A method of inverse guidance for striking a maneuvering target under information support

Abstract

The application discloses a kind of inversion guidance methods of striking mobile target under the support of prediction information, comprising the following steps: step one, establish relative guidance model;Step two, reverse design baseline guidance law;Step three, target trajectory tracking;Step four, target trajectory prediction;Step five, design time collaborative guidance law;The application combines inversion guidance strategy with relative guidance framework, designs baseline guidance law based on relative residual flight trajectory and front angle, solves theoretical closedness problem, meets terminal acceleration constraint, avoids command singularity;Interacting multiple model filtering is used to track target, polynomial regression is used to predict trajectory, dynamic adjustment prediction interval algorithm is combined, residual flight time is calculated using radar information support, and engineering applicability is improved;Collaborative bias item is introduced on the basis of baseline guidance law to form time collaborative guidance law, realizes multi-missile collaboration, fully utilizes composite seeker and data link, and effectively solves the problem of mobile target strike.

Description

Technical Field

[0001] This invention relates to the field of anti-ship missile terminal guidance law design technology, specifically to an inversion guidance method for striking maneuvering targets supported by predictive information. Background Technology

[0002] In modern military confrontation, the effective engagement of maneuvering targets is crucial. Existing techniques for engaging maneuvering targets, such as those relying on predicted impact points, assuming linear target motion, and specific switching logic, generally suffer from the following shortcomings: 1. Existing methods lack rigorous closed-loop derivation, making it difficult to construct a universally applicable guidance framework. This results in insufficient theoretical closure and an inability to adapt to complex and ever-changing target motion scenarios. In engineering practice, their adaptability to complex maneuvering scenarios is poor. Faced with high speed, high maneuverability, and variable flight trajectories, they cannot function accurately and stably, exhibiting poor engineering applicability; 2. When engaging maneuvering targets, the collision triangle condition requires the relative velocity vector to be precisely aligned with the line of sight. This is fundamentally different from the zero-control condition for engaging stationary targets. This difference undermines the guidance laws proposed by existing methods. In the process of multiple missiles coordinating to strike mobile targets, it is difficult to meet the terminal acceleration constraints. Once the terminal acceleration exceeds the reasonable range, it is very easy to trigger strange guidance commands, resulting in missile loss of control or failure to accurately hit the target, which seriously affects the strike effect. 3. Although most anti-ship missiles are now equipped with composite seekers and two-way data link systems, which can receive guidance information from radar platforms, existing technologies have not fully explored and utilized the information provided by these advanced devices, and have not effectively developed time-coordinated guidance technologies that are compatible with them. This makes it impossible to achieve precision strikes by leveraging the advantages of multiple missiles in the face of mobile targets, and it is difficult to provide a practical solution to deal with the challenges of complex battlefield environments and highly mobile targets. Summary of the Invention

[0003] The purpose of this invention is to provide an inversion guidance method for striking maneuvering targets supported by predictive information, so as to solve the problems mentioned in the background art.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a method for inverse guidance of striking maneuvering targets supported by predictive information, comprising the following steps: Step 1, establishing a relative guidance model; Step 2, designing a baseline guidance law in reverse; Step 3, tracking the target trajectory; Step 4, predicting the target trajectory; Step 5, designing a time-coordinated guidance law.

[0005] In step one above, a kinematic model of the missile and the maneuvering target in a relative frame is constructed as a relative guidance model;

[0006] In step two above, based on the relative guidance model constructed in step one, the relative residual flight trajectory is introduced, and the baseline guidance law that satisfies the terminal constraint is derived through reverse design.

[0007] In step three above, based on the target observation information acquired by radar, a target state equation is established to describe the target motion characteristics, a measurement equation is established to correlate the target state with the radar observation information, and an interactive multi-model filtering algorithm is used to track the trajectory of the maneuvering target.

[0008] In step four above, based on the target trajectory tracking data obtained in step three, a multinomial regression algorithm combined with dynamically adjusted prediction intervals is used to predict the future trajectory of the target.

[0009] In step five above, based on the target future trajectory prediction results in step four, the remaining flight time is calculated using numerical methods. A time-coordinated bias term is introduced based on the baseline guidance law designed in step two, and a time-coordinated guidance law is designed to achieve coordinated strikes of multiple missiles against maneuvering targets.

[0010] Preferably, in step one, the specific steps are: defining the relative velocity vector and the relative velocity unit vector as follows:

[0011] (1)

[0012] in, It is a relative velocity vector. It is a unit vector of relative velocity. The magnitude of the relative velocity;

[0013] relative velocity vector Differentiation yields:

[0014] (2)

[0015] in, Indicates tangential relative acceleration. This is the normal relative acceleration;

[0016] The missile-target kinematic equations can be characterized as:

[0017] (3)

[0018] (4)

[0019] (5)

[0020] in, Line of sight vector The rotational angular velocity vector, Relative velocity vector The angular velocity vectors of rotation are expressed as follows:

[0021] (6)

[0022] Define relative leading angle Relative velocity vector With line of sight vector The included angle between them, relative to the leading angle, satisfies:

[0023] (7)

[0024] in, For a unit vector, differentiating the above equation yields the relative leading angle derivative as follows:

[0025] (8)

[0026] To analyze the dynamics of the line-of-sight angle, the line-of-sight angular velocity vector is given here. The derivative is:

[0027] (9)

[0028] in, This refers to interference caused by the target's maneuver.

[0029] Preferably, in step two, specifically: let the relative remaining flight trajectory be... ,in The length of the missile's trajectory in the relative frame at the terminal moment. Let be the length of the missile's trajectory in the relative frame at the current moment. Then, the relative remaining trajectory is:

[0030] (10)

[0031] in To be relative to the front angle The relevant functions, Designed as:

[0032] (11)

[0033] in For guidance parameters, It represents the length of the missile's trajectory in a relative frame of reference, not the actual trajectory length, therefore With relative forward angle related,

[0034] remember Differentiate equation (10):

[0035] (12)

[0036] As can be seen from the definition of relative remaining flight trajectory, there is Established, among which To obtain the relative velocity magnitude, substituting this condition into equation (12) yields the relative leading angle derivative:

[0037] (13)

[0038] According to the control quantity Based on the relationship with the relative lead angle, a baseline guidance law satisfying equation (13) can be designed as follows:

[0039] (14)

[0040] in .

[0041] Preferably, in step two, the terminal constraints include zero miss distance constraint, zero terminal relative forward angle constraint, and bounded terminal acceleration constraint.

[0042] Preferably, in step three, the target state equation is established as follows:

[0043] (15)

[0044] in and state matrix Noise driving matrix The target maneuver model will be determined by the selected target maneuver model, which includes a constant velocity model, a constant acceleration model, and a current statistical model. This is system noise;

[0045] make , The relative distance to the target. For the azimuth information, the measurement equation is established as follows:

[0046] (16)

[0047] in , and These are the components of the target in the radar observation system. For measuring noise.

[0048] Preferably, in step three, the process of using the interactive multi-model filtering algorithm to track the trajectory of a maneuvering target specifically includes the following steps:

[0049] (a) Input interaction: Based on the filtering information of each sub-model at the previous time step And the model switching probability from the previous time step, respectively, calculate the state input information of the individual model at the current time step:

[0050] (17)

[0051] (18)

[0052] in and The models are respectively State estimation and state covariance matrix after data interaction For the mixture probability of the model:

[0053] (19)

[0054] in Model of the previous time step The probability, The elements of the model transition probability matrix represent the target transition from the first... The motion model is transferred to the first... The probability of a motion model;

[0055] (b) Filtering: Based on the state information of each subsystem model obtained after input interaction. Covariance Matrix By combining system measurement information with extended Kalman filtering of the subsystem models, the state estimation results of each subsystem model are finally obtained. and covariance matrix ;

[0056] (c) Model probability update: After completing the parallel filtering of the subsystem model, calculate the new model transformation probability based on the filtering residual information:

[0057] (20)

[0058] in For the model The likelihood function follows a Gaussian distribution:

[0059] (twenty one)

[0060] in The filtering residuals for each subsystem model, The variance of the residuals;

[0061] (d) Output interaction: Through the updated model probabilities Filtered estimated values ​​of each subsystem and covariance matrix The final state estimate can be obtained. and covariance matrix :

[0062] (twenty two)

[0063] (twenty three)

[0064] Preferably, in step four, the process of dynamically adjusting the prediction interval is as follows: first, an initial multinomial regression model is trained; then, the latest tracking data is obtained cyclically and the training set is updated; when the remaining flight time meets the preset conditions, the multinomial model is retrained and the future trajectory is predicted.

[0065] Preferably, in step five, the numerical method for calculating the remaining flight time specifically involves: calculating the remaining flight time based on the relative remaining flight trajectory and solving it using the Runge-Kutta algorithm.

[0066] Preferably, the formula for calculating the remaining flight time is:

[0067] (twenty four)

[0068] in For the remaining flight time, It is a relative velocity vector. For the relative remaining flight trajectory, is the integral variable relative to the remaining flight trajectory.

[0069] Preferably, in step five, designing the time-coordinated guidance law specifically involves: for missiles The cooperative guidance law for striking mobile targets is designed as follows:

[0070] (25)

[0071] in To ensure the convergence of the strike time error, the bias term, For the consistency error of remaining flight time, for:

[0072] (26)

[0073] in For constant parameters, The preset convergence time is determined by the specified convergence distance. To facilitate guidance law design, three scalar functions are given as follows: , ,in ,Right now .

[0074] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention combines the inversion guidance strategy with the relative guidance framework, designs a baseline guidance law based on the relative remaining flight trajectory and lead angle, solves the theoretical closure problem, satisfies terminal acceleration constraints, and avoids command singularities; it uses interactive multi-model filtering to track targets, employs a polynomial regression algorithm combined with dynamically adjusted prediction intervals to predict trajectories, and utilizes radar information to support the calculation of remaining flight time, thus improving engineering applicability; it introduces a cooperative bias term to extend the baseline guidance law to form a time-coordinated guidance law, realizing multi-missile coordination, making full use of composite seekers and data links, and effectively solving the problem of striking maneuvering targets. Attached Figure Description

[0075] Figure 1 This is the kinematic model of the present invention in a relative frame;

[0076] Figure 2 The target position tracking error curve;

[0077] Figure 3 The root mean square error curve for the target position;

[0078] Figure 4 Simulation results for target trajectory prediction;

[0079] Figure 5 for Simulation results of time-coordinated guidance law;

[0080] Figure 6 Simulation results for different target maneuver modes;

[0081] Figure 7 This is a flowchart of the method of the present invention;

[0082] Figure 4 In the image, (a) is the target location prediction error curve; (b) is the target location prediction root mean square error curve.

[0083] Figure 5 In the image, (a) missile flight trajectory; (b) relative distance versus remaining flight time curve; (c) relative lead angle versus consistency error curve; (d) control acceleration curve;

[0084] Figure 6 In the image, (a) missile flight trajectory; (b) curve of relative distance versus remaining flight time; (c) curve of relative lead angle versus time of impact error; and (d) curve of control acceleration. Detailed Implementation

[0085] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0086] Please see the appendix Figure 1 - Appendix Figure 7 The present invention provides an embodiment of an inverse guidance method for striking maneuvering targets supported by predictive information, comprising the following steps: Step 1, establishing a relative guidance model; Step 2, designing a baseline guidance law in reverse; Step 3, tracking the target trajectory; Step 4, predicting the target trajectory; Step 5, designing a time-coordinated guidance law.

[0087] In step one above, a kinematic model of the missile and the maneuvering target in a relative frame is constructed as a relative guidance model. Specifically, the relative velocity vector and the relative velocity unit vector are defined as follows:

[0088] (1)

[0089] in, It is a relative velocity vector. It is a unit vector of relative velocity. The magnitude of the relative velocity;

[0090] relative velocity vector Differentiation yields:

[0091] (2)

[0092] in, Indicates tangential relative acceleration. This is the normal relative acceleration;

[0093] The missile-target kinematic equations can be characterized as:

[0094] (3)

[0095] (4)

[0096] (5)

[0097] in, Line of sight vector The rotational angular velocity vector, Relative velocity vector The angular velocity vectors of rotation are expressed as follows:

[0098] (6)

[0099] Define relative leading angle Relative velocity vector With line of sight vector The included angle between them, relative to the leading angle, satisfies:

[0100] (7)

[0101] in, For a unit vector, differentiating the above equation yields the relative leading angle derivative as follows:

[0102] (8)

[0103] To analyze the dynamics of the line-of-sight angle, the line-of-sight angular velocity vector is given here. The derivative is:

[0104] (9)

[0105] in, Interference caused by the target's maneuver;

[0106] In step two above, based on the relative guidance model constructed in step one, a relative residual flight trajectory is introduced. A baseline guidance law satisfying terminal constraints is derived through reverse engineering. Terminal constraints include zero miss distance constraint, zero terminal relative lead angle constraint, and bounded terminal acceleration constraint. Specifically, let the relative residual flight trajectory be... ,in The length of the missile's trajectory in the relative frame at the terminal moment. Let be the length of the missile's trajectory in the relative frame at the current moment. Then, the relative remaining trajectory is:

[0107] (10)

[0108] in To be relative to the front angle The relevant functions, Designed as:

[0109] (11)

[0110] in For guidance parameters, It represents the length of the missile's trajectory in a relative frame of reference, not the actual trajectory length, therefore With relative forward angle related,

[0111] remember Differentiate equation (10):

[0112] (12)

[0113] According to the definition of relative remaining flight trajectory, we know that Established, among which To obtain the relative velocity magnitude, substituting this condition into equation (12) yields the relative leading angle derivative:

[0114] (13)

[0115] According to the control quantity Based on the relationship with the relative lead angle, a baseline guidance law satisfying equation (13) can be designed as follows:

[0116] (14)

[0117] in ;

[0118] In step three above, based on the target observation information acquired by radar, a target state equation is established to describe the target's motion characteristics, a measurement equation is established to correlate the target state with the radar observation information, and an interactive multi-model filtering algorithm is used to track the trajectory of the maneuvering target; wherein, the target state equation is established as follows:

[0119] (15)

[0120] in and state matrix Noise driving matrix The target maneuver model will be determined by the selected target maneuver model, which includes a constant velocity model, a constant acceleration model, and a current statistical model. This is system noise;

[0121] make , The relative distance to the target. For the azimuth information, the measurement equation is established as follows:

[0122] (16)

[0123] in , and These are the components of the target in the radar observation system. For measuring noise;

[0124] The process of using the interactive multi-model filtering algorithm to track the trajectory of a maneuvering target includes the following steps:

[0125] (a) Input interaction: Based on the filtering information of each sub-model at the previous time step And the model switching probability from the previous time step, respectively, calculate the state input information of the individual model at the current time step:

[0126] (17)

[0127] (18)

[0128] in and The models are respectively State estimation and state covariance matrix after data interaction For the mixture probability of the model:

[0129] (19)

[0130] in Model of the previous time step The probability, The elements of the model transition probability matrix represent the target transition from the first... The motion model is transferred to the first... The probability of a motion model;

[0131] (b) Filtering: Based on the state information of each subsystem model obtained after input interaction. Covariance Matrix By combining system measurement information with extended Kalman filtering of the subsystem models, the state estimation results of each subsystem model are finally obtained. and covariance matrix ;

[0132] (c) Model probability update: After completing the parallel filtering of the subsystem model, calculate the new model transformation probability based on the filtering residual information:

[0133] (20)

[0134] in For the model The likelihood function follows a Gaussian distribution:

[0135] (twenty one)

[0136] in The filtering residuals for each subsystem model, The variance of the residuals;

[0137] (d) Output interaction: Through the updated model probabilities Filtered estimated values ​​of each subsystem and covariance matrix The final state estimate can be obtained. and covariance matrix :

[0138] (twenty two)

[0139] (twenty three)

[0140] In step four above, based on the target trajectory tracking data obtained in step three, a multinomial regression algorithm combined with dynamic adjustment of the prediction interval is used to predict the future trajectory of the target. The specific process of dynamically adjusting the prediction interval is as follows: first, an initial multinomial regression model is trained, then the latest tracking data is obtained cyclically and the training set is updated. When the remaining flight time meets the preset conditions, the multinomial model is retrained and the future trajectory is predicted.

[0141] In step five above, based on the target future trajectory prediction results from step four, the remaining flight time is calculated using numerical methods. A time-coordinated bias term is introduced based on the baseline guidance law designed in step two to design a time-coordinated guidance law, enabling coordinated multi-missile strikes against maneuvering targets. Specifically, the numerical method for calculating the remaining flight time involves calculating the remaining flight time based on the relative remaining flight trajectory and solving it using the Runge-Kutta algorithm. The formula for calculating the remaining flight time is:

[0142] (twenty four)

[0143] in For the remaining flight time, It is a relative velocity vector. For the relative remaining flight trajectory, For the integral variable relative to the remaining flight trajectory;

[0144] The specific design time-coordinated guidance law is as follows: For missiles... The cooperative guidance law for striking mobile targets is designed as follows:

[0145] (25)

[0146] in To ensure the convergence of the strike time error, the bias term, The remaining flight time consistency error, for:

[0147] (26)

[0148] in For constant parameters, The preset convergence time is determined by the specified convergence distance. To facilitate guidance law design, three scalar functions are given as follows: , ,in ,Right now .

[0149] Theoretical verification 1:

[0150] To verify that the baseline guidance law proposed in this invention enables the closed-loop system to achieve zero miss distance, zero terminal relative lead angle, and bounded terminal acceleration constraint, the following theoretical verification is performed:

[0151] Zero off-target constraint: for the function Finding the limit yields:

[0152] (27)

[0153] function Continuous and bounded We can obtain:

[0154] (28)

[0155] because Therefore, the relative remaining flight trajectory will decrease strictly monotonically from the initial value to zero, and due to the auxiliary function And it is bounded, therefore when From time to time Therefore, the closed-loop system based on the guidance law satisfies the zero miss distance constraint;

[0156] Zero terminal relative leading angle constraint:

[0157] The auxiliary function is introduced as follows:

[0158] (29)

[0159] Substituting the derivative of the relative leading angle into (29), we get:

[0160] (30)

[0161] It can be verified that when the guidance parameters meet the requirements... At that time, for ,function Bounded and satisfied By the properties of continuous bounded functions, there exists a constant. and This makes the following equation true:

[0162] (31)

[0163] The above formula can be rearranged as follows:

[0164] (32)

[0165] Integrating the above differential inequality from the initial time to the current time:

[0166] (33)

[0167] in As the initial value relative to the remaining flight trajectory, combined with It can be known that:

[0168] (34)

[0169] It can be seen that the closed-loop system of the guidance terminal always satisfies:

[0170] (35)

[0171] The above results demonstrate that the relative lead angle will converge to zero at the guidance terminal moment.

[0172] Bounded terminal acceleration constraints: Analyzing the control acceleration at the terminal moment, and utilizing the relationship between the line-of-sight angular velocity and the relative lead angle, the equation can be... Rewritten as:

[0173] (36)

[0174] The guidance terminal is always available According to L'Hospital's rule:

[0175] (37)

[0176] in The magnitude of the relative velocity at the terminal moment, since as well as It can be known that when have Known For about A continuous function, therefore it exists on the interval [0, 1]. Within this interval, the following relationship holds:

[0177] (38)

[0178] in , To make the constant sufficiently small, substitute the auxiliary function (29) into it and rearrange:

[0179] (39)

[0180] In the interval Solve the above differential inequality internally:

[0181] (40)

[0182] in To enter the interval with a relative forward angle The relative remaining flight trajectory at that time simplifies equation (40):

[0183] (41)

[0184] when The time expression (41) is equivalent to:

[0185] (42)

[0186] because as well as Therefore, the above formula means Substituting this result into equation (36) yields the following:

[0187] (43)

[0188] The above equation shows that the rotational angular velocity of the relative velocity vector converges to zero at the terminal moment, therefore the normal acceleration in the relative frame converges to zero, and the original acceleration of the missile at the guidance terminal moment is:

[0189] (44)

[0190] It is known that the missile retains a component to compensate for the target's maneuver at the terminal moment, therefore the terminal control acceleration is bounded. Furthermore, the guidance law is derived in reverse from the analytical solution of the remaining flight trajectory, i.e. The fact that this holds true consistently indicates that the relative remaining flight trajectory is globally accurate.

[0191] Theoretical verification 2:

[0192] To verify that the cooperative guidance law proposed in this invention enables a closed-loop system to achieve time-coordinated guidance against maneuvering targets, the following theoretical verification is performed:

[0193] Substituting the designed time-coordinated guidance law into the relative lead angle dynamics, we can obtain:

[0194] (45)

[0195] Differentiating the relative remaining flight trajectory, we have:

[0196] (46)

[0197] use The derivative of the relative remaining flight trajectory with respect to the relative flight trajectory can be solved as follows:

[0198] (47)

[0199] Depend on It can be seen that the remaining flight time is currently as follows:

[0200] (48)

[0201] Therefore, the consistency error in striking mobile targets will converge to zero;

[0202] The final form of the feedback guidance law for striking maneuvering targets is analyzed, and the designed guidance law is reorganized as follows:

[0203] (49)

[0204] in It can also be regarded as a time-varying proportional coefficient, and its expression is:

[0205] (50)

[0206] The proportional coefficient in the designed guidance law It is the relative front angle The function, and can obtain Therefore, the terminal time ratio coefficient Greater than Similarly, this can explain the relative lead angle and the terminal characteristics of the control acceleration. The above analysis shows the generality and uniformity of the inversion guidance strategy for both stationary and maneuvering targets.

[0207] Experimental Example 1:

[0208] To verify the effectiveness of the proposed interactive multi-model filtering algorithm, multinomial regression, and dynamically adjusted prediction interval algorithm, the following simulation experiments were conducted: The target motion models used were constant velocity (CV) model, constant acceleration (CA) model, and current statistical (CS) model, respectively. The system noise was set to [value missing] in the simulation. For the CV model and the CA model, the noise covariance matrix is ​​selected as follows: For the CS model, the maneuver frequency is set to 1 / 20, and the radar measurement noise is... ,in The ship target maneuvers in the horizontal plane at a constant speed, and its lateral acceleration perpendicular to the velocity direction is set as follows: The results of running 200 Monte Carlo simulations are as follows: Figure 2 and Figure 3 As shown; Figure 2 The filtered estimation error curve for target trajectory tracking is given. Figure 3 The root mean square error curve for target trajectory tracking is given. As can be seen from the figure, the target... and The position tracking errors in both directions are less than 1.2m and 1.3m, and the root mean square errors are less than 6.1m, indicating that the interactive multi-model filter exhibits high tracking accuracy and robustness when the target is maneuvering. Based on the above target trajectory tracking data, a multinomial regression algorithm is used to predict the target's trajectory at future moments. The prediction time is set to 15s in the simulation. The prediction error curves for 200 Monte Carlo simulations are shown below. Figure 4 As shown, it is clear that the prediction error gradually increases with the increase of the prediction time. When the prediction time exceeds 10 seconds, and The position prediction errors in all directions are greater than 10m. The above simulation results demonstrate the effectiveness of the designed polynomial regression and dynamic adjustment prediction interval algorithm, and also illustrate the necessity of dynamically adjusting the prediction interval in guidance applications.

[0209] Experimental Example 2:

[0210] To verify the effectiveness of the time-coordinated guidance law proposed in this invention, the following simulation experiment was conducted: the target maneuver mode was the same as in Experiment 1, and the guidance parameters were selected as follows. The predicted data interval is initialized to s, Figure 5 The flight trajectories, relative distances and remaining flight times, relative lead angles and consistency error curves, and missile control acceleration curves of the four missiles are presented. This indicates that all missiles successfully hit the target simultaneously, and the remaining flight times of the four missiles converged uniformly, further demonstrating that the designed guidance law successfully achieved coordinated guidance of maneuvering targets. Because the designed trajectory prediction algorithm requires dynamic adjustment of the prediction interval, the update of the target trajectory data at the moment of prediction information switching leads to discontinuities in the remaining flight time curves. Figure 5 (c) The consistency error is also affected, ultimately resulting in a non-smooth missile control acceleration curve. Furthermore, Figure 5 (c) indicates that the consistency error converges to an acceptable range and the relative lead angle eventually converges to zero, satisfying the guidance terminal constraint. It should be noted that when the flight time is greater than 30s, the missile state curve gradually smooths out and the control acceleration converges to zero at the terminal moment. This shows that the trajectory prediction algorithm does not affect the guidance performance at the terminal moment.

[0211] Experimental Example 3:

[0212] To fully verify the guidance law performance, simulations of strike time control were conducted using different target maneuvering modes. Considering the ship-target motion characteristics in the horizontal plane, the target velocity and lateral maneuvering acceleration are shown in Table 1. Figure 6 The missile-target trajectory, relative distance and remaining flight time, relative lead angle and impact time error curves, and control acceleration curves are presented. The designed guidance law is designed in a relative frame, and the obtained theoretical results fully consider the influence of the target's maneuvering modes. Simulation results show that, despite the target employing different maneuvering modes, the missile achieves the desired impact time. The fact that the target was hit at time s demonstrates the robustness of the designed guidance law against maneuvering targets. Figure 6 The escape direction of the target differs significantly under different maneuvering modes, but the remaining flight time still maintains high estimation accuracy, indicating that the designed trajectory prediction algorithm provides accurate target information. It should be noted that once the strike time error converges... Figure 6 The control acceleration did not strictly converge to zero, but retained a component used to compensate for the target's maneuver.

[0213] Table 1 Simulation conditions

[0214] Based on the above, the advantages of this invention are as follows: When used, it combines the inversion guidance strategy with a relative guidance framework, designs a baseline guidance law based on the relative remaining flight trajectory and relative lead angle, derives the closed-loop system characteristics using a relative kinematic model to ensure theoretical closure; employs an interactive multi-model filtering algorithm, fusing constant velocity, constant acceleration, and the current statistical model to accurately track various motion modes of maneuvering targets such as ships at sea; combines multinomial regression and dynamically adjusted prediction interval algorithms to update the target trajectory prediction model based on the remaining flight time, balancing the relationship between prediction accuracy and time, and providing support for the accurate calculation of the remaining flight time; and designs a time-coordinated guidance law with a time-coordinated bias term, achieving multi-missile time coordination through error feedback while ensuring bounded terminal acceleration, avoiding command singularities, and improving engineering applicability.

[0215] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A method for inversion guidance in striking maneuvering targets supported by predictive information, comprising the following steps: Step 1: Establish a relative guidance model; Step 2: Design a baseline guidance law in reverse; Step 3: Track the target trajectory; Step 4: Predict the target trajectory; Step 5: Design a time-coordinated guidance law; Its characteristics are: In step one above, a kinematic model of the missile and the maneuvering target in a relative frame is constructed as a relative guidance model. Specifically, the relative velocity vector and the relative velocity unit vector are defined as follows: （1） in, It is a relative velocity vector. It is a unit vector of relative velocity. The magnitude of the relative velocity; relative velocity vector Differentiation yields: （2） in, Indicates tangential relative acceleration. This is the normal relative acceleration; The missile-target kinematic equations can be characterized as: （3） （4） （5） in, Line of sight vector The rotational angular velocity vector, Relative velocity vector The angular velocity vectors of rotation are expressed as follows: （6） Define relative leading angle Relative velocity vector With line of sight vector The included angle between them, relative to the leading angle, satisfies: （7） in, For a unit vector, differentiating the above equation yields the relative leading angle derivative as follows: （8） To analyze the dynamics of the line-of-sight angle, the line-of-sight angular velocity vector is given here. The derivative is: （9） in, Interference caused by the target's maneuver; In step two above, based on the relative guidance model constructed in step one, a relative residual flight trajectory is introduced. A baseline guidance law satisfying terminal constraints is derived through reverse engineering. Terminal constraints include zero miss distance constraint, zero terminal relative lead angle constraint, and bounded terminal acceleration constraint. Specifically, let the relative residual flight trajectory be... ,in The length of the missile's trajectory in the relative frame at the terminal moment. Let be the length of the missile's trajectory in the relative frame at the current moment. Then, the relative remaining trajectory is: （10） in To be relative to the front angle The relevant functions, Designed as: （11） in For guidance parameters, It represents the length of the missile's trajectory in a relative frame of reference, not the actual trajectory length, therefore With relative forward angle related, remember Differentiate equation (10): （12） As can be seen from the definition of relative remaining flight trajectory, there is Established, among which To obtain the relative velocity magnitude, substituting this condition into equation (12) yields the relative leading angle derivative: （13） According to the control quantity Based on the relationship with the relative lead angle, a baseline guidance law satisfying equation (13) can be designed as follows: （14） in ; In step three above, based on the target observation information acquired by radar, a target state equation is established to describe the target motion characteristics, a measurement equation is established to correlate the target state with the radar observation information, and an interactive multi-model filtering algorithm is used to track the trajectory of the maneuvering target. In step four above, based on the target trajectory tracking data obtained in step three, a multinomial regression algorithm combined with dynamically adjusted prediction intervals is used to predict the future trajectory of the target. In step five above, based on the target future trajectory prediction results in step four, the remaining flight time is calculated using numerical methods. A time-coordinated bias term is introduced based on the baseline guidance law designed in step two, and a time-coordinated guidance law is designed to achieve coordinated strikes of multiple missiles against maneuvering targets.

2. The inversion guidance method for striking maneuvering targets supported by predictive information according to claim 1, characterized in that: In step three, the target state equation is established as follows: （15） in and state matrix Noise driving matrix The target maneuver model will be determined by the selected target maneuver model, which includes a constant velocity model, a constant acceleration model, and a current statistical model. This is system noise; make , The relative distance to the target. For the azimuth information, the measurement equation is established as follows: （16） in , and These are the components of the target in the radar observation system. For measuring noise.

3. The inversion guidance method for striking maneuvering targets supported by predictive information according to claim 1, characterized in that: Step three, which involves using the interactive multi-model filtering algorithm to track the trajectory of a maneuvering target, specifically includes the following steps: (a) Input interaction: Based on the filtering information of each sub-model at the previous time step And the model switching probability from the previous time step, respectively, calculate the state input information of the individual model at the current time step: （17） （18） in and The models are respectively State estimation and state covariance matrix after data interaction For the mixture probability of the model: （19） in Model of the previous time step The probability, The elements of the model transition probability matrix represent the target transition from the first... The motion model is transferred to the first... The probability of a motion model; (b) Filtering: Based on the state information of each subsystem model obtained after input interaction. Covariance Matrix By combining system measurement information with extended Kalman filtering of the subsystem models, the state estimation results of each subsystem model are finally obtained. and covariance matrix ; (c) Model probability update: After completing the parallel filtering of the subsystem model, calculate the new model transformation probability based on the filtering residual information: （20） in For the model The likelihood function follows a Gaussian distribution: （21） in The filtering residuals for each subsystem model, The variance of the residuals; (d) Output interaction: Through the updated model probabilities Filtered estimated values ​​of each subsystem and covariance matrix The final state estimate can be obtained. and covariance matrix : （22） （23） 4. The inversion guidance method for striking maneuvering targets supported by predictive information according to claim 1, characterized in that: In step four, the process of dynamically adjusting the prediction interval is as follows: first, an initial multinomial regression model is trained; then, the latest tracking data is obtained cyclically and the training set is updated; when the remaining flight time meets the preset conditions, the multinomial model is retrained and the future trajectory is predicted.

5. The inversion guidance method for striking maneuvering targets supported by predictive information according to claim 1, characterized in that: In step five, the numerical method for calculating the remaining flight time specifically involves: calculating the remaining flight time based on the relative remaining flight trajectory, and solving it using the Runge-Kutta algorithm.

6. The inversion guidance method for striking maneuvering targets supported by predictive information according to claim 5, characterized in that: The formula for calculating the remaining flight time is: （24） in For the remaining flight time, It is a relative velocity vector. For the relative remaining flight trajectory, is the integral variable relative to the remaining flight trajectory.

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