A trajectory prediction method under target large maneuvering condition based on fast transmission

Abstract

The application discloses a trajectory prediction method under target large maneuvering condition based on fast transfer, and the method is based on the fast transfer method, the control quantity approximate value in the target maneuvering process is obtained by directly solving the target flight dynamics and kinematics model, and then the target flight state is predicted, the control quantity approximate value in the target maneuvering process is directly solved from the motion model, and then the target flight state is predicted, compared with the traditional method, the prediction accuracy is greatly improved, the fast transfer method used in the application is compared with the traditional Monte Carlo targeting method, the analysis efficiency of the quantitative analysis of the uncertain parameter evolution is effectively improved, the motion state prediction method under the target large maneuvering condition based on the fast transfer method is proposed, the solving efficiency is greatly improved while the evolution precision is ensured, and the method is suitable for the control quantity calculation and prediction of the air / space target and the moving target.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of aerospace, and particularly relates to a trajectory prediction method under target large maneuvering condition based on fast transfer. BACKGROUND

[0002] With the continuous development of aerospace technology and the growing demand for tasks, the state parameter estimation of target aircraft under large maneuvering condition becomes more and more important, and its important role in influencing the trend of war is constantly verified. In the research of estimating the future target motion state parameters under large maneuvering condition by using the observation data obtained by the airborne radar, the traditional method is to use a variety of motion model matching fusion method, to match and approximate the radar observation data with the target motion model by assuming the target motion model (uniform motion, S maneuvering, etc.), and then to estimate the target by the matched motion model. However, the error of the estimation result is large under the condition of target large maneuvering. At the same time, in the process of target state estimation, the air and space target maneuvering flight can be characterized by a plurality of nonlinear equations in mathematics, and when analyzing the influence of a certain uncertain parameter on the nonlinear equation or equation group, a large number of sampling points at the nonlinear equation need to be solved. In the existing research, the traditional method is to use the Monte Carlo shooting method to realize it, and a large number of sampling point parameters are brought into the nonlinear equation for solving. However, the calculation and solving efficiency of this method is low, and it is difficult to meet the needs of the current war. Therefore, how to overcome these problems and use the observation data of the radar to estimate the future state of the target under large maneuvering condition with high precision and high efficiency has important research significance. SUMMARY

[0003] The present application aims to provide a trajectory prediction method under target large maneuvering condition based on fast transfer, to overcome the problems existing in the prior art,

[0004] To achieve the above-mentioned purpose, the present application provides the following technical scheme:

[0005] A trajectory prediction method under target large maneuvering condition based on fast transfer, comprising the following steps:

[0006] S1: establishing a target maneuvering flight kinematics model;

[0007] S2: establishing a target maneuvering dynamics model;

[0008] S3: constructing a mathematical model of fast transfer method;

[0009] S4: performing trajectory prediction of the target based on the maneuvering flight kinematics model, the maneuvering dynamics model and the mathematical model of fast transfer method.

[0010] Preferably, the method for establishing the target maneuvering flight kinematics model in S1 is specifically as follows: a north-east ground coordinate system is established based on the own aircraft and the enemy target aircraft, and a target maneuvering flight kinematics model is derived according to the geometric and angle relationship between the own aircraft and the enemy target aircraft.

[0011] Preferably, the method for calculating the position coordinates of the target relative to the ground is as follows:

[0012] The position coordinates of the target relative to the ground (N t ,E t ,D t ) are shown by the following formula:

[0013]

[0014] Wherein, N p , E p , D p are the coordinates of the own aircraft in the ground coordinate system, and α and β are the azimuth angle and the pitch angle in the geographic system respectively, and R is the relative distance between the target aircraft and the aircraft.

[0015] Preferably, the velocity of the target relative to the ground inertial coordinate system is as follows:

[0016]

[0017] Wherein, V Nt , V Et , V Dt are the velocities of the target aircraft relative to the ground in the geographic north direction, the geographic east direction and the direction of the earth's center respectively, and V Np , V Ep , V Dp are the velocities of the own aircraft relative to the ground in the geographic north direction, the geographic east direction and the direction of the earth's center respectively. are the differentials of the azimuth angle and the pitch angle in the geographic system respectively.

[0018] Preferably, the target maneuvering dynamics model in S2 is represented by the following two formulas:

[0019]

[0020]

[0021] Wherein, n x , n y and γ are the tangential overload, the normal overload and the roll angle around the velocity axis respectively, V, θ and ψ are the flight velocity, the flight path inclination angle and the heading angle of the corresponding velocity vector respectively, are the differentials of the flight velocity, the flight path inclination angle and the heading angle of the corresponding velocity vector respectively.

[0022] Preferably, the target maneuvering dynamics model is a three-degree-of-freedom dynamics model.

[0023] Preferably, the mathematical model for constructing the fast transfer method in S3 is specifically:

[0024] First, a set of state quantity parameters is obtained, a central state quantity nominal point is determined, the deviation values between the central state quantity nominal point and the remaining state points are calculated, one-step integration is performed on the central state quantity nominal value to obtain a state quantity nominal point at the next time, the deviation values are converted to obtain all the deviation values at the next time, and the deviations are substituted into the state quantity at the next time to obtain all the state quantity parameter sets at the next time, thereby completing the modeling of the fast transfer method.

[0025] Preferably, the method for converting the deviation values to obtain all the deviation values at the next time is Taylor polynomial expansion.

[0026] Preferably, S4 is specifically implemented as follows:

[0027] Based on four continuous time points, the motion states of the target at the four time points are obtained, first, the onboard radar of the aircraft captures the position and speed of the target aircraft from the first time point to the second time point, the position and speed of the target aircraft in the ground coordinate system are calculated based on the target maneuvering flight kinematics model, the control quantity at the first time point is calculated based on the target maneuvering dynamics model, the target motion state at the third time point is obtained based on the fast transfer method, the control quantity at the second time point is determined based on the target motion state at the third time point, and the state information of the target at the fourth time point is obtained based on the target motion state at the third time point and the control quantity at the second time point, thereby completing the maneuvering prediction of the target.

[0028] Preferably, the control quantity calculation method at the first time point is:

[0029]

[0030]

[0031] wherein V, θ and ψ are the flight speed, the flight path inclination angle and the heading angle of the corresponding speed vector of the aircraft, respectively corresponding to the differential of the flight speed, the flight path inclination angle and the heading angle of the corresponding speed vector, n x , n y and γ are the control quantity parameters at the first time point.

[0032] Compared with the prior art, the present application has the following beneficial effects: the present application provides a trajectory prediction method under target large maneuvering condition based on fast transfer, based on the fast transfer method, the control quantity approximation in the target maneuvering process is directly solved by approximating the target flight dynamics and kinematics model, and the target flight state is predicted, the present application directly solves the control quantity approximation in the target maneuvering process from the motion model, and then predicts the target flight state, compared with the traditional method, the prediction accuracy is greatly improved, the fast transfer method used in the present application, compared with the traditional Monte Carlo targeting method, the analysis efficiency of the evolution of uncertain parameters is significantly improved, the motion state prediction method under the target large maneuvering condition based on fast transfer proposed in the present application not only ensures the evolution accuracy, but also greatly improves the solving efficiency, and is also suitable for the control quantity calculation and prediction of air / space target (aircraft, missile, spacecraft) motion target. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 It is a schematic diagram of ground coordinate system and fighter coordinate system;

[0034] Figure 2 It is a quick evolution algorithm idea diagram of uncertain parameters;

[0035] Figure 3 It is a maneuvering trajectory prediction flowchart;

[0036] Figure 4 It is a maneuvering trajectory and data point and corresponding control quantity schematic diagram. DETAILED DESCRIPTION

[0037] The present application will be further described in detail below in combination with specific embodiments, which are an explanation of the present application rather than a limitation.

[0038] A trajectory prediction method under target large maneuvering condition based on fast transfer, characterized in that it comprises the following steps:

[0039] S1: establishing a target maneuvering flight kinematics model;

[0040] S2: establishing a target maneuvering dynamics model;

[0041] S3: constructing a mathematical model of fast transfer method;

[0042] S4: performing trajectory prediction of the target based on the maneuvering flight kinematics model, the maneuvering dynamics model and the mathematical model of fast transfer method.

[0043] The method for establishing the target maneuvering flight kinematics model in S1 is specifically as follows: a north-east ground coordinate system is established based on the own aircraft and the enemy target aircraft, and a target maneuvering flight kinematics model is derived according to the geometric and angle relationship between the own aircraft and the enemy target aircraft.

[0044] The method for calculating the position coordinates of the target relative to the ground is

[0045] The position coordinates (N t ,E t ,D t ) of the target relative to the ground are shown by the following formula:

[0046]

[0047] wherein N p , E p , D p are the coordinates of the own aircraft in the ground coordinate system, and α and β are the azimuth angle and the pitch angle in the geographic system respectively, and R is the relative distance between the target aircraft and the aircraft.

[0048] The velocity of the target relative to the ground inertial coordinate system is as follows:

[0049]

[0050] wherein V Nt , V Et , V Dt are the velocities of the target aircraft relative to the ground in the geographic north direction, the geographic east direction and the direction of the earth's center respectively, and V Np , V Ep , V Dp are the velocities of the own aircraft relative to the ground in the geographic north direction, the geographic east direction and the direction of the earth's center respectively; are the differentials of the azimuth angle and the pitch angle in the geographic system respectively.

[0051] The target maneuvering dynamics model in S2 is shown by the following two formulas:

[0052]

[0053]

[0054] wherein n x , n y and γ are the tangential overload, the normal overload and the roll angle around the velocity axis respectively, V, θ and ψ are the flight velocity, the flight path inclination angle and the heading angle of the corresponding velocity vector respectively, are the differentials of the flight velocity, the flight path inclination angle and the heading angle of the corresponding velocity vector respectively.

[0055] The target maneuvering dynamics model is a three-degree-of-freedom dynamics model.

[0056] The mathematical model for constructing the fast transfer method in S3 is specifically:

[0057] First, a set of state quantity parameters is obtained, a central state quantity nominal point is determined, the deviation values between the central state quantity nominal point and the remaining state points are calculated, one-step integration is performed on the central state quantity nominal value to obtain a state quantity nominal point at the next time, the deviation values are converted to obtain all the deviation values at the next time, and the deviation values are substituted into the state quantity at the next time to obtain all the state quantity parameter sets at the next time, thereby completing the modeling of the fast transfer method. The method for converting the deviation values to obtain all the deviation values at the next time is a Taylor polynomial expansion method.

[0058] S4 specifically implements the following steps:

[0059] Based on four continuous time points, the motion states of the target at the four time points are obtained. First, the onboard radar of the aircraft captures the position and speed of the target aircraft from the first time point to the second time point, the position and speed of the target aircraft in the ground coordinate system are calculated based on the target maneuvering flight kinematics model, the control quantity at the first time point is calculated based on the target maneuvering dynamics model, the target motion state at the third time point is obtained based on the fast transfer method, the control quantity at the second time point is determined based on the target motion state at the third time point, and the state information of the target at the fourth time point is obtained based on the target motion state at the third time point and the control quantity at the second time point, thereby completing the maneuvering prediction of the target. The control quantity calculation method at the first time point is as follows:

[0060]

[0061]

[0062] V, θ and ψ respectively represent the flight speed, the flight path inclination angle and the heading angle of the corresponding speed vector of the target aircraft, respectively representing the differentials of the flight speed, the flight path inclination angle and the heading angle of the corresponding speed vector, x y and γ are the control quantity parameters at the first time point.

[0063] Embodiment:

[0064] A target trajectory prediction method under a large target maneuvering condition based on a fast transfer method:

[0065] Step 1: Establish a target maneuvering flight kinematics model;

[0066] Step 2: Establish a target maneuvering dynamics model;

[0067] ​Step 3: Constructing the mathematical model of fast transfer method;

[0068] Step 4: Target maneuver estimation based on the maneuver kinematics model, the maneuver dynamics model and the mathematical model of fast transfer method.

[0069] In step 1, the coordinate system of the aircraft on the ground and the fighter is the North-East-Down coordinate system. Figure 1 The North-East-Down coordinate system is the coordinate system of the aircraft on the ground and the fighter.

[0070] From the geometric relationship, the position coordinates (N t ,E t ,D t ) of the target fighter relative to the ground can be obtained by the following formula:

[0071]

[0072] In the formula, α and β are the azimuth angle and the pitch angle in the geographic system, respectively. R is the relative distance between the target aircraft and the carrier aircraft, which is given by the radar data.

[0073] The velocity of the target relative to the ground inertial coordinate system can be obtained by differentiating both sides of formula (1) as follows:

[0074]

[0075] First, the radar data is processed to obtain the position of our fighter, the relative radial distance and velocity of the enemy fighter relative to our fighter, and the relative azimuth angle and pitch angle in the geographic system of our fighter relative to the enemy fighter. The position and velocity of the enemy fighter relative to the ground coordinate system can be obtained by formula (2).

[0076] In step 2, in the ground inertial coordinate system, the model of the fighter is a three-degree-of-freedom dynamics / kinematics model, which can be represented by the following two formulas:

[0077]

[0078]

[0079] In the formula, V represents the target flight speed.

[0080] In step 3, the thought diagram of the fast evolution algorithm of uncertain parameters (fast transfer) is shown in the figure. Figure 2 Assume that the nominal sampling of a certain uncertain parameter is and the parameters of the remaining N associated sampling points are Assume that the state vector increment of the N associated sampling points is i.e. The state deviation set of the evolution of the N uncertain parameters can be represented as Since the nominal state parameter x0 has been obtained from the evolution of the uncertain parameters, and the state deviation Δx0 of each uncertain parameter evolution has also been obtained, each point used in the range of uncertain parameters can be described as an associated individual x related to the nominal state x0. i Then any sampling point within the range of this uncertain parameter can be described as:

[0081]

[0082] In the formula, the symbol [·] indicates that the variable within the square brackets has a polynomial form.

[0083] Furthermore, a Taylor expansion is performed on the performance evaluation evolution function near the nominal point x0; and a Runge-Kutta integrator in polynomial form is used to map the initial polynomial state to the orbital state at a specific moment, obtaining a polynomial solution [x] with the initial state deviation Δx0 as the variable. f That is, an approximate solution to solution (1):

[0084]

[0085] In the formula, j = j1 + ... + j6 is the order of each term in the polynomial approximation solution, d represents the index value of the state vector, and x f =Φ(t) f ;t0,x0) means that at t f The time corresponds to the state of the uncertain point x0, [x f ] represents the solution of the polynomial. The corresponding Taylor expansion coefficients are given directly by the polynomial calculation tool.

[0086] Then, substitute the sets of states of other associated sampling points into the polynomial solution (6). It is possible to obtain the i-th sampling point at t f The set of approximate numerical solutions of the state at time t. Within the framework of polynomial algebra, the traditional Runge-Kutta numerical integration method can be easily generalized to its polynomial form, that is, all nonlinear solutions are transformed into polynomial operations.

[0087] In step 4, attached Figure 3 This is a flowchart for predicting maneuver trajectories. (Attached) Figure 4 This is a schematic diagram of the maneuver trajectory, data points, and corresponding control variables. (Based on the attached diagram...) Figure 4 It can be seen that there are four time points, and the fighter jet corresponds to four state variables X at times t1-t4 respectively. t1 ,X t2 ,X t3 ,X t4 The state quantity corresponds to the fighter jet's position and velocity, i.e., X. ti =[P i Vi ]。

[0088] Firstly, the radar can capture the position, speed and other state quantities of the fighter at t1-t2, at this time, the following two equations based on equation (3), equation (4) are used to calculate the control quantity u1 at t1. x1 ,n y1 ,γ1].

[0089]

[0090]

[0091] Next, the control quantity u2 at the next time is calculated, since the radar cannot detect the state quantity of the fighter at t3 at this time, the control quantity at t2 cannot be determined, so the control quantity at t2 needs to be guessed before the radar data at t3 is transmitted.

[0092] Let u2=u1+Δu=[n x2 +Δn x ,n y2 +Δn y ,γ2+Δγ]. Where Δn x ,Δn y ∈[-a,a],Δγ∈[-b,b]. Where a,b are determined according to the specific situation. And take 1000 random deviations in the interval, at this time, u1+Δu is substituted into the above two equations, and the state value of the fighter at t2 is further substituted into the above two equations, to obtain a series of guessed values of the state of the fighter at t3.

[0093] Further, the radar obtains the state information at t3, compares the guessed values with the observed values one by one, selects the guessed value with the relatively smallest error, and determines the control quantity u 2-comfirm at t2.

[0094] Since the time interval is short, the change of the control quantity of the fighter is considered to be small at this time, so it is assumed that the control quantity of the fighter at t3 is u3=u2, so u 2-comfirm and the state information of the fighter at t3 are substituted into equation (3), equation (4), and the state information of the fighter at t4 is obtained.

[0095] Although the embodiments of the present application are described above in combination with the drawings, the present application is not limited to the above specific embodiments and application fields, and the above specific embodiments are only illustrative and guiding, but not limiting. Those skilled in the art can make many forms under the guidance of the specification without departing from the scope protected by the claims of the present application, which are all included in the protection of the present application.

Claims

1. A trajectory prediction method for targets under conditions of rapid transfer and large maneuvering, characterized in that, Includes the following steps: S1: Establish a kinematic model of the target maneuvering flight; S2: Establish the target maneuver dynamics model; S3: Construct a mathematical model for the fast delivery method; S4: Target trajectory prediction based on mathematical models of maneuvering flight kinematics, maneuvering dynamics, and rapid transfer methods; The method for establishing the target maneuvering flight kinematic model in S1 is characterized by: constructing a corresponding northeast-northeast coordinate system based on our carrier aircraft and the enemy target aircraft, and deriving the target maneuvering flight kinematic model based on the geometric and angular relationship between our carrier aircraft and the enemy target aircraft. The method for calculating the target's position coordinates relative to the ground is as follows: Target position coordinates relative to the ground As shown in the following formula: （1） in, N p , E p , D p These are the coordinates of our aircraft in the ground coordinate system. These are the azimuth and elevation angles of the geographic system, respectively. This refers to the relative distance between the target aircraft and the carrier aircraft. The target's velocity relative to the ground inertial coordinate system is as follows: （2） in V Nt , V Et , V Dt The target aircraft's velocity relative to the ground in its ground inertial coordinate system is oriented north, east, and at the geocentric direction. V Np , V Ep , V Dp The velocity relative to the ground in the geographic north, geographic east, and geocentric direction of our aircraft's ground inertial coordinate system; These are the differentials of the azimuth angle and the elevation angle of the geographic system, respectively. The target maneuver dynamics model in S2 is represented by the following two equations: （3） （4） In the formula, , γ and γ represent the tangential overload, normal overload, and roll angle about the velocity axis, respectively; , and These are the fighter jet's flight speed, track inclination angle, and the heading angle corresponding to the velocity vector. These correspond to the derivatives of flight speed, track inclination angle, and the heading angle of the corresponding velocity vector, respectively. The target maneuver dynamics model is a three-degree-of-freedom dynamics model; The mathematical model for constructing the fast transfer method in S3 is as follows: First, obtain the set of state variables parameters, determine a central state variable nominal point, calculate the deviation value between the central state variable nominal point and the other state points, then perform a one-step integration on the central state variable nominal value to obtain the state variable nominal point at the next time step, transform the deviation value to obtain all the deviation values ​​at the next time step, and then substitute the deviations into the state variables at the next time step to obtain all the state variable parameter sets at the next time step, thus completing the relevant modeling of the fast transfer method.

2. The trajectory prediction method for a target under high-speed maneuvering conditions based on rapid transmission according to claim 1, characterized in that, The method used to transform the deviation values ​​to obtain all deviation values ​​for the next time step is the Taylor polynomial expansion method.

3. The trajectory prediction method for a target under high-speed maneuvering conditions based on rapid transmission according to claim 1, characterized in that, The specific implementation steps of S4 are as follows: Based on four consecutive time points, the target's motion state at each of the four moments is acquired. First, the airborne radar of our carrier aircraft acquires the position and velocity of the fighter jet from the first time point to the second time point. Based on the target maneuvering flight kinematics model, the position and velocity of the target fighter jet in the ground coordinate system are calculated. Based on the target maneuvering dynamics model, the control quantity at the first time point is calculated. Then, the target's motion state at the third time point is acquired using a rapid transfer method. The control quantity at the second time point is determined based on the target's motion state at the third time point. Finally, based on the target's motion state at the third time point and the control quantity at the second time point, the target's state information at the fourth time point is obtained, thus completing the target's maneuver prediction.

4. The trajectory prediction method for a target under high-speed maneuvering conditions based on rapid transmission according to claim 3, characterized in that, The method for calculating the control quantity at the first time point is as follows: （5） （6） in , and These are the fighter jet's flight speed, track inclination angle, and the heading angle corresponding to the velocity vector. These correspond to the derivatives of flight speed, track inclination angle, and the heading angle of the corresponding velocity vector, respectively. n x , n y and γ These are the control parameters at the first time point.

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