On-line real-time characteristic parameter identification and trajectory prediction method for uncontrolled vehicle based on measured trajectory parameters

Abstract

The application discloses a method for aerodynamic parameter identification and trajectory prediction of an uncontrolled aircraft based on a section of measured trajectory parameters, which comprises the following steps: firstly, according to the nature of the measured trajectory data and the characteristics of the subsequent flight trajectory of the aircraft, a simplified motion state equation suitable for online rapid calculation of the aircraft is established, and a trajectory filtering aerodynamic parameter identification model is established by applying a unscented Kalman filtering algorithm; then, a section of the measured trajectory data is input into the above model to complete trajectory filtering and identification of the drag compliance coefficient and the lift compliance coefficient of the aircraft; finally, the filtering state value of the last point and the identified compliance coefficient are taken as initial values for subsequent flight trajectory calculation to realize the prediction of the subsequent flight trajectory. The application can realize trajectory filtering and aerodynamic parameter identification on a section of measured trajectory parameters in real time, quickly and accurately predict the subsequent flight trajectory of the aircraft, and has the characteristics of high trajectory calculation precision, small calculation amount and short calculation time.

Description

Technical Field

[0001] This invention pertains to the field of external ballistic calculation technology for uncontrolled aircraft, and in particular, to a method for online real-time characteristic parameter identification and trajectory prediction of uncontrolled aircraft based on a segment of measured ballistic parameters. Background Technology

[0002] For various uncontrolled aircraft (such as artillery shells and rockets), once a ballistic model is established, a definite trajectory can be calculated given a set of parameters (such as structural parameters, aerodynamic coefficients, and launch condition parameters), called the "theoretical trajectory." This process is called trajectory calculation. In practical engineering applications, the theoretical trajectory can be obtained before the aircraft is fired. Taking artillery shells as an example, after the projectile is launched, its actual initial velocity, aerodynamic coefficients, initial disturbance, and other parameters not only differ from the given theoretical values, but also vary between each projectile, resulting in random differences in the actual trajectory of each projectile. In this sense, the actual trajectory of each projectile can be called a "random trajectory." By using certain sensors or external measuring equipment (such as missile-borne satellite signal receivers or ballistic tracking radars), the actual trajectory of each projectile can be measured, that is, the relevant information of the random trajectory can be obtained. For a set of measured ballistic data, one or two ballistic characteristic parameters can be selected to characterize the random information of the trajectory. Ballistic filtering techniques are used to identify these characteristic parameters from the measured data, effectively obtaining the random ballistic characteristics of the projectile. By combining these characteristic parameters with trajectory calculations, the subsequent flight trajectory of the projectile can be predicted; this process is called "ballistic prediction." Clearly, ballistic prediction differs from trajectory calculation. The core of ballistic prediction lies in the identification (or extraction) of ballistic characteristic parameters. The randomness of the actual trajectory of a projectile is reflected in the differences in the ballistic characteristic parameters of each projectile.

[0003] Therefore, ballistic calculation is the process of calculating the flight trajectory of a projectile using an external ballistic model under known or predetermined conditional parameters. These conditional parameters include initial velocity, launch angle, projectile aerodynamic coefficients, projectile structural parameters, and meteorological parameters. Ballistic prediction, on the other hand, is based on ballistic calculation. It involves using ballistic filtering techniques to identify characteristic ballistic parameters and predict subsequent trajectories based on a segment of measured projectile motion information. This process often emphasizes real-time performance or requires online processing. For example, for a long-range howitzer, after firing, a segment of ballistic data on the ascent phase can be obtained using ballistic tracking radar. For projectile flight control, we need to accurately predict its actual impact point before the projectile lands (or even before entering the descent phase) using this ballistic data. Under these conditions, we can select the drag coincidence coefficient and lift coincidence coefficient from the aforementioned filtering model as ballistic characteristic parameters, that is, the equivalent of all random disturbances on the trajectory as changes in the drag coefficient. Earlier, when constructing the Kalman filter, these coincidence coefficients were treated as state variables. Their optimal estimates could be obtained using measured ballistic data, thereby correcting the original drag and lift coefficients (theoretical values). Then, ballistic calculations were performed to quickly obtain the actual impact point of the projectile. Since the actual impact point is known before the projectile's actual landing point, there is time to implement flight control, altering its trajectory to bring it closer to the target. Ballistic prediction has wide applications in modern projectiles and rockets, especially in controlled and intelligent projectiles, effectively improving accuracy, reducing dispersion, and increasing range. As mentioned above, the foundation of ballistic prediction is aerodynamic parameter identification.

[0004] Currently, the main methods for aerodynamic parameter identification are the parametric differential method (also known as the CK method) and the maximum likelihood method. These methods divide the trajectory into many small segments, treating the Mach number and aerodynamic parameters as constants in each segment. Typically, there are ten to twenty measurement data points in each segment. Aerodynamic parameters are identified by establishing and solving a set of conjugate equations, yielding the aerodynamic parameters corresponding to the Mach number in that segment. Smoothing techniques are then used to obtain a smooth curve showing the aerodynamic parameters changing with the Mach number. However, the more variables and undetermined parameters there are in the original equation set, the more the number of equations in the conjugate equation set will increase dramatically. Furthermore, the measured trajectory needs to be divided into several small segments, and after identifying the aerodynamic parameters in each segment, smoothing techniques are used to achieve data smoothing. The computational data volume is very large, and the time consumption is long. This method is suitable for data processing after firing tests but cannot meet the requirements of online, real-time, and rapid aerodynamic parameter identification for closed-loop firing correction systems.

[0005] Currently, ballistic calculations for conventional artillery shells are difficult to perform accurately and in real-time due to the existence of dispersion caused by random factors. Since conventional shells are area-effect weapons, the average ballistic effect is usually the primary concern. Therefore, their ballistic calculations are mostly based on predetermined aerodynamic ballistic parameters, calculating the theoretical baseline trajectory offline under known firing conditions. This method of offline calculation of theoretical baseline trajectories is insufficient to accurately predict the actual flight trajectory of uncontrolled aircraft based on measured ballistic parameters. Summary of the Invention

[0006] The purpose of this invention is to provide a method for online real-time characteristic parameter identification and trajectory prediction of uncontrolled aircraft based on a set of measured ballistic parameters.

[0007] The technical solution to achieve the objective of this invention is as follows: Firstly, this invention provides a method for online real-time characteristic parameter identification and trajectory prediction of an uncontrolled aircraft based on a segment of measured ballistic parameters, comprising the following steps:

[0008] Step 1: Select the aerodynamic parameters of the uncontrolled aircraft as characteristic parameters and establish a ballistic filtering aerodynamic parameter identification model. First, based on the properties of the measured ballistic data and the characteristics of the subsequent flight trajectory of the uncontrolled aircraft, a simplified five-degree-of-freedom rigid body motion state equation is established. Then, the unscented Kalman filter algorithm is applied to linearize and discretize the established simplified rigid body motion state equation, and finally, a Kalman ballistic filtering aerodynamic parameter identification model is established.

[0009] Step 2: Use the ballistic filtering aerodynamic parameter identification model established in Step 1 to filter the measured ballistic parameters of a segment, and identify the drag compliance coefficient and lift compliance coefficient of the uncontrolled aircraft to obtain the initial conditions and drag and lift compliance coefficients for calculating the subsequent flight trajectory.

[0010] Step 3: Using the initial conditions and coincidence coefficients obtained in Step 2 for trajectory calculation, predict the subsequent flight trajectory to obtain the actual flight trajectory and impact point information of the uncontrolled aircraft.

[0011] In a second aspect, the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method described in the first aspect.

[0012] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0013] Compared with the prior art, the present invention has the following significant advantages: (1) The method of the present invention applies the unscented Kalman filtering algorithm to perform ballistic filtering on a section of measured ballistic data, thereby reducing the noise of the measurement data; the method fully considers the theoretical dynamic model of the physical system, uses the theoretical model for prediction, and then uses the measurement results for correction, thereby improving the accuracy of the state value; it overcomes the shortcomings of traditional data smoothing methods and least squares methods, which do not consider the characteristics of the physical system itself and the data test error, but only perform pure digital processing. (2) The method of the present invention applies the established unscented Kalman ballistic filtering aerodynamic parameter identification model, which can identify and process the actual drag compliance coefficient and lift compliance coefficient of the uncontrolled aircraft in flight that are affected by various factors based on the measured section of flight ballistic parameters, thereby accurately predicting the subsequent actual flight trajectory of the uncontrolled aircraft; the algorithm is simple to process and has a fast calculation speed, avoiding the large number of conjugate equations established by the parameter differentiation method and the maximum likelihood method, and the need to process in segments first, and then smooth the identified parameters, etc., which are complex in processing and have a large number of equations to solve, and are not suitable for the requirements of online real-time fast processing. (3) The simplified five-degree-of-freedom motion state equations of the uncontrolled aircraft established by the method of the present invention fully consider the influence of the gyro effect on the lateral motion of the uncontrolled aircraft, and use the identified actual drag coincidence coefficient and lift coincidence coefficient for ballistic calculation, resulting in high accuracy of the calculated ballistic landing point; in addition, the ballistic calculation can take a large step size (e.g., 50 milliseconds), and the ballistic calculation time is very short (it can be completed within tens of milliseconds under the current computer hardware environment), which is very suitable for online real-time fast and accurate ballistic calculation; it overcomes the fact that the six-degree-of-freedom ballistic model and the mass ballistic model in current ballistics are suitable for calculating their theoretical reference ballistics offline under known firing conditions based on determined aerodynamic ballistic parameters, but it is difficult to perform accurate ballistic calculations for any actual uncontrolled aircraft flying in the air; and the six-degree-of-freedom ballistic model requires a very small calculation step size (about a few milliseconds), a large amount of calculation, and too long a calculation time, which is not suitable for the requirement of online real-time fast ballistic calculation; it also overcomes the fact that the simple mass ballistic model does not consider the influence of the gyro effect on the lateral motion of the uncontrolled aircraft, and although the ballistic calculation is fast, the calculation accuracy is poor.

[0014] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0015] Figure 1 This is a flowchart of the aerodynamic parameter identification and trajectory prediction method based on a measured ballistic parameter of the present invention.

[0016] Figure 2 It is a graph showing the change of the measured horizontal distance and its filtered value over time.

[0017] Figure 3 It is a graph showing the change of the measured value of the input ballistic height and its filtered value over time.

[0018] Figure 4 It is a graph showing the change of the input side deviation measured value and its filter value over time.

[0019] Figure 5 It is a graph showing the change of the measured horizontal velocity value and its filtered value over time.

[0020] Figure 6 It is a graph showing the change of the measured vertical velocity and its filter value over time.

[0021] Figure 7 It is a graph showing the change of the measured input lateral velocity and its filtered value over time.

[0022] Figure 8 It is a graph showing the changes in the drag and lift coefficients over time.

[0023] Figure 9 It is a graph showing the predicted trajectory changes of an uncontrolled aircraft during its subsequent flight.

[0024] Figure 10 It is a curve showing the predicted trajectory deviation of the uncontrolled aircraft during its subsequent flight.

[0025] Figure 11 It is a curve showing the predicted trajectory and velocity changes of an uncontrolled aircraft. Detailed Implementation

[0026] Combination Figure 1 The present invention provides an online real-time aerodynamic parameter identification and trajectory prediction method based on a segment of measured ballistic parameters, the steps of which are as follows:

[0027] The first step is to analyze a section of ballistic data obtained from actual measurements. Based on the characteristics of subsequent flight trajectories and the state equations describing the flight of uncontrolled aircraft in external ballistics, a simplified motion state equation adapted for online rapid calculation of uncontrolled aircraft is established. An unscented Kalman filter algorithm is applied to establish an unscented Kalman ballistic filter aerodynamic parameter identification model.

[0028] (1) Taking into full account the influence of the gyro effect on the lateral motion of the uncontrolled aircraft, and considering the correction of the trajectory by the actual drag coefficient and lift coefficient, a simplified five-degree-of-freedom motion state equation for the uncontrolled aircraft under non-standard conditions was established, as shown in equations (1) to (12).

[0029]

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041] The auxiliary equations and expressions for force and torque are as follows:

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055] δ r =arccos(v r ξ / v r )

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063]

[0064] w x = -wcos(α) W -α N )

[0065] w z = -wsin(α) W -α N )

[0066]

[0067] g0 = 9.78034 × (1 + 5.28001 × 10) -3 ·sin 2 Λ1)

[0068] c x =c x0 (1+k·δ r 2 ) = c x0 +c x2 ·δ r 2 c y ≈c′ y ·δ r m z ≈m′ z ·δ r

[0069]

[0070] In the formula: v is the flight speed of the uncontrolled aircraft; θ a ψ2 is the velocity elevation angle (also known as the trajectory inclination angle); ψ2 is the velocity direction angle (also known as the trajectory deflection angle); ω ξ ω η ω ζ The rotational angular velocity of the uncontrolled aircraft; The vertical axis elevation angle (also known as the vertical swing angle); γ is the longitudinal axis azimuth angle (also known as the azimuth sway angle); γ is the roll angle of the uncontrolled aircraft; x, y, z are the spatial coordinates of the uncontrolled aircraft (horizontal distance, trajectory altitude, sideslip); V x V y V z t represents the three components of the uncontrolled aircraft's flight velocity (horizontal velocity, vertical velocity, and lateral velocity); t represents the flight time. M represents the three components of the resultant force acting on the uncontrolled aircraft in the ballistic coordinate system; ξ M η M ζ Let δa be the three components of the resultant torque acting on the uncontrolled aircraft in the missile axis coordinate system; m be the mass of the uncontrolled aircraft; A be the equatorial moment of inertia; C be the polar moment of inertia; δ2 be the directional angle of attack; δ1 be the elevation angle of attack; b be the azimuth angle of attack. cx b is the resistance compliance coefficient; cy η is the lift coefficient; d is the maximum cross-sectional diameter of the uncontrolled aircraft; l is the length of the uncontrolled aircraft; η is the rifling twist; S is the maximum cross-sectional area of ​​the uncontrolled aircraft; g is the acceleration due to gravity; ρ is the air density; w x For wind, w z For crosswinds; c x ,c y ,c z These are the drag coefficient, lift coefficient, and lateral force coefficient of an uncontrolled aircraft, respectively; m z ,m′ zz ,m′ y ,m′ xz These are the derivatives of the static moment coefficient, pitch damping moment coefficient, Magnus moment coefficient, and roll damping moment coefficient of the uncontrolled aircraft, respectively; Ω E Λ is the Earth's rotational angular velocity; R is the local latitude; E h0 represents the average radius of the Earth; h0 represents altitude.

[0071] (2) Establish the filtered state equation, and take the state variables of the uncontrolled aircraft as:

[0072]

[0073] The simplified rigid body ballistic model is rewritten in state-space form, for

[0074]

[0075] In the formula:

[0076]

[0077] f5=v cos2sinθa f6 = v sinψ2,

[0078]

[0079] f 11 =0,f 12 =0

[0080] (3) Establish the filter measurement equation

[0081] For uncontrolled aircraft, the measurable ballistic parameters are:

[0082] Z = [v x v y v z xy zωξ] T (15)

[0083] Since the directly measured data are the three components of position and velocity of the uncontrolled aircraft, while the filtered model uses the ballistic tilt angle θ... a And the ballistic deflection angle ψ2. Therefore, the measurement equation of the ballistic filtering system can be expressed as:

[0084]

[0085] In the formula: n is the measurement noise.

[0086] Since the state variables X is a 12×1 matrix, Z is a 7×1 matrix, and n is a 7×1 matrix.

[0087] The variance matrix of the measurement noise n is

[0088]

[0089] In the formula: the symbol σ represents the standard deviation.

[0090] (4) Establishing an unscented Kalman filter discrete-time nonlinear system

[0091] Given a discrete-time nonlinear system with n state variables, denoted as

[0092] X k+1 =f(X) k ,u k ,t k )+w k (18) In the formula: w k ~(0,Q k ), representing the variance of the process noise, u k This represents the control vector.

[0093] The system measurement equation can be written as:

[0094] y k =h(X) k ,t k )+v k (19)

[0095] In the formula: v k ~(0,R k ), representing the variance of the measurement noise.

[0096] (5) Initialization of the filtering system

[0097] Initial values ​​for optimal estimation of given state variables

[0098]

[0099] The initial values ​​for the optimal estimate of the covariance of the state variables are given.

[0100]

[0101] (6) Calculation of state variables and covariance of the filtering system

[0102] The following steps can be used to propagate the estimates and covariance of state variables from one measurement point (point k-1) to the next measurement point (point k).

[0103] (a) In order to propagate from step (k-1) to step k, the optimal estimate at step (k-1) is used. Covariance Construct point σ, for

[0104]

[0105] In the formula: n is the number of state variables.

[0106] (b) By transforming the σ point using the known nonlinear function f(·) (i.e., the reduced-order rigid body ballistic system), we can obtain...

[0107]

[0108] In other words, As an initial value, the reduced-order rigid body ballistic equations are integrated, with an integration step size of Δt = t. k -t k-1 σ point is obtained Change value

[0109] (c) Using the unscented transformation, the predicted value of the optimal estimate of the state variables at time k is obtained.

[0110]

[0111] (d) Similarly, the predicted value of the covariance at time k is obtained using the unscented transform.

[0112]

[0113] (7) Updating the measurement equations of the filtering system

[0114] (a) Constructing the σ point using the latest optimal estimates of the state variables, we have

[0115]

[0116] (b) By performing a nonlinear transformation on the σ point using the measurement equation, we can obtain...

[0117]

[0118] (c) Find the approximate mean of the measured quantity

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[0120] (d) Find the approximate covariance of the measured quantity

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[0122] (e) Estimate the cross-covariance between the state variables and the measured quantities.

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[0124] (f) Kalman gain and basic recursive formula

[0125]

[0126] The second step involves inputting a segment of measured ballistic data into the unscented Kalman ballistic filter aerodynamic parameter identification model established in the first step, and then performing ballistic filtering and identifying the drag and lift coefficients.

[0127] Step 2-1: Apply equations (18) and (19) to establish a nonlinear filtering system;

[0128] Step 2-2: Initialize the state variables and covariance matrix elements using equations (20) and (21);

[0129] Steps 2-3, using equations (22) to (25), propagate the estimated values ​​and covariance of the state variables from one measurement point (the (k-1)th point) to the next measurement point (the kth point);

[0130] Steps 2-4: Apply equations (26) to (31) to update the measurement equations and obtain the optimal estimates of each state variable.

[0131]

[0132] That is, the resistance coefficient was identified. and lift coefficient

[0133] The third step is to filter the last bit of ballistic value. The coefficient of resistance to identification Coefficient of Lift As the initial condition for subsequent flight trajectory calculation, the simplified motion state equations (1) to (12) of the uncontrolled aircraft are applied to predict the subsequent flight trajectory, and the result is obtained for any point t on the subsequent flight trajectory of the uncontrolled aircraft. j ballistic information at the location and the coordinates of the landing point of the uncontrolled aircraft (X C Z C ).

[0134] The present invention will be further described in detail below with reference to embodiments:

[0135] Example

[0136] The online real-time aerodynamic parameter identification and trajectory prediction method based on a set of measured ballistic parameters includes the following:

[0137] 1. Input a set of measured ballistic parameters

[0138] Taking a segment of ballistic data (20140114-01) of an uncontrolled aircraft measured by a GPS satellite positioning device on January 14, 2014, as an example, parameters for 6 seconds (measurement interval of 100 milliseconds) between 12 and 18 seconds are taken, specifically including the horizontal distance x. k Ballistic high k Lateral deviation z k Horizontal speed Vertical speed and lateral velocity As time changes, respectively as Figure 2-7 The solid black line in the figure represents the measured ballistic parameters, which include measurement error noise from the GPS satellite positioning device. Figure 4 , Figure 7 As can be seen from the first graph, there are obvious oscillations in the data due to measurement error noise. In the other graphs, the oscillations are not as obvious because the values ​​are larger and the measurement error noise is relatively smaller.

[0139] 2. Calculation and identification of measured ballistic parameters, drag and lift coefficients.

[0140] According to the second step of the specific implementation method, the measured ballistic parameters are filtered using the input 6-second measurement data, and parameter identification is performed to obtain the drag compliance coefficient and lift compliance coefficient that integrate various influences on the ballistic trajectory.

[0141] Figure 2-7 The dashed lines in the diagram represent the filtered values ​​of the input parameters, which are the horizontal distances. ballistic high Lateral deviation Horizontal speed Vertical speed and lateral velocity Changes over time. Figure 2-7 As can be clearly seen from the dotted line, this method performs ballistic filtering on a segment of measured ballistic data, reducing the noise in the measurement data. Furthermore, the filtered value fully considers the theoretical dynamic model of the physical system, uses the theoretical model for prediction, and then uses the measurement results for correction, thereby improving the accuracy of the state value.

[0142] Figure 8 The graphs show the variation of the identified drag and lift coefficients over time. It can be seen that after a period of dynamic adjustment between the measured ballistic parameters and the theoretical estimates, the identified drag and lift coefficients gradually converge and tend towards a certain constant value.

[0143] 3. Obtain initial ballistic values ​​for subsequent flight trajectory calculations.

[0144] The ballistic filtering value, drag compliance coefficient, and lift compliance coefficient at the last point in the ballistic filtering and aerodynamic parameter identification process are used as the initial values ​​for subsequent flight trajectory calculations.

[0145] Figures 2-8 The ballistic filter value, drag compliance factor, and lift compliance factor at 18 seconds are as follows: Horizontal range filter value The value is 3722.9m, and the ballistic high-filter value is [missing information]. 2004.1m, side-biased filter value -30.0m, horizontal velocity filter value The vertical velocity filter value is 190.3m. The lateral velocity filter value is 16.2m. -0.1m, resistance compliance factor The coefficient of performance is 0.9389 and the lift factor is consistent with the performance factor. It is 1.0011.

[0146] 4. Prediction of subsequent flight trajectory and impact coordinates of uncontrolled aircraft

[0147] Using the simplified motion state equations of the uncontrolled aircraft and the initial values ​​for the above trajectory calculations, the fourth-order Runge-Kutta method is employed for numerical calculations to predict the subsequent flight trajectory and obtain the landing point coordinates of the uncontrolled aircraft.

[0148] Figures 9-11 The dashed line represents the predicted trajectory, drift, and velocity curves of the uncontrolled aircraft's subsequent flight path. The landing coordinates (X, X) of the uncontrolled aircraft are calculated. C Z C The measured coordinates of the uncontrolled aircraft's landing point are (7658.6m, 10.7m), while the actual measured coordinates are (7670.3m, 9.1m). This indicates that the method for predicting the subsequent actual flight trajectory based on a segment of the uncontrolled aircraft's measured flight trajectory parameters has high calculation accuracy and can meet engineering application requirements.

Claims

1. A method for identifying characteristic parameters and predicting the trajectory of an uncontrolled aircraft based on a segment of measured ballistic parameters, characterized in that, Includes the following steps: Step 1: Select the aerodynamic parameters of the uncontrolled aircraft as characteristic parameters and establish a ballistic filtering aerodynamic parameter identification model. First, based on the properties of the measured ballistic data and the characteristics of the subsequent flight trajectory of the uncontrolled aircraft, a simplified five-degree-of-freedom rigid body motion state equation is established. Then, the unscented Kalman filter algorithm is applied to linearize and discretize the established simplified rigid body motion state equation, and finally, a Kalman ballistic filtering aerodynamic parameter identification model is established. The specific steps for establishing the ballistic filtering aerodynamic parameter identification model are as follows: Step 1-1: Taking the uncontrolled aircraft as the object, establish a simplified five-degree-of-freedom rigid body motion state equation, specifically: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) The auxiliary equations and expressions for force and torque are as follows: ； ； ； ； ； ； ； ； ； ； ； ； ， ， ； ； ； ； ； ； ； ； ； ； ； ； ； ； ， ， ； ， ； In the formula: The flight speed of an uncontrolled aircraft; For the velocity elevation angle; The velocity direction angle; , , The rotational angular velocity of the uncontrolled aircraft; The vertical axis represents the elevation angle; The vertical axis direction angle; For uncontrolled aircraft, this refers to the roll angle. , , The spatial coordinates of the uncontrolled aircraft; , , The three components of the flight speed of an uncontrolled aircraft; For flight time; , , The three components of all the resultant forces acting on the uncontrolled aircraft in the ballistic coordinate system; , , The three components of the resultant torque acting on the uncontrolled aircraft in the projectile axis coordinate system; The mass of an uncontrolled aircraft; The moment of inertia is the rotational inertia at the equator; The moment of inertia is the polar rotational inertia; Angle of attack for direction; For high and low angles of attack; This is the resistance compliance coefficient; This is the lift coefficient; The maximum cross-sectional diameter of the uncontrolled aircraft. For the length of uncontrolled aircraft, For rifling twist, This represents the maximum cross-sectional area of ​​an uncontrolled aircraft. It is the acceleration due to gravity; For air density, For the wind, Crosswind; These are the drag coefficient, lift coefficient, and lateral force coefficient of an uncontrolled aircraft, respectively. These are the static moment coefficient, pitch damping moment coefficient derivative, Magnus moment coefficient derivative, and roll damping moment coefficient derivative of the uncontrolled aircraft, respectively. This is the Earth's rotational angular velocity; The latitude is the local latitude. The average radius of the Earth; Because of its high altitude; Step 1-2: Establish the filtered state equation. The state variables of the uncontrolled aircraft are taken as: (13) The simplified rigid body ballistic model is rewritten in state-space form, for (14) In the formula: ， ， ， ， ， ， ， ， ， ， ， ； Steps 1-3: Establish the filter measurement equation For uncontrolled aircraft, the measurable ballistic parameters are: (15) Since the directly measured data consists of the three components of position and velocity of the uncontrolled aircraft, while the filtered model uses the ballistic tilt angle... and ballistic deflection Therefore, the measurement equation of the ballistic filtering system is expressed as follows: (16) In the formula: For measuring noise; Due to state variables For 12 1-dimensional matrix, as one 3D matrix as one 3D matrix; Measurement noise The variance matrix is (17) In the formula: symbol Indicates standard deviation; Steps 1-4: Establish the unscented Kalman filter discrete-time nonlinear system Given with A discrete-time nonlinear system with n state variables, denoted as […]. (18) In the formula: , representing the variance of process noise. Represents the control vector; The system measurement equation can be written as: (19) In the formula: , representing the variance of the measurement noise; Steps 1-5: Initialization of the filtering system Initial values ​​for optimal estimation of given state variables (20) The initial values ​​for the optimal estimate of the covariance of the state variables are given. (21) Steps 1-6: Calculation of the state variables and covariance of the filtering system The following steps can be used to propagate the estimates and covariance of state variables from one measurement point to the next. (1) In order to obtain from the first Step to spread to the first Step, using the first Optimal estimation of steps Covariance structure Point, for (22) In the formula: The number of state variables; (2) Using known nonlinear functions right By transforming the point, we can obtain (23) In other words, As initial values, the reduced-order rigid body ballistic equations are integrated, with an integration step size of exactly . ,get point Change value ; (3) Obtain the first digit using the unscented transformation. The predicted value of the optimal estimate of the state variable at time step is obtained. (24) (4) Similarly, the first step is to use the unscented transformation to obtain the result. The predicted value of the time covariance is obtained. (25) Steps 1-7: Updating the measurement equations of the filter system (1) Construct using the latest optimal estimates of state variables Point, have (26) (2) Using measurement equations to By performing a nonlinear transformation on the point, we can obtain (27) (3) Find the approximate mean of the measured quantity. (28) (4) Find the approximate covariance of the measured quantity (29) (5) Estimate the cross-covariance between the state variables and the measured quantities. (30) (6) Kalman gain and basic recurrence relation (31) Step 2: Use the ballistic filtering aerodynamic parameter identification model established in Step 1 to filter the measured ballistic parameters of a segment, and identify the drag compliance coefficient and lift compliance coefficient of the uncontrolled aircraft to obtain the initial conditions and drag and lift compliance coefficients for calculating the subsequent flight trajectory. Step 3: Using the initial conditions and coincidence coefficients obtained in Step 2 for trajectory calculation, predict the subsequent flight trajectory to obtain the actual flight trajectory and impact point information of the uncontrolled aircraft.

2. The method for identifying characteristic parameters and predicting the trajectory of an uncontrolled aircraft based on a segment of measured ballistic parameters as described in claim 1, characterized in that, The ballistic data measured in step 1 includes data corresponding to each moment. Spatial coordinates ( , , ) and three-dimensional velocity ( , , ),in = 1,2, …, n, where n is the number of measurement points.

3. The method for identifying characteristic parameters and predicting the trajectory of an uncontrolled aircraft based on a segment of measured ballistic parameters as described in claim 1, characterized in that, Step 2 involves filtering the measured ballistic parameters and identifying the drag and lift compliance coefficients. Step 2-1: Apply equations (18) and (19) to establish a nonlinear filtering system; Step 2-2: Initialize the state variables and covariance matrix elements using equations (20) and (21); Steps 2-3, using equations (22) to (25), propagate the estimated values ​​and covariance of the state variables from one measurement point to the next. Steps 2-4, using equations (26) to (31), update the measurement equations to obtain the optimal estimates of each state variable. (32) That is, the resistance coefficient was identified. and lift coefficient .

4. The method for identifying characteristic parameters and predicting the trajectory of an uncontrolled aircraft based on a segment of measured ballistic parameters as described in claim 1, characterized in that, Step 3, predicting the subsequent flight trajectory, specifically involves: The last bit of ballistic filtering value The coefficient of resistance to identification Lift compliance factor As the initial condition for subsequent flight trajectory calculation, the simplified rigid body motion state equation (1) of the uncontrolled aircraft is applied to predict the subsequent flight trajectory, and the result is obtained for any point on the subsequent flight trajectory of the uncontrolled aircraft. Ballistic information at the location ( , , , , , ) and the coordinates of the landing point of the uncontrolled aircraft ( , ).

5. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1-4.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1-4.

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