Trajectory prediction and coordinated interception method, system, equipment and medium for maneuverable targets

Abstract

The present application discloses a trajectory prediction and coordinated interception method, system, equipment and medium for maneuverable targets, relating to the field of aircraft guidance technology. The method includes establishing a control system model for the maneuverable target, obtaining a target observation trajectory sequence and filtering it to obtain a target historical trajectory sequence; fitting the coefficients in the initial target increment function model based on the target historical trajectory sequence, and obtaining a target trajectory prediction sequence based on the fitted target increment function model; using the expected intercept point as the mid-range guidance target point of each interceptor missile, using MPSP to plan the mid-range guidance trajectory that meets the attack angle constraint, and determining the mid-range guidance trajectory; delaying the time for the delayed interceptor missile to enter terminal guidance through pulse maneuvers to achieve mid-range guidance time coordination; and adjusting the line of sight angular acceleration using a line of sight angular acceleration control amount to make the hit time of each interceptor missile consistent. The present application can improve the interception accuracy of maneuverable targets.

Description

Technical Field

[0001] The present application relates to the field of aircraft guidance technology, and in particular to a trajectory prediction and collaborative interception method, system, equipment and medium for maneuverable targets. Background Art

[0002] In recent years, coordinated interception has become increasingly common in air combat defense systems. When faced with fast-flying, highly maneuverable targets, the success rate of interception using a single interceptor missile is often very low, making it highly likely that the target will penetrate defenses. Building a defense system using multiple interceptor missiles fully leverages the high degree of integration, integrated linkage, complementary strengths, and information sharing capabilities of these groups. This effectively increases the probability of interception, reduces operational costs, and enhances anti-interference capabilities, significantly enriching the limited mission modes of traditional single-interceptor missile operations. Key improvements currently include achieving saturation attacks, improving target search and identification capabilities, collaborative battlefield situational awareness, and multi-source acquisition of target information. By configuring multiple interceptor missiles for different missions, they can leverage the strategic advantages of increased numbers, enhance guidance precision, and significantly improve the accuracy of interception against highly maneuverable targets.

[0003] When developing coordinated interception strategies for highly maneuverable, high-speed targets, most papers employ a real-time interception approach. This requires the defender to make a series of critical decisions within the target's extremely short attack window to mitigate the attacker's evasive maneuvers, resulting in a very low margin for error. Furthermore, these strategies fail to consider time delays introduced by factors such as human control, hardware requirements, and guidance law design. In real-world scenarios, once the attacker's aircraft enters interception range, the defender's interception window is very short, and the time delays introduced by each link in the interception process are significant. Once factors such as decision errors and excessive delays become significant enough to compromise intercept quality, the attacker can maneuver to evade the defender's interception and successfully penetrate. Therefore, increasing the interceptor missile's interception range to extend the interception window, predicting the target's trajectory for predictive interception, and developing a coordinated interception strategy to ensure that the interception domain covers the target's reachable area are currently the primary challenges in intercepting highly maneuverable targets and represent key objectives in interception strategy development.

[0004] Accurately predicting the flight trajectory of maneuvering enemy aerial targets can provide reliable data support for battlefield operational decision-making, which is crucial for achieving air superiority. Target trajectory prediction is primarily divided into target tracking and trajectory extrapolation. Radhakrishnan first proposed a method for locating and tracking a single target using position information from a single observation platform. This method requires continuous measurement of the target's position to determine the target's state parameters. Jiang Haonan et al., based on the observability theory of linear systems, proposed necessary and sufficient conditions for target observability in different motion states. Zhao Yanli et al. established three basic motion models for target trajectory tracking: uniform velocity, uniform acceleration, and coordinated turning. In terms of trajectory prediction, Zhao Shuaibing et al. proposed a motion trajectory prediction algorithm based on a polynomial Kalman filter and applied it to ship track prediction. In the field of target trajectory prediction, Zhai Dailiang et al. used a composite function of first-order polynomials and trigonometric functions to fit the changing curves of target aerodynamic parameters, but the prediction results were unsatisfactory. Han Chunyao et al. used an autoregressive moving average model to predict target altitude, but this model is limited to one dimension and cannot be extended to three dimensions.

[0005] Compared to traditional single-missile interception, cooperative interception strategies emphasize the allocation of tasks and targets, translating an increase in the number of missiles into an improvement in interception success rate. Zhao Jianbo et al. analyzed cooperative interception strategies and studied the communication issues they present. Zhang Da et al. investigated the terminal constraints in cooperative interception guidance. However, none of these cooperative interception strategies consider the relationship between the missile interception domain and the target reachable domain, and their interception accuracy needs to be improved. Summary of the Invention

[0006] The purpose of this application is to provide a trajectory prediction and collaborative interception method, system, device and medium for maneuverable targets to solve the problem of low interception accuracy of existing maneuverable targets.

[0007] To achieve the above objectives, this application provides the following solutions:

[0008] In a first aspect, the present application provides a trajectory prediction and coordinated interception method for a maneuverable target, comprising:

[0009] Acquiring historical observation data of a maneuverable target, establishing a control system model of the maneuverable target based on the historical observation data, and obtaining a target observation trajectory sequence within a set time period based on the control system model; the control system model includes an observation equation and a state equation;

[0010] Based on the control system model, the target observation trajectory sequence is filtered using a Kalman filter algorithm to obtain a target historical trajectory sequence within a set time period;

[0011] Constructing an initial target incremental function model, fitting the coefficients in the initial target incremental function model based on the target historical trajectory sequence within a set time period to obtain a fitted target incremental function model, and obtaining a target trajectory prediction sequence based on the fitted target incremental function model;

[0012] Determining an estimated intercept point based on the target trajectory prediction sequence, using the estimated intercept point as the intermediate guidance target point for each interceptor missile, and performing intermediate guidance trajectory planning between the intermediate guidance target point of each interceptor missile and the current position of the interceptor missile to meet the attack angle constraint, thereby determining the intermediate guidance trajectory;

[0013] Based on the mid-range guidance trajectory, the time for the interceptor missile to be delayed to enter terminal guidance is delayed by pulse maneuvering to control the mid-range guidance time coordination of multiple interceptor missiles; the interceptor missile to be delayed is the interceptor missile other than the interceptor missile with the latest expected mid-range and terminal handover time;

[0014] The line-of-sight angular acceleration and the line-of-sight angular acceleration control amount of each of the interceptor missiles that enter terminal guidance in a coordinated manner are determined, and the line-of-sight angular acceleration is adjusted based on the line-of-sight angular acceleration control amount to make the hit time of each of the interceptor missiles consistent, thereby completing the coordinated interception of the maneuverable target.

[0015] In a second aspect, the present application provides a trajectory prediction and coordinated interception system for maneuverable targets, comprising:

[0016] a target observation trajectory sequence determination module, configured to obtain historical observation data of a maneuverable target, establish a control system model of the maneuverable target based on the historical observation data, and obtain a target observation trajectory sequence within a set time period based on the control system model; the control system model includes an observation equation and a state equation;

[0017] A target historical trajectory sequence determination module is used to filter the target observation trajectory sequence using a Kalman filter algorithm based on the control system model to obtain a target historical trajectory sequence within a set time period;

[0018] The target trajectory prediction sequence determination module is used to construct an initial target incremental function model, fit the coefficients in the initial target incremental function model based on the target historical trajectory sequence within a set time period, obtain the fitted target incremental function model, and obtain the target trajectory prediction sequence based on the fitted target incremental function model;

[0019] a mid-range guided missile trajectory determination module, configured to determine an estimated interception point based on the target trajectory prediction sequence, use the estimated interception point as the mid-range guided missile target point for each interceptor missile, and perform mid-range guided missile trajectory planning between the mid-range guided missile target point for each interceptor missile and the current position of the interceptor missile, satisfying the attack angle constraint, to determine the mid-range guided missile trajectory;

[0020] a mid-range guidance time coordination control module, configured to delay the time for the delayed interceptor missile to enter terminal guidance through pulse maneuvers based on the mid-range guidance trajectory, so as to control the mid-range guidance time coordination of multiple interceptor missiles; the delayed interceptor missile is the interceptor missile other than the interceptor missile with the latest expected mid-range terminal handover time;

[0021] The hit time control module is used to determine the line of sight angular acceleration and the line of sight angular acceleration control value of each interceptor missile that enters the terminal guidance in a coordinated manner, and adjust the line of sight angular acceleration based on the line of sight angular acceleration control value to make the hit time of each interceptor missile consistent and complete the coordinated interception of the maneuverable target.

[0022] In a third aspect, the present application provides a computer device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of any one of the above-mentioned methods for trajectory prediction and collaborative interception of maneuverable targets.

[0023] In a fourth aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any of the above-mentioned methods for trajectory prediction and collaborative interception of maneuverable targets.

[0024] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0025] The present application provides a trajectory prediction and coordinated interception method, system, equipment and medium for maneuverable targets. By establishing a control system model of the maneuverable target, a target trajectory observation sequence is obtained, and Kalman filtering is performed to obtain a target historical trajectory sequence. The target trajectory prediction sequence is fitted based on a target incremental function model, thereby improving the accuracy of the target trajectory prediction sequence, thereby improving the interception accuracy of the maneuverable target; the target trajectory prediction sequence is extrapolated to obtain an expected interception point, and a mid-range guidance target point is set according to the expected interception point. Based on the proportional guidance method, mid-range guidance trajectory planning that meets the attack angle constraint is performed, so that the interceptor missile has the largest possible interception range, thereby improving the interception accuracy; mid-range guidance time coordination is achieved by pulse maneuvering the delayed interceptor missile during the mid-range guidance period, and finally, terminal guidance time coordination is achieved by controlling the interceptor missile's line of sight angular acceleration at a set distance from the target, thereby making the hit times of the two interceptor missiles on the maneuverable target tend to be consistent, thereby improving the interception accuracy of the maneuverable target. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0027] Figure 1 This is a flow chart of a trajectory prediction and collaborative interception method for a maneuverable target in one embodiment of the present application;

[0028] Figure 2 Schematic diagram of the geometric relationship of the maneuverable target provided in this application in the observation coordinate system;

[0029] Figure 3 for Figure 1 A schematic diagram of a maneuverable target trajectory prediction result provided in another embodiment;

[0030] Figure 4 A schematic diagram of a maneuverable target trajectory prediction error result provided by another embodiment of the present application;

[0031] Figure 5 A schematic diagram of the change in pitch attack angle of an intercepting missile during mid-course guidance provided in one embodiment of the present application;

[0032] Figure 6 A schematic diagram of the change in the yaw attack angle of an intercepting missile during the mid-course guidance process provided by one embodiment of the present application;

[0033] Figure 7A schematic diagram showing the functional relationship between the delay time and the delay level D of an interceptor missile pulse maneuver provided in another embodiment of the present application;

[0034] Figure 8 A schematic diagram of changes in the estimated impact time of terminal guidance provided by another embodiment of the present application;

[0035] Figure 9 A schematic diagram of the change in the estimated impact time difference of terminal guidance provided by another embodiment of the present application;

[0036] Figure 10 A schematic diagram of the trajectory of a projectile in the entire interception process provided by another embodiment of the present application;

[0037] Figure 11 A schematic diagram of the functional modules of a trajectory prediction and coordinated interception system for maneuverable targets provided in another embodiment of the present application;

[0038] Figure 12 A schematic diagram of the structure of a computer device provided in one embodiment of the present application.

[0039] Reference numerals:

[0040] Target observation trajectory sequence determination module-1, target historical trajectory sequence determination module-2, target trajectory prediction sequence determination module-3, mid-range guidance trajectory determination module-4, mid-range guidance time coordination control module-5, and hit time control module-6. DETAILED DESCRIPTION

[0041] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0042] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0043] In order to meet the range requirements of the mission, the missile adopts a segmented guidance method. The overall trajectory includes the active segment, the mid-range guidance segment, and the terminal guidance segment. The quality of the mid-range and terminal guidance handover greatly affects the interception success rate.

[0044] In an exemplary embodiment, Figure 1As shown, a method for trajectory prediction and coordinated interception of maneuverable targets is provided. The method is executed by a computer device, specifically a computer device such as a terminal or a server, or a terminal and a server. In the embodiment of the present application, the method is applied to a server as an example for description, and includes the following steps S1 to S6. Among them:

[0045] Step S1, obtaining historical observation data of a maneuverable target, establishing a control system model of the maneuverable target based on the historical observation data, and obtaining a target observation trajectory sequence within a set time period based on the control system model; the control system model includes an observation equation and a state equation.

[0046] Specifically, before tracking the trajectory of a maneuverable target, a control system model for the maneuverable target must be established in the observation coordinate system. Since most aircraft maneuvers involve lateral turns, a constant acceleration turn (CA) model is chosen to model the target, and the target trajectory observation problem is considered as an approximate linear control system. Taking the x-axis as an example, the initial control system model established based on kinematic analysis is as follows:

[0047]

[0048] Where t is time, x T is the coordinate, V T is the target speed, V T,x Indicates the target speed in the x direction; a T is the target acceleration, a T,x The target acceleration in the x direction is represented by w, which is the system noise. This application uses a single radar platform for observation. The observation data include the target elevation angle α, azimuth angle β and target distance r. The geometric relationship of the target in the observation coordinate system is as follows: Figure 2 shown.

[0049] Select the position coordinate information x of the maneuverable target T ,y T ,z T As the observed value,

[0050]

[0051] Formula (2) is the observation equation of the target, where and is the actual observed target position information (i.e., target position observation value), x T 、y T and z T is the target’s true position information (i.e., the target’s true position value), and v is the observation noise. The observable quantities of the radar base station are the target’s elevation angle α, azimuth angle β, and distance information r T, calculate the target position x in the observation coordinate system based on the observation quantities α, β and R T 、y T 、z T As shown in formula (3), the observed value is and The observation noise can be expressed as the following formula (4):

[0052]

[0053]

[0054] in, and Represent the observed values ​​of target elevation, azimuth and distance information respectively; α, β and r T Represent the true values ​​of target elevation, azimuth, and distance information respectively; Δα, Δβ, and Δr T Represent the observation noise of target elevation, azimuth and distance information respectively.

[0055] Combining equations (1) and (2) to establish the target control system model, the established target control system model is as follows:

[0056]

[0057] Among them, k is the discrete time point, X T,k represents the target state at time k; F T,k-1 is the target state transfer matrix at time k-1; X T,k-1 represents the target state at time k-1; G k-1 represents the system noise distribution matrix at time k-1; w k-1 represents the k-1 system noise vector; Z k represents the target state observation at time k; H k-1 represents the k-1 moment measurement matrix; v k represents the observation noise at time k. In general, the system noise G, w and observation noise v are independent of each other, all of which are zero-mean Gaussian white noise, and the corresponding covariance matrices are Q and R respectively. In addition, w and v are independent of the initial state. T,k 、F T,k , G k-1 and Z k The details are as follows:

[0058]

[0059]

[0060] After obtaining the current trajectory of the target through radar observation, a series of coordinate points can be obtained. That is, the target observation trajectory sequence, where Observe the trajectory sequence of the target Subsequent filtering is performed to obtain historical coordinate trajectories (S1, S2, S3, ..., S n ), where S k =(x T,k ,y T,k ,z T,k ),k=1,2,...,n。

[0061] Step S2: Based on the control system model, a Kalman filter algorithm is used to filter the target observation trajectory sequence to obtain a target historical trajectory sequence within a set time period.

[0062] Specifically, after trajectory tracking begins, the initial filtering condition can be determined as follows:

[0063]

[0064] Among them, the system observation value at time k = 0 As an initial estimate The actual initial value is X T,0 , the initial estimation error is ΔX T,0|0 , P0 is its covariance matrix. Estimation is performed based on the system state at time k-1 to obtain the estimated value and its corresponding covariance G k-1 and Q k-1 They are the noise distribution matrix and noise covariance at time k-1, and the state transfer matrix F at time k-1 is used. T,k-1 , we can get the predicted state and its covariance matrix:

[0065]

[0066] in, represents the Kalman filter estimation value at time k obtained by estimating the state at time k-1; P kk-1 Represents the k-time estimation error covariance matrix obtained by estimating the state at time k-1; represents the transpose of the target state transfer matrix at time k; represents the transpose of the system noise distribution matrix at time k-1; F T,k-1 is the state transition matrix at time k-1; represents the Kalman filter observation value at time k-1 obtained based on the state observation at time k-1, P k-1|k-1 represents the k-1 moment error covariance matrix obtained based on the k-1 moment state observation; Represents the single-step estimation error. Calculate the filter update value and its error covariance matrix P k|k as follows:

[0067]

[0068] in, is the filtering error; W k represents the filter gain matrix at time k; H k is the measurement matrix at time k; is the transpose of the measurement matrix at time k; R k Represents the noise covariance matrix of the observation at time k. Repeat the above process during the target trajectory observation, and continuously iterate the gain matrix W according to the input and output values ​​of the Kalman filter. k , optimize the observation value Z k Estimated value X T,k The weight distribution between them can reduce the target trajectory tracking error and filter the noise signal generated during the observation process. Repeat step S2 to observe the target sequence in the three directions of x, y, and z. Perform filtering, and the filtering results (S1, S2, S3, ..., S n ) can be used as the target historical trajectory sequence for subsequent trajectory extrapolation.

[0069] Step S3: construct an initial target incremental function model, fit the coefficients in the initial target incremental function model based on the target historical trajectory sequence within a set time period, obtain the fitted target incremental function model, and obtain the target trajectory prediction sequence based on the fitted target incremental function model.

[0070] As an optional implementation, in step S3, an initial target incremental function model is constructed, and the coefficients of the initial target incremental function model are fitted based on the target historical trajectory sequence within the set time period to obtain the fitted target incremental function model, specifically including:

[0071] Step S31, obtaining the first target historical trajectory data in the target historical trajectory sequence within a set time period, and performing a differential operation on the target historical trajectory sequence within the set time period and the first target historical trajectory data to obtain an incremental data sequence; Step S32, fitting the incremental data sequence with a polynomial function to obtain the initial target incremental function model; Step S33, fitting the polynomial function coefficients and transcendental function parameters in the initial target incremental function model using the least squares method; Step S34, iteratively optimizing the fitted polynomial function coefficients and transcendental function parameters using the gradient descent method and the LM algorithm to obtain optimized polynomial function coefficients and optimized transcendental function parameters; Step S35, determining the fitted target incremental function model based on the optimized polynomial function coefficients and optimized transcendental function parameters.

[0072] Specifically, it is assumed that the target historical trajectory data sequence (S1, S2, S3, ..., S k ), where S i =(x T,i ,y T,i ,z T,i ), i=1,2,3,...,k represents a series of coordinate points in the current trajectory of the target, and the timestamps corresponding to the flight trajectory data sequence are (t1, t2,..., t k First, the target historical trajectory sequence is preprocessed, and the data in the acquired target historical trajectory data sequence is differentially calculated with the first target historical trajectory data in the sequence to obtain an incremental data sequence (0, S 2|1 ,S 3|1 ,...,S k|1 ), where S k|1 is the difference between the kth coordinate point and the initial point; then use the incremental function f x (t), f y (t) and f z (t) Fit the incremental data sequence to extrapolate the incremental data sequence at the future moment (S n+1|1 ,S n+2|1 ,S n+3|1 ,...), then perform the sum operation on the incremental data sequence and the first target historical data in the intercepted target historical trajectory sequence to restore the target trajectory sequence and obtain the predicted future target trajectory sequence The trajectory prediction is completed.

[0073] A polynomial function is used to fit the time series data of each axial position, and the initial target increment function model for target trajectory extrapolation is defined as follows:

[0074]

[0075] Among them, f x (t), f y (t), f z (t) represents the target position increment function in the x-axis, y-axis and z-axis directions respectively; f x1 (t), f y1 (t), f z1 (t) represents the polynomial function in the x-axis, y-axis and z-axis directions respectively; f x2 (t), f y2 (t), f z2 (t) represents the transcendental function in the x-axis, y-axis and z-axis directions respectively; a0, a1, ..., an represent the polynomial coefficients in the x-axis direction; a n+1 ,...,a n+q Represents the transcendental function parameters in the x-axis direction; b0, b1, ..., b n Represents the polynomial coefficient in the y-axis direction; b n+1 ,...,b n+q Represents the transcendental function parameters in the y-axis direction; c0, c1, ..., c n Represents the polynomial coefficient in the z-axis direction; c n+1 ,...,c n+q represents the transcendental function parameter in the z-axis direction; t represents time.

[0076] After obtaining the incremental data sequence based on the target trajectory observation, the parameters in the initial target incremental function model are obtained based on the least squares method, gradient descent method, and LM algorithm. The following will take the x-axis direction as an example to explain in detail:

[0077] The data increment sequence (0, x) in the x-axis direction is obtained by trajectory observation. 21 ,x 31 ,…,x k1 ), construct an n-order polynomial model as shown in the following formula (12):

[0078] f x1 (t) = a0 + a1t + a2t 2 +…+a n t n (12)

[0079] Among them, a0, a1, ..., a n are the polynomial coefficients, and then the polynomial function parameters are obtained based on the least squares fitting method, and the polynomial function is defined at the time point t i The squared residual δ at is:

[0080]

[0081] Based on the least squares method and formula (12), the equation is as follows:

[0082]

[0083] According to the known incremental data sequence (0,x 21 ,x 31 ,…,x k1 ) Construct the equation system AX a =b, where

[0084]

[0085] The least squares solution X of the equation can be obtained from equations (14) and (15): a for:

[0086] X a =(A T A) -1 A T b(16)

[0087] In order to ensure that the equations formed by formula (15) have a solution, the dimension of the incremental data sequence must be greater than the degree of the polynomial function, that is, k>n. According to formula (16), the coefficients of the polynomial function (a0, a1, ..., a n ), similarly, the transcendental function parameters (a n+1 ,…,a n+q ), and finally the fitted polynomial function and transcendental function can be obtained.

[0088] After establishing the polynomial function and transcendental function, the gradient descent method and LM algorithm are used to optimize their parameters. The parameter optimization problem is defined as follows according to formula (11):

[0089]

[0090] Among them, t i is the time as the independent variable, and the parameters to be optimized include the polynomial function coefficients (a0, a1, a2, ... a n ) and transcendental function parameters (a n+1 ,…a n+q ). According to the above Kalman filter, the historical trajectory increment sequence (0,x 2|1 ,x 3|1 ,…x k|1 ), the initial parameter a is obtained by fitting based on the least squares method. i (0), i=1,…,n+q, and then optimize the polynomial coefficients and transcendental function parameters based on the gradient descent method. According to formula (11), the function L to be optimized is constructed:

[0091]

[0092] The gradient calculation expression of the function to be optimized L is as follows:

[0093]

[0094] Construct the initial parameter matrix a 0 =[a0 (0) …a n (0) a n+1 (0) …a n+q (0) ] T Then, according to the gradient descent method and LM algorithm, the parameter matrix a is obtained (i) The update iteration formula is as follows:

[0095]

[0096] Among them, μ is the penalty factor, I is the identity matrix, and the penalty factor is updated according to the value of the intermediate variable ρ. The calculation formula of the intermediate variable ρ is as follows:

[0097]

[0098] in,

[0099] The specific formula for updating the penalty factor according to the value of ρ is as follows:

[0100]

[0101] According to previous research results, v=2 is set.

[0102] After the above steps, the incremental sequence function f for future trajectory prediction is fitted x (t), f y (t), f z (t), and then substitute the predicted timestamp to get the trajectory increment sequence of the target at the future moment (S k+1|1 ,S k+2|1 ,S k+3|1 ,...), and perform difference calculation with the initial value to finally obtain the target prediction trajectory sequence (S k+1 ,S k+2 ,S k+3 ,...).

[0103] Step S4: Based on the target trajectory prediction sequence, an estimated intercept point is determined. This estimated intercept point is used as the mid-range guidance target point for each interceptor missile. A Model Predictive Static Programming (MPSP) algorithm is used to perform mid-range guidance trajectory planning between each interceptor missile's mid-range guidance target point and the interceptor missile's current position, satisfying the angle of attack constraint. The interceptor missile's angle of attack is the velocity angle of the interceptor missile as it approaches the target.

[0104] As an optional implementation, in step S4, a model static prediction planning algorithm is used to perform intermediate-range guided missile trajectory planning between the intermediate-range guided target point of each interceptor missile and the current position of the interceptor missile, satisfying the attack angle constraint, to determine the intermediate-range guided missile trajectory, specifically including:

[0105] Step S41 , preprocessing the nonlinear control system of each interceptor missile, and determining the initial terminal output attack angle error of the interceptor missile based on the preprocessed nonlinear control system.

[0106] Step S42: obtaining an initial control quantity sequence based on the initial terminal output attack angle error of the interceptor missile.

[0107] Step S43: Input the initial control quantity sequence into the nonlinear control system of the interceptor missile to obtain the current terminal output attack angle error, and iteratively optimize the initial control quantity sequence based on the current terminal output attack angle error to obtain the optimal control quantity sequence.

[0108] In step S44, the optimal control variable sequence is used as the input of the nonlinear control system of each interceptor missile to control the terminal output angle of attack error of each interceptor missile at the mid-terminal intersection to approach zero, thereby obtaining a mid-range guided trajectory that satisfies the angle of attack constraint. A zero terminal output angle of attack error satisfies the angle of attack constraint.

[0109] Specifically, we get the target prediction trajectory sequence (S k+1 ,S k+2 ,S k+3 ,...), then select the expected intercept point S f =(x T,f ,y T,f ,z T,f ), k≤f is used as the target point of the mid-range guidance of the interceptor. In the mid-range guidance phase, the MPSP-based proportional guidance method is selected as the interceptor guidance law. f =(x T,f ,y T,f ,z T,f) to plan a guided missile trajectory that satisfies the angle of attack constraint. The normal acceleration of the interceptor missile in the yaw and pitch directions is selected as the input of the interceptor missile's nonlinear control system. The terminal output is the attack angle of the interceptor missile when it approaches the target. The trajectory planning problem with the attack angle constraint is transformed into an optimal control problem with terminal constraints. The MPSP algorithm is used to introduce a static Lagrangian operator, which converts the optimal control problem with terminal constraints into a static optimization problem. The analytical control quantity correction for the terminal error is quickly obtained. The nonlinear control system of the interceptor missile is approximately linearized and discretized:

[0110]

[0111] Among them, F M is the interceptor missile state transfer matrix; h is the observation matrix; X M,k is the state variable of the interceptor missile at time k; X M,k+1 is the interceptor missile state variable at time k+1, U is the system input control quantity; Y is the system output; k=1,2…N represents discrete points; N corresponds to the terminal output point; Y N For terminal output; set the expected terminal output to Y N * , the terminal output error expression is as follows:

[0112] ΔY N =Y N -Y N * (twenty four)

[0113] The goal of the MPSP algorithm is to use the existing terminal error output to obtain a better control quantity, and then continuously iterate to obtain the optimal solution of the control quantity, so that the terminal output error gradually decreases with the iteration of the control quantity, and the actual terminal output tends to the expected terminal output. Based on the minimum deviation theory, the terminal output Y N Performing a high-order Taylor expansion and ignoring high-order small terms yields:

[0114]

[0115] Where d represents the derivative.

[0116] The terminal output deviation can be represented by the state quantity deviation of the Nth step. At the same time, the state quantity deviation dX of the kth step (1≤k≤N) M,k Performing Taylor expansion and ignoring second-order and higher terms yields:

[0117]

[0118] That is, the k-th step state quantity deviation dX k The state deviation dX in the k-1 step can be M,k-1and the k-th step control quantity deviation dU k It can be obtained that the terminal output deviation dY N The initial state deviation dX M,k and control quantity deviation dU k It is expressed as follows:

[0119] dY N =AdX M,1 +B1dU1+B2dU2+...+B N-1 dU N-1 (27)

[0120] Among them, the initial state quantity X M,1 Is a fixed value, that is, the initial state deviation dX M,1 =0, so the above formula can be simplified to:

[0121] dY N =B1dU1+B2dU2+…B N-1 dU N-1 (28)

[0122] in,

[0123]

[0124] Among them, B k It is an intermediate variable and has no actual meaning.

[0125] At this point, the constraints on the terminal output can be transformed into constraints on the control quantity. Next, the terminal error dY N Solve the control quantity sequence U, select the minimum control deviation as the performance function, and finally transform the nonlinear problem of this control into a static optimization problem composed of equations (24) and (28) by introducing the Lagrange operator. The control quantity deviation of the kth step is obtained by the Lagrange multiplier method:

[0126] dU k =R k -1 B k T A λ -1 dY N ,k=1,2,…N-1 (30)

[0127] in, Combined with the initial value of the control quantity, the k-th step control quantity U is obtained k for:

[0128] U k =U k 0 -dU k =Uk 0 -R k -1 B k T A λ -1 dY N (31)

[0129] Since it is necessary to obtain the optimal control sequence that meets the terminal error output requirements, it is necessary to repeat the above process and iterate the solved control sequence. N Optimize the control sequence U k , after iterative optimization, the optimal control sequence U k As the system input, the interceptor terminal outputs the attack angle Y N Equal to the predetermined angle of attack The terminal attack angle output error ΔY=0, that is, a mid-course guidance trajectory that meets the attack angle constraint is obtained, which allows the interceptor missile to enter the terminal guidance stage with a predetermined posture and obtain the largest possible interception range under the overload limit.

[0130] Step S5, based on the intermediate guidance trajectory, delaying the time for the interceptor missile to be delayed to enter terminal guidance through pulse maneuvering to control the coordination of the intermediate guidance time of multiple interceptor missiles; the interceptor missile to be delayed is the interceptor missile other than the interceptor missile with the latest expected intermediate and terminal handover time.

[0131] As an optional implementation, in step S5, based on the intermediate guidance trajectory, the time for the delayed interceptor missile to enter terminal guidance is delayed by pulse maneuvering, specifically including:

[0132] A trajectory of a set distance is intercepted from the intermediate-range guided missile trajectory as a pulse maneuvering section; the pulse maneuvering section includes a constant acceleration turning stage and a proportional guidance stage; wherein the delayed interceptor missile performs a lateral constant acceleration turning flight in the constant acceleration turning stage, and the delayed interceptor missile flies according to the proportional guidance method in the proportional guidance stage, so as to delay the time when the delayed interceptor missile enters terminal guidance.

[0133] Specifically, the coordinated intercept is accomplished by two interceptors. The prerequisite for establishing a coordinated terminal guidance and encirclement interception configuration is that both interceptors enter the terminal guidance phase at approximately the same time. After completing trajectory planning based on the MPSP algorithm, the interceptors perform pulse maneuvers to delay the time for a single interceptor to enter terminal guidance, thereby achieving time coordination for the mid-range guidance of the two interceptors. Assuming the first interceptor's estimated mid-range terminal handover time is later than that of the second interceptor, the second interceptor performs pulse maneuvers to increase the mid-range guidance range, thereby increasing the time required for the mid-range guidance phase while maintaining a relatively constant speed, ultimately entering the terminal guidance phase at the same time as the first interceptor.

[0134] A section of the guided missile trajectory obtained based on the MPSP algorithm is intercepted as the pulse maneuver section. After the initial and end points of the pulse maneuver section are determined, the time it takes to pass through the flight section before the maneuver is Δt. initial The pulse maneuver phase includes the constant acceleration turning phase and the proportional guidance phase; the time delay level D is defined, and the interceptor missile begins to perform a lateral constant acceleration turn after entering the pulse maneuver phase. The constant acceleration turn duration t man Satisfy t man =D·Δt initial , so D can be used as the control quantity of the interceptor missile's pulse maneuvering degree. After the interceptor missile completes the turn, switch to the proportional guidance method, and the target is the end of the pulse maneuvering segment. Select the normal acceleration a in the horizontal plane of the interceptor missile. M,h As the control quantity, the flight control of the interceptor missile during the entire pulse maneuver phase is as follows:

[0135]

[0136] Where K is the navigation ratio of the proportional guidance method; a man is the turning acceleration of the interceptor missile during the pulse maneuver; V M is the interceptor missile speed; is the rate of change of the interceptor missile's line of sight angle. Replacing the original MPSP-planned trajectory with the interceptor missile's pulse maneuver trajectory increases the interceptor missile's flight range and delays mid-course guidance, with the degree of delay controlled by D. During mid-course guidance, the estimated time for each interceptor missile to transition between mid-course and terminal phases is predicted. Pulse maneuvers are then performed based on this estimated time, ultimately allowing both interceptors to enter terminal guidance at the same time, achieving time coordination during the mid-course guidance phase.

[0137] Step S6, determining the line-of-sight angular acceleration and the line-of-sight angular acceleration control amount of each of the interceptor missiles that enter terminal guidance in a coordinated manner, and adjusting the line-of-sight angular acceleration based on the line-of-sight angular acceleration control amount to make the hit time of each of the interceptor missiles consistent, thereby completing the coordinated interception of the maneuverable target.

[0138] Specifically, in the coordinated terminal guidance phase under the impact time constraint, after completing the mid-range missile trajectory planning and impulse maneuvering, the interceptor missile switches to the terminal guidance phase when it is sufficiently close to the target (approximately 10,000 meters). Under the impact time constraint, a coordinated encirclement guidance strategy of two missiles is adopted. During the encirclement process, the interceptor missiles approach the target from the left and right sides respectively, so that at least one interceptor missile can intercept the target at a predetermined attack angle with a small required overload. The terminal guidance phase adopts the proportional guidance method, and the missile-target attack and defense confrontation model is as follows:

[0139]

[0140] Where M represents the interceptor missile; T represents the target; x, y, z are the position coordinates; θ and ψ are the velocity angles in pitch and yaw directions respectively; q h ,q v V is the angle of sight of the interceptor missile looking at the target in pitch and yaw directions respectively; M is the interceptor missile speed; V T is the target speed; K is the navigation ratio used in proportional guidance.

[0141] The core concept of the overload-limited cooperative strategy is to maximize the interceptable coverage area of ​​the interceptor missile, which is essentially an optimization problem. The terminally guided cooperative interception strategy ultimately achieves the following goals:

[0142] (1) The common interception area of ​​the two interceptor missiles can cover the reachable area of ​​the target after maneuvering to the greatest extent.

[0143] (2) The intersection area of ​​the interception domains of two interceptor missiles should be as small as possible.

[0144] (3) At least one interceptor missile should be able to successfully intercept the target.

[0145] After building the terminal guidance cooperative interception configuration according to equation (33), the time coordination of the two interceptor missiles is achieved through the interceptor missile line of sight angle direction overload control. The three-dimensional relative kinematic equation for a single interceptor missile intercepting a maneuverable target is established as follows:

[0146]

[0147] Among them, [a M,r ,a M,y ,a M,z ] and [a T,r ,a T,y ,a T,z ] are the accelerations of the interceptor missile and the maneuverable target in the line of sight coordinate system; r is the relative distance between the interceptor missile and the target; is the relative speed between the interceptor and the target; Relative acceleration between interceptor missile and target; q v ,q h are the interceptor missile’s sight angles in pitch and yaw directions respectively. The interceptor missile’s acceleration a in the sight angle direction is used. M,r As the control variable in the time-coordinated guidance law, the remaining flight time t go It can be approximated as:

[0148]

[0149] Combining formula (34) and taking its derivative, we can get:

[0150]

[0151] Consider a situation where n interceptor missiles are coordinated to capture and intercept. At the moment of impact, the sight angle and angular velocity of each interceptor missile satisfy:

[0152]

[0153] Combining equations (33) and (35), the relative kinematic equation between the i-th interceptor missile and the target is as follows:

[0154]

[0155] in:

[0156]

[0157] Calculation can be obtained:

[0158]

[0159] in, The interceptor missile sight angle direction control quantity is defined by The design of can achieve the time coordination of interceptor missiles. When multiple interceptor missiles are guided in a coordinated manner, the hit time of a single interceptor missile is expressed as:

[0160] t f,i =t i +t go,i (41)

[0161] Among them, t i is the moment when the interceptor missile completes the mid-terminal handover, that is, the moment when the terminal guidance begins, t go,i is the estimated remaining flight time of the interceptor missile. The t i Same, then t f,i Convergence is equivalent to t go,i tend to be consistent. f,i Taking the derivative we get:

[0162]

[0163] Through The design guarantees the hit time t f,i Construct the coordinated guidance control quantity:

[0164]

[0165] in, ξ i >0( and ξ i is an intermediate coefficient and has no practical significance).

[0166] make The three-dimensional time coordinated guidance law can be obtained, that is, the interceptor missile line of sight angle direction control quantity is:

[0167]

[0168] Where i represents the i-th interceptor missile; j represents the j-th interceptor missile; a i,r Represents the interceptor missile sight angle direction control quantity; r i Indicates the relative distance between the interceptor missile and the maneuverable target; q v,i Indicates the sight angle of the interceptor missile in the pitch direction; represents the interceptor missile’s line-of-sight angular velocity in the pitch direction; q h,i Indicates the sight angle of the interceptor missile in the yaw direction; It represents the line-of-sight angular rate of the interceptor missile in the yaw direction; represents the cooperative guidance control quantity; t f,i represents the time when the i-th interceptor missile hits; t f,j represents the time when the jth interceptor missile hits; and ξ i represents the intermediate coefficient; sgn represents the sign function.

[0169] Acceleration command in the direction of sight This can make the hit times of the two interceptor missiles tend to be consistent, and ultimately the two interceptor missiles can intercept the target from the left and right sides respectively and hit the target at the same time.

[0170] Beneficial effects of this application:

[0171] 1) The target trajectory prediction sequence is fitted based on the target increment function model, which improves the accuracy of the target trajectory prediction sequence and thus improves the interception accuracy of maneuverable targets.

[0172] 2) The target trajectory prediction sequence is extrapolated to obtain the expected interception point. The mid-range guidance target point is set according to the expected interception point. The mid-range guidance trajectory is planned based on the proportional guidance method to meet the attack angle constraint, so that the interceptor missile can obtain the largest possible interception range, thereby improving the interception accuracy.

[0173] 3) Mid-range guidance time coordination is achieved by pulse maneuvering the delayed interceptor missile during the mid-range guidance period. Finally, terminal guidance time coordination is achieved by controlling the interceptor missile's line-of-sight angular acceleration at a set distance from the target. This makes the hit times of the two interceptor missiles on the maneuverable target more consistent, thereby improving the interception accuracy of the maneuverable target.

[0174] In an exemplary embodiment, a coordinated interception method for maneuverable targets is used to intercept a maneuverable target, and the following results are obtained:

[0175] 1) Obtain the trajectory prediction result of the maneuverable target as follows Figure 3 As shown, X represents the x-direction position, Y represents the y-direction position, and Z represents the z-direction position, with the unit being km. Set the time step dt = 0.01s, perform trajectory tracking for a window length of 3000, and then perform trajectory prediction for a window length of 10000. The final result is as follows Figure 3 As shown, it is observed that the trajectory prediction error meets the requirements of cooperative interception guidance.

[0176] 2) The prediction error results of maneuverable target trajectory are as follows Figure 4 As shown, the time step dt = 0.01s, the target is tracked with a window length of 3000, and then the trajectory is predicted with a window length of 10000. The final result is as follows Figure 4 As shown in the figure, the trajectory prediction accuracy reaches more than 95%, and the target trajectory prediction error meets the set requirements. The accuracy can be used for subsequent mid-range guidance trajectory planning and terminal guidance coordinated capture.

[0177] 3) Obtain the change of attack angle during the mid-range guidance process as follows Figure 5 and Figure 6 As shown in Figure 1, θ is the interceptor missile's pitch angle of attack, and ψ is its yaw angle of attack, both in degrees. t is time, in seconds. The MPSP algorithm is used to iterate the interceptor missile's guidance control variable sequence online. The resulting optimal control variable sequence can control the interceptor missile to enter the terminal guidance phase at a predetermined attack angle.

[0178] 4) The functional relationship between the interceptor missile pulse maneuver delay time and delay level D is obtained as follows: Figure 7 As shown, where D is the delay level and t is the pulse maneuver delay time, in seconds. Figure 7 It can be seen that after different degrees of interceptor missile pulse maneuvers, the mid-range guidance time difference of 0 to 11 seconds can be smoothed out.

[0179] 5) The change of the estimated hit time of terminal guidance is as follows: Figure 8 As shown by Figure 8 It can be seen that under the control of the interceptor missile's line-of-sight acceleration in the terminal guidance stage, the estimated hit times of the two interceptor missiles tend to be consistent.

[0180] 6) The schematic diagram of the change of the estimated time difference of terminal guidance is as follows: Figure 9 As shown by Figure 9 It can be seen that the vertical axis is the hit time difference, which decreases from 0.4 seconds to 0.06 seconds, almost to 0. That is, under the control of the interceptor missile's line of sight acceleration in the terminal guidance stage, the expected hit time difference between the two interceptor missiles gradually shrinks to close to 0.

[0181] 7) Obtain the interception process trajectory diagram as follows Figure 10As shown, X represents the x-axis position, Y represents the y-axis position, and Z represents the z-axis position, all in kilometers. After the two interceptors reached the intercept altitude through the active phase, they performed mid-course guidance, meeting the angle-of-attack constraint. They approached the target from the left and right sides, respectively. Under the overload limit of 8 g, they used impulse maneuvers to adjust the timing of their entry into the terminal guidance phase to achieve time coordination. After entering terminal guidance, the two interceptors used proportional guidance under the time-to-hit constraint, ultimately successfully intercepting the target. To illustrate the full trajectory, the x-axis and y-axis have significantly different dimensions, resulting in a sharper trajectory. However, if the dimensions were the same, the trajectory would appear smooth and curved.

[0182] Based on the same inventive concept, the embodiments of the present application also provide a trajectory prediction and collaborative interception system for maneuverable targets for implementing the aforementioned trajectory prediction and collaborative interception method for maneuverable targets. The implementation solution provided by this device is similar to the implementation solution described in the aforementioned method. Therefore, the specific limitations of one or more embodiments of the trajectory prediction and collaborative interception system for maneuverable targets provided below can be found in the limitations of the trajectory prediction and collaborative interception method for maneuverable targets above, and will not be repeated here.

[0183] In an exemplary embodiment, Figure 11 As shown, a trajectory prediction and coordinated interception system for maneuverable targets is provided, including: a target observation trajectory sequence determination module 1, a target historical trajectory sequence determination module 2, a target trajectory prediction sequence determination module 3, a mid-range guidance trajectory determination module 4, a mid-range guidance time coordinated control module 5 and a hit time control module 6.

[0184] The target observation trajectory sequence determination module 1 is used to obtain historical observation data of the maneuverable target, establish a control system model of the maneuverable target based on the historical observation data, and obtain the target observation trajectory sequence within a set time period based on the control system model; the control system model includes an observation equation and a state equation.

[0185] The target historical trajectory sequence determination module 2 is used to filter the target observation trajectory sequence based on the control system model using a Kalman filter algorithm to obtain the target historical trajectory sequence within a set time period.

[0186] The target trajectory prediction sequence determination module 3 is used to construct an initial target incremental function model, fit the coefficients in the initial target incremental function model based on the target historical trajectory sequence within a set time period, obtain the fitted target incremental function model, and obtain the target trajectory prediction sequence based on the fitted target incremental function model.

[0187] The mid-range guided missile trajectory determination module 4 is used to determine the expected interception point based on the target trajectory prediction sequence, and use the expected interception point as the mid-range guided target point of each interceptor missile. The model static prediction planning algorithm is used to plan the mid-range guided missile trajectory between the mid-range guided target point of each interceptor missile and the current position of the interceptor missile so as to meet the attack angle constraint and determine the mid-range guided missile trajectory.

[0188] The mid-range guidance time coordination control module 5 is used to delay the time for the delayed interceptor missile to enter terminal guidance through pulse maneuvers based on the mid-range guidance trajectory, so as to control the mid-range guidance time coordination of multiple interceptor missiles; the delayed interceptor missile is the interceptor missile other than the interceptor missile with the latest expected mid-range and terminal handover time.

[0189] The hit time control module 6 is used to determine the line of sight angular acceleration and the line of sight angular acceleration control value of each of the interceptor missiles that enter the terminal guidance in a coordinated manner, and adjust the line of sight angular acceleration based on the line of sight angular acceleration control value to make the hit time of each of the interceptor missiles consistent, thereby completing the coordinated interception of the maneuverable target.

[0190] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Figure 12 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O) and a communication interface. The processor, memory and input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a trajectory prediction and collaborative interception method for a maneuverable target is implemented.

[0191] Those skilled in the art will understand that Figure 12 The structure shown in the figure is merely a block diagram of a portion of the structure related to the solution of the present application and does not constitute a limitation on the computer device to which the solution of the present application is applied. A specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement. In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps of the above-mentioned method embodiments when executing the computer program.

[0192] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0193] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0194] Those skilled in the art will understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, database or other media used in the embodiments provided in this application may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory may include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0195] The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may include, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic units, data processing logic units based on quantum computing, and the like.

[0196] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0197] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A trajectory prediction and coordinated interception method for maneuverable targets, characterized in that: The trajectory prediction and coordinated interception method for maneuverable targets includes: Acquiring historical observation data of a maneuverable target, establishing a control system model of the maneuverable target based on the historical observation data, and obtaining a target observation trajectory sequence within a set time period based on the control system model; the control system model includes an observation equation and a state equation; Based on the control system model, the target observation trajectory sequence is filtered using a Kalman filter algorithm to obtain a target historical trajectory sequence within a set time period; Constructing an initial target incremental function model, fitting the coefficients in the initial target incremental function model based on the target historical trajectory sequence within a set time period to obtain a fitted target incremental function model, and obtaining a target trajectory prediction sequence based on the fitted target incremental function model; Determining an estimated intercept point based on the target trajectory prediction sequence, using the estimated intercept point as the intermediate guidance target point for each interceptor missile, and performing intermediate guidance trajectory planning between the intermediate guidance target point of each interceptor missile and the current position of the interceptor missile to meet the attack angle constraint, thereby determining the intermediate guidance trajectory; Based on the mid-range guidance trajectory, the time for the interceptor missile to be delayed to enter terminal guidance is delayed by pulse maneuvering to control the mid-range guidance time coordination of multiple interceptor missiles; the interceptor missile to be delayed is the interceptor missile other than the interceptor missile with the latest expected mid-range and terminal handover time; The line-of-sight angular acceleration and the line-of-sight angular acceleration control amount of each of the interceptor missiles that enter terminal guidance in a coordinated manner are determined, and the line-of-sight angular acceleration is adjusted based on the line-of-sight angular acceleration control amount to make the hit time of each of the interceptor missiles consistent, thereby completing the coordinated interception of the maneuverable target.

2. The trajectory prediction and coordinated interception method for maneuverable targets according to claim 1, characterized in that: The expression of the control system model is: Among them, X T,k represents the target state at time k; F T,k-1 is the target state transfer matrix at time k-1; X T,k-1 represents the target state at time k-1; G k-1 represents the system noise distribution matrix at time k-1; w k-1 represents the system noise vector at time k-1; Z k represents the target state observation at time k; H k-1 represents the k-1 moment measurement matrix; v k represents the observation noise at time k.

3. The trajectory prediction and coordinated interception method for maneuverable targets according to claim 1, characterized in that: Constructing an initial target incremental function model, fitting the coefficients of the initial target incremental function model based on the target historical trajectory sequence within the set time period to obtain a fitted target incremental function model, specifically including: Obtaining the first target historical trajectory data in the target historical trajectory sequence within a set time period, and performing a differential operation between the target historical trajectory sequence within the set time period and the first target historical trajectory data to obtain an incremental data sequence; Fitting the incremental data sequence using a polynomial function to obtain the initial target incremental function model; Using the least squares method to fit the polynomial function coefficients and transcendental function parameters in the initial target incremental function model; The gradient descent method and LM algorithm are used to iteratively optimize the fitted polynomial function coefficients and transcendental function parameters to obtain the optimized polynomial function coefficients and the optimized transcendental function parameters; Based on the optimized polynomial function coefficients and the optimized transcendental function parameters, the fitted target incremental function model is determined.

4. The method for trajectory prediction and coordinated interception of maneuverable targets according to claim 1, characterized in that: The expression of the initial target increment function model is: Among them, f x (t), f y (t), f z (t) represents the target position increment function in the x-axis, y-axis and z-axis directions respectively; f x1 (t), f y1 (t), f z1 (t) represents the polynomial function in the x-axis, y-axis and z-axis directions respectively; f x2 (t), f y2 (t), f z2 (t) represents the transcendental function in the x-axis, y-axis and z-axis directions respectively; a0, a1, ..., an represent the polynomial coefficients in the x-axis direction; a n+1 ,...,a n+q Represents the transcendental function parameters in the x-axis direction; b0, b1, ..., b n Represents the polynomial coefficient in the y-axis direction; b n+1 ,...,b n+q Represents the transcendental function parameters in the y-axis direction; c0, c1, ..., c n Represents the polynomial coefficient in the z-axis direction; c n+1 ,...,c n+q represents the transcendental function parameter in the z-axis direction; t represents time.

5. The method for trajectory prediction and coordinated interception of maneuverable targets according to claim 1, characterized in that: The model static prediction planning algorithm is used to plan the missile trajectory between the missile's target point and the missile's current position, satisfying the angle of attack constraint. The trajectory of the missile is determined by: pre-processing the nonlinear control system of each interceptor missile, and determining the initial terminal output attack angle error of the interceptor missile based on the pre-processed nonlinear control system; Based on the initial terminal output attack angle error of the interceptor missile, the initial control quantity sequence is obtained; Inputting the initial control quantity sequence into the nonlinear control system of the interceptor missile to obtain a current terminal output angle of attack error, and iteratively optimizing the initial control quantity sequence based on the current terminal output angle of attack error to obtain an optimal control quantity sequence; The optimal control quantity sequence is used as the input of the nonlinear control system of each interceptor missile to control the terminal output attack angle error of each interceptor missile at the mid-terminal intersection to approach zero, thereby obtaining a mid-range guided trajectory that meets the attack angle constraint.

6. The trajectory prediction and coordinated interception method for maneuverable targets according to claim 1, characterized in that: Based on the intermediate-range guided missile trajectory, the time for the delayed interceptor missile to enter terminal guidance is delayed by pulse maneuvers, specifically including: A trajectory of a set distance is intercepted from the intermediate-range guided missile trajectory as a pulse maneuvering section; the pulse maneuvering section includes a constant acceleration turning stage and a proportional guidance stage; wherein the delayed interceptor missile performs a lateral constant acceleration turning flight in the constant acceleration turning stage, and the delayed interceptor missile flies according to the proportional guidance method in the proportional guidance stage, so as to delay the time when the delayed interceptor missile enters terminal guidance.

7. The trajectory prediction and coordinated interception method for maneuverable targets according to claim 1, characterized in that: The expression of the interceptor missile line of sight angle direction control quantity is: Where i represents the i-th interceptor missile; j represents the j-th interceptor missile; a i,r Represents the interceptor missile sight angle direction control quantity; r i Indicates the relative distance between the interceptor missile and the maneuverable target; q v,i Indicates the sight angle of the interceptor missile in the pitch direction; represents the interceptor missile’s line-of-sight angular velocity in the pitch direction; q h,i Indicates the sight angle of the interceptor missile in the yaw direction; It represents the line-of-sight angular rate of the interceptor missile in the yaw direction; represents the cooperative guidance control quantity; t f,i represents the time when the i-th interceptor missile hits; t f,j represents the time when the jth interceptor missile hits; and ξ i represents the intermediate coefficient; sgn represents the sign function.

8. A trajectory prediction and coordinated interception system for maneuverable targets, characterized in that: The trajectory prediction and coordinated interception system for maneuverable targets includes: a target observation trajectory sequence determination module, configured to obtain historical observation data of a maneuverable target, establish a control system model of the maneuverable target based on the historical observation data, and obtain a target observation trajectory sequence within a set time period based on the control system model; the control system model includes an observation equation and a state equation; A target historical trajectory sequence determination module is used to filter the target observation trajectory sequence using a Kalman filter algorithm based on the control system model to obtain a target historical trajectory sequence within a set time period; The target trajectory prediction sequence determination module is used to construct an initial target incremental function model, fit the coefficients in the initial target incremental function model based on the target historical trajectory sequence within a set time period, obtain the fitted target incremental function model, and obtain the target trajectory prediction sequence based on the fitted target incremental function model; a mid-range guided missile trajectory determination module, configured to determine an estimated interception point based on the target trajectory prediction sequence, use the estimated interception point as the mid-range guided missile target point for each interceptor missile, and perform mid-range guided missile trajectory planning between the mid-range guided missile target point for each interceptor missile and the current position of the interceptor missile, satisfying the attack angle constraint, to determine the mid-range guided missile trajectory; a mid-range guidance time coordination control module, configured to delay the time for the delayed interceptor missile to enter terminal guidance through pulse maneuvers based on the mid-range guidance trajectory, so as to control the mid-range guidance time coordination of multiple interceptor missiles; the delayed interceptor missile is the interceptor missile other than the interceptor missile with the latest expected mid-range terminal handover time; The hit time control module is used to determine the line of sight angular acceleration and the line of sight angular acceleration control value of each interceptor missile that enters the terminal guidance in a coordinated manner, and adjust the line of sight angular acceleration based on the line of sight angular acceleration control value to make the hit time of each interceptor missile consistent and complete the coordinated interception of the maneuverable target.

9. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the trajectory prediction and collaborative interception method for maneuverable targets as described in any one of claims 1 to 7.

10. 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 for trajectory prediction and coordinated interception of a maneuverable target according to any one of claims 1 to 7 is implemented.

Images