Aircraft 4D trajectory prediction method and system based on equivalent guidance law

Abstract

The present invention relates to the field of track prediction technology, and in particular to a method and system for predicting a 4D track of an aircraft based on an equivalent guidance law, wherein the aircraft speed parameters and acceleration parameters are obtained based on ADS-B track data; the nonlinear mapping relationship between the aircraft track data and the equivalent guidance law is obtained based on the aircraft speed parameters, acceleration parameters and equivalent guidance parameters and in combination with the center of mass dynamics equation in the track coordinate system, wherein the equivalent guidance parameters include aircraft engine thrust, angle of attack and roll angle, and the equivalent guidance law is the center of mass motion curve of the aircraft equivalent guidance parameters changing with time; the nonlinear mapping relationship is used to predict and output the 4D track corresponding to the equivalent guidance parameters of the aircraft at the target time. The present invention realizes aircraft track prediction through the equivalent guidance law and based on the center of mass dynamics and kinematic models, and realizes aircraft track prediction that reflects the essence of target dynamic characteristics and has high accuracy without relying on prior information such as target models and parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of track prediction, and in particular to a method and system for predicting a 4D track of an aircraft based on an equivalent guidance law. Background Art

[0002] 4D trajectory prediction is a key technology of the air traffic management (ATM) system. Accurate 4D trajectory prediction is of great significance for improving the efficiency of air traffic management and ensuring air traffic safety. According to the different means of aircraft trajectory generation, there are two main categories of existing 4D trajectory prediction methods: one is the trajectory prediction method based on dynamics and kinematic models, and the other is the trajectory prediction method based on curve interpolation fitting models. The advantage of the former is that it can reflect the essential characteristics of aircraft motion. When the constructed model is sufficiently precise and accurate, the prediction accuracy is high, but the disadvantage is that it requires a large amount of prior information such as models and parameters. The advantage of the latter is that it does not require a large amount of prior information such as physical models and parameters, and the obtained trajectory is relatively continuous and smooth, but the disadvantage is that it does not reflect the essential characteristics of aircraft motion enough, and the prediction accuracy depends on the model and number of nodes of the curve. Therefore, there is an urgent need for a high-precision prediction method that does not rely on prior information such as target models and parameters and can realize the essential characteristics of aircraft motion to meet the application requirements of air traffic management systems. Summary of the invention

[0003] To this end, the present invention provides an aircraft 4D trajectory prediction method and system based on the equivalent guidance law, which realizes aircraft trajectory prediction through the equivalent guidance law and based on the center of mass dynamics and kinematic models, and realizes aircraft trajectory prediction that reflects the essence of target dynamic characteristics and has higher accuracy without relying on prior information such as target models and parameters.

[0004] According to the design scheme provided by the present invention, on the one hand, a method for predicting a 4D trajectory of an aircraft based on an equivalent guidance law is provided, comprising:

[0005] Acquire aircraft speed parameters and acceleration parameters based on ADS-B track data, wherein the track data includes the aircraft's geodetic longitude and latitude, pressure altitude, ground speed, altitude change rate and heading angle; speed parameters include speed magnitude, speed inclination and heading angle; acceleration parameters include speed change rate, speed inclination change rate and heading angle change rate;

[0006] The nonlinear mapping relationship between the aircraft track data and the equivalent guidance law is obtained based on the aircraft speed parameters, acceleration parameters and equivalent guidance parameters and combined with the mass center dynamics equation in the track coordinate system. The equivalent guidance parameters include the aircraft engine thrust, angle of attack and roll angle. The equivalent guidance law is the mass center motion curve of the aircraft equivalent guidance parameters changing with time.

[0007] The nonlinear mapping relationship between the aircraft track data and the equivalent guidance law is used to predict and output the 4D track corresponding to the equivalent guidance parameters of the aircraft at the target time.

[0008] As the aircraft 4D track prediction method based on the equivalent guidance law of the present invention, further, the aircraft speed parameters and acceleration parameters are obtained based on the ADS-B track data, including:

[0009] First, the geodetic longitude and latitude and pressure altitude are converted to earth-fixed coordinates, and the geocentric distance and geocentric longitude and latitude are obtained based on the conversion relationship between earth-fixed coordinates and spherical coordinates;

[0010] Next, the aircraft position parameters are obtained based on the distance from the center of the earth and the longitude and latitude of the center of the earth, and the speed parameters are obtained based on the ground speed and the rate of change of altitude;

[0011] Then, the data sequence of the speed parameter changing with time is obtained, and the interpolation model of the speed parameter is constructed by using the spline interpolation method;

[0012] Finally, the time first-order derivative of the data series is interpolated based on the interpolation model to obtain the acceleration parameters at the corresponding moment.

[0013] As the aircraft 4D track prediction method based on the equivalent guidance law of the present invention, further, the interpolation model of the speed parameter is constructed by using the spline interpolation method, which includes:

[0014] The velocity parameter is divided into several intervals by using cubic spline interpolation function, a cubic function is constructed in each interval, and the connection between each cubic function is smooth, wherein the smooth connection includes: the 0th order derivative, the first order derivative and the second order derivative of the cubic function at the endpoint of each interval are continuous.

[0015] As an aircraft 4D track prediction method based on the equivalent guidance law of the present invention, further, according to the aircraft speed parameters, acceleration parameters and equivalent guidance parameters and in combination with the center of mass dynamic equation in the track coordinate system, a nonlinear mapping relationship between the aircraft track data and the equivalent guidance law is obtained, including:

[0016] Firstly, the center-of-mass dynamic equation of the aircraft in the track coordinate system is constructed based on the aircraft velocity parameters, acceleration parameters, equivalent guidance parameters, aircraft mass, lift, atmospheric drag, earth's rotation angular velocity and gravitational acceleration;

[0017] Next, the center-of-mass dynamic equation is simplified by setting the earth's rotation angular velocity to 0; the aerodynamic coefficient of the aerial target is set to satisfy the parabolic drag polar line, and the aerodynamic coefficient model is constructed based on the lift coefficient and drag coefficient;

[0018] Then, the simplified center-of-mass dynamics equation is optimized based on the aerodynamic coefficient model, and the nonlinear mapping relationship between the aircraft track data and the equivalent guidance law is obtained by solving the optimized center-of-mass dynamics equation.

[0019] As the aircraft 4D track prediction method based on the equivalent guidance law of the present invention, further, the aerodynamic coefficient model is expressed as: Among them, C L is the lift coefficient, C D is the drag coefficient, C D0 , K are aerodynamic coefficients, and α is the aircraft angle of attack.

[0020] As the aircraft 4D track prediction method based on the equivalent guidance law of the present invention, further, the simplified center of mass dynamics equation is optimized based on the aerodynamic coefficient model, including:

[0021] The atmospheric density, aircraft wing reference area and speed are obtained, and the lift coefficient and drag coefficient in the aerodynamic coefficient model are combined to represent the lift and atmospheric drag in the center of mass dynamics equation.

[0022] As the aircraft 4D track prediction method based on the equivalent guidance law of the present invention, further, the optimized center of mass dynamic equation is solved, including:

[0023] Firstly, the unknown model parameters are estimated based on the aircraft speed parameters, acceleration parameters and equivalent guidance parameters, and using the aircraft's straight and level flight state. The unknown model parameters include: aircraft mass, aircraft wing reference area and aerodynamic coefficients.

[0024] Then, the estimated unknown model parameters are verified using the preset inference formula of the aircraft engine thrust, and the expected unknown model parameter estimation results are obtained based on the verification results, so as to establish a nonlinear mapping relationship between the aircraft track data and the equivalent guidance law based on the estimation results.

[0025] Furthermore, the present invention also provides an aircraft 4D track prediction system based on equivalent guidance law, comprising: a motion data acquisition module, a mapping relationship construction module and a track prediction output module, wherein:

[0026] A motion data acquisition module is used to acquire aircraft speed parameters and acceleration parameters based on ADS-B track data, wherein the track data includes the aircraft's geodetic longitude and latitude, pressure altitude, ground speed, altitude change rate and heading angle; the speed parameters include speed magnitude, speed inclination and heading angle; and the acceleration parameters include speed change rate, speed inclination change rate and heading angle change rate;

[0027] A mapping relationship building module is used to obtain a nonlinear mapping relationship between the aircraft track data and the equivalent guidance law based on the aircraft speed parameters, acceleration parameters and equivalent guidance parameters and in combination with the mass center dynamics equation in the track coordinate system, wherein the equivalent guidance parameters include the aircraft engine thrust, angle of attack and roll angle, and the equivalent guidance law is a mass center motion curve of the aircraft equivalent guidance parameters changing with time;

[0028] The track prediction output module is used to predict and output the 4D track corresponding to the equivalent guidance parameters of the aircraft at the target time by using the nonlinear mapping relationship between the aircraft track data and the equivalent guidance law.

[0029] Beneficial effects of the present invention:

[0030] The present invention is based on ADS-B track data and uses a spline interpolation method to obtain position parameters, velocity parameters and acceleration parameters; the nonlinear mapping relationship between track data and the equivalent guidance law is obtained by constructing a simplified center-of-mass dynamics equation based on the equivalent guidance law of the aircraft in the track coordinate system, and the equivalent guidance law is obtained by solving it using numerical methods such as Newton iteration; the current equivalent guidance law parameters are substituted into the simplified center-of-mass dynamics equation based on the equivalent guidance law, and numerical integration is performed to realize the 4D track prediction of the aircraft. Based on dynamic and kinematic models and using equivalent guidance laws, the essence of the target dynamic characteristics and high-precision track prediction are realized without relying on prior information such as target models and parameters, and the track prediction can be applied to non-cooperative aircraft, and has good application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a schematic diagram of the aircraft 4D trajectory prediction process based on the equivalent guidance law in the embodiment;

[0032] Figure 2 It is a schematic diagram of a three-dimensional track curve and a speed curve in the embodiment;

[0033] Figure 3 It is a schematic diagram of the acceleration parameter curve in the embodiment;

[0034] Figure 4 It is a schematic diagram of the equivalent guidance law curve in the embodiment;

[0035] Figure 5 Schematic diagram of the comparison between the predicted track and the original track in the embodiment. DETAILED DESCRIPTION

[0036] In order to make the purpose, technical solutions and advantages of the present invention clearer and more understandable, the present invention is further described in detail below in conjunction with the accompanying drawings and technical solutions.

[0037] In view of the problem described in the background art that the existing 4D trajectory prediction of aircraft requires a large amount of prior information such as model parameters and does not adequately reflect the essential characteristics of aircraft motion, the embodiments of the present invention refer to Figure 1 As shown, a method for aircraft 4D trajectory prediction based on an equivalent guidance law is provided, which includes the following contents:

[0038] S101. Acquire aircraft speed parameters and acceleration parameters based on ADS-B track data, wherein the track data includes the aircraft's geodetic longitude and latitude, pressure altitude, ground speed, altitude change rate, and heading angle; the speed parameters include speed magnitude, speed inclination, and heading angle; and the acceleration parameters include speed change rate, speed inclination change rate, and heading angle change rate.

[0039] Specifically, the aircraft speed parameters and acceleration parameters are obtained based on ADS-B track data, which can be designed to include the following contents:

[0040] First, the geodetic longitude and latitude and pressure altitude are converted to earth-fixed coordinates, and the geocentric distance and geocentric longitude and latitude are obtained based on the conversion relationship between earth-fixed coordinates and spherical coordinates;

[0041] Next, the aircraft position parameters are obtained based on the distance from the center of the earth and the longitude and latitude of the center of the earth, and the speed parameters are obtained based on the ground speed and the rate of change of altitude;

[0042] Then, the data sequence of the speed parameter changing with time is obtained, and the interpolation model of the speed parameter is constructed by using the spline interpolation method;

[0043] Finally, the time first-order derivative of the data series is interpolated based on the interpolation model to obtain the acceleration parameters at the corresponding moment.

[0044] The parameter data contained in the ADS-B track data usually include the aircraft's geodetic longitude L, latitude B and pressure altitude H, ground speed v d , height change rate v h The above parameter data are converted into geocentric longitude λ, latitude φ, geocentric distance r, speed v, speed inclination θ and heading angle σ in the track coordinate system.

[0045] First, the latitude and longitude of the earth can be converted into the fixed coordinates (X, Y, Z)

[0046]

[0047] Where N is the radius of curvature of the mortise circle

[0048]

[0049] In the formula, a e is the semi-major axis of the Earth, and e is the eccentricity of the Earth.

[0050] Then, convert the ground-fixed coordinates (X, Y, Z) into spherical coordinates

[0051]

[0052] The speed is

[0053]

[0054] The velocity inclination is

[0055]

[0056] After obtaining the data sequence of velocity parameters (including velocity magnitude v, velocity inclination angle θ and heading angle σ) changing with time, the interpolation model of velocity parameters is constructed by cubic spline interpolation. The first-order derivative of the interpolation model with respect to time is calculated and then interpolated to obtain the acceleration parameter (velocity change rate) at the corresponding moment. Speed ​​angle change rate and the rate of change of heading angle ).

[0057] Among them, the interpolation model of speed parameters is constructed by using spline interpolation method, which may include:

[0058] The velocity parameter is divided into several intervals by using cubic spline interpolation function, a cubic function is constructed in each interval, and the connection between each cubic function is smooth, wherein the smooth connection includes: the 0th order derivative, the first order derivative and the second order derivative of the cubic function at the endpoint of each interval are continuous.

[0059] In the cubic spline interpolation function, there are n+1 nodes a=t in the interval [a,b] 0 <t 1 <···<t n =b, the function values ​​corresponding to the nodes are y 0 ,y 1 ,y 2 ,···,y n If there is a function S(t) passing through all nodes that satisfies: (1) S(t i )=y i ,i=0,1,···,n;(2) has a continuous second-order derivative S(t)∈C in the interval [a,b] 2 [a,b]; (3) in [t i-1 ,t i ], i = 1, 2, ···, n. is a cubic polynomial. Then S(t) is a cubic spline interpolation function, which is a cubic polynomial function in each subinterval, that is,

[0060] S(t)=a i+b i t+c i t 2 +d i t 3 (6)

[0061] Each cubic polynomial contains 4 unknown coefficients, so a total of 4n parameters must be determined.

[0062] Using the second-order derivative of S(t), S″(t i )=M i (i=0,1,···,n) represents S(t), then

[0063]

[0064] Since S(t) is in each small interval [t i-1 ,t i ], i = 1, 2, ···, n. Each cubic polynomial contains 4 unknown coefficients, so a total of 4n parameters need to be determined. According to the continuous property of S(t) in [a, b] and at node t i The continuous properties of the first and second order derivatives can provide 3n-3 conditions, and S(t) satisfies the interpolation conditions, so there are 4n-2 conditions in total. However, to finally determine S(t), two boundary conditions are required.

[0065] Usually, a boundary condition can be added to each end point of the interval [a, b]. The following are three common ones:

[0066] (1) The first-order derivative values ​​at both ends are known, that is, S′(t 0 ) = f 0 ′,S′(t n ) = f n ′;

[0067] (2) The second-order derivative values ​​at both ends are known, that is, S″(t 0 ) = f 0 ″,S″(t n ) = f n ″;

[0068] (3) Natural boundary condition S″(t 0 )=S″(t n )=0

[0069] Based on the 4n conditions obtained above, a tridiagonal matrix equation system is constructed and solved using the pursuit method, and then the expression (7) of the cubic spline interpolation function on each small interval is calculated. After obtaining the interpolation model, the model can be substituted into equation (8) to calculate its derivative curve.

[0070]

[0071] S102. Obtain a nonlinear mapping relationship between the aircraft track data and the equivalent guidance law based on the aircraft speed parameters, acceleration parameters and equivalent guidance parameters and in combination with the center of mass dynamics equation in the track coordinate system, wherein the equivalent guidance parameters include the aircraft engine thrust, angle of attack and roll angle, and the equivalent guidance law is a center of mass motion curve of the aircraft equivalent guidance parameters changing with time.

[0072] Specifically, the nonlinear mapping relationship between the aircraft track data and the equivalent guidance law is obtained based on the aircraft speed parameters, acceleration parameters and equivalent guidance parameters and combined with the center of mass dynamics equation in the track coordinate system, which can be designed to include the following contents:

[0073] Firstly, the center-of-mass dynamic equation of the aircraft in the track coordinate system is constructed based on the aircraft velocity parameters, acceleration parameters, equivalent guidance parameters, aircraft mass, lift, atmospheric drag, earth's rotation angular velocity and gravitational acceleration;

[0074] Next, the center-of-mass dynamic equation is simplified by setting the earth's rotation angular velocity to 0; the aerodynamic coefficient of the aerial target is set to satisfy the parabolic drag polar line, and the aerodynamic coefficient model is constructed based on the lift coefficient and drag coefficient;

[0075] Then, the simplified center-of-mass dynamics equation is optimized based on the aerodynamic coefficient model, and the nonlinear mapping relationship between the aircraft track data and the equivalent guidance law is obtained by solving the optimized center-of-mass dynamics equation.

[0076] Among them, the simplified center of mass dynamics equation is optimized based on the aerodynamic coefficient model and can be designed to include:

[0077] The atmospheric density, aircraft wing reference area and speed are obtained, and the lift coefficient and drag coefficient in the aerodynamic coefficient model are combined to represent the lift and atmospheric drag in the center of mass dynamics equation.

[0078] Assuming that the earth is a homogeneous sphere and considering the earth's rotation, the atmospheric model adopts an interpolation model. The center of mass dynamic equation of the aircraft in the track coordinate system is:

[0079]

[0080] Where T is the engine thrust, α is the angle of attack, m is the mass of the aircraft, L is the lift, D is the atmospheric drag, γ is the roll angle, ω e is the angular velocity of the earth's rotation, and g is the gravitational acceleration. If the additional acceleration caused by the earth's rotation is not considered (10 -5 magnitude), we only need to replace ω in the above formula e Set it to 0, and the equation can be simplified to

[0081]

[0082] The lift force L can be expressed by the lift coefficient C L express

[0083]

[0084] Where: ρ represents the atmospheric density; S is the reference area of ​​the wing. Similarly, drag can be expressed by the drag coefficient C D express

[0085]

[0086] In actual situations, the aerodynamic coefficient is obtained by two-dimensional interpolation based on the aerodynamic model data table. However, in the overall design and analysis, it can be simplified to assume that the aerodynamic coefficient of the aerial target approximately satisfies the parabolic drag pole, and then the aerodynamic coefficient model is constructed.

[0087]

[0088] Where: C D0 , K and is a constant. Substituting the aerodynamic model into equation (10) yields

[0089]

[0090] Where T, α, γ determine the motion curve of the center of mass of the aircraft, and the curve of T, α, γ changing with time is called the equivalent guidance law of the aircraft.

[0091] Furthermore, the optimized center of mass dynamics equation is solved and can be designed to include the following contents:

[0092] Firstly, the unknown model parameters are estimated based on the aircraft speed parameters, acceleration parameters and equivalent guidance parameters, and using the aircraft's straight and level flight state. The unknown model parameters include: aircraft mass, aircraft wing reference area and aerodynamic coefficients.

[0093] Then, the estimated unknown model parameters are verified using the preset inference formula of the aircraft engine thrust, and the expected unknown model parameter estimation results are obtained based on the verification results, so as to establish a nonlinear mapping relationship between the aircraft track data and the equivalent guidance law based on the estimation results.

[0094] From equation (14), we can see that in addition to the known motion state parameters and equivalent guidance law parameters, there are also unknown model parameters: mass m, windward cross-sectional area S, aerodynamic coefficient C D0 , K and Based on public information, reasonable assumptions about the model parameters can be made using the aircraft's straight and level flight state.

[0095] Assume that it is known that the aircraft usually cruises at a constant speed at a height H and a speed v. Then we have

[0096]

[0097] If the assumed model parameters satisfy the conditions of formula (16), it proves that the parameter speculation is more reasonable, where α should be taken near the favorable angle of attack (i.e., the angle of attack corresponding to the maximum lift-to-drag ratio).

[0098]

[0099] After obtaining the motion state parameters and model parameters at any time, according to equation (14), solving the equivalent guidance law T, α, γ of the aircraft is actually solving the nonlinear equation system (17)

[0100]

[0101] Equation (17) is a transcendental equation, which usually cannot be solved analytically. It can be solved by numerical methods such as Newton iteration.

[0102] Due to the influence of various error factors such as track data error, model error and algorithm error, the solved equivalent guidance law usually contains a certain amount of noise. The moving window curve fitting algorithm can be used to filter out the noise influence and extract the slower long-term changes of the equivalent guidance law value.

[0103] S103, using the nonlinear mapping relationship between the aircraft track data and the equivalent guidance law, predict and output the 4D track corresponding to the equivalent guidance parameters of the aircraft at the target time.

[0104] After obtaining a relatively accurate equivalent guidance law at the current moment, it can be assumed that the equivalent guidance law of the aircraft is a constant or a slowly time-varying parameter in the short future period. The equivalent guidance law at the current moment as the target moment is substituted into equation (14), and numerical integration methods such as Runge-Kutta can be used to predict the trajectory within a given future time range.

[0105] Furthermore, based on the above method, an embodiment of the present invention also provides an aircraft 4D track prediction system based on an equivalent guidance law, comprising: a motion data acquisition module, a mapping relationship construction module and a track prediction output module, wherein:

[0106] A motion data acquisition module is used to acquire aircraft speed parameters and acceleration parameters based on ADS-B track data, wherein the track data includes the aircraft's geodetic longitude and latitude, pressure altitude, ground speed, altitude change rate and heading angle; the speed parameters include speed magnitude, speed inclination and heading angle; and the acceleration parameters include speed change rate, speed inclination change rate and heading angle change rate;

[0107] A mapping relationship building module is used to obtain a nonlinear mapping relationship between the aircraft track data and the equivalent guidance law based on the aircraft speed parameters, acceleration parameters and equivalent guidance parameters and in combination with the mass center dynamics equation in the track coordinate system, wherein the equivalent guidance parameters include the aircraft engine thrust, angle of attack and roll angle, and the equivalent guidance law is a mass center motion curve of the aircraft equivalent guidance parameters changing with time;

[0108] The track prediction output module is used to predict and output the 4D track corresponding to the equivalent guidance parameters of the aircraft at the target time by using the nonlinear mapping relationship between the aircraft track data and the equivalent guidance law.

[0109] In order to verify the effectiveness of this solution, the following is a further explanation based on experimental data:

[0110] Taking a certain section of the track of a reconnaissance aircraft with ICAO number 43c39c as an example, the effectiveness of the algorithm is verified. The three-dimensional curves of latitude and longitude and speed of the entire track are as follows: Figure 2 As shown in (a) and (b) in Figure 1, the track contains 278 points and lasts for about 5250 seconds. The first half of the track data (139 points) is used to solve the equivalent guidance law, and the second half of the data is used to evaluate the 4D track prediction accuracy.

[0111] First, a cubic spline interpolation model of speed, speed inclination and heading angle is constructed. The first-order derivative of time is calculated and interpolated to obtain the corresponding change rate. The change rates of speed, speed inclination and heading angle are as follows: Figure 3 As shown in (a), (b) and (c).

[0112] According to the open source information and the model parameter balance under the condition of fixed straight and level flight, the dynamic model parameters of the reconnaissance aircraft are set as follows: aerodynamic coefficient C D0 =0.015, K = 0.15, mass m = 108000 (kg), windward cross-sectional area S = 238.5 (m 2 ). The calculated equivalent guidance law curves including engine thrust, angle of attack and roll angle are as follows: Figure 4 As shown in (a), (b) and (c).

[0113] The 139th point trajectory is used as the initial state variable, and the smoothed equivalent guidance law is used as the control input. The trajectory is predicted by Runge-Kutta integration using equation (14). The predicted trajectory is compared with the original trajectory in the dimensions of altitude, latitude, speed and heading angle. Figure 5 As shown in (a), (b), (c) and (d).

[0114] It can be seen from the above experimental results that when the equivalent guidance law of the aircraft's subsequent track is a slow time-varying parameter (that is, the aircraft does not perform large maneuvers), the scheme in this case can obtain a highly accurate predicted track. It is predicted that the altitude error will be about 700 meters after about 3000 seconds, the longitude and latitude errors will be about 0.06 degrees, the speed error will be about 20m / s, and the heading angle error will be about 0.15 degrees. It can be verified that without relying on prior information such as target models and parameters, the essence of the target dynamic characteristics and high-precision track prediction can be achieved. It can be applied to non-cooperative aircraft, can improve air traffic management efficiency and air traffic safety, and has good application prospects.

[0115] Unless otherwise specifically stated, the relative steps, numerical expressions and values ​​of the components and steps set forth in these embodiments do not limit the scope of the present invention.

[0116] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0117] The units and method steps of each example described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described in the above description according to function. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. A person of ordinary skill in the art may use different methods to implement the described functions for each specific application, but such implementation is not considered to be beyond the scope of the present invention.

[0118] Those skilled in the art will appreciate that all or part of the steps in the above method can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium, such as a read-only memory, a disk or an optical disk. Optionally, all or part of the steps in the above embodiment can also be implemented using one or more integrated circuits, and accordingly, each module / unit in the above embodiment can be implemented in the form of hardware or in the form of software function modules. The present invention is not limited to any specific form of combination of hardware and software.

[0119] Finally, it should be noted that the above-described embodiments are only specific implementations of the present invention, which are used to illustrate the technical solutions of the present invention, rather than to limit them. The protection scope of the present invention is not limited thereto. Although the present invention is described in detail with reference to the above-described embodiments, ordinary technicians in the field should understand that any technician familiar with the technical field can still modify the technical solutions recorded in the above-described embodiments within the technical scope disclosed by the present invention, or can easily think of changes, or make equivalent replacements for some of the technical features therein; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A method for predicting 4D aircraft trajectory based on equivalent guidance law, characterized in that: Include: Acquire aircraft speed parameters and acceleration parameters based on ADS-B track data, wherein the track data includes the aircraft's geodetic longitude and latitude, pressure altitude, ground speed, altitude change rate and heading angle; speed parameters include speed magnitude, speed inclination and heading angle; acceleration parameters include speed change rate, speed inclination change rate and heading angle change rate; According to the aircraft speed parameters, acceleration parameters and equivalent guidance parameters and in combination with the center-of-mass dynamics equation in the track coordinate system, the nonlinear mapping relationship between the aircraft track data and the equivalent guidance law is obtained, wherein the equivalent guidance parameters include the aircraft engine thrust, angle of attack and roll angle, and the equivalent guidance law is the center-of-mass motion curve of the aircraft equivalent guidance parameters changing with time; the process of obtaining the nonlinear mapping relationship between the aircraft track data and the equivalent guidance law includes: firstly, based on the aircraft speed parameters, acceleration parameters, equivalent guidance parameters, aircraft mass, lift The center-of-mass dynamic equation of the aircraft in the track coordinate system is constructed by taking into account the force, atmospheric drag, the earth's rotation angular velocity and gravitational acceleration; then, the center-of-mass dynamic equation is simplified by setting the earth's rotation angular velocity to 0; the aerodynamic coefficient of the aerial target is set to satisfy the parabolic drag polar line, and an aerodynamic coefficient model is constructed based on the lift coefficient and the drag coefficient; then, the simplified center-of-mass dynamic equation is optimized based on the aerodynamic coefficient model, and the nonlinear mapping relationship between the aircraft track data and the equivalent guidance law is obtained by solving the optimized center-of-mass dynamic equation; The nonlinear mapping relationship between the aircraft track data and the equivalent guidance law is used to predict and output the 4D track corresponding to the equivalent guidance parameters of the aircraft at the target time.

2. The aircraft 4D trajectory prediction method based on equivalent guidance law according to claim 1, characterized in that: Obtain aircraft speed and acceleration parameters based on ADS-B track data, including: First, the geodetic longitude and latitude and pressure altitude are converted to earth-fixed coordinates, and the geocentric distance and geocentric longitude and latitude are obtained based on the conversion relationship between earth-fixed coordinates and spherical coordinates; Next, the aircraft position parameters are obtained based on the distance from the center of the earth and the longitude and latitude of the center of the earth, and the speed parameters are obtained based on the ground speed and the rate of change of altitude; Then, the data sequence of the speed parameter changing with time is obtained, and the interpolation model of the speed parameter is constructed by using the spline interpolation method; Finally, the time first-order derivative of the data series is interpolated based on the interpolation model to obtain the acceleration parameters at the corresponding moment.

3. The aircraft 4D trajectory prediction method based on equivalent guidance law according to claim 2 is characterized in that: The interpolation model of speed parameters is constructed using spline interpolation method, including: The velocity parameter is divided into several intervals by using cubic spline interpolation function, a cubic function is constructed in each interval, and the connection between each cubic function is smooth, wherein the smooth connection includes: the 0th order derivative, the first order derivative and the second order derivative of the cubic function at the endpoint of each interval are continuous.

4. The aircraft 4D trajectory prediction method based on equivalent guidance law according to claim 1, characterized in that: The aerodynamic coefficient model is expressed as: Among them, C L is the lift coefficient, C D is the drag coefficient, C D0 , K are aerodynamic coefficients, and α is the aircraft angle of attack.

5. The aircraft 4D trajectory prediction method based on equivalent guidance law according to claim 1 or 4, characterized in that: The simplified center of mass dynamics equation is optimized based on the aerodynamic coefficient model, including: The atmospheric density, aircraft wing reference area and speed are obtained, and the lift coefficient and drag coefficient in the aerodynamic coefficient model are combined to represent the lift and atmospheric drag in the center of mass dynamics equation.

6. The aircraft 4D trajectory prediction method based on equivalent guidance law according to claim 5, characterized in that: Solve the optimized center of mass dynamics equation, including: Firstly, the unknown model parameters are estimated based on the aircraft speed parameters, acceleration parameters and equivalent guidance parameters, and using the aircraft's straight and level flight state. The unknown model parameters include: aircraft mass, aircraft wing reference area and aerodynamic coefficients. Then, the estimated unknown model parameters are verified using the preset inference formula of the aircraft engine thrust, and the expected unknown model parameter estimation results are obtained based on the verification results, so as to establish a nonlinear mapping relationship between the aircraft track data and the equivalent guidance law based on the estimation results.

7. An aircraft 4D trajectory prediction system based on equivalent guidance law, characterized in that: It includes: motion data acquisition module, mapping relationship construction module and track prediction output module, among which, A motion data acquisition module is used to acquire aircraft speed parameters and acceleration parameters based on ADS-B track data, wherein the track data includes the aircraft's geodetic longitude and latitude, pressure altitude, ground speed, altitude change rate and heading angle; the speed parameters include speed magnitude, speed inclination and heading angle; and the acceleration parameters include speed change rate, speed inclination change rate and heading angle change rate; The mapping relationship building module is used to obtain the nonlinear mapping relationship between the aircraft track data and the equivalent guidance law based on the aircraft speed parameters, acceleration parameters and equivalent guidance parameters and in combination with the center of mass dynamics equation in the track coordinate system, wherein the equivalent guidance parameters include the aircraft engine thrust, angle of attack and roll angle, and the equivalent guidance law is the center of mass motion curve of the aircraft equivalent guidance parameters changing with time; the process of obtaining the nonlinear mapping relationship between the aircraft track data and the equivalent guidance law includes: first, based on the aircraft speed parameters, acceleration parameters, equivalent guidance parameters, aircraft The center-of-mass dynamic equation of the aircraft in the track coordinate system is constructed by taking into account the mass, lift, atmospheric drag, angular velocity of the earth's rotation and gravitational acceleration; then, the center-of-mass dynamic equation is simplified by setting the angular velocity of the earth's rotation to 0; the aerodynamic coefficient of the aerial target is set to satisfy the parabolic drag polar line, and an aerodynamic coefficient model is constructed based on the lift coefficient and the drag coefficient; then, the simplified center-of-mass dynamic equation is optimized based on the aerodynamic coefficient model, and the nonlinear mapping relationship between the aircraft track data and the equivalent guidance law is obtained by solving the optimized center-of-mass dynamic equation; The track prediction output module is used to predict and output the 4D track corresponding to the equivalent guidance parameters of the aircraft at the target time by using the nonlinear mapping relationship between the aircraft track data and the equivalent guidance law.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

9. An electronic device, characterized in that: include: at least one processor, and a memory coupled to the at least one processor; The memory stores a computer program, and the computer program can be executed by the at least one processor to implement the method according to any one of claims 1 to 6.

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