4d trajectory modeling method based on conditional markov process

Abstract

The application relates to a 4D flight path modeling method based on a conditional Markov process, and the main steps are as follows: (1) pre-processing of flight management system (FMS) and global positioning system (GPS) data; (2) motion mode identification in a flight path, multi-flight path data clustering and waypoint marking; (3) establishing a 4D flight path closed model based on waypoint information; (4) optimal parameter estimation of the 4D flight path model based on dynamic time warping (DTW) loss; and (5) evaluating the prediction degree of the 4D flight path model. Compared with the existing 4D flight path modeling method, the application has good physical and mathematical interpretability, can fully utilize the waypoint information mined from historical flight path data, can obtain optimal estimation of unknown parameters of the 4D flight path model, is suitable for flight path modeling and flight path prediction with varying flight time, has fast calculation speed, high model prediction precision and can effectively evaluate the prediction ability of the 4D flight path model.

Description

Technical Field

[0001] The present invention relates to aircraft track modeling technology, and in particular to a high-precision 4D track modeling method capable of utilizing waypoint information. Background Art

[0002] Aircraft trajectory modeling and automated control play a fundamental and critical role in air traffic control systems. They underpin applications such as trajectory prediction, trajectory planning, air traffic optimization, flight path optimization, conflict warning and avoidance, and abnormal trajectory detection. Trajectory modeling based on waypoint knowledge is a development trend in the next generation of air traffic management.

[0003] Aircraft trajectory is influenced by numerous complex factors, including flight control inputs, aerodynamic performance, engine performance, airflow, air pressure, temperature, and load. Given the uncertainty in the trajectory caused by these factors, trajectory modeling often assumes that the motion state has Markov properties. However, the Markov process relies solely on the initial state, process noise, and the state transition matrix, and cannot effectively integrate waypoint or destination information from the flight trajectory. Therefore, a commonly used trajectory inference method is a two-step approach: first, an initial trajectory is generated using traditional prediction or filtering methods without prior information, and then prior knowledge (waypoints, destinations) is incorporated to improve trajectory prediction performance. In recent years, trajectory prediction methods based on neural networks and deep learning have attracted widespread attention in the industry. These methods utilize large amounts of historical trajectory data to learn and capture the motion patterns of aircraft flight paths. However, the main challenge encountered by these methods is the lack of interpretability of the models, resulting in a "black box" state.

[0004] Existing methods lack clarity and accuracy in trajectory models. To improve the efficiency and safety of air traffic control, there is an urgent need to establish a clear and precise trajectory model that accurately depicts the motion of aircraft at different moments in three dimensions (longitude, latitude, and altitude), also known as a 4D trajectory model.

[0005] Compared with trajectory modeling through additional constraints, the newly proposed conditional Markov process in academia directly establishes a motion model using waypoint information, which can more accurately describe the flight trajectory. Here, the conditional Markov process is a natural and systematic theoretical generalization of the Markov process. Based on the conditional Markov process, how to establish a 4D trajectory model by learning historical trajectory data, optimize unknown parameters in the model, evaluate the matching degree between the trajectory model and the actual trajectory data, and realize model selection based on the evaluation results, etc., are all difficult problems faced in civil aviation applications. However, the corresponding processing technology for these problems has not appeared in public literature and patents. Therefore, the patent of this invention is a brand-new trajectory modeling technology.

[0006] This paper proposes a 4D trajectory modeling method based on a conditional Markov process. Compared with existing methods, this method has the following advantages: 1) the model has a clear and explicit kinematic meaning; 2) it fully utilizes the distribution of waypoint states and segment durations; 3) it learns a 4D trajectory model based on the aircraft's historical trajectory data, where unknown parameters of the model are automatically optimized through an algorithm without requiring manual selection or setting; 4) it evaluates the match between the 4D trajectory model and the actual trajectory; and 5) it achieves fast and highly accurate trajectory prediction. Summary of the Invention

[0007] The purpose of the present invention is to overcome the shortcomings of existing track modeling methods and design a 4D track modeling method that can fully utilize waypoint information; design a corresponding optimization algorithm to optimize the unknown parameters of the model based on track training data; and provide reasonable evaluation criteria to effectively evaluate the matching degree between the track model and the actual track.

[0008] In order to achieve the above technical objectives, the present invention designs a 4D trajectory modeling, optimization and evaluation method based on the conditional Markov process, which is implemented using the following technical solutions.

[0009] 1) Preprocessing of the large amount of collected Flight Management System (FMS) and Global Positioning System (GPS) data. The preprocessing includes:

[0010] Data cleaning, dimension standardization, abnormal altitude data removal, etc. are performed to finally obtain the track data.

[0011] 2) Based on the longitude, latitude, and time dimension (3D) information of the pre-processed track data, the motion mode (e.g., linear motion or turning motion) within each track is identified.

[0012] 3) Select one or more consecutive aircraft motion phases of interest, extract the flight paths within the phases of interest based on altitude and time (2D) information, perform cluster analysis on the flight path data, obtain the clustering results of the flight path data, and mark the waypoints of different flight paths in the same type of flight paths to obtain the flight path duration.

[0013] 4) Based on the conditional Markov process and the joint probability density of waypoint status and flight segment duration, 4D trajectory modeling is performed on the trajectory data containing waypoint information.

[0014] 5) Under the dynamic time warping (DTW) loss, the unknown parameters in the 4D trajectory model are optimized according to the trajectory training data to obtain the trajectory model with the optimal parameters.

[0015] 6) Under the DTW similarity evaluation criteria, the trajectory test data is used to verify the prediction ability of the established 4D trajectory model for the motion state, and the model selection for 4D trajectory modeling is carried out according to the prediction ability.

[0016] Compared with the prior art, the present invention has the following advantages:

[0017] 1) The 4D trajectory modeling method provided by the present invention has the ability to clarify kinematic meaning and learn knowledge from historical data. Driven by historical trajectory data, it can use waypoint information to establish a 4D trajectory model with physical and mathematical interpretability.

[0018] 2) The present invention effectively solves the modeling problem of variable-duration tracks and realizes 4D track modeling in four joint dimensions: longitude, latitude, altitude, and time.

[0019] 3) The present invention can optimize the unknown parameters of the 4D track model based on the track training data.

[0020] 4) The present invention establishes an evaluation index for the matching degree between the 4D track model and the track test data. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a diagram of the overall technical framework provided by an embodiment of the present invention.

[0022] Figure 2 The present invention provides a flowchart of an aircraft data preprocessing method.

[0023] Figure 3 This is a flow chart of a 3D flight mode recognition method provided by an embodiment of the present invention.

[0024] Figure 4 This is a flow chart of a track clustering and waypoint marking method provided by an embodiment of the present invention.

[0025] Figure 5 This is a flow chart of a 4D trajectory modeling method provided by an embodiment of the present invention.

[0026] Figure 6 This is a flow chart of a method for optimally estimating unknown parameters of a 4D trajectory model provided by an embodiment of the present invention.

[0027] Figure 7 This is a flow chart of a method for calculating the prediction goodness of a 4D trajectory model provided by an embodiment of the present invention.

[0028] Figure 8 The present invention provides 71 4D real training tracks of a civil aviation training aircraft in the descent-landing-taxi-parking phase. The data is used as training data to establish a 4D track model and generate a recommended track diagram (excluding process noise).

[0029] Figure 9 The embodiment of the present invention provides 64 4D real test tracks of a civil aviation training aircraft in the descent-landing-taxi-parking section, and according to the initial state and Figure 6 The same 4D track model in is used to generate track plots (with random process noise). DETAILED DESCRIPTION

[0030] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly describes the methods and drawings required for use in the embodiments of the present invention. It is apparent that the methods and drawings described below are merely some embodiments of the present invention, and a person of ordinary skill in the art can derive other drawings and similar methods based on these drawings without inventive effort.

[0031] The present invention provides a high-precision 4D track modeling method that can fully utilize the aircraft's historical track, waypoint status, and flight segment duration information. The overall framework of this method is shown in the attached Figure 1 .

[0032] The specific steps include:

[0033] Step 1: Preprocessing of FMS and GPS data. Please refer to the attached Figure 2 .

[0034] Data preprocessing is required for the raw data (.csv format) collected by FMS and GPS. First, identify and delete data with empty records. Then, perform dimensional conversion and standardization to ensure that the units of the data are consistent with the requirements of the track model. Finally, eliminate abnormal altitude data caused by large errors in the sensor. These steps help improve the accuracy and consistency of the data and lay the foundation for reliable track modeling. It should be emphasized that the 4D track modeling method provided in the embodiment of the present invention takes into account the geographic coordinate system, but the method is also applicable to other commonly used coordinate systems such as the Earth-centered Earth-fixed coordinate system and the spatial rectangular coordinate system.

[0035] Specific process:

[0036] Table 1

[0037] Original data unit Standardized units Unit conversion formula feet / ft meter / m 1ft=0.3048m Kt Meters per second / mps 1Kt=0.5144444mps feet per minute / fpm Meters per second / mps 1 fpm = 0.00508 mps

[0038] Since the present invention takes into account the position, speed, and acceleration of the aircraft in three dimensions of longitude / Lon, latitude / Lat, and altitude / Alt that change with time, the present invention mainly uses GPS data: local date / Lcl Data, local time / LclTime, latitude / Lat (degrees / deg), longitude / Lon (degrees / deg); FMS data: MSL mean sea level pressure altitude / Alt (feet / ft), ground speed / GndSpd (kt / kt), vertical speed / VSpd (feet per minute / fpm), and track angle / TRK (degrees / deg).

[0039] Preprocessing of the raw data. First, delete the data with empty or NaN records. Then, standardize the dimensions of the raw data according to Table 1. Calculate the speed LonSpd (in mps) in the longitude direction and the speed LatSpd (in mps) in the latitude direction based on the ground speed GndSpd and the track angle TRK:

[0040] LatSpd mps =GndSpd mps ×cosd(TRK),

[0041] LonSpd mps =GndSpd mps ×sind(TRK).

[0042] Then, according to the WGS84 ellipsoid model of the earth, the speed unit "meters per second / mps" in the longitude and latitude directions is converted to "degrees per second / dps". The unit conversion formula is:

[0043]

[0044] in, represents the distance from the center of the Earth to the surface at the corresponding latitude. The equatorial radius (major axis) is a = 6378137 m, and the distance from the North Pole to the center of the Earth (minor axis) is b = 6356752.3142 m. cosd and sind represent the sine and cosine functions, respectively, calculated in degrees. The acceleration in each dimension is calculated by taking the difference in velocity along each dimension.

[0045] Since changes in atmospheric conditions and sensor measurement errors affect the accuracy of altitude data during flight, FMS data occasionally experience abnormal fluctuations in altitude values. Therefore, it is necessary to correct or remove abnormal data to reduce the adverse effects of abnormal fluctuations in altitude data on the estimation of unknown parameters of the 4D track model. For example, abnormal altitude data (excessive altitude changes within a unit time interval T=1s) are deleted to improve the quality of track data. Finally, by performing the above preprocessing on the original data, track data sampled at a time interval of T=1s is obtained (there may be missing sampling data at the sampling time). Track data preprocessing is the basis for subsequent flight mode recognition, track clustering, 4D track modeling and other steps.

[0046] Step 2: 3D flight mode recognition, please refer to the attached Figure 3 .

[0047] In the daily operations of civil aviation, it's easy to effectively identify and classify aircraft flight patterns based on longitude, latitude, and time (3D). Considering the actual application scenarios of civil aviation, common aircraft motion patterns include uniform turning, uniform straight-line motion, and uniformly accelerated straight-line motion. Of course, other more complex motion patterns, such as variable turning models, the Singer model, a physical model for variable acceleration motion, and models based on flight dynamics, can also be similarly included in the recognition scope. Here, we use the three most common motion patterns mentioned above as examples to briefly explain flight pattern recognition.

[0048] Specific process:

[0049] First, the track angle / TRK in the track data is used to determine whether the track has turned. For example, the cumulative change in TRK during n consecutive observation times can be calculated (which can be easily achieved through convolution operation). When the cumulative change in TRK exceeds the set threshold, it is considered that a turning motion has occurred.

[0050] Secondly, for linear motion, the cumulative change of ground speed / GndSpd during n consecutive observation times can be calculated (which can be easily achieved through convolution operation) and compared with the set threshold. If it is less than the threshold, it is considered to be uniform linear motion, and if it is greater than the threshold, it is considered to be uniformly accelerated linear motion.

[0051] Finally, based on the start and end times of different flight modes within each track, the flight segment duration of the flight mode can be obtained.

[0052] Step 3: Track data clustering and waypoint marking, refer to the attached Figure 4 .

[0053] According to the change in altitude, the flight phases of an aircraft can be divided into: takeoff phase (Takeoff), cruise phase (Cruise), descent phase (Descent), landing phase (Landing), taxiing phase (Taxiing), and parking phase (Parking).

[0054] For the aircraft movement phase of interest, it is necessary to perform cluster analysis on the track data in the corresponding phase to obtain various tracks with different navigation tasks and mark the waypoints in the same track. Figure 8 ) shows the 4D trajectory modeling of the descent-landing-taxi-parking phase. This paper considers the sampling interval as T = 1 s。

[0055] Specific process:

[0056] First, one or more consecutive flight phases of interest are selected, and the aircraft motion phases of interest are extracted based on the altitude and time (2D) information. Based on the airport longitude, latitude, and altitude, the track classes with the same landing airport location can be determined.

[0057] Secondly, for the track data from the same airport, we clustered the data using the 3D flight pattern of each track. Specifically, a 3D flight pattern typically includes multiple segments of linear motion and / or turning motion. Using the flight pattern of each segment as a track feature, we performed cluster analysis on multiple tracks to obtain track clustering results.

[0058] Finally, the class of interest in the cluster is selected, and the aircraft state in the mth flight mode in the ith track (each state includes position, speed, and acceleration in longitude, latitude, and altitude) is recorded as

[0059]

[0060] Among them, the initial state of the mth flight mode in the i-th track is and terminal state It is recorded as the waypoint state, and the duration of the mth 3D flight mode segment is recorded as N m,i There are K tracks in total, and each track has M different track segments. It should be emphasized here that the state of the waypoint is related to the duration of the flight segment. To avoid ambiguity, the present invention stipulates

[0061]

[0062] K similar tracks are randomly divided into training group and test group, each containing K1 and K0 tracks.

[0063] Step 4: 4D track modeling, refer to the attached Figure 5 process.

[0064] Based on the conditional Markov process, the trajectory segments of different motion modes are modeled, and the information of waypoint status and flight segment duration is integrated to perform 4D trajectory modeling.

[0065] Specific process:

[0066] Consider using a linear transfer model (including various motion modes such as uniform speed straight line, uniform acceleration straight line, uniform speed turn, etc.) to initially model the motion mode of the mth track segment:

[0067]

[0068] in, Represents the state at the kth moment in the mth track segment, assuming A total of M different track segments are considered, and the starting point in the mth track segment is The duration of the flight segment is N m , the state transfer matrix is Obviously, the above motion model only depends on the starting point, duration, and state transition matrix.

[0069]

[0070] If the waypoint status of the mth track segment is known According to the conditional Markov process, the state of the waypoint (end point) of the mth track segment is integrated A motion model with waypoint information can be obtained:

[0071]

[0072] in,

[0073]

[0074] Notice: and May contain unknown parameters.

[0075] For example, consider uniform or uniformly accelerated linear motion. is a constant coefficient matrix, There are three dimensions in longitude, latitude and altitude respectively. three unknown variance parameters;

[0076] Consider the uniform turning motion. is a constant coefficient matrix containing the unknown angular velocity ω, Unknown parameters are also included

[0077] Compared with the motion model without waypoint information, the motion model with waypoint information can more accurately describe the actual motion law of the aircraft. Due to the uncertainty of the actual track, the waypoint status of the mth track segment includes the starting point and end point Duration N m By learning the clustered similar track data, we can get the joint probability density of the waypoint status and the flight duration.

[0078]

[0079] For a given initial aircraft state According to the above probability model, all waypoint states can be and the duration of the track segment N m Perform posterior statistical inference, where m=1,...,M.

[0080] In particular, if it is assumed that each track segment is connected at a given waypoint (i.e. or ) is conditionally independent, the above joint probability density can be expressed as

[0081]

[0082] In the attached Figure 8 and attached Figure 9 In this paper, the measured data of civil aviation training aircraft are used for analysis. and For Gaussian distribution, use the track training data to learn the unknown parameters of the density function and use the conditional expectation Waypoint status and the duration of the track segment N m Make an estimate (N m rounded up).

[0083] By combining the motion model containing the waypoint information, the joint probability density of the waypoint status and the flight segment duration, the 4D track model of the embodiment of the present invention is obtained.

[0084] Step 5: Estimation of optimal parameters of 4D trajectory model, refer to the attached Figure 6 process.

[0085] Dynamic Time Warping (DTW) measures the similarity between two time series of different lengths. It is commonly used in time series data analysis and pattern matching, and is particularly suitable for processing time series with a certain degree of offset and deformation. The core idea of ​​DTW is to find the optimal alignment between two series through dynamic programming to minimize the distance or dissimilarity between them.

[0086] The present invention proposes using DTW to measure the distance between the training track data and the model-generated track data. Under the DTW loss, the unknown parameters in the conditional Markov model are optimized based on the track training data to obtain a 4D track model with optimal parameters.

[0087] Specific process:

[0088] First, define the 4D track model established in step 4 as

[0089]

[0090] in, is the initial state of the aircraft in the first flight phase, and They represent the estimated states of the starting point and the ending point (i.e., the waypoint) of the mth track segment, represents the estimated duration of the mth flight segment, and θ represents all unknown parameters in the 4D trajectory model. Next, according to steps 1 to 3, K1 training trajectories are obtained:

[0091]

[0092] in Denote the initial state of the i-th training track in the first flight phase, i = 1, ..., K1. Then, based on the DTW loss, the following (nonlinear) optimization problem is established:

[0093]

[0094] Among them, due to There is randomness in Represents a random sequence The nth independent realization of , where N is the number of Monte Carlo times.

[0095] For the above optimization problem, a variety of standard optimization algorithms can be used to find numerical solutions, such as the "interior point method". As an estimate of the unknown parameter θ. Finally, Substitution Obtain a 4D trajectory model with optimal parameters

[0096] Step 6: 4D track model evaluation, refer to the attached Figure 7 process.

[0097] According to the DTW similarity evaluation criteria, the prediction ability of the established trajectory model is verified on the test data, and the model selection in the modeling process in step 4 is performed based on the prediction performance.

[0098] Specific process:

[0099] First, use steps 1 to 3 to obtain K0 test tracks:

[0100]

[0101] in, is the initial state of the jth test track in the first flight phase, j = 1, ..., K0. The predicted track is calculated using the DTW metric With test track The similarity between them is calculated, and the average similarity is calculated (i.e. the prediction goodness η of the 4D trajectory model)

[0102]

[0103] in Represents a random sequence The nth independent realization of , where N represents the number of Monte Carlo times. Finally, according to the prediction goodness η of the 4D trajectory model, the motion model in step 4 is fed back to achieve model selection.

[0104] The above are only some specific embodiments of the present invention. The specific contents or common knowledge known in the scheme are not described in detail here (including but not limited to abbreviations, abbreviations, and units commonly used in the art). It should be pointed out that the above embodiments do not limit the present invention in any way. For those skilled in the art, any technical solution obtained by equivalent replacement or equivalent transformation falls within the scope of protection of the present invention. The scope of protection claimed in this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A 4D trajectory modeling method based on conditional Markov process, characterized in that: The method comprises the following steps: Step 1) Preprocessing the large amount of collected flight management system and global positioning system data, including data cleaning, dimension normalization, and abnormal altitude data removal, to finally obtain track data; Step 2) identifying the motion pattern within each track based on the longitude, latitude, and time dimension information of the pre-processed track data; Step 3) Select one or more consecutive aircraft motion phases of interest, extract the flight paths within the aircraft motion phase of interest based on altitude and time information, perform cluster analysis on the flight path data, obtain clustering results of the flight path data, and mark the waypoints of different flight path segments in the same type of flight path to obtain the flight segment duration; Step 4) 4D track modeling is performed on the track data containing the waypoint information based on the conditional Markov process and the joint probability density of the waypoint status and the flight segment duration; Step 5) Under the dynamic time warping (DTW) loss, the unknown parameters in the 4D trajectory model are optimized according to the trajectory training data to obtain a trajectory model with optimal parameters; Step 6) Under the DTW similarity evaluation criteria, the trajectory test data is used to verify the prediction ability of the established 4D trajectory model for the motion state, and the model selection for 4D trajectory modeling is performed based on the prediction ability.

2. The method according to claim 1, characterized in that In the method, step 1) is to first identify and delete data with empty records; then, perform dimension conversion and standardization to ensure that the units of the data are consistent with the requirements of the track model; and finally, eliminate abnormal altitude data caused by large errors in the sensor. Specifically, First, delete the data with empty or NaN records. Then, standardize the dimensions of the original data according to Table 1. Calculate the speed LonSpd along the longitude and LatSpd along the latitude based on the ground speed GndSpd and the track angle TRK, respectively. The units are meters per second (mps): LatSpd mps =GndSpd mps ×cosd(TRK), LonSpd mps =GndSpd mps ×sind(TRK). Then, according to the WGS84 ellipsoid model of the earth, the speed unit "meters per second mps" in the longitude and latitude directions is converted into "degrees per second dps". The unit conversion formula is: in, represents the distance from the center of the earth to the surface at the corresponding latitude, the equatorial radius, that is, the length of the major axis of the earth's ellipsoid model, a = 6378137m, the distance from the North Pole to the center of the earth, that is, the length of the minor axis of the earth's ellipsoid model, b = 6356752.3142m, cosd and sind represent the sine and cosine functions calculated in degrees deg, respectively; the acceleration in each dimension is obtained by calculating the difference of the velocity in each dimension; the abnormal data is corrected or eliminated; finally, by performing the above preprocessing on the original data, the track data sampled at the time interval T = 1s is obtained.

3. The method according to claim 1, characterized in that Step 2) of the method is to effectively identify and classify the flight mode of the aircraft based on longitude, latitude, and time dimensions; the movement modes include uniform turning, uniform straight line, and uniformly accelerated straight line movement; Specifically, first, the track angle TRK in the track data is used to determine whether the track has turned. The cumulative change of TRK during n consecutive observation times is calculated. When the cumulative change of TRK exceeds the set threshold, it is considered that a turning motion has occurred. Secondly, for linear motion, the cumulative change of ground speed GndSpd during n consecutive observation times is calculated and compared with the set threshold. If it is less than the threshold, it is considered to be uniform linear motion; if it is greater than the threshold, it is considered to be uniformly accelerated linear motion. Finally, the flight segment duration of the flight mode is obtained based on the start and end times of different flight modes within each track.

4. The method according to claim 1, wherein Step 3) of the method is to perform cluster analysis on the track data in the corresponding stage for the aircraft movement phase of interest, obtain various tracks with different navigation tasks, and mark the waypoints in the same track; Specifically, one or more consecutive flight phases of interest are selected, the aircraft motion phases of interest are extracted based on altitude and time information, and the track classes with the same landing airport location are determined based on the airport longitude, latitude, and altitude; Secondly, for the track data of the same airport, the 3D flight pattern of each track is used to cluster them. Specifically, the 3D flight pattern contains multiple segments of linear motion and / or turning motion. The flight pattern of the track segment is used as the track feature, and cluster analysis is performed on multiple tracks to obtain track clustering results. Finally, the class of interest in the cluster is selected, and the aircraft state in the mth flight mode in the i-th track is recorded as Among them, the initial state of the mth flight mode in the i-th track is and terminal state It is recorded as the waypoint state, and the duration of the mth 3D flight mode segment is recorded as N m,i There are K tracks in total, and each track has M different track segments. It should be emphasized here that the state of the waypoints is related to the duration of the flight segment. To avoid ambiguity, determine K similar tracks are randomly divided into training group and test group, each containing K1 and K0 tracks.

5. The method according to claim 1, wherein In step 4) of the method, a linear transfer model is used, which includes uniform straight line, uniformly accelerated straight line, and uniform turning motion modes; Initially model the motion pattern of the mth track segment: in, Represents the state at the kth moment in the mth track segment, assuming A total of M different track segments are considered, and the starting point in the mth track segment is The duration of the flight segment is N m , the state transfer matrix is Obviously, the above initial model only depends on the starting point, duration, and state transition matrix; in order to avoid ambiguity, determine If the waypoint status of the mth track segment is known According to the conditional Markov process, the waypoints of the mth track segment are integrated, that is, the end point of the mth track segment, and the state A motion model with waypoint information can be obtained: in, Since the real track is uncertain, the waypoint status of the mth track segment includes the starting point and end point Duration N m It also has uncertainty; by learning the clustered similar track data, the joint probability density of the waypoint status and the flight duration is obtained For a given initial aircraft state According to the above joint probability density model, all waypoint states can be and the duration of the track segment N m Perform posterior statistical inference, where m = 1, ..., M; The 4D trajectory model is obtained by combining the motion model containing waypoint information, the joint probability density of waypoint status and flight segment duration.

6. The method according to claim 3, characterized in that In the method, the cumulative change amount of TRK and the cumulative change amount of GndSpd are achieved through convolution operation.

7. The method according to claim 5, characterized in that described and contains unknown parameters; Consider uniform or uniformly accelerated linear motion. is a constant coefficient matrix, There are three dimensions in longitude, latitude and altitude respectively. three unknown variance parameters; Consider the uniform turning motion. is a constant coefficient matrix containing the unknown angular velocity ω, Unknown parameters are also included 8. The method according to claim 5, characterized in that Assume that each track segment is at a given connecting waypoint; that is, or After conditional independence, the joint probability density is expressed as It assumes and For Gaussian distribution, use the track training data to learn the unknown parameters of the density function and use the conditional expectation Waypoint status and the duration of the track segment N m To estimate, N m Round up.

9. The method according to claim 1, characterized in that The method includes step 5), optimizing unknown parameters in the 4D track model according to track training data under dynamic time warping (DTW) loss to obtain a track model with optimal parameters; specifically, First, define the 4D track model established in step 4) as in, is the initial state of the aircraft in the first flight phase, and Represent the starting point and end point of the mth track segment, i.e., the waypoint, the state estimation, represents the estimated duration of the mth flight segment, and θ represents all unknown parameters in the 4D trajectory model. Secondly, according to steps 1) to 3), K1 training trajectories are obtained: in Denote the initial state of the i-th training track in the first flight phase, i = 1, ..., K1; then, based on the DTW loss, the following nonlinear optimization problem is established: Among them, due to There is randomness in Represents a random sequence The nth independent realization of , where N represents the number of Monte Carlo times; For the above optimization problems, a variety of standard optimization algorithms are used to find numerical solutions; the optimal solution As an estimate of the unknown parameter θ; finally, Substitution Obtain a 4D trajectory model with optimal parameters 10. The method according to claim 1, characterized in that The method includes step 6), using track test data to verify the prediction ability of the established 4D track model for the motion state under the DTW similarity evaluation criterion, and selecting a model for 4D track modeling based on the prediction ability; specifically, first, using steps 1) to 3) to obtain K0 test tracks: in, is the initial state of the jth test track in the first flight phase, j = 1, ..., K0; the predicted track is calculated using the DTW metric With test track The similarity between them is calculated, and the average similarity is calculated, that is, the prediction goodness η of the 4D track model. in Represents a random sequence The nth independent realization of , N represents the number of Monte Carlo times; finally, according to the prediction goodness η of the 4D trajectory model, the motion model in step 4) is fed back to realize model selection.

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