to assist the air traffic management system and users in initiating trajectory negotiation based on flight preferences and airspace traffic environment (2) A spatiotemporal weighted pattern mining algorithm is proposed, which accurately identifies potential flight conflicts and flight combinations with low flight efficiency from user-proposed trajectories.
The method is then validated in the airspace by imposing various constraints The remainder of the paper is organized as follows.Section 2 systematically introduces the system architecture for trajectory prediction, negotiation, and verification.The mining process of the spatiotemporal weighted algorithm is described in Section 3. The experimental test results are shown in Section 4. The conclusion of the paper is presented in Section 5.

Trajectory Prediction, Negotiation, and Verification System
2.1.Trajectory Prediction Method.In trajectory-based operations, the airspace users will negotiate with the air traffic management system during the preflight and in-flight 2 International Journal of Aerospace Engineering phases.As shown in Figure 1, the airspace user must first predict the four-dimensional trajectory of the aircraft based on its flight performance, flight plan, and meteorological conditions [17].
The trajectory prediction refers to the estimation of future longitude, latitude, altitude, and time based on the flight plan of the aircraft, the expected environmental conditions, and the performance model of the aircraft.The four-dimensional trajectory is derived by integrating time into the three-dimensional trajectory, which consists of two parts: the horizontal flight profile and the vertical flight profile [18].The horizontal flight profile consists of segments of straight flight and segments of curved flight.There are two types of turning segment: fly-by and flyover.When calculating the horizontal flight profile, the waypoint information from the flight plan is retrieved first, and then, the waypoints are connected sequentially to form straight-line segments.Since the great circle route is the shortest distance on the surface of the sphere, it is used to connect adjacent waypoints; the horizontal flight profile is then obtained by adding turn segments at the turn positions according to the heading changes between the great circle routes [19,20].
When calculating the vertical flight profile, the aircraft is initially regarded as a mass point, and the relationship between the force acting on the aircraft and the rate of change of potential energy and kinetic energy is expressed through the energy equation, and a full energy model is established, as shown in where Thr represents the thrust and D represents the drag.This paper uses the aircraft performance data provided by the base of aircraft data (BADA) database to calculate the thrust and drag, m represents the aircraft mass, g 0 represents the gravitational acceleration, h represents the geodetic altitude, and V TAS represents the true airspeed.
Then, the velocity in the vertical direction of the aircraft is calculated by controlling the thrust and speed of the aircraft, as shown in To eliminate the influence of meteorological conditions, the rate of climb or descent (ROCD) is used to express the rate of climb and descent of the aircraft, as shown in where H p represents the barometric altitude, T represents the atmospheric temperature, ΔT represents the temperature difference, and f M represents the energy sharing factor, which indicates the amount of energy allocated for climbing or descending, as shown in Finally, the four-dimensional trajectory from the departure airport to the arrival airport is predicted.

Trajectory Negotiation Architecture
2.2.1.Trajectory Negotiation Initiated by User.Trajectory negotiation can effectively satisfy user flight preferences and reduce flight delay, so this paper proposes a trajectory negotiation architecture based on references [21,22] that allows airspace users to initiate trajectory negotiation requests during the preflight and in-flight stages.Before the flight, the airspace user utilizes the FMS to calculate the four-dimensional trajectory based on aircraft performance, flight plan, and other data and then transmits the flight trajectory to the trajectory negotiation system through the data link.During flight, the airspace user monitors the airspace traffic environment and airspace meteorological conditions.If a better route is available or an emergency such as airborne equipment failure occurs, the FMS system will recalculate the four-dimensional trajectory based on the current flight status and aircraft performance, and the new trajectory is transmitted to the trajectory negotiation system through the data link.After receiving the flight trajectories sent by the users, the trajectory negotiation system verifies the user-requested flight trajectory to ensure the minimum flight separation constraints are met.When the requested trajectory satisfies constraints, the air traffic management system will send the trajectory permission to the user, who will then send the confirmation information to conclude the trajectory negotiation procedure, as shown in Figure 2. When the requested trajectory proposed by the 3 International Journal of Aerospace Engineering user violates the minimum separation constraints, it indicates the presence of a potential flight conflict; the ATM will allocate the airspace constraints in coordination with the airspace traffic environment and send the airspace constraints to the aircraft through the data link [23,24].The FMS system will then recalculate the requested flight trajectory and send it to the trajectory negotiation system for trajectory verification.The air traffic management system will continuously adjust the airspace constraints until an agreement is reached with the user.

Trajectory Negotiation Initiated by ATM.
The main objective of the air traffic management system is to reduce flight conflicts and flight delays.However, airspace convective weather and no-fly zones, among other factors, often cause flight delays and decrease flight efficiency.Therefore, the air traffic management system must identify flight combinations in the airspace with close flight intervals and long flight delays and then negotiate with these users to adjust the user's flight trajectory to improve airspace operation efficiency.During the trajectory negotiation process, the trajectory negotiation system transmits the airspace constraints (including speed, altitude, and time) to the user through the data link.After receiving the airspace constraints, the FMS system is used to calculate the requested flight trajectory based on the aircraft's performance, constraints, and status.When the requested flight trajectory violates the air-space constraints sent by the trajectory negotiation system, the user will negotiate with the air traffic management system to adjust the airspace constraints and recalculate the flight trajectory until an agreement is reached, as shown in Figure 3.When the requested trajectory satisfies the airspace constraint, the FMS system will send it to the trajectory negotiation system for verification.If the verification fails, the air traffic management system and the user will negotiate to adjust the airspace constraint until they reach an agreement.When the trajectory system passes the verification, it will send the permission information to the airspace user, who will then be able to fly based on the updated trajectory, thereby enhancing the flight efficiency.

Trajectory Verification Architecture.
To ensure the safety of airspace operations, the trajectory negotiation system must verify the flight trajectories proposed by users.The trajectory negotiation system receives the flight trajectory information sent by users through the data link and then verifies the user's flight trajectory at each moment by calculating the horizontal and vertical distances between the user's flight trajectories in the airspace [6].If the flight interval between users is less than the minimum flight separation constraint, it indicates that potential flight conflicts between aircrafts exist.Therefore, the ATM must negotiate with users to adjust flight trajectory and ensure flight safety within the airspace.As shown in Figure 4 4 International Journal of Aerospace Engineering between aircrafts satisfies the minimum flight separation constraint, the time is updated until the trajectory verification is complete.

Problem Description of Trajectory Negotiation and
Verification.In trajectory-based operations, fourdimensional trajectory negotiation and verification can detect flight conflicts, reduce flight delay, and improve airspace operation efficiency.Therefore, before or during flight, the user transmits the four-dimensional trajectory to the air traffic management system.Then, in order to ensure flight safety, after receiving the user's proposed flight trajectory, the air traffic management system verifies whether the proposed flight trajectory satisfies the set horizontal and vertical flight separation constraints.Secondly, in the process of airspace operation, meteorological hazards, no-fly zones, etc., will cause the aircraft to deviate from the economic speed and altitude, causing flight delay and reducing flight efficiency; therefore, the ATM must identify flight combinations with a long flight delay and close flight interval so that the air traffic management system and users can negotiate to adjust flight trajectories and reduce flight congestion and flight delay.Therefore, how to quickly and accurately identify flight combinations that violate the minimum flight separation constraint from a large number of trajectory information at different times to ensure flight safety and how to identify flight combinations with close flight intervals and long flight delays in the airspace, in order to improve flight efficiency, have great significance.

Spatiotemporal Weighted Pattern Mining Algorithm
This paper proposes a spatiotemporal weighted pattern mining algorithm based on the works of Kiran et al. and Kelin et al. [25,26] to improve airspace operation efficiency and ensure flight safety.As shown in Figure 5, this algorithm identifies flight combinations that violate minimum separation constraints by first analyzing the flight trajectory proposed by users, so that the air traffic management system and users can negotiate to adjust the flight trajectory, eliminate flight conflicts, and ensure flight safety.Second, the algorithm can obtain flight combinations with close flight intervals and long flight delay by analyzing the flight trajectory and the user's flight delay information in airspace with heavy traffic and then negotiate with the user to adjust the flight trajectory to increase flight efficiency.
3.1.Algorithm Definition.In order to explain the operation process of algorithm in detail, the hypothetical data in a similar format to experimental data are used in this paper, as shown in Tables 1-3.Among them, Table 1 is the flight database, which represents the users of the airspace at various times.In order to detect flight conflict and ensure flight safety, this paper first mines the item sets that satisfy the interval constraints from the trajectory information proposed by users.The mining process begins by reading the three-dimensional position coordinates of aircrafts in the airspace at various times.Second, this paper uses the trajectory information provided by users to compare whether the horizontal and vertical intervals between aircrafts satisfy the minimum separation constraints at each moment and then identifies the flight combinations that violate the minimum flight separation constraints.
As shown in the pseudocode in Algorithm 1, the algorithm uses each item as an extension item at different times, beginning with the first item to determine the flight intervals between the extension item and the remaining items in the line.If the horizontal and vertical distances between the item 7 International Journal of Aerospace Engineering and the extension item are less than the minimum flight separation constraints, the item will be considered the extension item's predecessor.When the item is identical to the extension item, it will move backward.When the horizontal and vertical distances between the subsequent item and the extension item are less than the minimum flight separation constraints, the subsequent item is considered a candidate for the extension item.
This paper proposes a precursor pruning strategy to increase the algorithm's mining efficiency by removing candidate items during the algorithm's execution.When the flight intervals between the predecessor item of the extension item and each candidate item of the extension item are less than the minimum flight separation constraints, the candidate can be eliminated, thereby accelerating the algorithm's execution.The candidates are then sequentially added to the current expansion item for recursive expansion until the candidates' list is empty.Finally, each output in the expansion item is the combination of aircraft whose horizontal and vertical intervals satisfy the minimum flight separation constraints.Theorem 9. Assuming E is the extension item, C T is the candidate item set of E and P T is the predecessor item set of E. For any candidate item C C ∈ C T , there is a predecessor item P P ∈ P T , satisfying hor dis P,C ≤ sep hor &ver dis P,C ≤ sep ver 7 The sep hor and sep ver represent the minimum horizontal and vertical flight separation constraints, respectively, and then, the candidate item C can be previously extended by the predecessor item P, and C can be pruned.
Proof (proof of contradiction).For extension item E, P P ∈ P T and C C ∈ C T are the precursor and candidate items for E, respectively.If items PE and PC also satisfy the horizontal and vertical interval constraints, the item PEC can be obtained when extending P. The item EC satisfy the horizontal and vertical interval constraints when extending E. Considering that each item appears once, the EC item obtained by expanding item E is a subset of the PEC item, which contradicts the hypothesis.Therefore, the original Theorem 9 holds.
To describe the mining process in detail, the horizontal and vertical intervals are set in this paper (for example, se p hor = 5 nm and sep ver = 300 m), and the minimum weight constraint min WS = 120 is set at the same time.Then, based on the three-dimensional position information, the 1.Input: The location and weight information of aircrafts at different times in the airspace 2. Output: Flight combinations satisfying flight interval constraints at different times

For extension in item sets
Calculate the flight intervals between the expansion item and other items at the same time; If the horizontal and vertical intervals satisfy the interval constraints and this item is in front of the extension item add to predecessors Else if the horizontal and vertical intervals satisfy the interval constraints and this item is located after the extension add to candidates End if Use pruning strategy to remove some candidates Add candidate to the extension recursively until the candidates of the extension are empty End for Algorithm 1: Spatiotemporal mining algorithm.
International Journal of Aerospace Engineering algorithm calculates the relationship between the horizontal and vertical intervals of aircrafts and the set horizontal and vertical separation constraints and places flight combinations that satisfy the minimum separation constraints simultaneously with adjacent combinations in parentheses.Using time t 4 as an example, f 1 is used as an extension to calculate the horizontal and vertical intervals between f 1 and f 2 , f 3 , and f 4 firstly, the intervals between f 1 and f 2 violate the set minimum separation constraints, then delete f 2 , and both f 3 and f 4 satisfy the horizontal and vertical minimum separation constraints with f 1 , then f 3 and f 4 are candidates for f 1 , and then, the f 3 is added as an extension item, so the current extension item is f 1 f 3 ; then, calculate that f 4 , f 1 , and f 3 all satisfy the horizontal and vertical minimum separation constraints, and the f 4 is added to the current expansion item, that is, f 1 f 3 f 4 .At this point, the candidate item is empty, which means that the flight combination f 1 f 3 f 4 that satisfies the minimum separation constraints is output, as shown in Figure 6.
When f 3 is used as the extension item, the intervals between f 1 f 3 and f 3 f 4 satisfy the set minimum separation constraints.Thus, f 1 is used as the predecessor item of the extension item f 3 , and f 4 is used as the candidate item of the extension item f 3 .However, since the precursor f 1 and candidate f 4 satisfy the minimum separation constraints, this candidate f 4 is deleted; that is, there is no output when f 3 is used as an extension, as shown in Figure 7.
The flight combinations that satisfy the minimum separation constraints at various times are then identified.As shown in Table 4, the distances between the items in brackets within the same time in the table are all less than the minimum separation constraints set by the algorithm.

Spatiotemporal Weighted Data Mining.
In order to support the ATM system to initiate trajectory negotiation, alleviate airspace congestion; after obtaining the flight combinations that satisfy the separation constraints, the flight delay time of each flight is used as the weight information.This paper identifies the flight combinations that satisfy the flight intervals and weight constraint simultaneously   Item set To identify flight combinations that satisfy both the intervals and weight constraint, each item is read from the flight combinations that satisfy the interval constraints at each moment, and the MWS and BNWS values are filled for each item, where MWS represents the weighted sum of the items that occur at the same time moment and BNWS represents the maximum sum of weights behind the item at each time, as shown in Table 5.Then, when the expansion item is empty, each item that satisfies the interval constraints is read from the flight combinations, along with a check to determine whether the item appears only once.If it only appears once, the BNWS of the item is assigned to the candidate item; if another item with the same name is read, it is determined if the items are at the same time.If it is located at different times, the item's weight is added to the MWS, and the item's BNWS is determined based on whether or not it only appears once at that time.If the item is present at the same time, the values of BNWS and the temporarily stored BNWS are compared, and the larger BNWS is used as the item's temporary BNWS.If the item appears for the last time at this moment, the BNWS of the item is computed, and a single candidate item is generated, as shown in Table 6.
When the extension item is not empty, the precursor pruning strategy is employed to first remove candidate    10 International Journal of Aerospace Engineering items.Second, the algorithm described above is used to calculate BNWS for extension items and candidate items, and then, candidates are generated if the extension item is not empty.After calculating the single candidate of the extension item, the proposed candidate pruning strategy is applied to prune the single candidate item to increase the algorithm's efficiency.The min WS represents the minimum weight sum constraint, then the combination of candidate C and subsequent items is still less than the minimum constraint, and C can be pruned.
Proof (proof of contradiction).For candidate item C that satisfies weight constraint, MWS C represents the sum of weights of C items in the database, and BNWS C represents the maximum weight of subsequent items that appear with item C at the same time.If MWS C + BNWS C is less than min WS , it means that the item sets combined with item C and subsequent items still violate the weight constraint, which contradicts the hypothesis.Therefore, the original Theorem 10 holds.
After a single candidate has been determined, each item is individually identified as an extension item.In the mining process, when the extension item is empty, the single candi-date item generated above is used as an extension item, the items following the extension item are used as candidates for recursive mining, and the predecessor pruning strategy is used to delete the candidate items to reduce the computational complexity of the algorithm.When the extension item is not empty, the candidate items are added to the extension item as new extension items in turn, and the candidate item's subsequent items are used as new candidate items.At the same time, the predecessor pruning strategy is used to remove candidate items, and then, recursive mining is performed.Finally, the algorithm identifies flight combinations that satisfy the intervals and weight constraint, as shown in Table 7.

Analysis of Experimental Results
In order to verify the effectiveness of the spatiotemporal weighted pattern mining algorithm proposed for fourdimensional trajectory negotiation and verification, the trajectory negotiation initiated by the user and the air traffic management system is tested, respectively.The experimental platform is a laptop with an i5 2.5 GHz processor, Windows 10 operating system, and 8 GB of memory.
4.1.Trajectory Negotiation Initiated by the User.In order to explain the user-initiated trajectory negotiation process in detail, this paper assumes that there are flights f 1 -f 5 in the airspace, with the departure and destination airports and expected departure time listed in Table 8.As depicted in Figure 8, the flight plan is then formulated for airspace users through collaborative allocation based on the route resources in the airspace and is represented by a series of waypoints.
In trajectory-based operations, the airspace user calculates the four-dimensional trajectory based on the flight plan information and the aircraft performance, including take-off weight, aerodynamic performance, and engine thrust; the four-dimensional trajectories of flights f 1 -f 5 are shown in Figure 9; the time information of the four-dimensional Therefore, the air traffic management system must negotiate with the user to adjust the airspace constraints based on the mining results, in order to resolve the flight conflict and ensure the safety of airspace operation.
After identifying flight combinations that violate the minimum flight separation constraints in the airspace based on the four-dimensional trajectory information proposed by the user, the air traffic management system negotiates with the user to allocate the airspace constraints according to the airspace traffic environment.Then, the cruise altitude of the f 2 is adjusted through negotiation, as shown in Table 9.
After trajectory negotiation, the f 2 recalculates the trajectory and sends it to the air traffic management system, and then, the flight conflicts are detected by identifying the flight combinations that violate the flight separation constraints.As shown in Figure 11, there are no flight conflicts in the airspace, thereby ensuring the safety of airspace operations.

Trajectory Negotiation Initiated by Air Traffic
Management System.To improve airspace operation efficiency, the air traffic management system monitors the operational status of air traffic, so as to detect the airspace congestion caused by the aircrafts with close flight interval and long flight delay in time.For aircraft flying through congested airspace, the air traffic management system needs to negotiate with users to adjust flight trajectories, reduce flight delays, and alleviate airspace congestion.
In order to explain the trajectory negotiation process initiated by ATM, this paper assumes the user's departure and destination airports and planned departure time in the airspace, as shown in Table 10.Then, each airspace user is assigned a flight plan based on the airspace route resources.As shown in Figure 12, different colors represent the flight plans of different users, where the airport is represented by the five-pointed star, the waypoint by triangle, and the flight route by the dotted line.
After obtaining the flight plan, the airspace user calculates the four-dimensional flight trajectory based on the flight plan, aircraft performance, and other information, as shown in Figure 13.The color gradient curve represents the user's four-dimensional flight trajectory, with different    Then, this paper mines the four-dimensional trajectory and flight delay information of users in the airspace by setting different horizontal and vertical interval constraints and minimum weight constraint, as shown in Table 11.The flight combination identified by mining is zero when the minimum horizontal and vertical interval constraints are set, indicating that there are no flight conflicts in the airspace.When a smaller flight interval and a larger weight constraint are set, the algorithm identifies fewer flight combinations, whereas when a larger flight interval and a smaller weight constraint are set, it identifies more flight combinations.
Therefore, the air traffic management system can adjust the flight intervals and weight constraint according to different traffic environments flexibly.When airspace traffic is severely congested and route resources are limited, smaller horizontal and vertical interval constraints and larger weight constraint can be imposed to negotiate with users and give priority to flights with significant delays and close flight intervals.When the flight density in the airspace is low, and there are sufficient available route resources, larger horizontal and vertical intervals and smaller weight constraint can be set and then negotiated to solve the flights with lighter flight delay, so as to improve the efficiency of airspace operations, alleviate airspace traffic congestion, and decrease flight delay.

Conclusions
This paper first develops a framework for trajectory prediction, negotiation, and verification to ensure flight safety and improve flight efficiency in trajectory-based operations.Secondly, a spatiotemporal weighted pattern mining algorithm is proposed for trajectory negotiation and verification.Experimental results indicate that the algorithm can identify flight combinations that violate the minimum flight separation constraints during trajectory verification and that flight combinations that satisfy the set constraints are accurately identified according to the different airspace operating states, so as to support the air traffic management system and users to manage the flight trajectory collaboratively.Additionally, collaborative decision-making between the air traffic management system and users is being considered, including airspace resource allocation and fourdimensional trajectory optimization.

Figure 2 :
Figure 2: Flow chart of the trajectory negotiation initiated by airspace user.

Figure 8 :
Figure 8: Schematic diagram of the flight plan.

Figure 9 :
Figure 9: Schematic diagram of the four-dimensional flight trajectory before negotiation.

Theorem 10 .
For candidate item C C ∈ C T , MWS C represents the weights sum of candidate item C at various times, and BNWS C represents the maximum weight sum of the subsequent item of candidate item C, satisfying MWS C + BNWS C < min WS 8

Figure 10 :
Figure 10: Schematic diagram of flight trajectory mining results.

Figure 11 :
Figure 11: Schematic diagram of four-dimensional trajectory after negotiation.

igure 14 :
Schematic diagram of flight delay.

Table 2
is a spatiotemporal database that uses time (s), latitude ( °), longitude ( °), and altitude (m) to represent the position information of each aircraft at different times; t represents the different flight times, f represents the different aircraft in the airspace, and data in brackets represents the latitude, longitude, and altitude of the aircraft at different
Definition 4. The spatiotemporal weighted item set X indicates that the horizontal and vertical intervals between items in the weighted itemset are less than the set requirements for the horizontal and vertical intervals, the unit of horizontal interval is nautical miles, and the unit of vertical interval is meters, which is∀x a , x b ∈ X, a ≠ b, hor dis x a ,x b ≤ sep hor && ver dis x a ,x b ≤ sep ver 5 Example 4. If sep hor = 5 nm and sep ver = 300 m, at the t 2 moment, and hor dis f 3 ,f 4 = 1 188 nm and ver dis f 3 ,f 4 = 84 m, then f 3 f 4 is a spatiotemporal item set.Example 5.At the t 3 moment, MWS f 2 f 3 = ω f 2 + ω f 3 = 9 + 13 = 22.Definition 6. BNWS X represents the maximum weight after item set X in the dataset, and the unit is minutes.Example 6.At the t 5 moment, BNWS f 2 f 3 = BNWS f 2 f 3 , t 5 = 25.Definition 8.For extension item x in the dataset, the interval constraint is satisfied with the preceding item p, which is hor dis x,p ≤ sep hor && ver dis x,p ≤ sep ver 6Then, take p as the predecessor of x.Example 8.At the t 2 moment, if f 4 is an extension item and hor dis f 3 ,f 4 ≤ sep hor and ver dis f 3 ,f 4 ≤ sep ver are satisfied, then f 3 is the predecessor of f 4 .
Aerospace Engineering Definition 2. The weight sum represents the sum of the corresponding weights in the item set X at all times of the dataset, and the unit is minutes: WS X = ∑ t i ∈t ws X, t i .Example 2. At time t 1 , t 4 , and t 5 , the combination of f 1 and f 4 satisfies the interval constraint WS f 1 f 4 = ws f 1 f 4 , t 1 + ws f 1 f 4 , t 4 + ws f 1 f 4 , t 5 = 20 + 23 + 22 + 26 + 19 + 25 = 135.Definition 3. The weighted item set X indicates that the weight sum of the item set X is larger than the set minimum weight sum constraint (min WS ), WS X ≥ min WS .Example 3. If min WS = 120 and WS f 4 = 121, then f 4 is a weighted item.Definition 5. MWS X represents the sum of the weights in the item set X that satisfy the interval constraint at the same time, and the unit is minutes: MWS X = ∑ x∈X ω x .Definition 7.For item x in the dataset, if MWS x + BNWS x ≥ min WS , then x is the candidate.Example 7. If min WS = 120, MWS f 1 = 95, and BNWS f 1 = 129, then MWS f 1 + BNWS f 1 = 224 > 120; hence, f 1 is a candidate item.
1. Input: Item sets that satisfy flight intervals constraints at different times 2. Output: Item sets satisfying flight intervals and weight constraint 3.For each extension Calculate the MWS and BNWS of the extension Generate single candidates Use a pruning strategy to prune some candidates Delete candidates that do not satisfy the weight constraint Sort Candidates Construct the precursor item and add the candidate item to the extension item for recursive mining until the candidate item is empty End for Algorithm 2: Spatiotemporal weighted pattern mining algorithm.

Table 6 :
Generation of single candidate.

Table 7 :
Item sets satisfying intervals and weight constraint.

Table 8 :
Flight information sheet.International Journal of Aerospace Engineering from the user's trajectory information; the pseudocode of the algorithm is shown in Algorithm 2.

Table 10 :
Flight information table.