Many-to-one intelligent cooperative guidance method based on coverage theory

Abstract

The invention discloses a many-for-one intelligent cooperative guidance method based on a coverage theory, and relates to the many-for-one intelligent cooperative guidance method based on the coverage theory. The objective of the invention is to solve the problem of possible insufficient overload capacity when a high-maneuverability target is intercepted in the prior art. According to the method, a classical acceleration-based cooperative guidance law is popularized to a three-dimensional space scene under the condition of given target coverage parameters, a three-dimensional acceleration coverage cooperative guidance model is established, an input and output sample database is constructed to train a neural network, and rapid and accurate estimation of the terminal guidance shift switching moment ZEM in the interception missile is realized; the method comprises the following steps: designing a coverage efficiency optimization index, carrying out optimization solution on a target coverage parameter, substituting the optimal parameter into a three-dimensional cooperative guidance law to obtain a virtual aiming point, attacking the virtual aiming point by adopting a PNG method to realize cooperative interception of a target, carrying out terminal guidance on the target by adopting an SSTAG method, reducing the miss distance of a terminal, and improving the interception hit rate. The method is applied to the field of collaborative guidance.

Description

Technical Field

[0001] The present invention relates to a multi-to-one intelligent cooperative guidance method based on the coverage theory. Background Art

[0002] The problem of cooperative interception guidance has received much attention in recent years and is a hot issue in the field of aerospace. Most of the previous studies were carried out for one-to-one interception scenarios and targets with weak maneuverability. However, in the case where the overload capabilities of the interceptor and the target are in equilibrium, the success probability of intercepting the target using the traditional one-to-one guidance law is greatly reduced. Therefore, in order to cope with the threat posed by targets with strong maneuverability to the defense and improve the interception hit rate, it is necessary to study how to achieve cooperative interception of the target by means of the cooperation of multiple interceptors in the case of equal maneuverability. Cooperative guidance laws can be roughly divided into cooperative guidance laws with attack time constraints, cooperative guidance laws with attack angle constraints, cooperative guidance laws based on game theory, and cooperative guidance laws based on coverage theory. It should be noted that most of the current studies on cooperative guidance laws are classical cooperative guidance laws considering interception time constraints and interception angle constraints. These cooperative guidance methods are only applicable to intercepting targets with weak maneuverability, and there may be problems with insufficient overload capabilities when intercepting highly maneuverable targets. When the overload capabilities of the interceptor and the target are in equilibrium, in order to ensure that the target is successfully intercepted by at least one interceptor, multiple interceptors need to achieve joint maneuvering area coverage of the target maneuvering area through a certain cooperative strategy. Therefore, the cooperative guidance of multiple interceptors based on the coverage theory may be the direction of future in-depth research. Summary of the Invention

[0003] The purpose of the present invention is to solve the problem of insufficient overload capabilities that may exist when intercepting targets with high maneuverability, and to propose a multi-to-one intelligent cooperative guidance method based on the coverage theory.

[0004] The specific process of a multi-to-one intelligent cooperative guidance method based on the coverage theory is as follows:

[0005] Step 1: Based on the current states of the interceptors and the target, solve the true standard intercept acceleration of the interceptors to intercept the target with zero control

[0006] Introduce the coverage probability, given the target coverage parameters (χ, ω), and based on the true standard intercept acceleration of the interceptors to intercept the target with zero control Online update the standard intercept acceleration a of each interceptor т,s,i ;

[0007] Based on the standard intercept acceleration a of each interceptor т,s,i Solve the three-dimensional remaining flight time t go,s,i , based on the three-dimensional remaining flight time t go,s,iGenerate a three-dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i );

[0008] Use the PNG method to attack the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ). Based on the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ), obtain the relative position and relative velocity between the interceptor and the target, and obtain the position, velocity, ballistic inclination angle, and ballistic deflection angle of the interceptor at the next moment based on the relative position and relative velocity between the interceptor and the target;

[0009] Based on the three-dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ), at the mid-course and terminal guidance handover moment, make the interceptor perform orbit recursion zero-control interception of the target in the current state, and use the relative distance between the interceptor and the target at the moment closest to the target as the zero-control miss distance ZEM at the mid-course and terminal guidance handover moment;

[0010] Step 2: Obtain a training set based on Step 1, and obtain a trained ZEM estimation network based on the training set; the specific process is as follows:

[0011] Step 2-1: Obtain a training set; the specific process is as follows:

[0012] 1) Change the initial position and initial velocity of the interceptor to obtain a new initial position and initial velocity of the interceptor;

[0013] 2) Traverse the target coverage parameters (χ, ω) within a given range to obtain new target coverage parameters (χ, ω);

[0014] 3) Based on the new initial position and initial velocity of the interceptor, and the new target coverage parameters (χ, ω), re-execute Step 1 to obtain a new three-dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i );

[0015] 4) Based on the new three-dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ), at the mid-course and terminal guidance handover moment, make the interceptor perform orbit recursion zero-control interception of the target in the current state, and use the relative distance between the interceptor and the target at the moment closest to the target as the zero-control miss distance ZEM at the mid-course and terminal guidance handover moment;

[0016] 5) Repeat steps 1)-4) to obtain M' zero-control miss distances ZEM at the mid-course and terminal guidance handover moment;

[0017] Step 2: Use the initial position, initial velocity of the new interceptor missile in the training set, and the new target coverage parameters (χ, ω) as a set of data as the input of the ZEM estimation network. The zero-effort miss ZEM of the interceptor missile at the mid-course and terminal guidance handover moment in the training set is used as the output of the ZEM estimation network. Train the ZEM estimation network to obtain a trained ZEM estimation network.

[0018] Step 3: Input the initial position and initial velocity of the interceptor missile to be measured into the trained ZEM estimation network, and the trained ZEM estimation network outputs the ZEM at the mid-course and terminal guidance handover moment.

[0019] Based on the ZEM at the mid-course and terminal guidance handover moment output by the trained ZEM estimation network and the line-of-sight angular rate Design the index function J;

[0020] Use the SQP optimization method to optimize the index function J, and find the optimal coverage parameters (χ L , ω L ) corresponding to the minimum value of the target index function J;

[0021] Substitute the optimal target parameters (χ L , ω L ) into Step 1 to calculate the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i );

[0022] Step 4: In the mid-course guidance stage, use the proportional navigation method to aim at the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) generated in Step 3 to perform cooperative interception on the target;

[0023] In the terminal guidance stage, use the anti-saturation super-twisting sliding mode guidance law to aim at the real position of the target to achieve cooperative interception of the target.

[0024] The beneficial effects of the present invention are as follows:

[0025] In the present invention, a three-dimensional cooperative guidance method based on coverage theory integrating neural network and optimization algorithm is proposed. First, under the condition of given target coverage parameters (χ, ω), the classical acceleration-based cooperative guidance law is extended to a three-dimensional space scenario, a three-dimensional acceleration coverage cooperative guidance model is established, and an input-output sample database is constructed based on this model to train a neural network to realize fast and accurate estimation of the ZEM of the interceptor missile at the mid-course and terminal guidance handover moment; on this basis, by designing the coverage effectiveness optimization index J and using the SQP algorithm for the target coverage parameters (χ L , ω L)Optimize and solve, and finally substitute the optimal parameters into the three-dimensional cooperative guidance law to obtain the virtual aiming point. Finally, use the PNG method to attack the virtual aiming point to achieve cooperative interception of the target. Finally, use the SSTAG method for terminal guidance of the target to further reduce the terminal miss distance and improve the interception hit rate. Using the method proposed by the present invention for cooperative interception of targets with equal potential overload capabilities can theoretically improve the calculation speed and interception success rate. Description of the Drawings

[0026] Figure 1 It is a flowchart of the present invention;

[0027] Figure 2 It is a one-to-many intelligent cooperative interception scenario based on the coverage theory.

[0028] Figure 3 It is a missile zero-control interception target diagram, where (x M,i , y M,i ) is the initial position of the i-th interceptor missile; (x T , y T ) is the initial position of the target; (x f,i , y f,i ) is the interception hit point; (x o,i , y o,i ) is the center of the trajectory of the target moving with acceleration ; r T,o,i = [(x o,i - x T ) 2 + (y o,i - y T ) 2 ) 1 / 2 is the trajectory radius of the target moving with acceleration ; α i is the central angle formed by the arc of the target's movement from the initial interception moment to the terminal moment; r M,f,i = [(x f,i - x M,i ) 2 + (y f,i - y M,i ) 2 ) 1 / 2 is the distance of the missile from the interception hit point; r T,f,i = [(x f,i - x T ) 2 + (y f,i - y T ) 2 ) 1 / 2 is the distance of the target from the interception hit point; V T represents the target speed, V M represents the interceptor missile speed; γM,i Denote the ballistic angle of the i-th interceptor; γ T Denote the target ballistic angle;

[0029] Figure 4 is the distribution diagram of the neural network training error;

[0030] Figure 5 is the diagram of the convergence of the north-axis coordinate of the virtual aiming point of the interceptor;

[0031] Figure 6 is the diagram of the convergence of the celestial-axis coordinate of the virtual aiming point of the interceptor;

[0032] Figure 7 is the diagram of the convergence of the east-axis of the virtual aiming point of the interceptor;

[0033] Figure 8 is the diagram of the engagement trajectory of the mid-course guidance in cooperative interception;

[0034] Figure 9 The engagement trajectory diagram of the terminal guidance in cooperative interception;

[0035] Figure 10 The distribution diagram of the terminal miss distance. Specific implementation manner

[0036] Specific implementation manner one: The specific process of a one-to-many intelligent cooperative guidance method based on the coverage theory in this implementation manner is as follows:

[0037] The present invention designs a one-to-many intelligent cooperative guidance method based on the coverage theory. In this method, according to the standard interception acceleration model, first, in the case of given target coverage parameters (χ, ω), the classical acceleration-based cooperative guidance law is extended to the three-dimensional space application scenario. Subsequently, an input-output database is established using the acceleration coverage cooperative guidance law in the three-dimensional scenario, and a neural network is trained to quickly estimate the zero effort miss (ZEM) at the handover moment between the mid-course and terminal guidance of the interceptor. Then, an optimization index J is designed, and the sequential quadratic programming method (SQP) is used to optimize the target coverage parameters (χ, ω) for this index. Finally, the optimal target coverage parameters (χ L , ω L ) are substituted into the acceleration coverage cooperative guidance law in the three-dimensional scenario to achieve the cooperative interception of the target. For the one-to-many cooperative interception problem under the equal potential overload capacity, the method proposed by the present invention can provide an effective solution.

[0038] Step 1. Based on the current states of the interceptor and the target, solve the true standard interception acceleration for the interceptor to intercept the target with zero control

[0039] Introduce the coverage probability. Given the target coverage parameters (χ, ω), based on the true standard interception acceleration of the interceptor to intercept the target with zero control Online update the standard interception acceleration a of each interceptor т,s,i ;

[0040] Based on the standard interception acceleration a of each interceptor т,s,i Solve the three-dimensional remaining flight time t go,s,i , and based on the three-dimensional remaining flight time t go,s,i Generate a three-dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i );

[0041] Use the PNG method to attack the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ), and based on the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) to obtain the relative position and relative velocity between the interceptor and the target, and based on the relative position and relative velocity between the interceptor and the target, obtain the position, velocity, ballistic inclination angle and ballistic deflection angle of the interceptor at the next moment;

[0042] Based on the three-dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ), at the mid-course and terminal guidance handover moment, make the interceptor perform orbit recursion zero control to intercept the target in the current state, and use the relative distance between the interceptor and the target at the moment closest to the target as the zero-effort miss ZEM at the mid-course and terminal guidance handover moment;

[0043] Step 2: Based on the training set obtained in Step 1, obtain a trained ZEM estimation network; the specific process is as follows:

[0044] Step 2-1: Obtain the training set; the specific process is as follows:

[0045] 1). Change the initial position and initial velocity of the interceptor to obtain new initial position and initial velocity of the interceptor;

[0046] 2). Traverse the target coverage parameters (χ, ω) in small step sizes within a given range to obtain new target coverage parameters (χ, ω);

[0047] 3). Based on the new initial position and initial velocity of the interceptor, and the new target coverage parameters (χ, ω), re-execute Step 1 to obtain a new three-dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i );

[0048] 4), Based on the new three-dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ), at the mid-course and terminal guidance handover moment, make the interceptor perform orbit propagation zero-control interception of the target in the current state, and take the relative distance between the interceptor and the target at the moment closest to the target as the zero-control miss distance ZEM at the mid-course and terminal guidance handover moment;

[0049] 5) Repeat steps 1)-4) to obtain M' zero-control miss distances ZEM at the mid-course and terminal guidance handover moments;

[0050] The new initial position and initial velocity of the interceptor, as well as the new target coverage parameters (χ, ω) are taken as a set of new inputs, and a set of new zero-control miss distances ZEM at the mid-course and terminal guidance handover moments are output;

[0051] 100,000 sets of new inputs correspond to 100,000 sets of new zero-control miss distances ZEM at the mid-course and terminal guidance handover moments;

[0052] Step Two: Use the new initial position, initial velocity of the interceptor and the new target coverage parameters (χ, ω) in the training set as a set of data as the input of the ZEM estimation network, and the corresponding zero-control miss distance ZEM of the interceptor at the mid-course and terminal guidance handover moment in the training set as the output of the ZEM estimation network, and train the ZEM estimation network to obtain a trained ZEM estimation network;

[0053] Step Three: Input the initial position and initial velocity of the interceptor to be measured into the trained ZEM estimation network, and the trained ZEM estimation network outputs the ZEM at the mid-course and terminal guidance handover moment;

[0054] Based on the ZEM at the mid-course and terminal guidance handover moment output by the trained ZEM estimation network and the line-of-sight angular rate Design the index function J;

[0055] Use the SQP optimization method to optimize the index function J to find the optimal coverage parameters (χ L , ω L ) corresponding to the minimum value of the target index function J;

[0056] Substitute the optimal target parameters (χ L , ω L ) into Step One to calculate the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i );

[0057] Step Four: In the mid-course guidance stage, use the proportional navigation guidance method (Proportional Navigation Guidance Law, PNG) to aim at the virtual aiming point (x T,s,f,i, y T,s,f,i , z T,s,f,i ), perform collaborative interception on the target;

[0058] In the terminal guidance stage, the anti-saturation super-twisting sliding mode guidance law (Saturated Super-Twisting Algorithm Sliding Mode Guidance Law, SSTAG) is adopted to aim at the real position of the target, so as to achieve the collaborative interception of the target, reduce the terminal miss distance of the collaborative interception, and improve the interception hit rate.

[0059] Specific implementation method 2: The difference between this implementation method and the first specific implementation method is that the specific process of the said step one is as follows:

[0060] Step one one: The dynamic model of the interceptor missile adopted is expressed in the northeast celestial coordinate system (the x-axis points east, the y-axis points north, and the z-axis points to the sky) as:

[0061]

[0062] Wherein,

[0063] x M , y M , z M are respectively the three-axis positions of the interceptor missile;

[0064] V M is the magnitude of the interceptor missile velocity; θ M is the ballistic inclination angle; ψ M is the ballistic deflection angle;

[0065] n x , n y , n z are respectively the components of the interceptor overload on the three axes in the velocity coordinate system (the x-axis of the velocity coordinate system coincides with the velocity vector of the center of mass of the missile body, the y-axis is in the longitudinal plane of the missile body, perpendicular to the x-axis, and the upward direction is positive, and the z-axis is perpendicular to the oxy plane, and the direction of the z-axis is determined by the right-hand rule);

[0066] g is the acceleration due to gravity;

[0067] are respectively the first derivatives of x M , y M , z M with respect to time;

[0068] are respectively the first derivatives of V M , θ M , ψ M with respect to time;

[0069] During the mid-course guidance and terminal guidance phases of the interception process, the process constraints are considered as the angle of attack constraint and the overload constraint, expressed as:

[0070]

[0071] Among them, is the aerodynamic combined overload, α max is the maximum angle of attack, n max is the maximum overload, and α is the angle of attack;

[0072] Steps 1-2: Based on the current state of the interceptor and the target ( Figure 3 ), solve for the true standard interception acceleration

[0073] of the interceptor to intercept the target with zero control. Steps 1-3: Introduce the coverage probability, given the target coverage parameters (χ, ω), and update the standard interception acceleration a т,s,i of each interceptor online based on the true standard interception acceleration

[0074] of the interceptor to intercept the target with zero control; T,s,i Steps 1-4: Based on the standard interception acceleration a go,s,i obtained from formula (14), solve for the remaining flight time t

[0075] of the interceptor to attack the target in three-dimensional space; go,s,i Then, solve for the three-dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) from the remaining flight time t;

[0076] Steps 1-5: Use the PNG method to attack the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) obtained in Step 1-4. Based on the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ), obtain the relative position and relative velocity between the interceptor and the target. Based on the relative position and relative velocity between the interceptor and the target, obtain n y and n z , where n x = 0;

[0077] Substitute n x , n y and n z into equation (1) to solve the differential equation of the dynamic model, and obtain the position, velocity, trajectory inclination angle, and trajectory deflection angle of the interceptor at the next moment;

[0078] Step 16: Repeat Steps 11 to 15 until the distance between the interceptor and the target reaches 100 km and stop. The stop time is used as the mid-course and terminal guidance handover time;

[0079] Based on the three-dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) corresponding to the stop time, at the mid-course and terminal guidance handover time, make the interceptor perform orbit propagation zero-effort interception of the target in the current state, and take the relative distance between the interceptor and the target at the moment closest to the target as the zero-effort miss distance ZEM at the mid-course and terminal guidance handover time.

[0080] Other steps and parameters are the same as those in the first specific implementation manner.

[0081] Specific implementation manner three: The difference between this implementation manner and the first or second specific implementation manner is that in Step 12, based on the current states of the interceptor and the target ( Figure 3 ), solve the true standard interception acceleration of the interceptor for zero-effort interception of the target

[0082] The specific process is as follows:

[0083] In the relative state relationship between the current missile and the target, if the missile can perform zero-effort interception of a target maneuvering with a constant acceleration , then is called the true standard interception acceleration of the target for the i-th interceptor missile M i . Figure 3 shows a schematic diagram of the interceptor performing zero-effort interception of a target maneuvering with a constant acceleration .

[0084] Step 121: For the missile to perform zero-effort interception of the target, it needs to satisfy

[0085]

[0086] In the formula, α i represents the central angle formed by the arc of the target's motion from the initial interception moment to the terminal moment, r T,o,i represents the trajectory radius of the target moving with an acceleration , r T,o,i = [(x o,i - x T ) 2 + (y o,i - y T ) 2 1 / 2 , (x o,i , y o,i ) is the center of the trajectory of the target moving with an acceleration , (x T , y T ​) is the target initial position, r M,f,i represents the distance of the missile from the interception hit point, r M,f,i =[(x f,i -x M,i ) 2 +(y f,i -y M,i ) 2 ) 1 / 2 , (x f,i , y f,i ) is the interception hit point, (x M,i , y M,i ) is the initial position of the i-th interceptor missile; V T represents the target speed, V M represents the interceptor missile speed; is the true standard interception acceleration of the target with respect to the i-th interceptor missile;

[0087] From Figure 3 the geometric relationship in

[0088]

[0089] y f,i =tan(γ M,i )×(x f,i -x M,i )+y M,i (5)

[0090]

[0091] In the formula,

[0092] r T,f,i represents the distance of the target from the interception hit point, r T,f,i =[(x f,i -x T ) 2 +(y f,i -y T ) 2 ) 1 / 2 ;

[0093] γ M,i represents the trajectory angle of the i-th interceptor missile;

[0094] γ T represents the target trajectory angle;

[0095] Step 1.2.2: Set the initial value of x f,i , and repeatedly execute formulas (3), (4), (5), and (6) using the Newton iteration method until x f,i converges to obtain the optimal value of x f,i ;

[0096] Steps One, Two, and Three: Based on the optimal x f,i The value is used to calculate the true standard intercept acceleration of the intercept missile for zero-control intercepting the target according to Formula (7);

[0097]

[0098] In the formula,

[0099]

[0100] x T,l,i is an intermediate variable.

[0101] Other steps and parameters are the same as those in the first or second specific implementation manners.

[0102] Specific Implementation Manner Four: The difference between this implementation manner and one of the first to third specific implementation manners is that: in Step One and Three, the coverage probability is introduced, and given the target coverage parameters (χ, ω), based on the true standard intercept acceleration of the intercept missile for zero-control intercepting the target the standard intercept acceleration a of each intercept missile is updated online т,s,i ;

[0103] The specific process is as follows:

[0104] Step One Thirty-One: Use f PDF (a T ) to represent the probability density function of the target acceleration. When the upper bound of the target maneuverability is known and t > t k , it is considered that the maneuver acceleration of the target follows a normal distribution, that is, a T (t) ~ N(a T (t k ), σ 2 ); when t £ t k it is not considered and does not exist;

[0105] Among them, σ is the standard deviation of the normal distribution; t is a future moment, t k is the current moment, a T (t) is the target acceleration at a future moment, a T (t k ) is the target acceleration at the current moment, and N() is the standard normal distribution;

[0106] Then the acceleration coverage probability of all intercept missiles for the target at the current moment is expressed as

[0107]

[0108] Among them, a T represents the current acceleration of the target, N m represents the total number of intercept missiles, and i represents the intercept missile number, Denote the current moment \(t\) k Acceleration coverage probability of all intercept missiles against the target; \(a\) T,max Is the upper bound of the target maneuverability Denote the target coverage process function, there is

[0109]

[0110] In the formula, \(a\) M,max Denote the maximum acceleration amplitude of the interceptor missile, \(\omega\) denotes the acceleration coverage parameter;

[0111] Step 132. Based on the acceleration coverage probability of all intercept missiles against the target at the \(k + 1\) moment Obtain the one that maximizes the overall coverage probability

[0112] The specific process is as follows:

[0113]

[0114] In the formula,

[0115] Denote \(t\) k + 1 moment acceleration coverage probability of all intercept missiles against the target;

[0116] Denote the true standard intercept acceleration array of each interceptor missile;

[0117] Define

[0118] Based on the principle of maximizing the overall coverage probability, use the gradient descent method to cooperate to intercept and cover the target (11), and get:

[0119]

[0120] In the formula, Denote the gradient function, Denote the first-order derivative of the true standard intercept acceleration with respect to time, \(j\) denotes the interceptor missile number, Denote the target coverage process function; Denote the true standard intercept acceleration of the target against the \(j\)th interceptor missile; \(\chi\) is the acceleration coverage parameter;

[0121] Step 133. Set the initial value of time \(t\) go,s,i ;

[0122] Based on the true standard intercept acceleration of the interceptor missile to intercept the target with zero control And the remaining flight time \(t\) go,s,i Obtain the expected standard intercept acceleration at the terminal interception moment The expression is as follows:

[0123]

[0124] In the formula, t go,s,i represents the remaining flight time of the i-th interceptor missile;

[0125] Steps One, Three, and Four: Use the expected standard interception acceleration as the standard interception acceleration of the updated interceptor missile,

[0126]

[0127] The other steps and parameters are the same as those in one of the specific embodiments One to Three.

[0128] Specific Embodiment Five: The difference between this embodiment and one of the specific embodiments One to Four is that: the standard interception acceleration a obtained based on formula (14) in Step One Four T,s,i Solve for the remaining flight time t of the interceptor missile attacking the target in three-dimensional space go,s,i ;

[0129] Then, from the remaining flight time t go,s,i Solve to obtain the three-dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i );

[0130] The specific process is as follows:

[0131] Step One Four One: Convert the interception scenario from the northeast celestial coordinate system to the target maneuvering coordinate system X V Y V Z V The X V axis points in the direction of the target velocity, the Y V axis points in the direction of the target velocity, and the Z V axis is determined according to the right-hand rule;

[0132] Obtain the expression of the position coordinates of the target changing with time in the target maneuvering coordinate system; expressed as:

[0133]

[0134] z TV (t go,s,i ) = z TV (0) (17)

[0135] In the target maneuvering coordinate system, the target only moves in the X V -Y V plane;

[0136] In the formula, x TV (tgo,s,i ) represents the X coordinate of the target in the target maneuvering coordinate system at the terminal interception moment, x V coordinate, x TV (0) represents the X coordinate of the target in the target maneuvering coordinate system at the initial moment, x V coordinate, y TV (t go,s,i ) represents the Y coordinate of the interceptor in the target maneuvering coordinate system at the terminal interception moment, y V coordinate, y TV (0) represents the Y coordinate of the interceptor in the target maneuvering coordinate system at the initial moment, y V coordinate, z TV (t go,s,i ) represents the Z coordinate of the interceptor in the target maneuvering coordinate system at the terminal interception moment, z V coordinate, z TV (0) represents the Z coordinate of the interceptor in the target maneuvering coordinate system at the initial moment, z V coordinate;

[0137] Step 142. Based on x TV (t go,s,i )、y TV (t go,s,i )、z TV (t go,s,i ) to obtain the flight time t of the interceptor attacking the target go,s,i ; The specific process is as follows:

[0138] For the case where a missile attacks a target along a straight path in three-dimensional space, there is

[0139]

[0140] In the formula, x MV (0) represents the x - coordinate of the interceptor in the target maneuvering coordinate system at the initial moment, y MV (0) represents the y - coordinate of the interceptor in the target maneuvering coordinate system at the initial moment, z MV (0) represents the z - coordinate of the interceptor in the target maneuvering coordinate system at the terminal interception moment, V M (0) represents the target speed at the initial moment;

[0141] Substitute Equation (15), Equation (16), and Equation (17) into Equation (18), and we get

[0142]

[0143] Solve Equation (19) to obtain:

[0144]

[0145] Among them:

[0146]

[0147] Where r(0) represents the relative distance between the interceptor and the target at the initial moment, and n s , m s are both intermediate variables, and r represents the relative distance between the interceptor and the target;

[0148] Step 143: Substitute the t obtained from Equation (20) go,s,i into Equations (15)-(18) to obtain the virtual aiming point;

[0149] Rotate the virtual aiming point from the target maneuvering coordinate system back to the northeast celestial coordinate system to obtain the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) in the northeast celestial coordinate system.

[0150] Other steps and parameters are the same as those in any one of Embodiments 1 to 4.

[0151] Specific Embodiment 6: The difference between this embodiment and any one of Embodiments 1 to 5 is that in Step 15, the PNG method is used to attack the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) obtained by solving in Step 14. Based on the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ), the relative position and relative velocity between the interceptor and the target are obtained. Based on the relative position and relative velocity between the interceptor and the target, n y and n z are obtained, and n x = 0;

[0152] Substitute n x , n y and n z into Equation (1) to solve the differential equation of the dynamic model, and obtain the position, velocity, ballistic inclination angle, and ballistic deflection angle of the interceptor at the next moment;

[0153] The specific process is as follows:

[0154] The three-dimensional proportional navigation method is described as:

[0155]

[0156] Where

[0157] is the rate of change of the line-of-sight inclination angle from the interceptor to the target;

[0158] LOS ε is the line-of-sight inclination angle from the interceptor to the target; LOS β is the line-of-sight deflection angle from the interceptor to the target;

[0159] is the line-of-sight deviation angle rate of the interceptor missile to the target;

[0160] They are respectively expressed as:

[0161]

[0162] Among them, V r is the relative velocity between the missile and the target, [x r , y r , z r is the relative position coordinates of the interceptor missile and the target, [V rx , V ry , V rz is the relative velocity vector of the interceptor missile and the target, N is the proportional navigation ratio, g is the gravitational acceleration at the current position, θ is the trajectory inclination angle of the interceptor missile, r is the relative distance between the interceptor missile and the target, is the first-order derivative of the relative distance between the interceptor missile and the target with respect to time, r β is the relative distance between the interceptor missile and the target in the northeast celestial coordinate system, n y is the overload of the y-axis (normal direction) of the interceptor missile, n z is the overload of the z-axis (lateral direction) of the interceptor missile;

[0163] Substitute the obtained n x , n y and n z into Equation (1) to solve the differential equation of the dynamic model, and obtain the position, velocity, trajectory inclination angle and trajectory deviation angle of the interceptor missile at the next moment.

[0164] Other steps and parameters are the same as those in any one of the first to fifth specific embodiments.

[0165] Specific Embodiment Seven: The difference between this embodiment and any one of the first to sixth specific embodiments is that: the value range of the target coverage parameters (χ, ω) in Step 21 is:

[0166]

[0167] In the formula, χ min represents the lower bound of the value range of χ, χ max represents the upper bound of the value range of χ, ω min represents the lower bound of the value range of ω, ω max represents the upper bound of the value range of ω.

[0168] Other steps and parameters are the same as those in any one of the first to sixth specific embodiments.

[0169] Embodiment 8: The difference between this embodiment and any one of Embodiments 1 to 7 is that: in Step 22, a new initial position, initial velocity of the interceptor missile and new target coverage parameters (χ, ω) in the training set are used as a set of data as the input of the ZEM estimation network, and the corresponding zero-effort miss distance ZEM of the interceptor missile at the mid-course and terminal guidance handover moment in the training set is used as the output of the ZEM estimation network to train the ZEM estimation network to obtain a trained ZEM estimation network;

[0170] The specific process is as follows:

[0171] The ZEM estimation network is a feedforward neural network (BackPropagationNeuralNetwork, BP);

[0172] The feedforward neural network includes an input layer, a hidden layer and an output layer;

[0173] Using a new initial position, initial velocity of the interceptor missile and new target coverage parameters (χ, ω) in the training set as a set of data as the input of the ZEM estimation network, and the corresponding zero-effort miss distance ZEM of the interceptor missile at the mid-course and terminal guidance handover moment in the training set as the output of the ZEM estimation network;

[0174] The number of nodes in the input layer of the ZEM estimation network is 3, the number of nodes in the hidden layer is 10, and the number of nodes in the output layer is 1;

[0175] The loss function used is the mean square error loss function, and the expression is:

[0176]

[0177] Among them, Y a represents the true value of the zero-effort miss distance ZEM of the interceptor missile at the mid-course and terminal guidance handover moment corresponding to the a-th group of new initial position, initial velocity of the interceptor missile and new target coverage parameters (χ, ω), and f(x a ) represents the predicted value of the zero-effort miss distance ZEM of the interceptor missile at the mid-course and terminal guidance handover moment corresponding to the a-th group of new initial position, initial velocity of the interceptor missile and new target coverage parameters (χ, ω), n represents the total number of groups composed of the new initial position, initial velocity of the interceptor missile and new target coverage parameters (χ, ω), and L(Y∣f(x)) represents the mean square error loss function;

[0178] The activation function selected is the Tanh activation function, and the expression is:

[0179]

[0180] During the neural network training process, the learning rate is adaptively changed according to the training error. Let the error be E, then the adaptive learning rate is expressed as

[0181]

[0182] Among them, η represents the adaptive learning rate, and E represents the difference in the ZEM at the mid-course and terminal guidance handover moment between the outputs of the feedforward neural network in two adjacent times. represents the first derivative of E;

[0183] Stop training until all data in the training set are trained, and obtain the trained ZEM estimation network.

[0184] And use the divided test set to verify the estimation accuracy of the trained ZEM estimation network.

[0185] Other steps and parameters are the same as those in any one of the specific embodiments one to seven.

[0186] Specific embodiment nine: The difference between this embodiment and any one of the specific embodiments one to eight is that in step three, the initial position and initial velocity of the interceptor to be measured are input into the trained ZEM estimation network, and the trained ZEM estimation network outputs the zero-effort miss distance ZEM of the interceptor at the mid-course and terminal guidance handover moment.

[0187] Based on the zero-effort miss distance ZEM of the interceptor at the mid-course and terminal guidance handover moment output by the trained ZEM estimation network and the line-of-sight angular rate Design the index function J;

[0188] Use the SQP optimization method to optimize the index function J, and find the optimal coverage parameters (χ L , ω L ) corresponding to the minimum value of the target index function J;

[0189] Substitute the optimal target parameters (χ L , ω L ) into step one to calculate the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i );

[0190] The specific process is as follows:

[0191] In the process of representing the coverage of the target acceleration, there are positive constants χ and a constant ω used to eliminate the errors at the coverage boundaries of different missiles. Optimize the target coverage parameters (χ, ω) to achieve the maximum coverage of the interceptor to the target.

[0192] Since in most current engineering application scenarios, the ZEM of the interceptor to the target at the end of the mid-course guidance and are selected as the mid-course and terminal guidance handover conditions. Therefore, in order to achieve the expectation that as many interceptors as possible meet the mid-course and terminal guidance handover conditions, the ZEM at the mid-course and terminal guidance handover moment and the line-of-sight angular rate After unifying the magnitudes and assigning weights, it is used as the index function for parameter optimization;

[0193] Input the initial position and initial velocity of the interceptor to be measured into the trained ZEM estimation network, and the trained ZEM estimation network outputs the zero-effort miss distance ZEM of the interceptor at the mid-course and terminal guidance handover moment;

[0194] Based on the zero-effort miss distance ZEM of the interceptor at the mid-course and terminal guidance handover moment and the line-of-sight angular rate output by the trained ZEM estimation network Design the index function J;

[0195] The index function J is expressed as:

[0196]

[0197] In the formula, J represents the index function, ε represents the weight value range of [0, 1], represents the line-of-sight angular rate, and ZEM represents the zero-effort miss distance of the interceptor at the mid-course and terminal guidance handover moment;

[0198] Use the SQP optimization method to optimize the target coverage parameters (χ, ω) of the index function J to obtain the optimal target coverage parameters (χ L , ω L ); It is described as:

[0199]

[0200] Substitute the obtained optimal target coverage parameters (χ L , ω L ) into Step 1 to obtain the virtual aiming point (x T , s,f,i , y T,s,f,i , z T,s,f,i ).

[0201] Other steps and parameters are the same as those in any one of the first to eighth specific embodiments.

[0202] Specific Embodiment Ten: The difference between this embodiment and any one of the first to ninth specific embodiments is that in the mid-course guidance stage of Step 4, the proportional navigation guidance law (PNG) is used to aim at the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) generated in Step 3 to perform cooperative interception on the target;

[0203] In the terminal guidance stage, the anti-saturation super-twisting sliding mode guidance law (Saturated Super-Twisting Al goThe rithm Sliding Mode Guidance Law, SSTAG) aims at the true position of the target to achieve cooperative interception of the target, reduce the terminal miss distance of cooperative interception, and improve the interception hit rate; among them, according to different scenarios, the acquisition method of the true position of the target is also different. The common acquisition methods include seeker capture and radar tracking. The present invention adopts the method of seeker capturing the target to obtain the true position of the target.

[0204] The specific process is as follows:

[0205] Step 4-1, in the mid-course guidance stage, the PNG method is used to attack the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) obtained by solving in Step 3 to achieve cooperative interception of the target; the specific process is as follows:

[0206] The three-dimensional proportional navigation method is described as:

[0207]

[0208] Among them,

[0209] is the rate of change of the line-of-sight inclination angle from the interceptor to the target;

[0210] LOS ε is the line-of-sight inclination angle from the interceptor to the target; LOS β is the line-of-sight deflection angle from the interceptor to the target;

[0211] is the rate of change of the line-of-sight deflection angle from the interceptor to the target;

[0212] They are respectively expressed as:

[0213]

[0214] Among them, V r is the relative velocity between the missile and the target, [x r , y r , z r is the relative position coordinates between the missile and the target, [V rx , V ry , V rz is the relative velocity vector between the interceptor and the target, N is the proportional navigation ratio, g is the gravitational acceleration at the current position, θ is the trajectory inclination angle of the interceptor, r is the relative distance between the interceptor and the target, is the first derivative of the relative distance between the interceptor and the target with respect to time, r β is the relative distance between the interceptor and the target in the northeast plane, a εis the normal acceleration of the interceptor missile, a β is the lateral acceleration of the interceptor missile;

[0215] Step 4.2: In the terminal guidance stage, the anti-saturation super-twisting sliding mode guidance law method is adopted to attack the real position of the target, so as to reduce the terminal miss distance of the interceptor missile;

[0216] The specific process is as follows:

[0217] Since keeping the line-of-sight angle unchanged can ultimately achieve the successful interception of the target. Therefore, the sliding mode surface is designed as:

[0218] σ = V q = 0 (30)

[0219] where, V q is the velocity of the interceptor missile in the direction perpendicular to the line of sight; σ is the sliding mode surface;

[0220] The model of the guidance system is written as:

[0221]

[0222] where, V R is the velocity in the line-of-sight direction, A Tq is the acceleration of the target in the direction perpendicular to the line of sight, R is the relative distance between the missile and the target, is the first derivative of σ; A Mq can be obtained from the anti-saturation super-twisting control law, and the expression is as follows:

[0223]

[0224] where, k1, k2, k3 are control coefficients, selected as positive constants, v is the integral variable function, is the first derivative of the integral variable function with respect to time, u is the control input, sat U (u) is the saturation function, v(t0) is the value of the integral variable function at the initial moment, and sgn() is the saturation function.

[0225] Other steps and parameters are the same as those in the first to ninth specific implementation manners.

[0226] The following embodiments are used to verify the beneficial effects of the present invention:

[0227] Embodiment 1:

[0228] The embodiment adopted in the present invention is the mid-course guidance process of multi-to-one cooperative interception, and a 4-to-1 cooperative interception scenario is adopted. The states of the 4 interceptor missiles in the northeast celestial coordinate system at the start of mid-course guidance are shown in Table 1.

[0229] Table 1 Initial states of the interceptor missiles

[0230] Intercept missile number Position (km) Velocity (m / s) Ballistic inclination angle (°) Ballistic deflection angle (°) 1 [-510,-665,22] 2300 -3.20 25.00 2 [-480,-680,35] 2950 -1.70 20.00 3 [-450,-640,35] 2950 -1.50 5.00 4 [-420,-620,32] 2950 -1.30 -5.00

[0231] The target adopts a maneuvering form that combines C-type and S-type maneuvers. The initial position is about 350 km - 400 km away from the interceptor, and the target speed is V T = 2100 m / s. The initial state of the target in the northeast celestial coordinate system is shown in Table 2.

[0232] Table 2 Initial State of the Target

[0233] Position (km) Velocity (m / s) [-929.3,-441.5,15.5] [656.875,-1772.1875,0]

[0234] The maximum overload capacity of the target can be expressed as:

[0235] a Tmax = 4g (34)

[0236] The overload capacity of 4 interceptors can be expressed as:

[0237] a Mmax = 6g (35)

[0238] The maximum angle of attack constraint of the interceptor is expressed as:

[0239]

[0240] First, randomly generate the initial positions of the interceptors at a relative distance of 350 km - 400 km between the missile and the target, and traverse the coverage parameter χ in the range of [800, 1200] with a step size of step χ = 4, and traverse the coverage parameter ω in the range of [0.6, 0.8] with a step size of step ω = 0.002. Perform a large number of calculations to solve the ZEM at the mid-course to terminal guidance handover moment for multiple interceptors. Take the initial state of the interceptor, including the initial position P0 = [x0, y0, z0] and the initial velocity V0 = [v x0 , v y0 , v z0 as the input, and take the ZEM at the mid-course to terminal guidance handover moment of the interceptor as the output to create a dataset. Then divide the generated dataset. The first 95% is used for the training of the BP neural network, and the last 5% is used as the test dataset. Check the trained neural network. The final error distribution is as Figure 4 shown. Among them, the samples with a training error lower than 5% account for 96.3% of the total number of samples, achieving the expected fitting effect.

[0241] Subsequently, use the SQP method in Step 3 to optimize the coverage parameters χ and ω. Among them, the weights in the index function and use the ZEM estimation network trained in the previous step to quickly estimate the ZEM. Finally, obtain the optimal combination of target coverage parameters as shown in Table 3.

[0242] Table 3 Optimal Target Coverage Parameters

[0243] Coverage parameter <![CDATA[χ L > <![CDATA[ω L > Value 1093.9 0.7479

[0244] Then, substitute the optimal target coverage parameters χ L and ω L , which are obtained by solving in the above steps, into the process of solving the virtual aiming point in Step 1. First, solve the standard interception acceleration of the interceptor missile against the target at the initial moment, as shown in Table 4.

[0245] Table 4 Standard Interception Acceleration

[0246] Intercept missile number (i) 1 2 3 4 <![CDATA[a T,s,i (m / s 2 )]]> -29.28 -9.76 9.76 29.28

[0247] Subsequently, through the standard interception acceleration a T,s,i , further adopt the remaining flight time estimation method in Step 1 to obtain the remaining flight times of each interceptor missile, as shown in Table 5.

[0248] Table 5 Remaining Flight Times of Interceptor Missiles

[0249] Intercept missile number (i) 1 2 3 4 <![CDATA[t gos,i (s) > 76.8 59.7 56.8 52.8

[0250] Based on this, the initial virtual aiming points of the interceptor missiles obtained by calculation are shown in Table 6:[[]]END]]

[0251] Table 6 Virtual Aiming Point Coordinates

[0252]

[0253]

[0254] Subsequently, adopt the PNG method to attack the virtual aiming point, set the guidance step size as dt = 0.1 s, and loop the above steps to achieve the cooperative interception of the target in the mid-course guidance stage. Taking interceptor missile 1 as an example, the convergence situation of its virtual aiming point is as Figures 5 - 7 shown.

[0255] Observe Figures 5 - 7 and know that at the mid-course and terminal guidance handover moment, the three-axis position coordinates of the virtual aiming point converge to the vicinity of the target position coordinates, and the target can be effectively intercepted. The mid-course engagement trajectory is as Figure 8 shown.

[0256] Take the moment when the relative distance between the missile and the target is 100 km as the mid-course and terminal guidance handover moment. At this time, the ZEM of the interceptor missile and are shown in Table 7:[[]]END]]

[0257] Table 7 Mid-course and Terminal Handover Condition Table

[0258]

[0259] Set ZEM < 10 km, As the handover condition criterion for entering the terminal guidance, it can be seen from Table 7 that interceptor 1 does not meet the mid-course handover condition, so it does not enter the terminal guidance. The terminal guidance engagement trajectories of interceptors 2, 3, and 4 are as Figure 9 shown.

[0260] Finally, a navigation error with a noise standard deviation of 100 m is applied to the target position during the mid-course guidance, and a noise with a standard deviation of 0.01° / s is applied to during the terminal guidance. 1000 Monte Carlo simulations are carried out for the entire cooperative interception process, and the distribution of the miss distance of the intercepting missile can be obtained as Figure 10 shown.

[0261] From Figure 10 it can be seen that the percentage of the terminal miss distance of the intercepting missile less than 0.6 m is 96.8%. The final result shows that the multi-to-one intelligent cooperative guidance method based on the coverage theory proposed by the present invention can achieve precise interception of targets with equal overload capabilities.

[0262] The present invention can also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention, but these corresponding changes and deformations should all fall within the protection scope of the appended claims of the present invention.

Claims

1. A multi-to-one intelligent cooperative guidance method based on coverage theory, characterized in that: The specific process of the method is as follows: Step 1. Based on the current state of the interceptor and the target, solve for the true standard intercept acceleration of the interceptor to intercept the target with zero control Introduce the coverage probability. Given the target coverage parameters (χ, ω), based on the true standard interception acceleration of the interceptor to intercept the target with zero control Online update the standard interception acceleration a of each interceptor т,s,i ; Based on the standard interception acceleration a of each interceptor missile т,s,i Solve for the three-dimensional remaining flight time t go,s,i , Based on the three-dimensional remaining flight time t go,s,i Generate a three-dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ); Use the PNG method to attack the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ). Based on the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ), obtain the relative position and relative velocity between the interceptor and the target, and based on the relative position and relative velocity between the interceptor and the target, obtain the position, velocity, ballistic inclination angle, and ballistic deflection angle of the interceptor at the next moment; Based on the three-dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ), at the mid-course and terminal guidance handover moment, the interceptor is used to perform orbital recursive zero-effort interception of the target in the current state, and the relative distance between the interceptor and the target at the moment closest to the target is used as the zero-effort miss distance ZEM at the mid-course and terminal guidance handover moment; Step 2: Obtain a training set based on Step 1, and obtain a trained ZEM estimation network based on the training set; the specific process is as follows: Step 2.1: Obtain a training set; the specific process is as follows: 1). Change the initial position and initial velocity of the interceptor missile to obtain a new initial position and initial velocity of the interceptor missile; 2). Traverse the target coverage parameters (χ, ω) within a given range to obtain new target coverage parameters (χ, ω); 3) Based on the new initial position and initial velocity of the interceptor missile, and the new target coverage parameters (χ, ω), re - execute step one to obtain a new three - dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ); 4), Based on the new three-dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ), at the mid-course and terminal guidance handover moment, the interceptor performs orbit propagation zero-effort interception of the target in the current state, and takes the relative distance between the interceptor and the target at the moment closest to the target as the zero-effort miss distance ZEM at the mid-course and terminal guidance handover moment; 5). Repeat steps 1)-4) to obtain M' zero-effort miss distances ZEM at the mid-course and terminal guidance handover moments; Step 2.2: Use the new initial position, initial velocity of the interceptor missile and the new target coverage parameters (χ, ω) in the training set as a set of data as the input of the ZEM estimation network, and use the corresponding zero-effort miss distance ZEM of the interceptor missile at the mid-course and terminal guidance handover moment in the training set as the output of the ZEM estimation network to train the ZEM estimation network and obtain a trained ZEM estimation network; Step 3: Input the initial position and initial velocity of the interceptor missile to be measured into the trained ZEM estimation network, and the trained ZEM estimation network outputs the ZEM at the mid-course and terminal guidance handover moment; The ZEM and line-of-sight angular rate at the mid-course and terminal guidance handover moment output by the trained ZEM estimation network Design the index function J; Use the SQP optimization method to optimize the objective function J and find the optimal coverage parameters (χ L , ω L ) corresponding to the minimum value of the objective function J; Substitute the optimal target parameters (χ L , ω L ) into the calculation of the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) in Step 1; Step 4, in the mid-course guidance stage, use the proportional navigation method to aim at the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) generated in Step 3, and conduct cooperative interception of the target; In the terminal guidance stage, an anti-saturation super-twisting sliding mode guidance law is adopted to aim at the true position of the target to achieve cooperative interception of the target.

2. The multi-to-one intelligent cooperative guidance method based on the coverage theory according to claim 1, characterized in that: The specific process of the above Step 1 is as follows: Step 1.1: The kinetic model of the interceptor missile adopted is expressed in the northeast celestial coordinate system as: Where, x M 、y M 、z M are respectively the three-axis positions of the interceptor missile; V M is the magnitude of the interceptor missile velocity; θ M is the ballistic inclination angle; ψ M is the ballistic deflection angle; n x 、n y 、n z are the components of the interceptor overload on the three axes in the velocity coordinate system, respectively; g is the acceleration due to gravity; are respectively x M , y M , z M the first-order derivative with respect to time; are respectively V M , θ M , ψ M the first-order derivative with respect to time; In the mid-course and terminal guidance stages of the interception process, the process constraints are considered as angle of attack constraints and overload constraints, expressed as: Among them, is the pneumatic combined overload, α max is the maximum angle of attack, n max is the maximum overload, and α is the angle of attack; Steps 1 and 2: Solve for the true standard intercept acceleration of the interceptor to intercept the target with zero control based on the current states of the interceptor and the target Step 13: Introduce the coverage probability. Given the target coverage parameters (χ, ω), based on the true standard interception acceleration of the interceptor to intercept the target with zero control Online update the standard interception acceleration a of each interceptor т,s,i ; Step 14. Based on the standard intercept acceleration a T,s,i Solve for the remaining flight time t of the interceptor attacking the target in three-dimensional space go,s,i ; Then, from the remaining flight time t go,s,i the three-dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) is obtained by solving; Step 15. Use the PNG method to attack the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) obtained by solving in Step 14. Based on the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ), obtain the relative position and relative velocity between the interceptor and the target. Based on the relative position and relative velocity between the interceptor and the target, obtain n y and n z , n x = 0; Substitute n x , n y and n z into Equation (1) to solve the differential equation of the kinetic model, and obtain the position, velocity, ballistic inclination angle, and ballistic deflection angle of the interceptor at the next moment; Step 1.6: Repeat steps 1.1 to 1.5 until the distance between the interceptor missile and the target reaches 100 km and stop, and the stop moment is used as the mid-course and terminal guidance handover moment; Based on the three-dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) corresponding to the stop moment, at the mid-course and terminal guidance handover moment, the interceptor performs orbit recursion zero-control interception of the target in the current state, and takes the relative distance between the interceptor and the target at the moment closest to the target as the zero-control miss distance ZEM at the mid-course and terminal guidance handover moment.

3. The multi-to-one intelligent cooperative guidance method based on the coverage theory according to claim 2, characterized in that: In the first and second steps, based on the current states of the interceptor and the target, solve the true standard interception acceleration of the interceptor to intercept the target with zero control The specific process is as follows: Step 1.2.1: The missile's zero-effort interception of the target needs to satisfy where α i represents the central angle formed by the circular arc of the target's motion from the initial interception moment to the terminal moment, r T,o,i represents the trajectory radius of the target moving with an acceleration of r T,o,i = [(x o,i - x T ) 2 + (y o,i - y T ) 2 1 / 2 , (x o,i , y o,i ) is the center of the trajectory of the target moving with an acceleration of , (x T , y T ) is the initial position of the target, r M,f,i represents the distance of the missile from the interception hit point, r M,f,i = [(x f,i - x M,i ) 2 + (y f,i - y M,i ) 2 1 / 2 , (x f,i , y f,i ) is the interception hit point, (x M,i , y M,i ) is the initial position of the i-th interceptor missile; V T represents the target speed, V M represents the interceptor missile speed; is the true standard interception acceleration of the target with respect to the i-th interceptor missile;​​ y f,i = tan(γ M,i ) × (x f,i - x M,i ) + y M,i (5) In the formula, r T,f,i represents the distance from the target to the intercept hit point, r T,f,i =[(x f,i -x T ) 2 +(y f,i -y T ) 2 1 / 2 ;​ γ M,i represents the ballistic angle of the i-th interceptor missile; γ T represents the target ballistic angle; Step 122: Set the initial value of x f,i , and repeatedly execute formulas (3), (4), (5), and (6) using the Newton iteration method until x f,i converges to obtain the optimal value of x f,i ; Steps One, Two, and Three: Based on the optimal x f,i The value is used to calculate the true standard intercept acceleration of the interceptor for zero-control interception of the target according to Equation (7). In the formula, x T,l,i is an intermediate variable.

4. A one-to-many intelligent cooperative guidance method based on the coverage theory according to claim 3, characterized in that: In step 13, the coverage probability is introduced. Given the target coverage parameters (χ, ω), based on the true standard interception acceleration of the interceptor for zero-control interception of the target Online update the standard interception acceleration a of each interceptor т , s, i; The specific process is as follows: Step 131: Use f PDF (a T ) to represent the probability density function of the target acceleration. When the upper bound of the target maneuverability is known and t > t k , it is considered that the maneuvering acceleration of the target follows a normal distribution, that is, a T (t) ~ N(a T (t k ), σ 2 ); where σ is the standard deviation of the normal distribution; t is a future moment, t k is the current moment, a T (t) is the target acceleration at a future moment, a T (t k ) is the target acceleration at the current moment, N() is the standard normal distribution; Then the acceleration coverage probability of all interceptor missiles against the target at the current moment is expressed as Where a T represents the current acceleration of the target, N m represents the total number of interceptors, i represents the interceptor number, represents the current time t k the acceleration coverage probability of all intercepting missiles on the target; a T,max is the upper bound of the target maneuverability, represents the target coverage process function, and there is where a M,max represents the maximum acceleration amplitude of the interceptor missile, and ω represents the acceleration coverage parameter; Step 132, based on the acceleration coverage probability of all intercept missiles for the target at time k + 1 Obtain the one that maximizes the overall coverage probability The specific process is as follows: In the formula, Denote t k The acceleration coverage probability of all intercepting missiles on the target at the moment of t+1; Represents the array of true standard interception accelerations of each interceptor missile; Definition Based on the principle of maximizing the overall coverage probability, the gradient descent method is used to cooperatively intercept and cover the target (11), and we get: In the formula, represents the gradient function, represents the first derivative of the true standard intercept acceleration with respect to time, j represents the interceptor number, represents the target coverage process function; represents the true standard intercept acceleration of the target with respect to the j-th interceptor; χ is the acceleration coverage parameter; Step 133: Set the initial value of time t go,s,i ; True standard intercept acceleration of the interceptor for zero-control intercepting the target and the remaining flight time t go,s,i The expected standard intercept acceleration at the terminal intercept moment is obtained The expression is as follows: where t go,s,i represents the remaining flight time of the i-th interceptor missile; Step 134: Use the expected standard intercept acceleration as the standard intercept acceleration of the updated interceptor 5. A one-to-many intelligent cooperative guidance method based on the coverage theory according to claim 4, characterized in that: In step 14, based on the standard interception acceleration a T,s,i Solve the remaining flight time tgo,s,i of the interceptor attacking the target in three-dimensional space; Then, from the remaining flight time t go,s,i Solve to obtain the three-dimensional virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ); The specific process is as follows: Step 141: Convert the interception scenario from the northeast celestial coordinate system to the target maneuvering coordinate system X V Y V Z V , X V axis points to the target velocity direction, Y V axis points to the direction of the target velocity, Z V axis is determined according to the right-hand rule; Obtain the expression of the position coordinates of the target changing with time in the target maneuvering coordinate system; expressed as: z TV (t go,s,i ) = z TV (0) (17) In the target maneuvering coordinate system, the target only moves in the X V -Y V plane; where x TV (t go,s,i ) represents the X V coordinate of the target in the target maneuvering coordinate system at the terminal interception time, x TV (0) represents the X V coordinate of the target in the target maneuvering coordinate system at the initial time, y TV (t go,s,i ) represents the Y V coordinate of the interceptor in the target maneuvering coordinate system at the terminal interception time, y TV (0) represents the Y V coordinate of the interceptor in the target maneuvering coordinate system at the initial time, z TV (t go,s,i ) represents the Z V coordinate of the interceptor in the target maneuvering coordinate system at the terminal interception time, z TV (0) represents the Z V coordinate at the initial time; Step 142: Based on x TV (t go,s,i )、y TV (t go,s,i )、z TV (t go,s,i ) to obtain the flight time t of the interceptor attacking the target go,s,i ; The specific process is as follows: For the case where the missile attacks the target along a straight path in three-dimensional space, there is where x MV (0) represents the x - coordinate of the interceptor in the target maneuvering coordinate system at the initial moment, y MV (0) represents the y - coordinate of the interceptor in the target maneuvering coordinate system at the initial moment, z MV (0) represents the z - coordinate of the interceptor in the target maneuvering coordinate system at the terminal interception moment, V M (0) represents the target velocity at the initial moment; Substitute equations (15), (16), and (17) into equation (18), and we get Solve equation (19) to obtain: Among them: where r(0) represents the relative distance between the interceptor and the target at the initial moment, and n s , m s are both intermediate variables, and r represents the relative distance between the interceptor and the target; Step 143: Substitute the t obtained from Equation (20) go,s,i into Equations (15) - (18) to obtain the virtual aiming point; The virtual aiming point is rotated back from the target maneuvering coordinate system to the northeast celestial coordinate system to obtain the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) in the northeast celestial coordinate system.

6. The multi-to-one intelligent cooperative guidance method based on the coverage theory according to claim 5, characterized in that: In the fifteenth step, the PNG method is used to attack the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) obtained by solving in the fourteenth step. Based on the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ), the relative position and relative velocity between the interceptor and the target are obtained. Based on the relative position and relative velocity between the interceptor and the target, n y and n z are obtained, and n x = 0; Substitute n x , n y and n z into Equation (1) to solve the differential equation of the kinetic model, and obtain the position, velocity, ballistic inclination angle, and ballistic deflection angle of the interceptor at the next moment; The specific process is as follows: The three-dimensional proportional navigation method is described as: Where, is the line-of-sight inclination rate of the interceptor missile to the target; LOS ε is the line-of-sight inclination angle from the interceptor to the target; LOS β is the line-of-sight deflection angle from the interceptor to the target; is the line-of-sight deviation angle rate of the interceptor missile to the target; They are respectively expressed as: Among them, V r is the relative velocity between the projectile and the target, [x r , y r , z r is the relative position coordinates of the interceptor and the target, [V rx , V ry , V rz is the relative velocity vector of the interceptor and the target, N is the proportional navigation ratio, g is the gravitational acceleration at the current position, θ is the ballistic inclination angle of the interceptor, r is the relative distance between the interceptor and the target, is the first derivative of the relative distance between the interceptor and the target with respect to time, r β is the relative distance between the interceptor and the target in the northeast-up coordinate system, Substitute the obtained \(n\) x , \(n\) y and \(n\) z into Equation (1) to solve the differential equation of the kinetic model, and obtain the position, velocity, flight path angle and drift angle of the interceptor at the next moment.

7. A one-to-many intelligent cooperative guidance method based on the coverage theory according to claim 6, characterized in that: The value range of the target coverage parameters (χ, ω) in Step 2.1 is: where χ min represents the lower bound of the value range of χ, and χ max represents the upper bound of the value range of χ, ω min represents the lower bound of the value range of ω, and ω max represents the upper bound of the value range of ω.

8. A multi-to-one intelligent cooperative guidance method based on the coverage theory according to claim 7, characterized in that: In Step 2.2, use the new initial position, initial velocity of the interceptor missile and the new target coverage parameters (χ, ω) in the training set as a set of data as the input of the ZEM estimation network, and use the corresponding zero-effort miss distance ZEM of the interceptor missile at the mid-course and terminal guidance handover moment in the training set as the output of the ZEM estimation network to train the ZEM estimation network and obtain a trained ZEM estimation network; The specific process is as follows: The ZEM estimation network is a feedforward neural network; The feedforward neural network includes an input layer, a hidden layer and an output layer; Take a set of data consisting of the new initial position, initial velocity of the interceptor missile in the training set, and the new target coverage parameters (χ, ω) as the input of the ZEM estimation network, and the zero-effort miss ZEM of the interceptor missile at the mid-course and terminal guidance handover moment in the training set as the output of the ZEM estimation network; The number of nodes in the input layer of the ZEM estimation network is 3, the number of nodes in the hidden layer is 10, and the number of nodes in the output layer is 1; The loss function adopted is the mean square error loss function, and the expression is: Among them, Y a represents the true value of the zero-effort miss (ZEM) of the interceptor at the mid-course to terminal guidance handover moment corresponding to the initial position, initial velocity of the a-th group of new interceptors and the new target coverage parameters (χ, ω), f(x a ) represents the predicted value of the zero-effort miss (ZEM) of the interceptor at the mid-course to terminal guidance handover moment corresponding to the initial position, initial velocity of the a-th group of new interceptors and the new target coverage parameters (χ, ω), n represents the total number of groups composed of the initial position, initial velocity of the new interceptors and the new target coverage parameters (χ, ω), and L(Y∣f(x)) represents the mean square error loss function; Select the activation function as the Tanh activation function. The adaptive learning rate is expressed as Among them, η represents the adaptive learning rate, and E represents the difference in the ZEM at the mid-course and terminal guidance handover moment between the outputs of the feedforward neural network in two adjacent times; represents the first derivative of E; Stop training until all the data in the training set are trained, and obtain the trained ZEM estimation network.

9. A one-to-many intelligent cooperative guidance method based on the coverage theory according to claim 8, characterized in that: In step 3, input the initial position and initial velocity of the interceptor missile to be measured into the trained ZEM estimation network, and the trained ZEM estimation network outputs the zero-effort miss ZEM of the interceptor missile at the mid-course and terminal guidance handover moment; Zero-effort miss ZEM and line-of-sight angular rate of the interceptor at the mid-course and terminal guidance handover moment based on the output of the trained ZEM estimation network Design the index function J; The SQP optimization method is used to optimize the objective function J to find the optimal coverage parameters (χ L , ω L ) corresponding to the minimum value of the objective function J; Substitute the optimal target parameters (χ L , ω L ) into the calculation of the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) in Step 1; The specific process is as follows: Input the initial position and initial velocity of the interceptor missile to be measured into the trained ZEM estimation network, and the trained ZEM estimation network outputs the zero-effort miss ZEM of the interceptor missile at the mid-course and terminal guidance handover moment; Zero-effort miss ZEM and line-of-sight angular rate of the interceptor at the mid-course and terminal guidance handover moment based on the output of the trained ZEM estimation network Design the index function J; The index function J is expressed as: In the formula, J represents the index function, ε represents the weight value range of [0, 1], represents the line-of-sight angular rate, and ZEM represents the zero-effort miss of the interceptor at the handover moment between mid-course and terminal guidance; The SQP optimization method is used to optimize the objective function J for the target coverage parameters (χ, ω), and the optimal target coverage parameters (χ L , ω L ) are obtained; it is described as: Substitute the obtained optimal target coverage parameters (χ L , ω L ) into Step 1 to obtain the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ).

10. A one-to-many intelligent cooperative guidance method based on the coverage theory according to claim 9, characterized in that: In the mid-course guidance stage of step 4, the proportional navigation method is used to aim at the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) generated in step 3 to conduct cooperative interception of the target; In the terminal guidance stage, adopt the anti-saturation super-twisting sliding mode guidance law to aim at the true position of the target to achieve cooperative interception of the target; The specific process is as follows: Step 4-1. In the mid-course guidance phase, use the PNG method to attack the virtual aiming point (x T,s,f,i , y T,s,f,i , z T,s,f,i ) obtained by solving in Step 3 to achieve cooperative interception of the target; Step 4.

2. In the terminal guidance stage, adopt the anti-saturation super-twisting sliding mode guidance law method to attack the true position of the target; The specific process is as follows: Design the sliding surface: σ = V q = 0 where V q is the velocity of the interceptor in the direction perpendicular to the line of sight; σ is the sliding mode surface; The model of the guidance system is written as: Among them, V R is the velocity in the line-of-sight direction, A Tq is the acceleration of the target along the direction perpendicular to the line of sight, R is the relative distance between the missile and the target, is the first derivative of σ; A Mq can be obtained from the anti-saturation super-twisting control law, and the expression is as follows: where k1, k2, and k3 are control coefficients, v is an integral variable function, is the first derivative of the integral variable function with respect to time, u is the control input, and sat U (u) is the saturation function, v(t0) is the value of the integral variable function at the initial time, and sgn() is the saturation function.

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