Civil aviation passenger plane track prediction method considering time window constraint

Abstract

The invention discloses a civil aircraft track prediction method considering time window constraint, which belongs to the technical field of air traffic and comprises the following steps: S1, information acquisition and model prediction; s2, time window boundary calculation; s3, potential motion space modeling; s4, coordinate system conversion; and S5, generating a total access probability. According to the method, the width of the time window is determined in a certain leg, and the potential motion space of the civil aviation passenger plane is determined according to the earliest departure time, the latest departure time, the earliest arrival time and the latest arrival time of the boundary time. And comparing a certain moment of the civil aircraft with the boundary moment of the time window, and determining a dynamic potential motion space of the civil aircraft. On the basis, after the coordinate axis is converted, discretization processing is carried out on the time window, and a total access probability function is obtained by using calculus. According to the method, the access probability of the civil aircraft in the potential space is accurately quantified, the air traffic safety can be effectively improved, the workload of a controller is reduced, and airspace resources are fully used.

Description

Technical Field

[0001] The invention belongs to the field of air traffic technology, and in particular relates to a civil aviation passenger aircraft track prediction method considering time window constraints. Background Art

[0002] With the rapid development of the civil aviation industry, the existing air traffic management system is unable to adapt to the growing demand for air transportation and the increasing number of civil aircraft, and the four-dimensional trajectory operation mode has emerged. Compared with the traditional air traffic management system, the four-dimensional trajectory operation can realize the accurate prediction, dynamic adjustment and safety management of the flight path of civil aircraft in the time and space dimensions, which helps to improve the efficiency, safety and environmental sustainability of air traffic. The increasing maturity of the four-dimensional trajectory operation mode has brought the date of promotion of this operation mode closer and closer. Therefore, how to solve the potential conflict risks caused by the uncertainty of the temporal and spatial position of civil aircraft under the four-dimensional trajectory operation mode has become the focus of attention of all parties. Research on trajectory prediction of civil aircraft is of great significance to improving operational safety and efficiency and making full use of airspace resources.

[0003] The Chinese patent document with publication number CN106846919A provides a four-dimensional trajectory dynamic prediction method based on ADS-B information update. Through network communication with the ADS-B receiver, the ADS-B data decoding module is used to obtain the real-time speed, altitude, longitude and latitude information of the flight, and the consistency check with the predicted trajectory is performed, thereby realizing dynamic, online and real-time trajectory prediction capabilities. It can provide important technical guarantees for the development of automation and intelligence of air traffic control and the realization of trajectory-based operation. However, the uncertainty of the flight trajectory of civil aircraft under four-dimensional trajectory operation is not only reflected in the flight segment, but also in the time and space of the waypoints connecting the two ends of the segment. In order to quantify the potential conflict risk caused by uncertainty, interval constraints must be performed. The potential motion space model under interval constraints is continued to be used to give the access probability of civil aircraft at any time and space coordinates, and finally a complete expression of the uncertainty of four-dimensional trajectory operation is achieved, which also provides strong support for subsequent safety management. The above-mentioned 4D trajectory dynamic prediction method is difficult to meet the high-precision requirements of 4D trajectory operation. The time window constraints of civil aviation aircraft at waypoints lead to uncertainty in trajectory prediction. Traditional methods do not consider the interval constraints of the time window, resulting in inaccurate modeling of the potential motion space.

[0004] Therefore, in view of the problems existing in the prior art, it is urgent to provide a civil aircraft trajectory prediction method considering the time window constraint, which is not only the core of civil aircraft conflict risk analysis, but also an important guarantee for ensuring flight safety. By predicting the future operation trajectory of civil aircraft, potential conflict risks can be discovered and handled in time, thereby avoiding accidents. Therefore, the prediction of trajectory distribution in the potential motion space under the time window constraint is of great significance to improving the safety and efficiency of air traffic management. Summary of the invention

[0005] In response to the problems in the related technology, the present invention proposes a civil aviation passenger aircraft trajectory prediction method taking into account the time window constraint, so as to solve the technical problems that the civil aviation passenger aircraft trajectory prediction method does not take into account the interval constraint of the time window, resulting in inaccurate modeling of the potential motion space.

[0006] The technical solution of the present invention is implemented as follows: a method for predicting the flight path of a civil aviation passenger aircraft considering time window constraints, comprising the following steps:

[0007] S1. Information acquisition and model prediction: determine the location information of waypoints and the aviation data of civil aviation aircraft; obtain the actual passing time of civil aviation aircraft, and use the track extrapolation model to predict the planned passing time of civil aviation aircraft;

[0008] S2. Time window boundary calculation: According to the average difference between the actual time of the waypoint and the planned time of the waypoint, the normal distribution standard deviation is calculated, and the time window width and boundary time are determined based on the 3σ principle;

[0009] S3. Latent motion space modeling: Generate the earliest departure time, latest departure time, earliest arrival time and latest arrival time of the flight segment according to the time window width and boundary time, and determine the potential motion space of civil aircraft at any time through geometric relationships;

[0010] S4. Coordinate system conversion: A new coordinate system is established with the expected position of the civil aviation passenger aircraft as the origin, the route direction is the positive direction of the x-axis, the ordinates of the starting waypoint and the ending waypoint are both 0, and the coordinates are rotated according to the route azimuth rotation angle;

[0011] S5. Total visit probability generation: define the point-passing probability function within the waypoint time window, calculate the straight-line distance from the space-time coordinate to the waypoint in the new coordinate system; perform double integrals with variable upper and lower limits on the space-time coordinates in the potential motion space based on the piecewise function of the time window to obtain the total visit probability function of civil airliners at any space-time coordinate.

[0012] During the flight mission, the present invention first determines the time window width of a certain section of a civil airliner, and the potential motion space of the civil airliner corresponding to the earliest departure time, the latest departure time, the earliest arrival time, and the latest arrival time at the boundary time is combined in pairs. A certain moment of the civil airliner is compared with the boundary time of the time window to determine the dynamic potential motion space of the civil airliner. On this basis, after converting the coordinate axis, the time window is discretized, and the total access probability function of the civil airliner in the potential motion space under the time window constraint is obtained using calculus. The present invention accurately quantifies the access probability of civil airliners in the potential space, which can effectively improve air traffic safety, reduce the workload of controllers, and make full use of airspace resources.

[0013] As a further improvement of the above scheme, in step S1, the location information of the waypoints includes the longitude and latitude coordinates of the starting waypoint A and the ending waypoint B, and the aviation data includes the actual time of flying over the starting waypoint A and the flight speed.

[0014] As a further improvement of the above scheme, in step S1, the track estimation model adopts an equiangular track estimation algorithm, including the following process:

[0015] S11. Calculate the angle between the equiangular route and the meridian according to the longitude and latitude coordinates of the starting waypoint A and the ending waypoint B:

[0016]

[0017] in, are the longitude and latitude coordinates of the starting waypoint A and the ending waypoint B respectively; θ is the angle between the equiangular route and the meridian;

[0018] S11. Calculate the distance between the starting waypoint A and the ending waypoint B:

[0019]

[0020] in, for and The difference between

[0021] S12. Predict the time when the civil aviation aircraft plans to pass the terminal waypoint B:

[0022]

[0023] Among them, T PB Indicates the time when the planned end waypoint B is passed, T TA Indicates the actual time of flying past the starting waypoint A, V A It is the actual flight speed when passing through the starting waypoint A.

[0024] As a further improvement of the above solution, in step S3, the potential motion space is determined by:

[0025] The earliest departure time and the latest arrival time, as well as the latest departure time and the earliest arrival time, are combined to form four sets of space-time constraints. The time when the civil airliner arrives at the upper segment and the upper and lower limits of the time window boundary are compared to determine the potential movement space of the civil airliner at any time based on the geometric relationship.

[0026] As a further improvement of the above scheme, in step S3, the time at which the civil aviation aircraft arrives at the flight segment is t, and the upper and lower limits of the time window boundary time are t 1 ,t 2 , the geometric relationships in the potential motion space include:

[0027] (1) When t<t 1 When , the potential motion space is a circular area centered on the starting waypoint A;

[0028] (2) When t 1 ≤t≤t 2 When , the potential motion space is the intersection of two circular areas;

[0029] (3) When t>t 2 When , the potential motion space is a circular area centered on the terminal waypoint B.

[0030] As a further improvement of the above scheme, in step S4, the transformed starting waypoint is defined as W i , the end waypoint is defined as W j , the coordinate system transformation includes the following processes:

[0031] S41. In the transformed coordinate system, the starting waypoint W i , End waypoint W j The ordinate y is 0, and the abscissa x is obtained by the following formula:

[0032]

[0033] Among them, μ X (t) is the mean value of the position of the civil aviation aircraft in the x direction at time t, μ Y (t) is the mean value of the position of the civil aviation aircraft in the y direction at time t; x i W is the starting waypoint i The horizontal axis, y i W is the starting waypoint i The vertical coordinate of j The end waypoint W j The horizontal axis, y j The end waypoint W j The vertical coordinate of

[0034] S42. Calculate the angle α of the x-axis rotation:

[0035]

[0036] S43. The new coordinates (x′, y′) of any point (x, y) after the coordinate system is rotated and transformed are obtained by the following formula:

[0037]

[0038] As a further improvement of the above solution, in step S5, the total access probability function is generated by the following steps:

[0039] A1. Construct a time window piecewise function of the difference between the latest departure time and the estimated time of the starting waypoint;

[0040] A2. Construct a time window piecewise function of the difference between the earliest arrival time and the estimated time of the terminal waypoint;

[0041] A3. Perform double integration on the range of moments within the time window to calculate the total access probability of the space-time coordinate point.

[0042] As a further improvement of the above scheme, the probability of a civil aviation aircraft passing through the starting waypoint or the ending waypoint at any time t follows a normal distribution, and the point-passing probability function is recorded as f(t); when the time-space coordinates of the starting and ending waypoints are determined, the access probability at any time-space coordinate (x, y, t) under the point constraint is recorded as p(x, y, t);

[0043] Note dep is any time within the time window of the starting waypoint, t arr is any time within the time window of the termination waypoint, with t dep ,t arr is the integration variable, and double integrals with variable upper and lower limits are performed;

[0044] In the case of tdep and t arr In the generated latent motion space, the access probability at any spatiotemporal coordinate (x, y, t) is related to tdep and t arr It is related to p(x,y,t,t dep ,t arr ).

[0045] As a further improvement of the above scheme, for the starting waypoint, the upper and lower limits of the integral are the time t corresponding to the spatiotemporal coordinates (x, y, t) of the access probability to be calculated in the time window of the starting waypoint dep_limit and the earliest departure time t dep_e ;

[0046] Among them, t dep_limitGiven as a piecewise function:

[0047]

[0048] in, is the average cruising speed; d dep is the straight-line distance from the time-space coordinate (x, y, t) to the starting waypoint; in the converted coordinate system, it is expressed as:

[0049]

[0050] For the starting waypoint, the upper and lower limits of the integral are the latest arrival time t arr_l The time and space coordinates (x, y, t) of the access probability to be sought correspond to the time t in the time window of the termination waypoint arr_limit ;

[0051] Among them, t arr_limit Given as a piecewise function:

[0052]

[0053] Among them, d arr is the straight-line distance from the time-space coordinate (x, y, t) to the end waypoint; in the converted coordinate system, it is expressed as:

[0054]

[0055] As a further improvement of the above scheme, the probability of a civil airliner visit at any spatiotemporal coordinate in the potential motion space is expressed as:

[0056]

[0057] Beneficial effects:

[0058] During the flight mission, the present invention first determines the time window width of a certain section of a civil airliner, and the potential motion space of the civil airliner corresponding to the earliest departure time, the latest departure time, the earliest arrival time, and the latest arrival time at the boundary time is combined in pairs. A certain moment of the civil airliner is compared with the boundary time of the time window to determine the dynamic potential motion space of the civil airliner. On this basis, after converting the coordinate axis, the time window is discretized, and the total access probability function of the civil airliner in the potential motion space under the time window constraint is obtained using calculus. The present invention accurately quantifies the access probability of civil airliners in the potential space, which can effectively improve air traffic safety, reduce the workload of controllers, and make full use of airspace resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a flow chart of the steps of the present invention. DETAILED DESCRIPTION

[0060] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] In the description of the present invention, it should be understood that the term "several" means "at least one", and the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise" and the like indicate directions or positional relationships based on the directions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the referred device or element must have a specific direction, be constructed and operated in a specific direction, and therefore cannot be understood as limiting the present invention.

[0062] Example:

[0063] like Figure 1 As shown, this embodiment provides a method for predicting the flight path of a civil aviation passenger aircraft considering time window constraints, comprising the following steps:

[0064] S1. Information acquisition and model prediction: determine the location information of waypoints and the aviation data of civil aviation aircraft; obtain the actual passing time of civil aviation aircraft, and use the track extrapolation model to predict the planned passing time of civil aviation aircraft;

[0065] Specifically, the location information of the waypoints includes the longitude and latitude coordinates of the starting waypoint A and the ending waypoint B, and the aviation data includes the actual time of flying over the starting waypoint A and the flight speed. In step S1, it should be noted that the track estimation algorithm includes a great circle track estimation algorithm, an equiangular track estimation algorithm, a track estimation algorithm based on Kalman filtering, a track estimation algorithm based on particle filtering, etc. In this embodiment, since the accuracy is relatively higher when the distance is closer when performing track estimation, the equiangular track estimation algorithm is more suitable for short-distance track estimation, and has the advantages of simple calculation and strong intuitiveness. Therefore, this embodiment adopts the equiangular track estimation algorithm, including the following process:

[0066] S11. Calculate the angle between the equiangular route and the meridian according to the longitude and latitude coordinates of the starting waypoint A and the ending waypoint B:

[0067]

[0068] in, are the longitude and latitude coordinates of the starting waypoint A and the ending waypoint B respectively; θ is the angle between the equiangular route and the meridian;

[0069] S11. Calculate the distance between the starting waypoint A and the ending waypoint B:

[0070]

[0071] in, for and The difference between

[0072] S12. Predict the time when the civil aviation aircraft plans to pass the terminal waypoint B:

[0073]

[0074] Among them, T PB Indicates the time when the planned end waypoint B is passed, T TA Indicates the actual time of flying past the starting waypoint A, V A It is the actual flight speed when passing through the starting waypoint A.

[0075] S2. Time window boundary calculation: According to the average difference between the actual time of the waypoint and the planned time of the waypoint, the normal distribution standard deviation is calculated, and the time window width and boundary time are determined based on the 3σ principle;

[0076] S3. Modeling of potential motion space: Generate the earliest departure time, latest departure time, earliest arrival time and latest arrival time of the flight segment according to the time window width and boundary time, and determine the potential motion space of the civil airliner at any time through geometric relationship; In this embodiment, in step S3, the potential motion space is determined by the following methods: Combine the earliest departure time with the latest arrival time, and the latest departure time with the earliest arrival time, respectively, to form four groups of spatiotemporal constraints; Compare the time when the civil airliner arrives at the upper limit of the flight segment and the upper and lower limits of the time window boundary time, and determine the potential motion space of the civil airliner at any time according to the geometric relationship.

[0077] Projecting the potential motion space onto the xOy plane, we can get an elliptical area, whose foci are the starting waypoint and the ending waypoint. With the midpoint of the segment as the origin of the coordinate axis, the direction from the starting waypoint to the ending waypoint as the positive x-axis direction, and the direction from the origin and perpendicular to the x-axis upward as the positive y-axis direction, the analytical equation is as follows:

[0078]

[0079] Where a and b are the major and minor semi-axes of the ellipse, respectively. The major semi-axis a is related to the maximum cruising speed v max , earliest departure time t dep_eand the latest arrival time t arr_l Related; short semi-axis b and maximum cruising speed v max , earliest departure time t dep_e , the latest arrival time t arr_l And the flight distance:

[0080] a=v max ·(t arr_l -t dep_e );

[0081]

[0082] In step S3, the time at which the civil aviation aircraft arrives at the flight segment is t, and the upper and lower limits of the time window boundary are t 1 ,t 2 , the geometric relationships in the potential motion space include:

[0083] (1) When t<t 1 When , the potential motion space is a circular area centered on the starting waypoint A;

[0084] (2) When t 1 ≤t≤t 2 When , the potential motion space is the intersection of two circular areas;

[0085] (3) When t>t 2 When , the potential motion space is a circular area centered on the terminal waypoint B.

[0086] S4. Coordinate system conversion: A new coordinate system is established with the expected position of the civil aviation passenger aircraft as the origin, the route direction is the positive direction of the x-axis, the ordinates of the starting waypoint and the ending waypoint are both 0, and the coordinates are rotated according to the route azimuth rotation angle;

[0087] In this embodiment, in step S4, the transformed starting waypoint is defined as W i , the end waypoint is defined as W j , the coordinate system transformation includes the following processes:

[0088] S41. In the transformed coordinate system, the starting waypoint W i , End waypoint W j The ordinate y is 0, and the abscissa x is obtained by the following formula:

[0089]

[0090] Among them, μ X (t) is the mean value of the position of the civil aviation aircraft in the x direction at time t, μ Y (t) is the mean value of the position of the civil aviation aircraft in the y direction at time t; x iW is the starting waypoint i The horizontal axis, y i W is the starting waypoint i The vertical coordinate of j The end waypoint W j The horizontal axis, y j The end waypoint W j The vertical coordinate of

[0091] S42. Calculate the angle α of the x-axis rotation:

[0092]

[0093] S43. The new coordinates (x′, y′) of any point (x, y) after the coordinate system is rotated and transformed are obtained by the following formula:

[0094]

[0095] S5. Total visit probability generation: define the point-passing probability function within the waypoint time window, calculate the straight-line distance from the space-time coordinate to the waypoint in the new coordinate system; perform double integrals of the space-time coordinates in the potential motion space with variable upper and lower limits based on the piecewise function of the time window, and obtain the total visit probability function of the civil aircraft at any space-time coordinate. In this embodiment, in step S5, the total visit probability function is generated by the following steps:

[0096] A1. Construct a time window piecewise function of the difference between the latest departure time and the estimated time of the starting waypoint;

[0097] A2. Construct a time window piecewise function of the difference between the earliest arrival time and the estimated time of the terminal waypoint;

[0098] A3. Perform double integration on the range of moments within the time window to calculate the total access probability of the space-time coordinate point.

[0099] In this embodiment, the probability of a civil aircraft passing through the starting waypoint or the ending waypoint at any time t follows a normal distribution, and the point-passing probability function is recorded as f(t); when the time-space coordinates of the starting and ending waypoints are determined, the access probability at any time-space coordinate (x, y, t) under the point constraint is recorded as p(x, y, t);

[0100] Note dep is any time within the time window of the starting waypoint, t arr is any time within the time window of the termination waypoint, with t dep ,t arr is the integration variable, and double integrals with variable upper and lower limits are performed;

[0101] In the case of tdep and t arrIn the generated latent motion space, the access probability at any spatiotemporal coordinate (x, y, t) is related to tdep and t arr It is related to p(x,y,t,t dep ,t arr ).

[0102] In this embodiment, for the starting waypoint, the upper and lower limits of the integral are respectively the time t corresponding to the spatiotemporal coordinates (x, y, t) of the access probability to be calculated in the time window of the starting waypoint dep_limit and the earliest departure time t dep_e ;

[0103] Among them, t dep_limit Given as a piecewise function:

[0104]

[0105] in, is the average cruising speed; d dep is the straight-line distance from the time-space coordinate (x, y, t) to the starting waypoint; in the converted coordinate system, it is expressed as:

[0106]

[0107] For the starting waypoint, the upper and lower limits of the integral are the latest arrival time t arr_l The time and space coordinates (x, y, t) of the access probability to be sought correspond to the time t in the time window of the termination waypoint arr_limit ;

[0108] Among them, t arr_limit Given as a piecewise function:

[0109]

[0110] Among them, d arr is the straight-line distance from the time-space coordinate (x, y, t) to the end waypoint; in the converted coordinate system, it is expressed as:

[0111]

[0112] In this embodiment, the probability of a civil airliner visit at any spatiotemporal coordinate in the potential motion space is expressed as:

[0113]

[0114] In the process of flight mission, the present embodiment first determines the time window width of a certain section of a civil airliner, and the potential motion space of the civil airliner corresponding to the earliest departure time, the latest departure time, the earliest arrival time, and the latest arrival time at the boundary time is determined in pairs. A certain moment of the civil airliner is compared with the boundary time of the time window to determine the dynamic potential motion space of the civil airliner. On this basis, after converting the coordinate axis, the time window is discretized, and the total access probability function of the civil airliner in the potential motion space under the time window constraint is obtained using calculus. The present invention accurately quantifies the access probability of civil airliners in the potential space, which can effectively improve air traffic safety, reduce the workload of controllers, and make full use of airspace resources.

[0115] According to the disclosure and teaching of the above description, those skilled in the art to which the present invention belongs may also make changes and modifications to the above embodiments. Therefore, the present invention is not limited to the specific embodiments disclosed and described above, and some modifications and changes to the invention should also fall within the scope of protection of the claims of the present invention. In addition, although some specific terms are used in this specification, these terms are only for the convenience of description and do not constitute any limitation to the present invention.

Claims

1. A method for predicting the flight path of a civil aircraft considering time window constraints, characterized in that: The following steps are involved: S1. Information acquisition and model prediction: determine the location information of waypoints and the aviation data of civil aviation aircraft; obtain the actual passing time of civil aviation aircraft, and use the track extrapolation model to predict the planned passing time of civil aviation aircraft; S2. Time window boundary calculation: According to the average difference between the actual time of the waypoint and the planned time of the waypoint, the normal distribution standard deviation is calculated, and the time window width and boundary time are determined based on the 3σ principle; S3. Latent motion space modeling: Generate the earliest departure time, latest departure time, earliest arrival time and latest arrival time of the flight segment according to the time window width and boundary time, and determine the potential motion space of civil aircraft at any time through geometric relationships; S4. Coordinate system conversion: A new coordinate system is established with the expected position of the civil aviation passenger aircraft as the origin, the route direction is the positive direction of the x-axis, the ordinates of the starting waypoint and the ending waypoint are both 0, and the coordinates are rotated according to the route azimuth rotation angle; S5. Total visit probability generation: define the point-passing probability function within the waypoint time window, calculate the straight-line distance from the space-time coordinate to the waypoint in the new coordinate system; perform double integrals with variable upper and lower limits on the space-time coordinates in the potential motion space based on the piecewise function of the time window to obtain the total visit probability function of civil airliners at any space-time coordinate.

2. A method for predicting the flight path of a civil aircraft considering time window constraints according to claim 1, characterized in that: In step S1, the location information of the waypoints includes the longitude and latitude coordinates of the starting waypoint A and the ending waypoint B, and the aviation data includes the actual time of flying over the starting waypoint A and the flight speed.

3. The method for predicting the flight path of a civil aircraft considering time window constraints according to claim 2, characterized in that: In step S1, the track estimation model adopts an equiangular track estimation algorithm, which includes the following processes: S11. Calculate the angle between the equiangular route and the meridian according to the longitude and latitude coordinates of the starting waypoint A and the ending waypoint B: in, are the longitude and latitude coordinates of the starting waypoint A and the ending waypoint B respectively; θ is the angle between the equiangular route and the meridian; S11. Calculate the distance between the starting waypoint A and the ending waypoint B: in, for and The difference between S12. Predict the time when the civil aviation aircraft plans to pass the terminal waypoint B: Among them, T PB Indicates the time when the planned end waypoint B is passed, T TA Indicates the actual time of flying past the starting waypoint A, V A It is the actual flight speed when passing through the starting waypoint A.

4. The method for predicting the flight path of a civil aircraft considering time window constraints according to claim 3, characterized in that: In step S3, the potential motion space is determined by: The earliest departure time and the latest arrival time, as well as the latest departure time and the earliest arrival time are combined respectively to form four sets of space-time constraints; the time when the civil airliner arrives at the upper segment and the upper and lower limits of the time window boundary are compared, and the potential movement space of the civil airliner at any time is determined based on the geometric relationship.

5. The method for predicting the flight path of a civil aircraft considering time window constraints according to claim 4, characterized in that: In step S3, the time at which the civil aviation aircraft arrives at any time on the flight segment is t, and the upper and lower limits of the time window boundary are t1 and t2 respectively. The geometric relationship of the potential motion space includes: (1) When t < t1, the potential motion space is a circular area centered on the starting waypoint A; (2) When t1≤t≤t2, the potential motion space is the intersection of two circular regions; (3) When t>t2, the potential motion space is a circular area centered on the terminal waypoint B.

6. A method for predicting the flight path of a civil aircraft considering time window constraints according to claim 5, characterized in that: In step S4, the transformed starting waypoint is defined as W i , the end waypoint is defined as W j , the coordinate system transformation includes the following processes: S41. In the transformed coordinate system, the starting waypoint W i , End waypoint W j The ordinate y is 0, and the abscissa x is obtained by the following formula: Among them, μ X (t) is the mean value of the position of the civil aviation aircraft in the x direction at time t, μ Y (t) is the mean value of the position of the civil aviation aircraft in the y direction at time t; x i W is the starting waypoint i The horizontal axis, y i W is the starting waypoint i The vertical coordinate of j The end waypoint W j The horizontal axis, y j The end waypoint W j The vertical coordinate of S42. Calculate the angle α of the x-axis rotation: S43. The new coordinates (x′, y′) of any point (x, y) after the coordinate system is rotated and transformed are obtained by the following formula:

7. A method for predicting the flight path of a civil aircraft considering time window constraints according to claim 6, characterized in that: In step S5, the total access probability function is generated by the following steps: A1. Construct a time window piecewise function of the difference between the latest departure time and the estimated time of the starting waypoint; A2. Construct a time window piecewise function of the difference between the earliest arrival time and the estimated time of the terminal waypoint; A3. Perform double integration on the range of moments within the time window to calculate the total access probability of the space-time coordinate point.

8. The method for predicting the flight path of a civil aircraft considering time window constraints according to claim 7, characterized in that: The probability of a civil aviation aircraft passing through the starting waypoint or the ending waypoint at any time t follows a normal distribution, and the point-passing probability function is recorded as f(t); when the time-space coordinates of the starting and ending waypoints are determined, the visit probability at any time-space coordinate (x, y, t) under the point constraint is recorded as p(x, y, t); Note dep is any time within the time window of the starting waypoint, t arr is any time within the time window of the termination waypoint, with t dep ,t arr is the integration variable, and double integrals with variable upper and lower limits are performed; In the case of tdep and t arr In the generated latent motion space, the access probability at any spatiotemporal coordinate (x, y, t) is related to tdep and t arr It is related to p(x,y,t,t dep ,t arr ).

9. A method for predicting the flight path of a civil aircraft considering time window constraints according to claim 8, characterized in that: For the starting waypoint, the upper and lower limits of the integral are the time and space coordinates (x, y, t) of the access probability to be calculated at the time t corresponding to the time window of the starting waypoint. dep_limit and the earliest departure time t dep_e ; Among them, t dep_limit Given as a piecewise function: in, is the average cruising speed; d dep is the straight-line distance from the time-space coordinate (x, y, t) to the starting waypoint; in the converted coordinate system, it is expressed as: For the starting waypoint, the upper and lower limits of the integral are the latest arrival time t arr_ l and the time-space coordinates (x, y, t) of the access probability to be sought at the time t corresponding to the termination waypoint time window arr_limit ; Among them, t arr_limit Given as a piecewise function: Among them, d arr is the straight-line distance from the time-space coordinate (x, y, t) to the end waypoint; in the converted coordinate system, it is expressed as:

10. The method for predicting the flight path of a civil aircraft considering time window constraints according to claim 1, characterized in that: The probability of a civil airliner visit at any spatiotemporal coordinate in the latent motion space is expressed as:

Images