A reverse-orbit cooperative guidance method based on virtual target points

Abstract

This disclosure provides a reverse-orbit cooperative guidance method based on virtual target points. The method includes: estimating the target velocity direction based on target observation information; assuming the target moves in the opposite direction of the missile with maximum maneuverability, calculating the attack time required for each missile to strike the target based on the geometric and kinematic relationships between the missile and the target, and taking the maximum value as the ideal attack time for the missile swarm; calculating the predicted hit point based on target observation information, target velocity direction, and ideal attack time; selecting a reverse-orbit strike mode or a lateral strike mode based on the positional relationship between the missile, the target, and the predicted hit point, and determining the strike angle; calculating the virtual target point for each missile based on the strike angle; and controlling each missile to fly towards the virtual target point and hit the target. Using this invention can improve the probability and effectiveness of target strikes.

Description

Technical Field

[0001] This invention relates to the field of multi-vehicle cooperative guidance and control technology, specifically to a reverse-orbit cooperative guidance method based on virtual target points. Background Technology

[0002] With the continuous development of near-space vehicles, especially high-speed near-space vehicles with high speed, high maneuverability, and strong penetration capabilities, they have become one of the most threatening weapons, posing a great challenge to guidance missions. Single-missile operations can no longer meet operational requirements, and multi-missile cooperative operations have become a current research trend. Various cooperative guidance strategies, such as attack time coordination, attack angle coordination, multi-constraint coordination, and cooperative guidance, have been proposed successively. Shi Heng and Zhu Jihong obtained the expected impact point as a virtual target point through iterative calculation, realizing the transformation of highly maneuvering targets into low-speed, small-maneuvering targets. Wang designed pitch acceleration to make the trajectory fall into the yaw plane, transforming the three-dimensional problem into a planar problem, and then designed yaw acceleration to achieve simultaneous strike on the target. You Hao et al. proposed a cooperative guidance law with dual constraints of time and angle based on sliding mode theory. By using consistency theory, they avoided the error caused by the estimation of remaining time and achieved high-precision strike on maneuvering targets. Wang designed a cooperative optimal guidance law for bang-bang maneuvering targets. Through rapid multi-model adaptive estimation of target acceleration and target acceleration switching time, he achieved accurate tracking of target acceleration and strike on the target.

[0003] In addition, many scholars have proposed coverage strategies that use multiple missiles to cover the target's reachable domain. Su, based on a linear model, achieved cooperative guidance for highly maneuverable targets by setting virtual aiming points for the missiles to cover the target's maneuverable domain. Xiao Wei and Chen applied the coverage strategy to nonlinear models in two-dimensional and three-dimensional scenarios, respectively, and added the concept of a standard ballistic trajectory to dynamically adjust the bias term coefficients. Liu, based on this, considered the optimal values ​​of the initial position of the missiles and the number of missile groups, and simulations verified that the method has good robustness to noise and errors. Bai applied the coverage strategy to heterogeneous missile groups, and used numerical methods to calculate the number of missile groups and initial positions required for coverage, achieving cooperative guidance of multiple missiles with less maneuverability than the target against highly maneuverable targets. Jiang Yong introduced the Apollonius circle into the coverage strategy, achieving cooperative guidance for targets with unknown maneuverability.

[0004] With the continuous development of communication jamming techniques, cutting off the enemy's communication network can disrupt their command and control functions and greatly weaken their coordination capabilities. Open-loop cooperative guidance has become an optional solution when inter-missile communication is restricted. However, all open-loop cooperative methods require pre-setting the attack time, and the reasonable setting of the ideal attack time has always been a challenge.

[0005] Meanwhile, current cooperative guidance methods primarily aim for at least one missile to hit the target. However, in scenarios where the speed and maneuverability of both attacking and defending forces are similar, even if the missile launch point is the same as the incoming missile target point, causing the speed directions of both sides to be opposite in the initial guidance phase, thus maintaining a high missile-target rendezvous speed, as the attack progresses, the target's maneuvering can easily shift from a head-on attack to a flanking attack or even a pursuit, reducing the rendezvous speed and lowering the attack success rate and the strike effect on the target. Adopting reverse-orbit guidance can improve the missile-target rendezvous speed, reduce the speed requirement for the missile, and ensure that the missile's normal overload is perpendicular to the missile-target line of sight, maximizing the efficiency of maneuvering to change the line-of-sight angle, thus reducing the required missile overload. Summary of the Invention

[0006] In view of this, the present invention provides a reverse-orbit cooperative guidance method based on virtual target points, which can improve the probability and effect of hitting the target.

[0007] To solve the above-mentioned technical problems, the present invention is implemented as follows.

[0008] A reverse-orbit cooperative guidance method based on virtual target points includes:

[0009] Step 1: Estimate the target velocity direction based on target observation information;

[0010] Step 2: Assuming the target moves in the opposite direction of the missile with maximum maneuverability, calculate the attack time required for each missile to strike the target based on the geometric and kinematic relationships between the missiles and the target, and take the maximum value as the ideal attack time T of the missile swarm. go ;

[0011] Step 3: Based on target observation information, target velocity direction, and ideal attack time T go Calculate the predicted hit point P pre ;

[0012] Step 4: Based on the missile, target, and predicted impact point P pre Based on the positional relationship between them, select the reverse trajectory attack method or the lateral attack method, and determine the attack angle; based on the attack angle, calculate the virtual target point P of each missile i. vir,i ;

[0013] Step 5: Control each missile to fly towards the virtual target point and hit the target.

[0014] Preferably, in step 1, the estimation of the target velocity direction based on the target observation information is as follows:

[0015] Based on target observation information, Kalman filtering is used to estimate the target velocity direction; in the Kalman filtering estimation, the constructed observation vector Z... k The component of the target velocity V in the direction of the projectile's line of sight was added.LOS :

[0016] Z k =[x obs,k y obs,k z obs,k V LOS ] T

[0017] In the formula, x obs,k ,y obs,k ,z obs,k The subscript indicates the k-th iteration, representing the target location being observed.

[0018] Then the observation matrix H k for:

[0019]

[0020] In the formula: I is the identity matrix, u LOS It is a unit vector in the direction of the bullet's line of sight.

[0021] Preferably, step 2 is as follows:

[0022] Let t be the attack time required for missile i to strike the target when the target is moving in the opposite direction of the missile with maximum maneuverability. go,i,max M s,i T s Let M be the projection points of missile i and the target's initial position onto the predicted strike surface S, respectively. s,i The positions of the y-axis and z-axis in the geodetic coordinate system are y M,i ,z M,i T s The positions of the y-axis and z-axis in the geodetic coordinate system are y T ,z T .

[0023] Two projection points M s,i ,T s The distance between them is expressed as

[0024]

[0025] Target projection point T s With the predicted hit point P pre The distance between them is:

[0026]

[0027] Among them, V T To estimate the target velocity based on target observation information, a T,max The target's maximum acceleration.

[0028] Target projection point T sThe distance between the target's initial position T and the target's initial position T is

[0029]

[0030] As the target maneuvers away from the missile, M s,i T s With P pre If they are on the same straight line, then the projection point M of missile i is... s,i With the predicted hit point P pre The distance is:

[0031]

[0032] Finally, the predicted hit point P is obtained. pre =(x pre ,y pre ,z pre The coordinates of ) are:

[0033]

[0034] In the formula, (x T ,y T ,z T ) represents the target position coordinates, β s The azimuth angle of the projected line of sight onto the predicted impact surface;

[0035] Assuming the missile flies directly towards a stationary target at the predicted impact point, the remaining flight time is estimated to be...

[0036]

[0037] In the formula, V M,i R represents the speed of missile i. M,i For missile i and the predicted hit point P pre The distance between them, N is the proportional guidance coefficient; σ i Let be the angle between the velocity of missile i and the line connecting the missile and the target.

[0038] The attack time t go,i,max Substituting into the above formula, we obtain the missile i and the predicted hit point P. pre Distance between:

[0039]

[0040] Finally, we obtained information about t. go,i,max equation

[0041]

[0042] Solve equations (III) to (VI) simultaneously to determine the attack time t required for the target's maximum maneuverability.go,i,max ;

[0043] Take the maximum attack time required for each missile as the ideal attack time T for the missile swarm. go .

[0044] Preferably, step 3 is as follows:

[0045] When the target moves in the same direction with maximum overload, its circular reachable radius R and the velocity deflection angle δ of the circular motion are:

[0046]

[0047] In the formula, a T,max V is the target's maximum maneuvering acceleration. T T represents the target's flight speed obtained from target observation information. go Ideal attack time;

[0048] The sphere formed by the maximum maneuver is approximated as a circular plane, and the distance between the center of the circular plane and the target is L = Rsinδ;

[0049] Combined with target location P T =(x T ,y T ,z T ), the trajectory inclination angle θ in the target velocity direction T and ballistic deflection The center position of the target's maximum maneuver range at time t is obtained as follows:

[0050]

[0051] (x o ,y o ,z o The predicted hit point P at time t is... pre .

[0052] Preferably, in step 4, the step of determining the missile, target, and predicted impact point P... pre The relative positions of the targets determine whether to use a counter-orbital strike or a lateral strike.

[0053] When the angle between the missile and the target meets the set first angle condition, it has the advantage of reverse trajectory strike and uses reverse trajectory strike as the strike method; otherwise, it uses lateral strike as the strike method.

[0054] When a lateral strike is selected, two lateral strike methods are further determined based on the second angle condition: one is to strike the target without changing the current angle of motion; the other is to calculate the strike angle based on the angle between the missile and the predicted impact point, and then use the calculated strike angle to measure the strike.

[0055] Preferably, in step 4, the step of determining the missile, target, and predicted impact point P... pre Based on the positional relationship between them, choose either a reverse-track attack or a lateral attack, and determine the attack angle as follows:

[0056] Let P be the virtual target point of missile i. vir,i With the predicted hit point P pre The line connecting the two points is the first line, and the angle between the first line and the reference direction on the predicted impact surface S is β. s.i The elevation angle between the target surface S and the target surface S is α. s,i Similarly, the target and predicted hit point P pre The corresponding included angle and elevation angle are defined as β. s.T and α s,T ;

[0057] The method of attack is determined by both equation (I) and equation (II):

[0058]

[0059] in, and The desired azimuth and elevation angles of the missile-target line-of-sight projection for guiding missile i; n is the number of missiles; y M,i ,z M,i Let y be the position of the projection point of missile i onto the predicted strike surface S in the geodetic coordinate system along the y and z axes; pre ,z pre To predict the hit point P pre The y-axis and z-axis positions; δ is the velocity deflection angle of the target when it moves in the same direction with maximum overload and is in circular motion.

[0060] Preferably, in step 4, the virtual target point P of each missile i is calculated based on the strike angle. vir,i for:

[0061] according to The expected attack direction vector is calculated as follows:

[0062]

[0063] The farthest position of the virtual target point is obtained from the distance r between the projectile and the target:

[0064]

[0065] In the formula, k1 is a scaling factor. Setting k1 < 1 ensures that the virtual target point is located between the missile and the target, thus obtaining the coordinates of the virtual target point:

[0066]

[0067] In the formula: k2 is the adjustment parameter, T go The ideal attack time is calculated in step 2. P represents the remaining flight time of missile i; t represents the current time; P represents the remaining flight time of missile i. T The coordinates are the target location.

[0068] Beneficial effects:

[0069] (1) Open-loop cooperative guidance methods all require pre-setting the attack time, and the reasonable setting of the ideal attack time has always been a challenge. Currently, the attack time is set manually, and there is no reasonable setting method. This invention proposes a method for calculating the ideal attack time based on the target's maneuvering range and missile guidance characteristics. The calculated ideal attack time is used to determine the predicted hit point, thereby improving the probability and effect of hitting the target.

[0070] (2) In order to achieve multi-constraint cooperative guidance, the present invention combines the target azimuth and the predicted hit point to set up a virtual target point, guiding the missile to strike the target under the desired constraints.

[0071] (3) When determining the virtual target point, the present invention determines the attack method as reverse trajectory attack or side attack based on the angle between the missile and the target. It fully utilizes the advantages of the missile's current position to set up a virtual target point to guide the missile to be constrained and surrounded by the target, thereby improving the success rate of the attack.

[0072] (4) Current cooperative guidance methods take successful target acquisition as the only constraint. This invention adds a constraint on the attack angle, making the attack mode a reverse-orbit guidance, which improves the strike effect and reduces the requirements for missile speed. Attached Figure Description

[0073] Figure 1 This is a schematic diagram of the reachable region of the target.

[0074] Figure 2 This is a schematic diagram of the reachable region of the target (Txy plane).

[0075] Figure 3 This is a terminal guidance scenario under ideal attack time.

[0076] Figure 4 This is a schematic diagram of the ideal attack time range.

[0077] Figure 5 This is a schematic diagram for guiding virtual target points.

[0078] Figure 6 The line connecting the virtual target point and the predicted impact area.

[0079] Figure 7 This is the trajectory of a missile swarm attacking a C-shaped maneuvering target.

[0080] Figure 8 This refers to the attack angle of a missile swarm against a C-shaped maneuvering target.

[0081] Figure 9 This is an overload command for missile swarm attacks on C-type maneuvering targets.

[0082] Figure 10 This represents the total miss distance of a missile swarm attacking a C-type maneuvering target.

[0083] Figure 11 This is the minimum miss distance for a missile swarm to strike a C-type maneuvering target.

[0084] Figure 12 This is a flowchart of the present invention. Detailed Implementation

[0085] This invention addresses the guidance problem of high-speed maneuvering targets in near-space within a three-dimensional environment, proposing a reverse-orbit cooperative guidance method based on virtual target points. By analyzing the target's maneuvering range and combining it with the missile's guidance characteristics, a method for calculating the ideal attack time of a missile swarm is proposed, thus transforming the guidance problem of high-speed maneuvering targets into the problem of hitting a point on a fixed plane in space at a specific time and angle. Subsequently, to address the high speed requirements of the missile, a virtual target point is selected in space to guide the missile based on the ideal attack time and angle. The hit angle meets the requirements of reverse-orbit guidance, improving the probability and effectiveness of target engagement.

[0086] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0087] A flowchart of the reverse-orbit cooperative guidance method based on virtual target points in this embodiment of the invention is shown. The method includes the following steps:

[0088] Step 1: Estimate the target velocity and direction based on the target observation information.

[0089] The seeker on a typical missile can only detect and obtain the target's position information and the magnitude of its velocity in the direction of the missile's line of sight. The target's velocity vector V... T This can be obtained through Kalman filtering:

[0090]

[0091] In the formula: v k For process noise, w k To observe noise.

[0092] The target's state vector X k Including the target's location P T =[x k y k z k ],speed and acceleration Since these steps involve parameters of the target, and the subscripts need to reflect the iteration number k, subscripts representing the target are not included for the sake of simplicity.

[0093]

[0094] Assuming the target undergoes uniformly accelerated motion, then the state transition matrix F k for

[0095]

[0096] In the formula: Δt is the observation time interval, and I is the identity matrix.

[0097] The target's observation information includes the target's position and the component of its velocity along the line of sight. Therefore, the observation vector Z... k for

[0098] Z k =[x obs,k y obs,k z obs,k V LOS ] T (4)

[0099] Observation matrix H k for

[0100]

[0101] In the formula: u LOS =[u x,k u y,k u z,k ] is the unit vector in the line-of-sight direction, obtained through the transformation matrix between the line-of-sight coordinate system and the ground coordinate system:

[0102]

[0103] In the formula: Let θ be the azimuth angle. L For elevation and elevation angles.

[0104] Applying the Kalman filter formula

[0105]

[0106] In the formula: G is the covariance matrix, Q is the prediction uncertainty, R is the sensor noise, K is the Kalman gain, and the subscript k|k-1 indicates the prediction of the state vector at time k in the (k-1)th iteration.

[0107] The estimated target speed is

[0108]

[0109] The target's trajectory inclination angle and trajectory deflection angle are further obtained as follows:

[0110]

[0111] Step 2: Calculate the predicted hit point P pre .

[0112] Specifically, in a multi-missile coordinated guidance scenario, similar to missiles, the target also possesses an approximately cone-shaped maximum maneuver range, i.e., the target's reachability domain, such as... Figure 1 , Figure 2 As shown:

[0113] The reachability domain is determined by the target's maneuver constraint a T,max Flight speed V T and flight time T go Decision. When the target maneuvers in the same direction with maximum overload, the radius of its circular motion and the velocity deflection angle are:

[0114]

[0115] In the formula: V T For V T The length of the module, T go Take the ideal attack time T obtained from step three. go It should be noted that step two is listed first here for smoother logical explanation. In actual work, step three is executed first to obtain T. go Then perform step 2 to calculate the predicted hit point P. pre .

[0116] Because the terminal guidance phase is short, the high-speed missile and target have extremely high speeds, and its maneuverability is limited, its maneuver angle δ is a small angle. Therefore, the sphere formed by the maximum maneuver can be approximated as a circular plane, with its diameter and distance from the target T being...

[0117]

[0118] Combined with the target's location P T =(x T ,y T ,z T The ballistic inclination angle θ in the target velocity direction obtained in step one. T and ballistic deflection The center position of the target's maximum maneuver range at time t is obtained as follows

[0119]

[0120] Here, (x) o,y o ,z o The predicted hit point P at time t is... pre As the distance between the projectile and the target decreases, the distance between the target and the predicted impact area also decreases, causing the predicted impact point to gradually converge to the actual impact point.

[0121] Step 3: Calculate the ideal attack time T go .

[0122] In open-loop cooperative guidance, setting the ideal attack time has always been a challenge. If the ideal attack time is set too long, it will exceed the missile's ability to adjust the attack time, resulting in the hit time being less than the ideal attack time or missing the target. If the time is set too short, it will exceed the missile's own flight capability and make it impossible to strike the target within the ideal attack time.

[0123] In the interception scenario, at the start of terminal guidance, the target's velocity direction is almost aligned with the line-of-sight direction. Target maneuvering causes lateral and longitudinal movement, extending the terminal guidance attack time. The attack time is longest when the target performs a C-shaped maneuver away from the missile with maximum overload. To design an ideal attack time that satisfies missile speed limitations while allowing sufficient maneuvering time to meet attack angle constraints, the attack time for each missile is calculated at the start of terminal guidance. Let t be the attack time required for missile i to strike the target when the target moves in the opposite direction to the missile with maximum maneuvering capability. go,i,max The predicted hit point is P. pre Then, in terminal guidance scenarios such as Figure 3 As shown in the figure. Plane S in the figure represents the predicted strike surface, and M represents the missile's position point. s,i T s Let M be the projection points of missile i and the target's initial position onto the predicted strike surface S, respectively. s,i The positions of the y-axis and z-axis in the geodetic coordinate system are y M,i ,z M,i T s The positions of the y-axis and z-axis in the geodetic coordinate system are y T ,z T .

[0124] The distance between two projection points can be expressed as

[0125]

[0126] From equations (10) and (11), the target projection point T can be obtained. s With the predicted hit point P pre The distance between them is

[0127]

[0128] Target projection point T sThe distance between the target's initial position T and the target's initial position T is

[0129]

[0130] As the target maneuvers away from the missile, M s,i T s With P pre If they are on the same straight line, then the projection point M of missile i is... s,i With the predicted hit point P pre The distance is:

[0131]

[0132] Finally, the predicted hit point P is obtained. pre =(x pre ,y pre ,z pre The coordinates of ) are

[0133]

[0134] In the formula, (x T ,y T ,z T ) represents the target position coordinates, β s The azimuth angle of the projected line of sight onto the predicted impact surface is denoted as .

[0135] βs=arctan[(z T -)z M,i / (y T -y M,i (18)

[0136] Here, the position parameters of missile i are used to calculate β. s That is, the β calculated for each missile s They are consistent.

[0137] Assuming the missile flies directly towards a stationary target at the predicted impact point, the remaining flight time t go for

[0138]

[0139] In the formula: r is the target distance, This is the derivative of the target range. When using proportional guidance to attack a target, the remaining flight time is estimated... for

[0140]

[0141] In the formula: R M,i For missile i and the predicted hit point P pre The distance between them, VM,i Let N be the velocity of missile i, N be the guidance coefficient, and σ be the velocity of missile i. i The angle between the missile's velocity and the line connecting the missile and its target can be expressed as:

[0142]

[0143] In the formula: R M,i For missile i and the predicted hit point P pre The distance vector between them, V M,i Let i be the velocity vector of missile i; To predict the hit point P pre The vector between two points relative to the target point. Let be the vector between missile i and the target.

[0144] Attack time t go,max Substituting into equation (20) yields

[0145]

[0146] Finally, we obtained a result about t. go,i,max equation

[0147]

[0148] The above formula means that the sum of the distances between the missile and the target and the predicted impact surface is equal to the missile-target distance.

[0149] By combining equations (15), (16), (22), and (23), the attack time t is obtained through numerical methods. go,i,max The maximum value in the bullet cluster is taken as the ideal attack time T for the bullet cluster. go .

[0150] It should be noted that the calculation of the attack time for a single missile already implicitly includes the condition that "the missile approaches the target in the shortest possible time." The assumption that "the target maneuvers away from the missile" extends the attack time to cover all possible target maneuvers; this time is actually the lower limit of the ideal attack time. Taking the maximum attack time of the missile swarm as the ideal attack time for the entire swarm is to ensure that this time meets the overload limits of each missile within the swarm. Let the maximum ideal attack time be T. go,max The attack time required for missile i to strike the target is

[0151] t go,i ∈[t go,i,min ,t go,i,max ](twenty four)

[0152] The minimum ideal attack time is t. go,max ,but

[0153] T go,i∈[t go,i,max ,T go,max (25)

[0154] Finally, the maximum value of the intersection of the ideal attack times of each missile is taken as the ideal attack time of the missile swarm:

[0155] T go =max(t) go,i,max (26)

[0156] Step 4: Calculate the virtual target point P vir,i .

[0157] In this step, based on the missile, the target, and the predicted impact point P... pre Based on the positional relationship between them, select the reverse trajectory attack method or the lateral attack method, and determine the attack angle; based on the attack angle, calculate the virtual target point P of each missile i. vir,i .

[0158] The guidance posture of a missile swarm is primarily achieved through guidance from virtual target points. By designing suitable virtual target points, missiles can leverage their maneuverability in the initial guidance phase, each surrounding the target at a specific angle, ultimately achieving a coordinated attack. Figure 5 As shown.

[0159] To achieve target encirclement, missiles should gradually converge on the target from all directions, with at least one missile in a head-on engagement position. At this point, regardless of which direction the target attempts to escape, at least one missile will attack in that direction; that is, the missile's velocity direction is opposite to the target's. In simpler terms, missile classification and control can be achieved by setting angle conditions. When the angle between the missile and the target meets the set first angle condition, it has the advantage of reverse-orbit strike. For example, if the angle between the missile and the target is small, a reverse-orbit strike is used; otherwise, a lateral strike is used.

[0160] When choosing a lateral strike, further distinctions can be made by setting a second angle condition to determine two lateral strike methods: one is to strike laterally without changing the current attack angle; the other is to calculate the attack angle based on the angle between the missile and the predicted impact point, and then use the calculated attack angle to measure and strike, thereby making full use of the advantages of missiles in different positions.

[0161] By setting virtual target points in the corresponding directions, missiles can be guided to form an encirclement of the target. The positional relationship between the line containing the virtual target point and the predicted strike surface is determined by the angle β between the line and the reference direction (set as the positive y-axis) on plane S. s and the angle of elevation α between the line and the plane S s To indicate, such as Figure 6 As shown. Therefore, in this preferred embodiment, according to βs and α s They jointly decide on the method of attack.

[0162] Specifically, the strategy is as follows: missiles whose azimuth is opposite to the target's maneuvering direction lack advantages in target position and speed, so their attack strategy changes from attacking the target head-on to attacking the target as much as possible; among missiles whose azimuth is the same as the target's maneuvering direction, the missile with the smallest difference in direction has the greatest advantage in attacking the target, therefore, α is set for this missile. s β s The missiles are positioned in the direction of the target's velocity to intercept the target, while the remaining missiles engage the target at the initial projected azimuth angle.

[0163]

[0164] The method of attack is determined by both equations (27) and (28). In the above equations, and The desired azimuth and elevation angles of the missile-target line-of-sight projection for guiding missile i; n is the number of missiles; y M,i ,z M,i Let y be the position of the projection point of missile i onto the predicted strike surface S in the geodetic coordinate system along the y and z axes; pre ,z pre To predict the hit point P pre The y-axis and z-axis positions; δ is the velocity deflection angle of the target when it moves in the same direction with maximum overload and is in circular motion.

[0165] when Satisfying the first condition of equation (28) and If the first condition of equation (27) is satisfied, then let To carry out a counter-attack;

[0166] when Satisfying the second condition of equation (28), and If the second condition of equation (27) is satisfied, then the missile angle becomes To launch a flanking attack;

[0167] when Satisfying the second condition of equation (28), and If the third condition of equation (27) is satisfied, the missile angle remains unchanged and a side attack is carried out.

[0168] according to The expected attack direction vector can be calculated as follows:

[0169]

[0170] The farthest position of the virtual target point is further obtained from the distance r between the projectile and the target:

[0171]

[0172] In the formula, k1 is a scaling factor. To ensure that the virtual target point is located between the missile and the target, and not to guide the missile backward, k1 < 1. The final coordinates of the virtual target point are obtained as follows:

[0173]

[0174] In the formula: k2 is an adjustment parameter; the larger k2 is, the more T go The ideal attack time calculated in the previous steps. Let k2 be the remaining flight time of missile i. The virtual target point is more sensitive to the error in the remaining attack time, but if k2 is too large, the transition from the virtual target point to the target will be uneven, resulting in an increase in the missile's required overload. Finally, the missile flies towards the virtual target point through three-dimensional proportional guidance and eventually hits the target.

[0175] Based on the above analysis, the present invention provides a reverse-orbit cooperative guidance method based on virtual target points, see [link to relevant documentation]. Figure 12 The process includes the following steps:

[0176] Step 1: Estimate the target velocity direction based on target observation information;

[0177] Step 2: Assuming the target moves in the opposite direction of the missile with maximum maneuverability, calculate the attack time required for each missile to strike the target based on the geometric and kinematic relationships between the missiles and the target, and take the maximum value as the ideal attack time T of the missile swarm. go ;

[0178] Step 3: Based on target observation information, target velocity direction, and ideal attack time T go Calculate the predicted hit point P pre ;

[0179] Step 4: Based on the missile, target, and predicted impact point P pre Based on the positional relationship between them, select the reverse trajectory attack method or the lateral attack method, and determine the attack angle; based on the attack angle, calculate the virtual target point P of each missile i. vir,i ;

[0180] Step 5: Control each missile to fly towards the virtual target point and hit the target.

[0181] The following section verifies the reverse-orbit cooperative guidance method based on virtual target points.

[0182] (1) Simulation condition settings

[0183] This invention takes near-space high-speed vehicles as the target of cooperative guidance. Considering that such targets often use C-shaped and S-shaped maneuvers during the penetration process to maximize their maneuverability and improve the probability of penetration, the proposed cooperative guidance method will be numerically analyzed and verified for two typical maneuver forms.

[0184] In the simulation, the missile swarm's velocity was set to 3000 m / s, with a maximum maneuver overload of 5.6. The target's velocity was set to 2000 m / s, with a maximum maneuver overload of 4. The initial missile-target distance was approximately 50 km, and the effective navigation ratio N was set to 4. The initial missile position was randomly generated based on the angles equally divided by the maximum boundary of the predicted strike surface, as shown in Table 1. The initial target position was located in the range [0, 0, 30000] m.

[0185] Table 1 Missile Initial Position

[0186]

[0187] (2) Comparative Simulation Analysis

[0188] When the target performs a C-shaped maneuver, the execution size is a. T , direction is γ T maneuver, that is

[0189]

[0190] Where η is the ratio of the target overload to its maximum overload.

[0191] Taking a target with η=1 as an example, the attack trajectory of the missile swarm on the target is as follows: Figure 7 As shown, the solid line trajectory uses the proposed Virtual Aiming Point Guidance (VAPG), while the dashed line trajectory uses True Proportion Navigation (TPN). Compared to the TPN method, VAPG achieves target engagement, with the attack angle as shown... Figure 8 As shown, three missiles successfully hit the target, and one of them had an attack angle of 179.4°, which improved the strike effect on the target compared to the TPN method.

[0192] Overload during missile swarm flight, such as Figure 9 As shown, it can be seen that the yaw acceleration of the two missiles that missed the target remained saturated throughout the flight, indicating that the attack on the target exceeded the attack capabilities of missiles 1 and 5. The overload saturation portion of the three missiles that successfully hit the target was relatively short, leaving sufficient maneuvering space to strike the target and adjust the attack angle.

[0193] To verify the effectiveness of the proposed method against C-shaped maneuvering targets, simulations were conducted on targets with different maneuver sizes and directions. The total miss distances of each missile against C-shaped maneuvering targets and the miss distance of the missile with the smallest miss distance in the missile group were obtained as follows: Figure 10 , Figure 11 As shown, when η≤0.7, the total miss distance of the missile swarm is small, meaning all missiles hit the target. When η>0.7, some missiles miss, but the minimum miss distance of the swarm is still less than 2m, ensuring a successful target hit. Individual missiles in the swarm may miss targets maneuvering in different directions, but the combined non-missing portions of all missiles can cover the entire maneuvering range of the target, thus achieving a successful target hit.

[0194] The specific embodiments described above only illustrate the design principles of the present invention. The shapes and names of the components in this description may differ and are not limited. Therefore, those skilled in the art can modify or make equivalent substitutions to the technical solutions described in the foregoing embodiments; and these modifications and substitutions do not depart from the inventive spirit and technical solutions of the present invention, and should all fall within the protection scope of the present invention.

Claims

1. A reverse-orbit cooperative guidance method based on virtual target points, characterized in that, include: Step 1: Estimate the target velocity direction based on target observation information; Step 2: Assuming the target moves in the opposite direction of the missile with maximum maneuverability, calculate the attack time required for each missile to strike the target based on the geometric and kinematic relationships between the missiles and the target, and take the maximum value as the ideal attack time for the missile swarm. ; Step 3: Based on target observation information, target velocity and direction, and ideal attack time. Calculate the predicted hit point ; Step 4: Based on the missile, target, and predicted impact point Based on the positional relationship between the missiles, the appropriate attack method (reverse trajectory or lateral attack) is selected, and the attack angle is determined; based on the attack angle, the calculations for each missile are performed. i virtual target point ; Step 5: Control each missile to fly towards the virtual target point and hit the target; Step 2 is as follows: When the target moves in the opposite direction of the missile with maximum maneuverability, the missile... i The attack time required to strike the target is , , missiles The initial position of the target is within the predicted strike area. The projection point on the surface, then The positions of the y-axis and z-axis in the geodetic coordinate system are: , , The positions of the y-axis and z-axis in the geodetic coordinate system are: , ; Two projection points , The distance between them is expressed as Target projection point With predicted hit point The distance between them is: in, To estimate the target velocity based on target observation information, The target's maximum acceleration. Target projection point relative to the initial position of the target The distance between them is (III) As the target maneuvers away from the missile, , and If they are on the same straight line, then the missiles projection point With predicted hit point The distance is: (IV) Finally, the predicted hit point was obtained. The coordinates are: In the formula, The target location coordinates, The azimuth angle of the projected line of sight onto the predicted impact surface; Assuming the missile flies directly towards a stationary target at the predicted impact point, the remaining flight time is estimated to be... : In the formula, For missiles speed magnitude, For missiles With predicted hit point The distance between them This is the proportional guidance coefficient; For missiles i The angle between the velocity and the line connecting the bullet and the target; The attack time Substituting into the above formula, we obtain the missile. i With predicted hit point Distance between: （V） Finally obtained about equation (WE) Solve together (III) to (VI) to determine the attack time required for the target's maximum maneuverability. ; The maximum required attack time for each missile is taken as the ideal attack time for the missile swarm. .

2. The method as described in claim 1, characterized in that, In step 1, the target velocity direction is estimated based on the target observation information as follows: Based on target observation information, Kalman filtering is used to estimate the target velocity direction; in the Kalman filtering estimation, the constructed observation vector... The component of the target velocity in the direction of the projectile's line of sight was added. : In the formula, The subscript indicates the position of the observed target. k The next iteration; Then the observation matrix for: In the formula: It is the identity matrix. It is a unit vector in the direction of the bullet's line of sight.

3. The method as described in claim 1, characterized in that, Step 3 is as follows: When a target maneuvers in the same direction with maximum overload, its circular reachable radius is... and the velocity deflection angle of circular motion for: In the formula, The target's maximum acceleration. The target's flight speed is obtained from target observation information. Ideal attack time; Approximating the spherical surface formed by the maximum maneuver as a circular plane, the distance between the center of the circular plane and the target is... ; Combined with target location Ballistic inclination angle in the direction of target velocity and ballistic deflection ,get The center position of the target's maximum maneuver range at any given time is: That is Predicted hit point at any given moment .

4. The method as described in claim 1, characterized in that, In step 4, the method based on the missile, target, and predicted impact point... The relative positions of the targets determine whether to use a counter-orbital strike or a lateral strike. When the angle between the missile and the target meets the set first angle condition, it has the advantage of reverse trajectory strike and uses reverse trajectory strike as the strike method; otherwise, it uses lateral strike as the strike method. When a lateral strike is selected, two lateral strike methods are further determined based on the second angle condition: one is to strike the target without changing the current angle of motion; the other is to calculate the strike angle based on the angle between the missile and the predicted impact point, and then use the calculated strike angle to measure the strike.

5. The method as described in claim 1, characterized in that, In step 4, the method based on the missile, target, and predicted impact point... Based on the positional relationship between them, choose either a reverse-track attack or a lateral attack, and determine the attack angle as follows: missile i virtual target point With predicted hit point The line connecting the two points is the first line, and the angle between the first line and the reference direction on the predicted impact surface S is . The elevation angle between the predicted strike surface S and the target surface is ; Similarly, target and predicted hit point The corresponding included angle is defined as ; The method of attack is determined by both equation (I) and equation (II): （I） (II) in, and For missiles i The desired azimuth and elevation angles of the projected line of sight during guided maneuvers; n For the number of missiles; , For missiles i In predicting the strike area The projection points on the surface are located on the y-axis and z-axis in the geodetic coordinate system; , To predict the hit point of y shaft and z Axis position; When a target is maneuvering in the same direction with maximum overload, the deflection angle of its circular motion velocity.

6. The method as described in claim 5, characterized in that, In step 4, the calculation of each missile is performed based on the attack angle. i virtual target point for: according to , The expected attack direction vector is calculated as follows: Based on the distance of the bullet to the target r Find the farthest position of the virtual target point: In the formula, Let be the proportionality coefficient. To ensure the virtual target point is located between the missile and the target, obtain the coordinates of the virtual target point: In the formula: To adjust the parameters, The ideal attack time is calculated in step 2. For missiles i The remaining flight time; The current time; The coordinates are the target location.

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