Multi-layer anti-missile cooperative combat mission planning modeling method

Abstract

The application discloses a multilayer anti-missile cooperative combat task planning modeling method, comprising the following modeling steps: S1, an anti-missile damage area numerical modeling method based on piecewise interpolation: a1, piecewise interpolation modeling of an anti-missile vertical damage area, a2, a vertical damage area model under different air route shortcuts, S2, an anti-missile launch area and launch depth calculation model based on backstepping calculation: b1, construction of a ballistic missile motion model, b2, construction of an anti-missile interceptor trajectory model, b3, backstepping calculation of an anti-missile vertical launch area and launch area depth, S3, an anti-missile defense area calculation model based on endpoint optimization: c1, a terminal anti-missile defense area calculation model, c2, a middle anti-missile defense area calculation model, the application proposes an anti-missile damage area numerical modeling method based on piecewise interpolation, and on the basis, an anti-missile launch area and launch depth model based on backstepping calculation and an anti-missile defense area calculation model based on endpoint optimization are completed.

Description

Technical Field

[0001] This invention relates to the field of anti-missile warfare technology, specifically a multi-layered anti-missile collaborative combat mission planning and modeling method. Background Technology

[0002] As an effective means of responding to and deterring ballistic missile attacks in actual combat, the anti-missile system is an important bargaining chip for both sides in seeking strategic balance. It has received attention from major military powers and military-sensitive countries and regions. Compared with aircraft targets, the high flight speed and small radar cross-section of ballistic missiles greatly compress the allowable preparation time for anti-missile operations. Moreover, due to the large number and variety of components that make up the anti-missile system, the coordination between combat entities is complex, and the data that needs to be processed in real time is enormous. This requires the anti-missile command and control system to have higher real-time performance and responsiveness. This puts great pressure on the terminal link of the anti-missile operation command and control link. There are many studies on the operational mission planning of the US anti-missile command and control system. Most of them are functional review literature. Domestic research on anti-missile operation deployment is mostly on single-type anti-missile equipment.

[0003] However, foreign anti-missile command and control systems almost never involve in-depth content such as structural framework, organization and operation, and interaction relationships. There is a lack of content on model construction and simulation of anti-missile collaborative combat mission planning. Domestic research is not very applicable to anti-missile operations with high timeliness, high accuracy and high integration requirements. There are few studies on anti-missile combat mission planning from the perspective of system-of-systems operations, and there are few studies that combine the latest developments of my country's air defense anti-missile system with the combat command system. Summary of the Invention

[0004] This invention provides a multi-layered anti-missile collaborative combat mission planning modeling method, which can effectively solve the problems mentioned in the background technology, such as the fact that foreign anti-missile command and control systems hardly involve in-depth content such as structural framework, organization and operation, and interaction relationships, and that there is a lack of content on model construction and simulation of anti-missile collaborative combat mission planning. Domestic research is not very applicable to anti-missile operations with high timeliness, high accuracy and high integration requirements. There are few studies on anti-missile combat mission planning from the perspective of system-of-systems operations, and there is a lack of research that combines the latest developments of my country's air defense anti-missile system with the combat command system.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a multi-layered anti-missile cooperative combat mission planning and modeling method, comprising the following modeling steps:

[0006] S1. Numerical model of anti-missile kill zone based on piecewise interpolation:

[0007] a1. Piecewise interpolation modeling of vertical kill zone of anti-missile systems;

[0008] a2. Vertical kill zone models under different flight route shortcuts;

[0009] S2. Calculation model of anti-missile launch zone and launch depth based on reverse calculation:

[0010] b1. Construct a ballistic missile motion model;

[0011] b2. Construct a trajectory model for an anti-missile interceptor;

[0012] b3. Calculate the vertical launch zone and depth of the anti-missile zone by reverse calculation;

[0013] S3. Calculation model of anti-missile defense zone based on endpoint optimization:

[0014] c1. Calculation model of the terminal anti-missile protection zone;

[0015] c2. Calculation model of mid-course anti-missile protection zone;

[0016] S4. Multi-layered anti-missile coordinated combat deployment planning model:

[0017] d1. Preliminary problem analysis;

[0018] d2. Constraints on multi-layered anti-missile coordinated combat deployment planning modeling;

[0019] d3. Objective function of multi-layered anti-missile coordinated combat deployment planning.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0021] 1. A numerical modeling method for the anti-missile kill zone based on piecewise interpolation was proposed. Based on this method, the anti-missile launch zone and launch depth models based on back-calculation and the anti-missile defense zone calculation model based on endpoint optimization were constructed.

[0022] 2. The protection zone coverage constraints of the multi-layer anti-missile coordinated combat deployment planning model were analyzed and demonstrated. The objective function of the multi-layer anti-missile coordinated combat deployment planning was constructed from two levels: single direction and threat sector. The construction of the multi-layer anti-missile coordinated combat deployment planning model was completed.

[0023] 3. Starting from the definition of operational deployment, this paper analyzes the types and basis of multi-layered anti-missile coordinated operational deployment, clarifies the requirements for multi-layered anti-missile coordinated operational deployment planning, designs the operational implementation process of task differentiation, force organization and force configuration in multi-layered anti-missile coordinated operational deployment planning, and clarifies the internal relationship between the three elements. Attached Figure Description

[0024] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0025] In the attached diagram:

[0026] Figure 1 This is a schematic diagram of the vertical kill zone of the anti-missile zero-path shortcut in the final stage of this invention;

[0027] Figure 2 This is a schematic diagram of the airspace loss in the vertical kill zone after interpolation processing according to the present invention;

[0028] Figure 3 This is the modified zero-path shortcut vertical kill zone of this invention;

[0029] Figure 4 This is the vertical kill zone of the anti-missile zero-path shortcut in the final stage of this invention;

[0030] Figure 5 This invention provides a numerical model of the vertical kill zone with a flight path shortcut of 20 km.

[0031] Figure 6 This is a schematic diagram of the reverse calculation of the vertical launch zone of the anti-missile system at the end of the present invention;

[0032] Figure 7 This is a schematic diagram of the final anti-missile protection zone of the present invention;

[0033] Figure 8 This is the vertical kill zone of the zero-path shortcut of the terminal anti-missile combat unit of this invention;

[0034] Figure 9 It is the foremost point of the "ground defense line" of the vertical kill zone of the anti-missile system at the end of this invention;

[0035] Figure 10 It is the last endpoint of the "ground defense line" corresponding to the vertical kill zone of the anti-missile system at the end of this invention;

[0036] Figure 11 This is the "ground defense line" corresponding to the vertical kill zone of the anti-missile system at the end of this invention;

[0037] Figure 12 This is a schematic diagram of the kill zone of the mid-course anti-missile combat unit of this invention;

[0038] Figure 13 It is the foremost point of the "ground defense line" of the mid-section anti-missile vertical kill zone in this invention;

[0039] Figure 14 It is the last endpoint of the "ground defense line" corresponding to the mid-section anti-missile vertical kill zone in this invention;

[0040] Figure 15 This is the "ground defense line" corresponding to the mid-course anti-missile vertical kill zone of this invention;

[0041] Figure 16This is a schematic diagram of the ballistic missile attack threat sector of the present invention;

[0042] Figure 17 This is a schematic diagram of the ground target segmentation method based on the anti-missile protection zone of the present invention;

[0043] Figure 18 This refers to the positional relationship between the high-altitude anti-missile protection zone at the end of this invention and the outer circle of the ground target. Detailed Implementation

[0044] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0045] Example: This invention provides a technical solution, a multi-layered anti-missile cooperative combat mission planning and modeling method, including the following modeling steps:

[0046] S1. Numerical model of anti-missile kill zone based on piecewise interpolation:

[0047] a1. Piecewise interpolation modeling of vertical kill zone of anti-missile systems;

[0048] a2. Vertical kill zone models under different flight route shortcuts;

[0049] S2. Calculation model of anti-missile launch zone and launch depth based on reverse calculation:

[0050] b1. Construct a ballistic missile motion model;

[0051] b2. Construct a trajectory model for an anti-missile interceptor;

[0052] b3. Calculate the vertical launch zone and depth of the anti-missile zone by reverse calculation;

[0053] S3. Calculation model of anti-missile defense zone based on endpoint optimization:

[0054] c1. Calculation model of the terminal anti-missile protection zone;

[0055] c2. Calculation model of mid-course anti-missile protection zone;

[0056] S4. Multi-layered anti-missile coordinated combat deployment planning model:

[0057] d1. Preliminary problem analysis;

[0058] d2. Constraints on multi-layered anti-missile coordinated combat deployment planning modeling;

[0059] d3. Objective function of multi-layered anti-missile coordinated combat deployment planning.

[0060] like Figure 1As shown in S1, the segmented interpolation modeling of the vertical kill zone of the anti-missile system adopts the profile method, and studies the vertical kill zone and the horizontal kill zone. The ballistic missile flies at high speed in the passive phase and carries out the attack in the manner of inclined ballistic trajectory.

[0061] In a1, the segmented interpolation modeling of the vertical kill zone of the anti-missile system adopts the data fitting method to comprehensively determine the formed spatial region. Based on the vertical kill zone of the O-path shortcut, the mathematical model of the vertical kill zone of the anti-missile combat unit is constructed by numerical processing of the vertical kill zone. The vertical kill zone of the O-path shortcut of the anti-missile combat unit when it encounters a typical ballistic target is the profile obtained by cutting the spatial kill zone with the plane of the path shortcut P=O.

[0062] Among them, BC is the far boundary of the kill zone, AB and CD are the high boundary and low boundary respectively, AE and DE are the high near boundary and low near boundary respectively, the far boundary BC and the low near boundary DE are two curves, and the other boundaries are straight lines. In the plane coordinate system SOH, O is the configuration point of the terminal anti-missile interceptor launch platform, OH is the altitude axis, and OS is the horizontal distance axis.

[0063] By reviewing and analyzing numerical algorithms and combining the shape characteristics of the anti-missile vertical kill zone, piecewise linear interpolation is used to numerically process the anti-missile vertical kill zone and characterize the kill zone.

[0064] The anti-missile system uses a multi-segment broken line connection to replace the curved boundaries of the vertical kill zone and the horizontal kill zone. As a result, the vertical kill zone of the anti-missile system will also change. The spatial loss F and G of the vertical kill zone after interpolation are the nodes that are inserted into the far boundary and low near boundary of the vertical kill zone of the anti-missile system. The shaded part is the spatial domain that changes after linear interpolation.

[0065] like Figure 2 As shown in the figure, F and G are the nodes inserted into the far and low near boundaries of the anti-missile vertical kill zone. The shaded area is the airspace that changes after linear interpolation. As can be seen from the figure, the most effective solution to reduce the impact of linear interpolation on the size of the kill zone is to increase the number of interpolation nodes. By increasing the number of interpolation nodes, the impact of linear interpolation on the size of the kill zone can be reduced. The more interpolation nodes there are, the higher the overlap between the processed kill zone and the original kill zone. Given that the far boundary of the anti-missile kill zone, especially the mid-course and terminal high-altitude kill zone, is relatively large, the change in the kill zone caused by interpolation can be ignored in actual combat. The interpolation nodes only need to be within a certain accuracy range.

[0066] When there is only one interpolation node, let the piecewise interpolation function be f(s), and the polynomial corresponding to the original curve be φ(s). Since the change in the kill zone after numerical processing is required to be minimal, i.e., within the interval [S...],... B S C Choose a value from ] such that Minimum, that is:

[0067]

[0068] The above operations can determine an interpolation node. The second and third new nodes are found in the same way until the change in the airspace range of the kill zone between adding a new node and not adding a node is not significant. The original irregular anti-missile kill zone is replaced by a regular polygon, which is also a planar region enclosed by the vertices of the polygon.

[0069] In A2, the construction of vertical kill zone models under different flight shortcuts is affected by terrain conditions, troop numbers, and ballistic missile operational deployment. An analysis is conducted on the vertical kill zones under different flight shortcuts to calculate the anti-missile launch area and launch depth under different flight shortcuts. The anti-missile space kill zone can be viewed as a combination of a cluster of vertical kill zones with equal flight shortcut intervals and discrete from each other. Given a clear numerical model of the vertical kill zone for the anti-missile combat unit 0 flight shortcut, other flight shortcuts P... i The corresponding vertical kill zone is calculated using the following method:

[0070] a2.1. Let S be the maximum heading distance among all feature points in the vertical kill zone of the zero-way shortcut. max The minimum heading distance is S min Flight shortcut P i The corresponding heading distance is S i Then we have:

[0071]

[0072] If S i min If the O-path shortcut vertical kill zone is reached, the next step can be directly entered. If S i >S max Then with P i The corresponding vertical kill zone does not exist;

[0073] If S min i max Then use a plane Cut the vertical kill zone of the zero-way shortcut and keep the distance less than S i Discarding regions and feature points, we get, for example: Figure 3 The corrected vertical kill zone is shown below;

[0074] a2.2. Calculate the route shortcut P based on the corrected vertical kill zone of the 0-way shortcut. i The feature point corresponding to the vertical kill zone, selected in the figure is point F(S). F H F ​​​If the route shortcut P is... i The corresponding feature points in the vertical kill zone are Then we have:

[0075]

[0076] Shortcut to the route P i Once all the feature points corresponding to the vertical kill zone have been calculated, the numerical model of the vertical kill zone corresponding to the route shortcut Pi can be obtained.

[0077] Example: A land-based anti-missile system is deployed 16 km before the ballistic missile's impact point. The interceptor launch point is at an altitude of 60 m. The initial flight time is t1 = 2 s, and the shutdown time is [not specified]. The shortcut of the incoming ballistic target is 20 km. Assume the Earth's radius Re = 6.371 × 10 [units unclear]. 6 m, gravitational acceleration at sea level g0 = 9.80665 m / s² 2 The characteristic data of the vertical kill zone of the flight path shortcut of this type of anti-missile equipment against typical ballistic targets in the ballistic coordinate system are shown in Table 1-1.

[0078] Table 1-1 Data on Vertical Kill Zone of a Shortcut Route in a Land-Based Anti-Missile Equipment Test Range

[0079]

[0080] The feature data points are fitted with a least-squares curve using a polynomial to form the final anti-missile vertical kill zone, as shown in the figure. Figure 4 As shown.

[0081] like Figure 5 As shown, the curved boundaries BC and DEF of the vertical kill zone of the 0-way shortcut are numerically processed to form a numerical model of the vertical kill zone of the 0-way shortcut. According to the above method and steps, the numerical model of the vertical kill zone with a 20km route shortcut is calculated.

[0082] Numerical modeling of the anti-missile kill zone based on piecewise interpolation is a new method for determining the anti-missile kill zone model. The constructed model has advantages such as high simulation accuracy, stable output results, and ease of computer implementation, laying a good foundation for subsequent calculations of anti-missile launch depth and protected area.

[0083] In b1, the ballistic missile motion model is constructed in the North-Sky-East coordinate system. In the local vertical coordinate system, the ballistic missile kinematic equations can be described as follows:

[0084]

[0085] Where y is the altitude of the ballistic missile flight, Y = C y qs

[0086] x is the range of the ballistic missile, X = C x qs

[0087] α is the angle of attack of the ballistic missile;

[0088] q is the flight kinetic pressure, q = ρv 2 / 2;

[0089] ρ is the atmospheric density, and its value varies with altitude y.

[0090] In b2, the trajectory model of the anti-missile interceptor is described in a Cartesian coordinate system with ground parameters. The duration from the anti-missile interceptor ejection tube to the ignition of the first-stage engine is t0, the initial velocity of the ejection tube is V0, and G is the acceleration due to gravity. Then, the velocity from the ejection tube to the ignition of the first-stage engine is:

[0091] V = V0 - Gt0(5)

[0092] Given the interceptor missile's average engine thrust p, the missile's mass m, V1 as the missile's velocity at the previous moment, and t... s Using the time step as the calculation step, the interceptor missile velocity is:

[0093]

[0094] In the formula, θ is the trajectory inclination angle of the interceptor missile.

[0095] Given the maximum thrust P2 and minimum thrust P1 of the anti-ballistic missile interceptor engine, the total engine operating time T1, and the engine operating time after ignition T, the thrust calculation formula can be determined as follows:

[0096]

[0097] Neglecting aerodynamic drag, the interceptor missile's velocity is:

[0098]

[0099] If we consider the effect of aerodynamic drag, then we have drag:

[0100]

[0101] Therefore, the interceptor missile's velocity is:

[0102]

[0103] In the formula, α is the angle of attack and β is the sideslip angle.

[0104] Assuming a ground-based interceptor missile engages a high-speed aerial target, and the interceptor missile's guidance uses a generalized proportional guidance method, then:

[0105]

[0106] Where K is the proportionality coefficient;

[0107] The relative velocity between the projectile and the target;

[0108] q represents the tilt angle of the bullet's line of sight;

[0109] The velocity of the angle of inclination of the bullet's line of sight;

[0110] The velocity of the angle of inclination of the bullet's line of sight;

[0111] n y n z These are the missile's longitudinal overload and lateral overload, respectively.

[0112] ballistic inclination velocity The calculation formula is:

[0113]

[0114] ballistic angular velocity The calculation formula is:

[0115]

[0116] By integrating the above formulas, we can obtain the missile's trajectory inclination angle and trajectory deflection angle.

[0117] In b3, for the feature points in the numerical model of the given vertical kill zone, the flight time t of the anti-missile interceptor to reach the feature points is calculated using the anti-missile interceptor trajectory model. df Let t be the time from the issuance of the launch command to the departure of the anti-missile interceptor from the launch device. dd The flight time of the ballistic missile from the characteristic launch point to the corresponding characteristic encounter point is:

[0118] t bdf =t df +t dd (14)

[0119] like Figure 6 As shown, the incoming ballistic missile and the ground defense target are clearly identified. Based on the ballistic missile reentry stage trajectory model, the launch point of the anti-missile interceptor can be determined by moving the launch point along the S-axis of the ground rectangular coordinate system. The characteristic launch points corresponding to each characteristic point of the kill zone can be determined by reverse calculation. After the characteristic launch points corresponding to all characteristic points of the terminal anti-missile vertical kill zone are determined, the adjacent characteristic launch points are connected to form an irregular polygon, which is the vertical launch zone corresponding to the vertical kill zone.

[0120] The anti-missile launch zone is determined, and the launch depth is calculated using simulation methods based on ballistic missile models and anti-missile interceptor models. In addition to giving the launch depth of anti-missile interception, the parameter of allowable launch time is further calculated. This parameter is used to characterize the remaining flight time of the incoming ballistic missile in the launch zone or the allowable decision time for the anti-missile combat commander, providing the anti-missile combat commander with more intuitive decision support.

[0121] In C1, terminal-phase ballistic missile defense (C-PBS) is the interception of ballistic targets during the reentry phase of an incoming ballistic missile. Given a specific launch point, direction of attack, and target type, the C-PBS protected zone can be described as the projection of the C-PBS kill zone onto the ground along the trajectory of the incoming ballistic missile. As long as the protected target is within this zone, it is protected from ballistic missile attack due to the interception action of the C-PBS unit. The C-PBS protected zone is as follows: Figure 7 As shown.

[0122] The shaded areas A′D′C′B′F′E′ in the diagram represent the protection zone of the terminal anti-missile combat unit against the incoming ballistic target. Figure 10 It can be intuitively seen that the terminal anti-missile protection zone is closely related to the kill zone of the anti-missile combat unit, the reentry angle of the ballistic missile, and the direction of the ballistic target's attack. Therefore, a calculation model analysis of the terminal anti-missile protection zone can be carried out.

[0123] c1.1 Basic ideas for constructing the terminal missile defense zone model;

[0124] The terminal missile defense kill zone can be viewed as a combination of a cluster of vertical kill zones with equal and discrete flight path intervals. If the flight path intervals are small enough, the terminal missile defense kill zone formed by the vertical kill zones obtained from this is infinitely close to the actual kill zone. Once the vertical kill zone corresponding to a certain flight path is determined, the "ground defense line" of the vertical kill zone against the incoming ballistic missile target can be calculated based on the flight trajectory of the incoming ballistic missile during the reentry phase. All the "ground defense lines" corresponding to the vertical kill zones are combined to form the terminal missile defense protection zone.

[0125] c1.2, The "ground defense line" corresponding to the terminal anti-missile vertical kill zone;

[0126] For ease of analysis, this section will use the vertical kill zone of the zero-course shortcut in terminal missile defense units as an example. Figure 8 The closed area ABCDEF connected by the red line in the middle is the vertical kill zone of the zero-path shortcut of the terminal anti-missile combat unit. As can be seen from the figure, the foremost point of the kill zone is C, and the last endpoint of the upper boundary of the kill zone is A.

[0127] c1.2.1 The terminal anti-missile vertical kill zone corresponds to the foremost point of the "ground defense line";

[0128] Let θ be the minimum ballistic inclination angle that a terminal anti-missile unit can counter a ballistic missile. min When the incoming ballistic missile's flight trajectory passes through point C, the foremost point of the farthest boundary of the kill zone, its curved trajectory intersects the S-axis at point G. m This refers to the foremost point of the theoretical "ground defense line." The ballistic missile's reentry trajectory is considered a straight line, and the angle between this straight trajectory and the S-axis is the minimum trajectory inclination angle θ that the terminal anti-missile unit can intercept during the reentry phase. min At this point, the intersection of the straight-line flight trajectory and the S-axis is G′. Therefore, point G′ is the foremost point of the "ground defense line" of the vertical kill zone. As shown in the diagram, the coordinates of G′ are (S, P, H). The foremost point of the "ground defense line" in the terminal phase anti-missile vertical kill zone is as follows: Figure 9 As shown.

[0129] c1.2.2 The terminal anti-missile vertical kill zone corresponds to the last endpoint of the "ground defense line";

[0130] Assuming the maximum elevation angle of the terminal anti-missile kill zone is greater than the maximum reentry angle of the ballistic missile, and let θ be the maximum trajectory inclination angle of the ballistic missile that the terminal anti-missile unit can intercept during the reentry phase. max When the incoming ballistic missile's flight trajectory passes through the final endpoint A of the kill zone's high boundary, the intersection point K of its curved trajectory and the S-axis is the final endpoint of the theoretical "ground defense line." Treating the ballistic missile's reentry phase trajectory as a straight line, the angle between this straight trajectory and the S-axis is the maximum trajectory inclination θ of the ballistic missile that the terminal anti-missile unit can intercept during the reentry phase. max At this point, the intersection of the straight-line flight trajectory and the S-axis is K′. Therefore, point K′ is the final endpoint of the vertical kill zone's "ground defense line." As shown in the diagram, the coordinates of K′ are... The terminal phase anti-missile vertical kill zone corresponds to the last endpoint of the "ground defense line," as shown in the example. Figure 10 As shown.

[0131] c1.2.3, The "ground defense line" corresponding to the terminal anti-missile vertical kill zone;

[0132] Based on the above analysis, the "ground defense line" corresponding to the vertical kill zone of the terminal anti-missile combat unit is the line K′G′ connecting points K′ and G′, with a length l of:

[0133]

[0134] The "ground defense line" corresponding to the terminal missile defense vertical kill zone is as follows: Figure 11 As shown.

[0135] c1.3 Calculate the shortcut P for different routes i The corresponding terminal anti-missile vertical kill zone;

[0136] Different route shortcuts P i The corresponding vertical kill zone calculation method can be performed by following the method described above to obtain the shortcut P for different flight paths. i The corresponding vertical kill zone.

[0137] c1.4 Calculate the “ground defense line” corresponding to the vertical kill zone of the anti-missile system at the end of different flight shortcuts;

[0138] Referring to the calculation method in c1.2, determine the foremost point of the "ground defense line" corresponding to the vertical kill zone of different flight shortcuts. and the last endpoint Their coordinates are respectively Then, the "ground defense line" corresponding to the vertical kill zone of different flight shortcuts can be determined, i.e. Point and Connecting the points Its length for:

[0139]

[0140] c1.5 Solve for the terminal missile defense zone;

[0141] Once the calculation results of the "ground defense line" corresponding to the vertical kill zone of each airway shortcut are determined, the least squares curve fitting of the foremost point and the last endpoint of the "ground defense line" can be performed using a polynomial to form the terminal anti-missile defense zone. If the airway shortcut interval ΔP is relatively small, the terminal anti-missile defense zone formed after least squares curve fitting will not differ much from the actual defense zone, and there is no need to perform secondary numerical processing on the defense zone boundary.

[0142] In C2, mid-course missile defense refers to the interception operations conducted by the missile defense unit against ballistic targets during the mid-course phase of an incoming ballistic missile's flight. The interception arc for a typical ballistic target by the mid-course missile defense unit is the flight trajectory after the ballistic missile's boost phase and before re-entry into the atmosphere, typically ranging in altitude from 200 km to 1500 km, with a kill zone exceeding 5000 km. Similar to terminal-phase missile defense, mid-course missile defense essentially involves launching an interceptor missile from a ground-based launcher. Under the guidance and control system, the interceptor missile encounters and destroys the incoming target within the mid-course missile defense kill zone. The basic principles of the terminal-phase missile defense protection zone calculation model are equally applicable to the mid-course missile defense protection zone.

[0143] When analyzing the calculation model of the mid-course anti-missile protection zone, it is crucial to grasp two key elements: the trajectory pattern of the incoming ballistic missile and the characteristics of the kill zone of the mid-course anti-missile combat unit. The kill zone of the mid-course anti-missile combat unit is as follows: Figure 12 As shown.

[0144] c2.1 The approach to constructing the mid-course anti-missile defense zone model;

[0145] The mid-course missile defense kill zone can be viewed as a combination of a cluster of vertical kill zones with equal and discrete flight path intervals. If the flight path interval ΔP is sufficiently small, the mid-course missile defense kill zone formed by the vertical kill zones obtained from this is infinitely close to the actual kill zone. When a certain flight path interval P... i Once the corresponding vertical kill zone is determined, the "ground defense line" of the vertical kill zone against the incoming ballistic missile can be calculated based on the mid-course flight trajectory of the incoming ballistic missile. All the "ground defense lines" corresponding to the vertical kill zones are combined to form the mid-course anti-missile defense zone.

[0146] c2.2, The "ground defense line" corresponding to the mid-course anti-missile vertical kill zone;

[0147] To facilitate problem analysis, we will use the vertical kill zone of the 0th flight path of the mid-course missile defense combat unit as an example. The closed area ABCDE is the vertical kill zone of the 0th flight path of the mid-course missile defense combat unit. As shown in the figure, the foremost point of the kill zone is C, and the last endpoint of the upper boundary of the kill zone is A.

[0148] c2.1.1 The mid-course anti-missile vertical kill zone corresponds to the foremost point of the "ground defense line";

[0149] Assume the incoming ballistic missile flies along a standard elliptical trajectory with a range of R. The highest point of the trajectory coincides with the foremost point C of the mid-course anti-missile kill zone. Then, the intersection point M of the incoming ballistic missile's trajectory and the S-axis is the foremost point of the theoretical "ground defense line." Since the range of the incoming ballistic missile is determined, the coordinates of point M can be accordingly determined.

[0150] Given the long range and high interception altitude of mid-course missile defense operations, when mid-course missile defense units are deployed forward, their kill zones often extend beyond the ground defense zone. Therefore, when analyzing the foremost point of the "ground defense line" corresponding to the mid-course missile defense vertical kill zone, redundancy is no longer emphasized. The foremost point of the "ground defense line" of the mid-course missile defense vertical kill zone is as follows: Figure 13 As shown.

[0151] c2.1.2 The mid-course anti-missile vertical kill zone corresponds to the last endpoint of the "ground defense line";

[0152] Assuming the maximum elevation angle of the mid-course anti-missile kill zone is greater than the maximum trajectory inclination angle of the ballistic missile, and the incoming ballistic missile's trajectory passes through point A, then the intersection point N of the ballistic missile's trajectory and the S-axis is the theoretical endpoint of the "ground defense line." Due to the instability of the ballistic missile's reentry trajectory, to enhance the redundancy and conservatism of the calculation results for the endpoint of the "ground defense line," a straight line is drawn through point A, and the angle between this line and the S-axis is θ, representing the maximum trajectory inclination angle of the ballistic missile that the mid-course anti-missile combat unit can handle. max At this point, the intersection of the straight line and the S-axis is N′. Therefore, point N′ is the final endpoint of the "ground defense line" of the mid-course anti-missile vertical kill zone. Analysis shows that the coordinates of N′ are...

[0153] The mid-course anti-missile vertical kill zone corresponds to the final endpoint of the "ground defense line," as shown below. Figure 14 As shown.

[0154] c2.1.3, The "ground defense line" corresponding to the mid-course anti-missile vertical kill zone;

[0155] Based on the above analysis, the "ground defense line" corresponding to the vertical kill zone of the mid-course anti-missile combat unit is the line N′M connecting points N′ and M, with a length l of:

[0156]

[0157] The "ground defense line" corresponding to the mid-course missile defense vertical kill zone is as follows: Figure 15 As shown.

[0158] c2.3 Calculate the shortcut P for different routes i The corresponding mid-course anti-missile vertical kill zone;

[0159] Different route shortcuts P i The corresponding vertical kill zone calculation method can be implemented according to the method in 4.4.1, which will yield the shortcut P for different flight paths. i The corresponding vertical kill zone.

[0160] c2.4 Calculate the "ground defense line" corresponding to the vertical kill zone of anti-missile systems in the mid-section of different flight shortcuts;

[0161] Referring to the calculation method in c2.2, determine the foremost point of the "ground defense line" corresponding to the vertical kill zone of different flight shortcuts. and the last endpoint Their coordinates are respectively Then, the "ground defense line" corresponding to the vertical kill zone of different flight shortcuts can be determined, i.e. The line connecting point M and point M Its length for:

[0162]

[0163] c2.5 Solving for the mid-course anti-missile protection zone;

[0164] Once the calculated results of the "ground defense line" corresponding to the vertical kill zone of the mid-course missile defense along each flight path shortcut are determined, a polynomial can be used to perform least-squares curve fitting on the foremost and last endpoints of the "ground defense line" to form the mid-course missile defense zone. It should be noted that, due to the large area and wide range of the mid-course missile defense zone, the value of the flight path shortcut interval ΔP can be appropriately increased, and the mid-course missile defense zone formed after least-squares curve fitting does not require numerical processing.

[0165] In S4, the multi-layer anti-missile coordinated combat deployment planning model is a process of constructing an objective function around the launch depth, taking into full account the constraints of the anti-missile protection zone, using the configuration position of the anti-missile combat units to which the multi-layer anti-missile system belongs as the variable.

[0166] d1. Preliminary problem analysis;

[0167] Before carrying out multi-layered anti-missile coordinated combat deployment planning and modeling, the key elements in the basis of the combat deployment planning should be analyzed and the analysis conclusions should be clearly given so as to provide basic conditions for the construction of the multi-layered anti-missile coordinated combat deployment planning model.

[0168] d1.1 Clarify the superior's intentions and the unit's operational tasks;

[0169] The intentions of higher authorities and the operational tasks of this level are usually reflected in the operational orders issued by higher authorities. Before implementing multi-level anti-missile coordinated operational deployment planning, a thorough and detailed study and analysis of the intentions of higher authorities and the operational tasks of this level should be carried out to clarify the analysis and judgment of higher authorities on the situation, the operational intentions and deployment attempts of higher authorities, the total number of troops involved in the operation and the situation of friendly forces, the nature of the operational tasks of this level, the targets to be protected and the main operational direction, the precautions required by higher authorities, and the methods of coordination with friendly forces.

[0170] d1.2. Clearly define the types of targets to be protected;

[0171] Based on the enemy's operational intentions, analyze and determine the main types of our own defensive targets. When studying the defensive targets, conduct in-depth analysis and judgment on the enemy's intention to use ballistic missiles to strike. Different operational intentions result in different main types of ballistic missile strike targets and different key defensive targets for our own side.

[0172] If the enemy's operational intent is military deterrence, then the missile defense targets are political and economic targets that have a huge impact on the morale and public spirit of our people.

[0173] If the enemy attempts to seize control of information, air, and sea on the battlefield, and weaken or even paralyze our offensive (counterattack) forces, the missile defense targets are our command and control systems, intelligence and reconnaissance systems, air defense positions, missile bases, important airports, naval bases, and port terminals.

[0174] Based on the above guidelines and the specific circumstances of your own protected targets, determine the type of protected target.

[0175] d1.3 Determine the key areas to be protected in anti-missile operations;

[0176] The types of ground targets within the responsibility protection zone of the multi-layered anti-missile system should be clearly defined. Based on the status and role of the protected targets, the key points of anti-missile operations should be determined. The strategic and operational status of the protected targets, as well as the degree of threat they pose to the enemy, determine the order in which the targets are protected.

[0177] On the one hand, due to the high cost and limited quantity of anti-missile resources, in order to ensure the key resources are used in a key manner, when determining the targets to be protected, it is necessary to give priority to the targets with strategic and operational importance.

[0178] On the other hand, when determining the targets to be protected, priority should be given to protecting targets that pose a serious threat to the enemy. Such targets are often the focus of enemy ballistic missile attacks. By analyzing the importance of the targets and the degree of threat to the enemy, the priority order of the targets to be protected can be determined. When our own anti-missile forces are limited, not all targets that may be attacked by the enemy can be protected. Therefore, it is necessary to comprehensively consider the status and role of the targets and the characteristics of the targets to determine the key targets to be protected.

[0179] d1.4 Analyze and judge the operational use of ballistic missiles;

[0180] The analysis and judgment of the enemy's ballistic missile operations mainly includes intelligence information such as the types of ballistic missiles the enemy may use, the activity area of ​​the ballistic missile launch system, the range of the ballistic missile's direction of attack, as well as the number of enemy ballistic missile launchers, penetration methods, and operational styles.

[0181] The type of ballistic missiles that the enemy may use is closely related to the location, shape, nature, and vulnerability of the target being defended. The ballistic missiles used by the enemy should be matched with the distance, nature, and shape of the target they are attacking in terms of range, power, and accuracy. If the target being defended is close to the enemy and has a small area, the enemy may use short-range or short-range ballistic missiles with high accuracy. If the target being defended has a large area and is far from the enemy, the enemy may use medium- and long-range ballistic missiles with high power and long range. If the target being defended has strong resilience and repair capabilities, the enemy will use ballistic missiles with high destructive power and wide damage range.

[0182] Most ballistic missile launch systems have a certain degree of mobility. In order to improve the surprise and effectiveness of the strike and increase the difficulty of defense, enemy ballistic missile launch sites are often distributed in a certain battlefield space and operate in a certain area. In order to improve the pertinence and effectiveness of multi-layer anti-missile coordinated combat deployment planning, it is necessary to make a basic judgment on the battlefield operation range of the enemy's ballistic missile launch system.

[0183] The ballistic missile threat sector is determined by the combined deployment and operational areas of the adversary's ballistic missile launch systems. For a given target, the potential direction of ballistic missile attack is always within a finite range. To accurately determine the range of ballistic missile attack, we first use the physical geometric center of the target as the center and the range of the potential incoming ballistic missiles to estimate the enemy's ballistic missile operational area. After estimating the potential operational area of ​​the enemy's ballistic missile launch system, we also need to consider the terrain and transportation conditions of the enemy's area to determine the actual operational range of the enemy's ballistic missile launch system. Connecting the target with the boundary points of the actual operational range, we thus determine the threat sector of the enemy's ballistic missiles to the target. The ballistic missile attack threat sector is as follows: Figure 16 As shown.

[0184] The number of enemy ballistic missiles and their launchers determines the maximum number of ballistic missiles the enemy can launch simultaneously during combat. Each anti-missile combat unit can only intercept a limited number of ballistic missiles at the same time. If the number of enemy ballistic missiles and their launchers is large, the number of ballistic missiles launched simultaneously will be greater, which will inevitably require more anti-missile combat units to intercept them simultaneously. If the number of enemy ballistic missiles and their launchers is small, then only a few anti-missile combat units are needed to intercept them.

[0185] The above describes the analytical and judgmental work that needs to be carried out in advance for the construction of a multi-layered anti-missile coordinated combat deployment planning model. Once the analytical conclusions are clear, the multi-layered anti-missile coordinated combat deployment planning model can be constructed based on the given anti-missile forces.

[0186] In d2, the constraints of multi-layer anti-missile coordinated combat deployment planning modeling;

[0187] The ability of the missile defense zone to cover ground targets is a prerequisite for missile defense deployment. Therefore, the constraints for multi-layered missile defense coordinated deployment planning and modeling should be based on the effective coverage of ground targets by the missile defense zones of each level of missile defense units. This assumes that the ground targets are a group of point-like targets, protected by a multi-layered missile defense system, including mid-course missile defense unit n. Z The terminal phase high-level and terminal phase low-level anti-missile combat units are n respectively. MG set, n MD To facilitate the description of the problem, this discussion and analysis will take the terminal high-level anti-missile combat unit as an example.

[0188] d2.1 Ground target segmentation based on the missile defense zone;

[0189] For large groups of ground targets, the protection zone formed by a single terminal-phase high-altitude anti-missile combat unit cannot provide complete coverage. To ensure effective protection of ground targets by terminal-phase high-altitude anti-missile firepower, a ground target segmentation method based on the anti-missile protection zone is adopted, dividing the ground targets into n groups. WY Each outer circle contains a certain number of point targets, and the outer circle can be completely covered by the terminal high-level missile defense zone. When dividing the group of targets, three points need to be explained: First, the number of point targets contained in the constructed outer circle is a parameter that the more the better. Under the premise that a certain outer circle is covered by the terminal high-level missile defense zone, the outer circle should include as many point targets as possible in the group of targets, so as to both meet the needs of missile defense operations and save missile defense resources.

[0190] Secondly, for important point targets among ground targets, in order to improve the protection effectiveness of the multi-layered anti-missile system, they should be covered in two or more adjacent outer circles as much as possible, so as to enhance the anti-missile firepower and protection effectiveness against important targets.

[0191] Thirdly, from the perspective of conserving anti-missile operational resources, the delineated circumcircle must be covered by the anti-missile operational unit's protected area, while also ensuring that the radius of the circumcircle is similar to the width of the protected area. A schematic diagram of the ground target segmentation based on the anti-missile protected area is shown below. Figure 17 As shown.

[0192] d2.2 Mathematical Model of Anti-missile Defense Zone Covering Ground Targets

[0193] With the i-th 1 i 1 <n MG Terminal phase high-altitude anti-missile combat unit protects the i-th zone 2 i 2 <n WY Taking the circumcircle of a ground target as an example, we analyze the mathematical model of the anti-missile protection zone covering ground targets. Let the i-th... 1 The terminal phase high-altitude anti-missile combat unit configuration point is O. MGi The center of the circumcircle of the final ground protection target is O. WYi The center O of the circumcircle of the ground-protected target. WYi XO with the origin WYi Y-coordinate system, Y-axis passes through O WYi The point points in the direction of the ballistic missile's main attack, and the X-axis passes through O. WYi Point O is defined as the point perpendicular to the Y-axis to the right. MGiConstruct a rectangular coordinate system SO for ground parameters with the origin as the origin. MGi If P is the axis, then the P-axis is parallel to the X-axis, and the S-axis coincides with the Y-axis.

[0194] Take the left-hand shortcut P MGii Draw a straight line perpendicular to the P-axis. The intersection point of this line and the front end of the terminal high-altitude missile defense zone is: The backend intersection is The point of intersection with the front end of the circumcircle of the ground-protected target is The backend intersection is Let l be the distance from the deployment point of the terminal anti-missile combat unit to the center of the circumcircle of the ground-protected target. MGii The terminal anti-missile combat unit is then positioned at XO. WYi The coordinate in the Y coordinate system is O MGi (0,l MGii If the missile defense zone of the terminal high-altitude missile defense unit covers the circumcircle of the ground coordinate system, then the following formula should be satisfied:

[0195]

[0196] Based on the calculation model of the terminal missile defense zone and considering the positional relationships, the following equation can be obtained by transforming the above equation:

[0197]

[0198] in:

[0199] --The shortcut is P MGii At that time, the coordinates of point C at the foremost point of the terminal high-altitude anti-missile kill zone on the S-axis;

[0200] --The shortcut is P MGii At that time, the coordinates of point C at the foremost point of the terminal high-altitude anti-missile kill zone on the H-axis;

[0201] θ min --The minimum trajectory inclination angle of a ballistic missile that the terminal phase anti-missile combat unit can intercept during reentry;

[0202] --The shortcut is P MGii At that time, the coordinates of the rear endpoint A of the high boundary of the terminal high-level anti-missile kill zone on the S-axis;

[0203] --The shortcut is P MGii At that time, the coordinates of the rear endpoint A of the high boundary of the terminal high-level anti-missile kill zone on the H-axis;

[0204] θ max--The maximum trajectory inclination angle of a ballistic missile during the reentry phase that the terminal phase anti-missile combat unit can counter;

[0205] For a given terminal phase high-altitude anti-missile combat unit and an incoming ballistic missile, S can be easily calculated using simulation tools following the steps in 4.4.1. CPMGii H CPMGii S APMGii H APMGii Parameters, combined with the known θ min and θ max Numerical values ​​form the constraints for the terminal high-altitude missile defense deployment planning and modeling. The positional relationship between the terminal high-altitude missile defense protection zone and the outer circle of the ground target is as follows: Figure 18 As shown.

[0206] The constraints for mid-course and terminal low-level anti-missile deployment planning and modeling are also carried out according to the above methods and steps. When involving their respective parameters, they must be determined based on the actual situation. After all calculations are completed, the constraints for multi-level anti-missile coordinated deployment planning and modeling are formed. The positional relationship between the terminal high-level anti-missile protection zone and the outer circle of the ground target is as follows: Figure 4-18 As shown.

[0207] d3. Objective function of multi-layered anti-missile coordinated combat deployment planning;

[0208] The objective function refers to the functional relationship between the target of interest and related factors. It is the form of the target to be pursued, expressed by design variables. The objective of the multi-layer anti-missile coordinated combat deployment plan is to maximize the launch depth or allow the longest launch time of the anti-missile combat units at each level of the multi-layer anti-missile system against incoming ballistic missiles, under the premise that the relevant constraints of the anti-missile protection zone are clear. The variables of the function are the deployment positions of each anti-missile combat unit.

[0209] Let d be the launch depth of the anti-missile combat unit of the multi-layered anti-missile system against the incoming ballistic missile. fs It represents the length of the trajectory of a ballistic missile within the anti-missile launch zone. Relatively speaking, the greater the anti-missile launch depth, the longer the incoming ballistic missile will fly within the anti-missile launch zone. Correspondingly, the anti-missile interceptor is allowed to fire more times at the incoming ballistic missile. Given a fixed probability of single-shot destruction by the anti-missile interceptor, increasing the number of allowed shots is an important way to improve the combat effectiveness of a multi-layer anti-missile system. Therefore, for multi-layer anti-missile coordinated operations, the anti-missile launch depth is a parameter that is better the greater it is.

[0210] Within the XOY coordinate system with the center of the circumcircle of the ground-protected target as the origin, the deployment position of the anti-missile combat unit always moves along the Y-axis. Therefore, by adjusting the Y-axis coordinate of the deployment position, the launch depth of the anti-missile combat unit against incoming ballistic missiles can be maximized. Thus, the objective function for multi-layered anti-missile coordinated combat deployment planning can be:

[0211] d fs =f(x,y) (21)

[0212] Where x is the abscissa of the anti-missile combat unit in the XOY coordinate system, and y is the ordinate of the anti-missile combat unit in the XOY coordinate system. Since the value of x is always 0 in the XOY coordinate system, equation (4-21) can also be expressed as:

[0213] d fs =f(0,y) (22)

[0214] As mentioned above, due to the anti-missile launch depth l fs To ensure that the parameters are as large as possible, a multi-layered anti-missile coordinated combat deployment planning mathematical model is proposed:

[0215]

[0216] The first two terms in the formula are constraints, and the third term is the objective function. This allows us to calculate the configuration position of the anti-missile combat unit when the launch depth of the incoming ballistic missile is maximized.

[0217] The above model is applicable to anti-missile combat scenarios where the direction of ballistic missile attack is relatively clear. If the ballistic missile may attack from multiple directions, threatening ground targets in the form of a certain fan angle, then the above model should be further processed. The specific steps are as follows:

[0218] d3.1 Calculate the shortcut path P of the kill zone for the anti-missile combat unit when an incoming ballistic missile is launched from the threat boundary. i According to P i The numerical value will P i n vertical kill zones are formed by cutting through the same route shortcut interval ΔP.

[0219] d3.2 Construct the objective function based on equation (23)

[0220] d3.3, Order The function value is maximized when the sum of the launch depths corresponding to all the vertical kill zones formed by the cuts is maximized.

[0221]

[0222] By using simulation to solve the above formula, the configuration points of the anti-missile combat units can be obtained. Then, by traversing the anti-missile combat units to which the multi-layer anti-missile system belongs, a sequence of multi-layer anti-missile coordinated combat deployment plans can be formed.

[0223] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-layered anti-missile cooperative combat mission planning and modeling method, characterized by: The modeling steps include the following: S1. Numerical model of anti-missile kill zone based on piecewise interpolation: a1. Piecewise interpolation modeling of vertical kill zone of anti-missile systems; a2. Vertical kill zone models under different flight route shortcuts; S2. Calculation model of anti-missile launch zone and launch depth based on reverse calculation: b1. Construct a ballistic missile motion model; b2. Construct a trajectory model for an anti-missile interceptor; b3. Calculate the vertical launch zone and depth of the anti-missile zone by reverse calculation; S3. Calculation model of anti-missile defense zone based on endpoint optimization: c1. Calculation model of the terminal anti-missile protection zone; c2. Calculation model of mid-course anti-missile protection zone; S4. Multi-layered anti-missile coordinated combat deployment planning model: d1. Preliminary problem analysis; d2. Constraints on multi-layered anti-missile coordinated combat deployment planning modeling; d3. Objective function of multi-layered anti-missile coordinated combat deployment planning; In the aforementioned c1, terminal missile defense is an interception operation carried out against ballistic targets during the reentry phase of an incoming ballistic missile. For a given ballistic missile launch point, direction of attack, and target type, the terminal missile defense protection zone can be described as the projection of the terminal missile defense combat unit's kill zone onto the ground along the trajectory of the incoming ballistic missile. c1.1 Basic ideas for constructing the terminal missile defense zone model; The terminal missile defense kill zone can be viewed as a combination of a cluster of vertical kill zones with equal flight path intervals and discrete from each other. If the flight path intervals are small enough, the terminal missile defense kill zone formed by the vertical kill zones obtained from this will be infinitely close to the actual kill zone. Once the vertical kill zone corresponding to a certain flight path is determined, the "ground defense line" of the vertical kill zone against the incoming ballistic missile target can be calculated based on the flight trajectory of the incoming ballistic missile during the reentry phase. All the "ground defense lines" corresponding to the vertical kill zones are combined to form the terminal missile defense protection zone. c1.2, the "ground defense line" corresponding to the terminal anti-missile vertical kill zone; In the vertical kill zone of the 0-way shortcut of the terminal anti-missile combat unit, the foremost point of the kill zone is C, and the last endpoint of the upper boundary of the kill zone is A. c1.2.1 The terminal anti-missile vertical kill zone corresponds to the foremost point of the "ground defense line"; Let θ be the minimum ballistic inclination angle that a terminal anti-missile unit can counter a ballistic missile. min When the incoming ballistic missile's flight trajectory passes through point C, the foremost point of the farthest boundary of the kill zone, its curved trajectory intersects the S-axis at point G. m This refers to the foremost point of the theoretical "ground defense line." The ballistic missile's reentry trajectory is considered a straight line, and the angle between this straight trajectory and the S-axis is the minimum trajectory inclination angle θ that the terminal anti-missile unit can intercept during the reentry phase. min At this point, the intersection of the straight-line flight trajectory and the S-axis is G′. Therefore, point G′ is the foremost point of the "ground defense line" of the vertical kill zone. Analysis shows that the coordinates of G′ are (S, P, H). c1.2.2 The terminal anti-missile vertical kill zone corresponds to the last endpoint of the "ground defense line"; Assuming the maximum elevation angle of the terminal anti-missile kill zone is greater than the maximum reentry angle of the ballistic missile, and let θ be the maximum trajectory inclination angle of the ballistic missile that the terminal anti-missile unit can intercept during the reentry phase. max When the incoming ballistic missile's flight trajectory passes through the final endpoint A of the kill zone's high boundary, the intersection point K of its curved trajectory and the S-axis is the final endpoint of the theoretical "ground defense line." Treating the ballistic missile's reentry phase trajectory as a straight line, the angle between this straight trajectory and the S-axis is the maximum trajectory inclination θ of the ballistic missile that the terminal anti-missile unit can intercept during the reentry phase. max At this point, the intersection of the straight-line flight trajectory and the S-axis is K′. Therefore, point K′ is the final endpoint of the vertical kill zone's "ground defense line." Analysis shows that the coordinates of K′ are... c1.2.3, The "ground defense line" corresponding to the terminal anti-missile vertical kill zone; Based on the above analysis, the "ground defense line" corresponding to the vertical kill zone of the terminal anti-missile combat unit is the line K′G′ connecting points K′ and G′, with a length l of: c1.3 Calculate the shortcut P for different routes i The corresponding terminal anti-missile vertical kill zone; Different route shortcuts P i The corresponding vertical kill zone calculation method can be performed by following the method described above to obtain the shortcut P for different flight paths. i The corresponding vertical kill zone; c1.4 Calculate the "ground defense line" corresponding to the vertical kill zone of the anti-missile system at the end of different flight shortcuts; Referring to the calculation method in c1.2, determine the foremost point of the "ground defense line" corresponding to the vertical kill zone of different flight shortcuts. and the last endpoint Their coordinates are respectively Then, the "ground defense line" corresponding to the vertical kill zone of different flight shortcuts can be determined, i.e. Point and Connecting the points Its length for: c1.5 Solve for the terminal missile defense zone; Once the calculation results of the "ground defense line" corresponding to the vertical kill zone of each flight path are determined, the least squares curve fitting of the foremost point and the last endpoint of the "ground defense line" can be performed using a polynomial to form the terminal anti-missile defense zone.

2. The multi-layered anti-missile cooperative combat mission planning and modeling method according to claim 1, characterized in that, In S1, the segmented interpolation modeling of the vertical kill zone of the anti-missile system adopts the profile method, and studies the vertical kill zone and the horizontal kill zone. The ballistic missile flies at high speed in the passive phase and carries out the attack in the manner of inclined ballistic trajectory. In the above a1, the segmented interpolation modeling of the vertical kill zone of the anti-missile system adopts the data fitting method to comprehensively determine the formed spatial region. Based on the vertical kill zone of the O-path shortcut, the mathematical model of the vertical kill zone of the anti-missile combat unit is constructed by numerical processing of the vertical kill zone. The vertical kill zone of the O-path shortcut of the anti-missile combat unit when it encounters a typical ballistic target is the cross section obtained by cutting the spatial kill zone with the plane of the path shortcut P=O. In the vertical kill zone of the terminal anti-missile 0-path shortcut, it is represented by the plane coordinate system SOH, where O is the configuration point of the terminal anti-missile interceptor launch platform, OH is the altitude axis, and OS is the horizontal distance axis. The kill zone is set with the far boundary BC, the high boundary AB and the low boundary CD, the high near boundary AE and the low near boundary DE. The far boundary BC and the low near boundary DE are two curves, and the other boundaries are straight lines. Piecewise linear interpolation is used to numerically process the vertical kill zone of the anti-missile system and characterize the kill zone. The anti-missile system uses a multi-segment broken line connection to replace the curved boundaries of the vertical kill zone and the horizontal kill zone, thereby performing interpolation processing. After interpolation processing, the vertical kill zone airspace is lost, and the interpolation nodes need to be within a certain accuracy range. When there is only one interpolation node, let the piecewise interpolation function be f(s), and the polynomial corresponding to the original curve be φ(s), that is, in the interval [S B S C Choose a value from ] such that Minimum, that is: The above operations can determine an interpolation node. Following this method, the second and third newly added nodes are found respectively. The original irregular anti-missile kill zone is replaced by a regular polygon, which is also a planar region enclosed by the vertices of the polygon.

3. The multi-layered anti-missile cooperative combat mission planning and modeling method according to claim 1, characterized in that, In section a2, the construction of vertical kill zone models under different flight shortcuts is affected by terrain conditions, troop numbers, and ballistic missile operational deployment. This is used to calculate the anti-missile launch area and launch depth under different flight shortcuts. The anti-missile space kill zone can be considered as a combination of a cluster of vertical kill zones with equal flight shortcut intervals and discrete from each other. Given a clear numerical model of the vertical kill zone for the anti-missile combat unit O flight shortcut, other flight shortcuts P... i The corresponding vertical kill zone is calculated using the following method: a2.

1. Let S be the maximum heading distance among all feature points in the vertical kill zone of the O-path shortcut. max The minimum heading distance is S min Flight shortcut P i The corresponding heading distance is S i Then we have: If S i min If the O route shortcut vertical kill zone allows direct entry into the next step; if S i >S max Then with P i The corresponding vertical kill zone does not exist;​ If S min i max Then use a plane Cut the vertical kill zone of the O-path shortcut and keep the distance less than S. i The region and feature points are discarded to obtain the corrected vertical kill zone;​​ a2.

2. Calculate the route shortcut P based on the corrected vertical kill zone of the O route shortcut. i The feature point corresponding to the vertical kill zone, and select a point F(S) in the vertical kill zone. F H F If the route shortcut P is... i The corresponding feature points in the vertical kill zone are Then we have: Shortcut to the route P i Once all feature points corresponding to the vertical kill zone have been calculated, the route shortcut P can be obtained. i The corresponding numerical model of the vertical kill zone.

4. The multi-layered anti-missile cooperative combat mission planning and modeling method according to claim 1, characterized in that, In b1, the ballistic missile motion model is constructed in the North-East coordinate system. In the local vertical coordinate system, the ballistic missile kinematic equations can be described as follows: Where y is the altitude of the ballistic missile flight, Y = C y qs x is the range of the ballistic missile, X = C x qs α is the angle of attack of the ballistic missile; q is the flight kinetic pressure, q = ρv 2 / 2; ρ is the atmospheric density, and its value varies with altitude y.

5. The multi-layered anti-missile cooperative combat mission planning and modeling method according to claim 1, characterized in that, In b2, the trajectory model of the anti-missile interceptor is constructed in a Cartesian coordinate system based on ground parameters. The duration from the anti-missile interceptor ejection tube to the ignition of the first-stage engine is t0, the initial velocity of the interceptor ejection tube is V0, and G is the acceleration due to gravity. Therefore, the velocity from the interceptor ejection tube to the ignition of the first-stage engine is: V = V0 - Gt0(5) Given the interceptor's engine average thrust p, the missile mass m, V1 as the missile velocity at the previous moment, and t... s Using the time step as the calculation step, the interceptor missile velocity is: In the formula, θ is the trajectory inclination angle of the interceptor missile; Given the maximum thrust P2 and minimum thrust P1 of the anti-ballistic missile interceptor engine, the total engine operating time T1, and the engine operating time after ignition T, the thrust calculation formula can be determined as follows: Neglecting aerodynamic drag, the interceptor missile's velocity is: Considering the effect of aerodynamic drag, we have the following drag: Therefore, the interceptor missile's velocity is: In the formula, α is the angle of attack and β is the sideslip angle; Assuming a ground-based interceptor missile engages a high-speed aerial target, and the interceptor missile's guidance uses a generalized proportional guidance method, then: Where K is the proportionality coefficient; The relative velocity between the projectile and the target; q represents the tilt angle of the bullet's line of sight; The velocity of the angle of inclination of the bullet's line of sight; The velocity of the angle of inclination of the bullet's line of sight; n y n z These are respectively the missile's longitudinal overload and lateral overload; ballistic inclination velocity The calculation formula is: ballistic angular velocity The calculation formula is: By integrating the above formulas, we can obtain the missile's trajectory inclination angle and trajectory deflection angle.

6. The multi-layered anti-missile cooperative combat mission planning and modeling method according to claim 1, characterized in that, In step b3, for the feature points in the numerical model of the predetermined vertical kill zone, the flight time t of the anti-missile interceptor to reach the feature points is calculated using the anti-missile interceptor trajectory model. df Let t be the time from the issuance of the launch command to the departure of the anti-missile interceptor from the launch device. dd The flight time of the ballistic missile from the characteristic launch point to the corresponding characteristic encounter point is: t bdf =t df +t dd (14) By clearly identifying the incoming ballistic missile and the ground-based target, and based on the ballistic missile reentry stage trajectory model, the launch point of the anti-missile interceptor can be determined by moving the launch point along the S-axis of the ground rectangular coordinate system. After determining the launch points corresponding to all the feature points of the terminal anti-missile vertical kill zone, the irregular polygon formed by connecting adjacent feature points is the vertical launch zone corresponding to the vertical kill zone. The anti-missile launch zone is determined. Based on the ballistic missile model and the anti-missile interceptor model, the launch depth is calculated using simulation methods. On the basis of the anti-missile interception launch depth, the allowable launch time parameter is further calculated. This parameter is used to characterize the remaining flight time of the incoming ballistic missile in the launch zone and the allowable decision time for the anti-missile combat commander.

7. The multi-layered anti-missile cooperative combat mission planning and modeling method according to claim 1, characterized in that, In the aforementioned C2, mid-course anti-missile defense refers to the interception operation carried out by the anti-missile combat unit against the ballistic target during the mid-course flight of the incoming ballistic missile. The interception arc of the mid-course anti-missile combat unit against a typical ballistic target is the flight trajectory of the ballistic missile after the end of the active phase and before re-entry into the atmosphere. The essence of mid-course anti-missile defense is that the anti-missile interceptor is launched from the ground launch device. Under the action of the guidance and control system, the interceptor encounters the incoming target in the mid-course anti-missile kill zone and destroys the target. When conducting calculation model analysis of the mid-course anti-missile protection zone, it is essential to grasp two key elements: the trajectory pattern of the incoming ballistic missile and the characteristics of the kill zone of the mid-course anti-missile combat unit. c2.1 The approach to constructing the mid-course anti-missile defense zone model; The mid-course missile defense kill zone can be viewed as a combination of a cluster of vertical kill zones with equal and discrete flight path intervals. If the flight path interval ΔP is sufficiently small, the mid-course missile defense kill zone formed by the vertical kill zones obtained from this is infinitely close to the actual kill zone. When a certain flight path interval P... i Once the corresponding vertical kill zone is determined, the "ground defense line" of the vertical kill zone against the incoming ballistic missile can be calculated based on the mid-course flight trajectory of the incoming ballistic missile. All the "ground defense lines" corresponding to the vertical kill zones are combined to form the mid-course anti-missile defense zone. c2.2, The "ground defense line" corresponding to the mid-course anti-missile vertical kill zone; In the vertical kill zone of the 0th route shortcut of the mid-course anti-missile combat unit, the closed area ABCDE is the vertical kill zone of the 0th route shortcut of the mid-course anti-missile combat unit. The foremost point of the kill zone is C, and the last endpoint of the upper boundary of the kill zone is A. c2.1.1 The mid-course anti-missile vertical kill zone corresponds to the foremost point of the "ground defense line"; Assume the incoming ballistic missile flies along a standard elliptical trajectory with a range of R. The highest point of the trajectory coincides with the foremost point C of the mid-course anti-missile kill zone. Then, the intersection M of the incoming ballistic missile's trajectory and the S-axis is the foremost point of the theoretical "ground defense line." Since the range of the incoming ballistic missile is determined, the coordinates of point M can be accordingly determined. c2.1.2 The mid-course anti-missile vertical kill zone corresponds to the last endpoint of the "ground defense line"; Assuming the maximum elevation angle of the mid-course anti-missile kill zone is greater than the maximum trajectory inclination angle of the ballistic missile, and the incoming ballistic missile's trajectory passes through point A, then the intersection point N of the ballistic missile's trajectory and the S-axis is the final endpoint of the theoretical "ground defense line." Draw a straight line through point A, and let the angle between this line and the S-axis be θ, which represents the maximum trajectory inclination angle of the ballistic missile that the mid-course anti-missile combat unit can counter. max At this point, the intersection of the straight line and the S-axis is N′. Therefore, point N′ is the final endpoint of the "ground defense line" of the mid-course anti-missile vertical kill zone. Analysis shows that the coordinates of N′ are... The mid-course anti-missile vertical kill zone corresponds to the last endpoint of the "ground defense line"; c2.1.3, The "ground defense line" corresponding to the mid-course anti-missile vertical kill zone; Based on the above analysis, the "ground defense line" corresponding to the vertical kill zone of the mid-course anti-missile combat unit is the line N′M connecting points N′ and M, with a length l of: c2.3 Calculate the shortcut P for different routes i The corresponding mid-course anti-missile vertical kill zone; Different route shortcuts P i The calculation method for the corresponding vertical kill zone can be implemented by referring to the method described above, and the shortcut P for different flight paths can be obtained. i The corresponding vertical kill zone; c2.4 Calculate the "ground defense line" corresponding to the vertical kill zone of anti-missile systems in the mid-section of different flight shortcuts; Referring to the calculation method in c2.2, determine the foremost point of the "ground defense line" corresponding to the vertical kill zone of different flight shortcuts. and the last endpoint Their coordinates are respectively Then, the "ground defense line" corresponding to the vertical kill zone of different flight shortcuts can be determined, i.e. The line connecting point M and point M Its length for: c2.5 Solving for the mid-course anti-missile protection zone; Once the calculation results of the "ground defense line" corresponding to the vertical kill zone of the mid-course missile defense in each flight path shortcut are determined, the mid-course missile defense zone can be formed by least-squares curve fitting of the foremost point and the last endpoint of the "ground defense line" using a polynomial. It should be noted that, since the mid-course missile defense zone has a large area and wide range, the value of the flight path shortcut interval ΔP can be appropriately increased, and the mid-course missile defense zone formed after least-squares curve fitting does not need to be numerically processed.

8. The multi-layered anti-missile cooperative combat mission planning and modeling method according to claim 1, characterized in that, In S4, the multi-layer anti-missile coordinated combat deployment planning model is a process of constructing an objective function around the launch depth, taking into full account the constraints of the anti-missile protection zone, using the configuration position of the anti-missile combat unit to which the multi-layer anti-missile system belongs as the variable. d1. Preliminary problem analysis; Before carrying out the multi-layered anti-missile coordinated combat deployment planning and modeling work, the key elements in the basis of the combat deployment planning are analyzed and the analysis conclusions are clearly given, so as to provide basic conditions for the construction of the multi-layered anti-missile coordinated combat deployment planning model. d1.1 Clarify the superior's intentions and the unit's operational tasks; The intentions of higher authorities and the operational tasks of this level are usually reflected in the operational orders issued by higher authorities. Before implementing the multi-level anti-missile coordinated operation deployment plan, a thorough and detailed study and analysis of the intentions of higher authorities and the operational tasks of this level should be carried out to clarify the analysis and judgment of higher authorities on the situation, the operational intentions and deployment attempts of higher authorities, the total number of troops involved in the operation and the situation of friendly forces, the nature of the operational tasks of this level, the targets to be protected and the main operational direction, the precautions required by higher authorities, and the methods of coordination with friendly forces. d1.

2. Clearly define the types of targets to be protected; Based on the enemy's operational intentions, analyze and determine the main types of our own defensive targets. When studying the defensive targets, conduct in-depth analysis and judgment on the enemy's intention to use ballistic missiles to strike. Different operational intentions result in different main types of ballistic missile strike targets and different key defensive targets for our own side. d1.3 Determine the key areas to be protected in anti-missile operations; The types of ground targets within the responsibility protection zone of the multi-layered anti-missile system should be clearly defined. Based on the status and role of the protected targets, the key points of anti-missile operations should be determined. The strategic and operational status of the protected targets, as well as the degree of threat they pose to the enemy, determine the order in which the targets are protected. When determining the targets to be protected, priority should be given to targets with high strategic and operational importance, and targets that pose a serious threat to the enemy should be protected first. d1.4 Analyze and judge the operational use of ballistic missiles; The analysis and judgment of the enemy's ballistic missile operations mainly includes intelligence information on the types of ballistic missiles that the enemy may use, the operational area of ​​the ballistic missile launch system, the range of the ballistic missile's direction of attack, as well as the number of enemy ballistic missile launchers, their penetration methods, and their operational patterns. The types of ballistic missiles that the enemy may use are closely related to the location, shape, nature, and vulnerability of the targets that our side is defending. The ballistic missiles used by the enemy should be matched with the distance, nature, and shape of the targets they are going to attack in terms of range, power, and accuracy. Enemy ballistic missile launch sites are often distributed in a certain battlefield space and operate in a certain area. It is necessary to make a basic judgment on the battlefield operation range of the enemy's ballistic missile launch system. For a given target to be protected, the possible direction of ballistic missile attack is always within a limited range. Now, taking the physical geometric center of the target to be protected as the center, the range of the possible ballistic missiles is used to estimate the activity area of ​​the enemy ballistic missiles. After estimating the possible activity range of the enemy ballistic missile launchers, it is also necessary to combine the terrain and traffic conditions of the enemy's area to determine the actual activity range of the enemy ballistic missile launch system. The target to be protected is then connected to the limit boundary point of the actual activity range, thereby determining the threat sector of the enemy ballistic missiles to the target to be protected. The number of enemy ballistic missiles and their launchers determines the maximum number of ballistic missiles the enemy can launch simultaneously during combat. The number of ballistic missiles that each anti-missile combat unit can intercept simultaneously is limited. If the number of enemy ballistic missiles and their launchers is large, the number of ballistic missiles launched simultaneously will be greater, which will inevitably require more anti-missile combat units to intercept them simultaneously. If the number of enemy ballistic missiles and their launchers is small, then only a few anti-missile combat units are needed to intercept them. The above describes the analytical and judgmental work that needs to be carried out in advance for the construction of a multi-layered anti-missile coordinated combat deployment planning model. Once the analytical conclusions are clear, the multi-layered anti-missile coordinated combat deployment planning model can be constructed based on the given anti-missile forces.

9. The multi-layered anti-missile cooperative combat mission planning and modeling method according to claim 1, characterized in that, In d2, the ability of the anti-missile protection zone to cover ground targets is a prerequisite for anti-missile operational deployment and a constraint condition for multi-layered anti-missile coordinated operational deployment planning and modeling. The analysis is based on the effective coverage of ground targets by the anti-missile protection zones of each level of anti-missile combat units. It is assumed that the ground targets are ground groups composed of several point targets, and these groups are protected by a multi-layered anti-missile system, including mid-course anti-missile combat unit n. Z The terminal phase high-level and terminal phase low-level anti-missile combat units are n respectively. MG set, n MD set; d2.1 Ground target segmentation based on the missile defense zone; A ground target group segmentation method based on the missile defense zone is adopted, dividing the ground target group into n WY Each circumcircle contains a certain number of point targets, and the circumcircle can be completely covered by the terminal high-level missile defense zone. d2.2 Mathematical model of the anti-missile protection zone covering ground targets; With the i-th 1 i 1 <nMG terminal phase high-altitude anti-missile combat unit coverage of the i-th 2 i 2 <n WY Taking the circumcircle of a ground target as an example, we analyze the mathematical model of the anti-missile protection zone covering ground targets. Let the i-th... 1 The terminal phase high-altitude anti-missile combat unit configuration point is O. MGi The center of the circumcircle of the final ground protection target is O. WYi The center O of the circumcircle of the ground-protected target. WYi XO with the origin WYi Y-coordinate system, Y-axis passes through O WYi The point points in the direction of the ballistic missile's main attack, and the X-axis passes through O. WYi Point O is defined as the point perpendicular to the Y-axis to the right. MGi Construct a rectangular coordinate system SO for ground parameters with the origin as the origin. MGi If P is the axis of the P axis, then the P axis is parallel to the X axis and the S axis coincides with the Y axis. Take the left-hand shortcut P MGii Draw a straight line perpendicular to the P-axis. The intersection point of this line and the front end of the terminal high-altitude missile defense zone is: The backend intersection is The point of intersection with the front end of the circumcircle of the ground-protected target is The backend intersection is Let l be the distance from the deployment point of the terminal anti-missile combat unit to the center of the circumcircle of the ground-protected target. MGii The terminal anti-missile combat unit is then positioned at XO. WYi The coordinate in the Y coordinate system is O MGi (0,l MGii If the missile defense zone of the terminal high-altitude missile defense unit covers the circumcircle of the ground coordinate system, then the following formula should be satisfied: Based on the calculation model of the terminal missile defense zone and the above positional relationships, the following equation can be obtained by transforming the above equation: in: --The shortcut is P MGii At that time, the coordinates of point C at the foremost point of the terminal high-altitude anti-missile kill zone on the S-axis; --The shortcut is P MGii At that time, the coordinates of point C at the foremost point of the terminal high-altitude anti-missile kill zone on the H-axis; θ min --The minimum trajectory inclination angle of a ballistic missile that the terminal phase anti-missile combat unit can intercept during reentry; --The shortcut is P MGii At that time, the coordinates of the rear endpoint A of the high boundary of the terminal high-level anti-missile kill zone on the S-axis; --The shortcut is P MGii At that time, the coordinates of the rear endpoint A of the high boundary of the terminal high-level anti-missile kill zone on the H-axis; θ max --The maximum trajectory inclination angle of a ballistic missile during the reentry phase that the terminal phase anti-missile combat unit can counter; For a given terminal phase high-altitude anti-missile combat unit and an incoming ballistic missile, simulation tools can be used to calculate... Parameters, combined with the known θ min and θ max The numerical values ​​then form the constraints for the terminal high-altitude anti-missile operation deployment planning and modeling. Then calculate the constraints for modeling the mid-course and terminal low-level anti-missile operational deployment plan; d3. Objective function of multi-layered anti-missile coordinated combat deployment planning; The objective function refers to the functional relationship between the target of interest and related factors, and the variable of the function is the deployment location of each anti-missile combat unit. Let d be the launch depth of the anti-missile combat unit of the multi-layered anti-missile system against the incoming ballistic missile. fs The length of the trajectory of a ballistic missile within the anti-missile launch zone is characterized by the length of its flight path. Relatively speaking, the greater the anti-missile launch depth, the longer the flight time of the incoming ballistic missile within the anti-missile launch zone. Correspondingly, the number of times the anti-missile interceptor is allowed to fire at the incoming ballistic missile is also greater. Within the XOY coordinate system with the center of the circumcircle of the ground-protected target as the origin, the deployment position of the anti-missile combat unit always moves along the Y-axis. Therefore, by adjusting the Y-axis coordinate of the deployment position, the launch depth of the anti-missile combat unit against incoming ballistic missiles can be maximized. Thus, the objective function for multi-layered anti-missile coordinated combat deployment planning can be: d fs =f(x,y) (21) Where x is the x-coordinate of the anti-missile combat unit in the XOY coordinate system; y represents the ordinate of the anti-missile combat unit in the XOY coordinate system; Since the x-value is always 0 in the XOY coordinate system, equation (4-21) can also be expressed as: d fs =f(0,y) (22) Due to the depth of the anti-missile launch... fs To ensure that the parameters are as large as possible, a multi-layered anti-missile coordinated combat deployment planning mathematical model is proposed: The first two terms in the formula are constraints, and the third term is the objective function. From this, the configuration position of the anti-missile combat unit can be calculated when the launch depth of the incoming ballistic missile is at its maximum. The above model is applicable to anti-missile combat scenarios where the direction of ballistic missile attack is relatively clear. If the ballistic missile may attack from multiple directions, threatening ground targets in the form of a certain fan angle, then the above model should be further processed. The specific steps are as follows: d3.1 Calculate the shortcut path P of the kill zone for the anti-missile combat unit when an incoming ballistic missile is launched from the threat boundary. i According to P i The numerical value will P i n vertical kill zones are formed by cutting through equal flight path shortcuts at intervals ΔP; d3.2 Construct the objective function based on equation (23) d3.3, Order The function value is maximized when the sum of the launch depths corresponding to all the vertical kill zones formed by the cuts is maximized. By using simulation to solve the above formula, the configuration points of the anti-missile combat units can be obtained. Then, by traversing the anti-missile combat units to which the multi-layer anti-missile system belongs, a sequence of multi-layer anti-missile coordinated combat deployment plans can be formed.

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