CN114740884A

CN114740884A - Double-pulse guidance method and device for short-range interception

Info

Publication number: CN114740884A
Application number: CN202210235480.4A
Authority: CN
Inventors: 陈万春; 于琦; 杨良; 赵石磊
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2022-03-11
Filing date: 2022-03-11
Publication date: 2022-07-12
Anticipated expiration: 2042-03-11
Also published as: CN114740884B

Abstract

The invention provides a double-pulse guidance method and a double-pulse guidance device for short-range interception, wherein the method comprises the following steps: establishing a kinetic equation of the interception missile and the target missile in the gliding section, and constructing a differential equation of the relative movement speed of the missile and the target missile in a sight line coordinate system based on the kinetic equation and a coordinate transformation matrix; establishing a dynamic equation of a boosting section, and predicting a terminal position vector and a speed vector of the boosting section; according to the terminal position vector and the speed vector of the boosting section ending moment, based on the strategy of the zero control interception triangle, obtaining a shutdown point parameter meeting the requirement of the zero control interception triangle at the sliding section; deducing the optimal ignition time of the second pulse of the interception bomb based on the performance index function of the ignition time of the second pulse of the interception bomb according to the shutdown point parameter, the position vector analytic expression and the boundary condition; and acquiring a double-pulse optimal guidance instruction based on the predicted values and the expected values of the speed inclination angle and the speed deflection angle at the shutdown time of the interceptor projectile and the second-pulse optimal ignition time of the interceptor projectile. The interception performance can be improved.

Description

Double-pulse guidance method and device for short-range interception

Technical Field

The invention relates to the technical field of guidance control, in particular to a double-pulse guidance method and device for short-range interception.

Background

With the continuous development of missile technology, the range of the missile and the power of the warhead are continuously increased, and the threat is increased. In order to reduce the damage effect of enemy missiles, an effective method is to use a back-guiding interception technology to intercept the enemy missiles. In the back-guidance interception process, in order to completely destroy a target missile, the direct collision between the own-launched interception missile and the target missile needs to be realized, but the relative speeds of the two parties are extremely high, so that a guidance control system with higher control precision and an interception missile guidance law with better performance are needed.

In order to intercept remote enemy missiles and even intercontinental ballistic missiles in the middle flight section outside the atmosphere, a guidance control system is required to accurately control the speed and the direction of the interception missiles. However, the intercepting bullet at the present stage generally uses a solid rocket engine, so that the adjustment of the thrust and the working time cannot be realized, and the intercepting capability of the intercepting bullet is limited. In order to improve the intercepting capability of the intercepting bullet, the double-pulse solid rocket engine becomes the leading edge of the power research of the intercepting bullet, and the interval between two working pulses can be flexibly adjusted by utilizing the double-pulse solid rocket engine, so that the requirements of more working scenes are met, and therefore a new guidance law needs to be designed aiming at the characteristics of the double-pulse solid rocket engine to improve and realize the intercepting capability of the double-pulse solid rocket engine.

Disclosure of Invention

In view of this, the present invention provides a double-pulse guidance method and apparatus for short-range interception, so as to improve the interception performance of an interception bullet.

In a first aspect, an embodiment of the present invention provides a double-pulse guidance method for short-range interception, including:

establishing a kinetic equation of the interception missile and the target missile in the gliding section under a local ground coordinate system, and establishing a differential equation of the relative movement speed of the missile and the target missile under a sight line coordinate system based on the kinetic equation and a coordinate conversion matrix of the sight line coordinate system and the local ground coordinate system;

establishing a dynamic equation of a boosting section, and predicting a terminal position vector and a speed vector of the boosting section;

according to an end point position vector and a velocity vector of an interception bullet boosting section ending moment, based on a strategy of a zero control interception triangle, obtaining shutdown point parameters meeting the requirement of the zero control interception triangle at a gliding section, wherein the shutdown point parameters comprise an interception bullet velocity inclination angle and a velocity deflection angle;

deducing the optimal ignition time of the second pulse of the interception bomb based on a preset performance index function of the ignition time of the second pulse of the interception bomb according to the shutdown point parameter, the position vector analytical formula and the boundary condition;

and acquiring a double-pulse optimal guidance instruction based on the predicted values and the expected values of the speed inclination angle and the speed deflection angle at the shutdown time of the interceptor projectile and the second-pulse optimal ignition time of the interceptor projectile.

With reference to the first aspect, an embodiment of the present invention provides a first possible implementation manner of the first aspect, where the establishing a kinetic equation of the target missile and the interception missile in the taxiing section under the local ground coordinate system includes:

respectively acquiring the earth center distance vectors of the interception missile and the target missile according to the earth center distance of the origin of a local ground coordinate system of the sliding section and the position vectors of the interception missile and the target missile under the local ground coordinate system;

determining gravity acceleration vectors of the interception missile and the target missile under a local ground coordinate system respectively based on the earth-center distance vector and the earth-center gravity constant;

and acquiring kinetic equations of the intercepting missile and the target missile respectively under a local ground coordinate system based on the gravity acceleration vector.

With reference to the first possible implementation manner of the first aspect, an embodiment of the present invention provides a second possible implementation manner of the first aspect, where the constructing a differential equation of the projectile relative movement velocity in the line-of-sight coordinate system based on the kinetic equation and a coordinate transformation matrix of the line-of-sight coordinate system and the local ground coordinate system includes:

acquiring a sight elevation angle and a sight declination expression of a sight coordinate system based on the components of the position vectors in the kinetic equation and the relative positions of the interception missile and the target missile;

constructing a coordinate transformation matrix of a sight line coordinate system and a local ground coordinate system according to the sight line elevation angle and the sight line deflection angle expression;

acquiring velocity component equations of the interception missile and the target missile respectively under a sight line coordinate system based on the coordinate transformation matrix, the velocity vector of the interception missile in the kinetic equation and the velocity vector of the target missile in the kinetic equation;

constructing a bullet relative motion velocity equation under a sight coordinate system according to the sight elevation angle and sight declination expression, the relative position between the interception bullet and the target missile and respective velocity component equations;

and carrying out differential operation on the relative movement velocity equation of the bullet, and constructing the differential equation of the relative movement velocity of the bullet under a sight line coordinate system.

With reference to the first aspect, an embodiment of the present invention provides a third possible implementation manner of the first aspect, where the establishing a dynamic equation of the boost section and predicting an end position vector and a velocity vector of the boost section include:

acquiring an orbit inclination angle and a rising intersection right ascension of an orbit plane based on the angular momentum of the interception projectile in the earth center inertial coordinate system;

establishing a boosting section dynamic model based on a projectile relative motion velocity differential equation, an interception projectile operation parameter and an interception projectile velocity in a track plane;

and determining an end point position vector and a velocity vector of the ending moment of the boosting section of the interceptor missile based on the dynamic model of the boosting section.

With reference to the third possible implementation manner of the first aspect, an embodiment of the present invention provides a fourth possible implementation manner of the first aspect, where the determining, based on a boost section dynamics model, an end position vector and a velocity vector of an end time of a boost section of a containment bomb includes:

simplifying the derivative of the speed of the interception bomb in the boosting section dynamic model to obtain a speed simplified derivative;

and integrating the speed simplified derivative to obtain the speed of the boosting section ending moment of the interception bomb.

With reference to the fourth possible implementation manner of the first aspect, an embodiment of the present invention provides a fifth possible implementation manner of the first aspect, where the integrating the simplified derivative of the velocity vector to obtain the velocity vector at the ending time of the missile blocking boosting section includes:

constructing an intermediate variable representing the ending moment of the boosting section, and acquiring a derivative of the intermediate variable according to an intercepting bullet trajectory inclination angle equation in a dynamic model of the boosting section;

integrating the derivative of the intermediate variable to obtain a boosting speed integral term and a boosting section terminal trajectory inclination angle;

and acquiring a velocity vector of the intercepting bullet boosting section at the ending moment based on the acquired boosting speed integral term value and the boosting section terminal trajectory inclination angle.

With reference to the first aspect, an embodiment of the present invention provides a sixth possible implementation manner of the first aspect, where the establishing a dynamic equation of the boost section and predicting an end position vector and a velocity vector of the boost section includes:

fitting the interception bullet trajectory inclination angle based on a derivative equation of the interception bullet trajectory inclination angle in the boosting section dynamic model;

acquiring an end point position equation of the boosting section of the interceptor projectile and an included angle equation of a connecting line between an end point position vector and the earth center to the ascending intersection point based on the fitted angle of inclination of the trajectory of the interceptor projectile;

and determining the end point position vector and the velocity vector of the ending moment of the boosting section of the intercepting bullet based on the track inclination angle, the ascent intersection point right ascension, the end point velocity of the boosting section of the intercepting bullet, the end point trajectory inclination angle of the boosting section, the end point position equation and the included angle equation of the end point position vector and the connecting line from the geocenter to the ascent intersection point.

In a second aspect, an embodiment of the present invention further provides a double-pulse medium guidance law device for short-range interception, including:

the differential equation building module is used for building a kinetic equation of the interception missile and the target missile in the gliding section under a local ground coordinate system, and building a differential equation of the relative movement speed of the missile and the target missile under the line of sight coordinate system based on the kinetic equation and a coordinate conversion matrix of the line of sight coordinate system and the local ground coordinate system;

the prediction module is used for establishing a boosting section kinetic equation and predicting a terminal position vector and a velocity vector of the boosting section;

the shutdown point parameter acquisition module is used for acquiring shutdown point parameters meeting the zero control interception triangle at the gliding section based on the strategy of the zero control interception triangle according to the end point position vector and the speed vector of the boosting section ending time of the intercepted missile, wherein the shutdown point parameters comprise an intercepted missile speed inclination angle and a speed deflection angle;

the derivation module is used for deriving the optimal ignition time of the second pulse of the interception bomb based on a preset performance index function of the ignition time of the second pulse of the interception bomb according to the shutdown point parameter, the position vector analytic expression and the boundary condition;

and the optimal instruction acquisition module is used for acquiring a double-pulse optimal guidance instruction based on the predicted values and the expected values of the speed inclination angle and the speed deflection angle at the shutdown time of the interception bullet and the second pulse optimal ignition time of the interception bullet.

In a third aspect, an embodiment of the present application provides a computer device, which includes a memory, a processor, and a computer program stored on the memory and executable on the processor, and the processor implements the steps of the above method when executing the computer program.

In a fourth aspect, the present application provides a computer-readable storage medium, on which a computer program is stored, and the computer program, when executed by a processor, performs the steps of the method described above.

According to the double-pulse guidance method and device for short-range interception, provided by the embodiment of the invention, a differential equation of the relative movement speed of the missile target under a sight line coordinate system is constructed by establishing a kinetic equation of an interception missile and a target missile in a gliding section under a local ground coordinate system and based on the kinetic equation and a coordinate conversion matrix of the sight line coordinate system and the local ground coordinate system; establishing a dynamic equation of a boosting section, and predicting a terminal position vector and a speed vector of the boosting section; according to an end point position vector and a velocity vector of an interception bullet boosting section ending moment, based on a strategy of a zero control interception triangle, obtaining shutdown point parameters meeting the requirement of the zero control interception triangle at a gliding section, wherein the shutdown point parameters comprise an interception bullet velocity inclination angle and a velocity deflection angle; deducing the optimal ignition time of the second pulse of the interception bomb based on a preset performance index function of the ignition time of the second pulse of the interception bomb according to the shutdown point parameter, the position vector analytical formula and the boundary condition; and acquiring a double-pulse optimal guidance instruction based on the predicted values and the expected values of the speed inclination angle and the speed deflection angle at the shutdown time of the interceptor projectile and the second-pulse optimal ignition time of the interceptor projectile. Therefore, the position and the speed of the terminal point of the boosting section are analyzed to obtain the position and the speed of the engine of the boosting section at the shutdown time, and the double-pulse optimal guidance instruction is deduced according to the optimal control theory, so that the optimality of the guidance instruction can be met, and the interception capability and the reliability of the intercepted bomb are improved.

In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.

FIG. 1 is a schematic flow chart of a double-pulse guidance method for short-range interception provided by an embodiment of the invention;

FIG. 2 is a schematic diagram of a relationship between a line-of-sight coordinate system and a local ground coordinate system according to an embodiment of the present invention;

FIG. 3 is a schematic diagram illustrating operational parameters of an intercepting bomb provided by an embodiment of the invention;

FIG. 4 is a schematic diagram of three-dimensional interception in a local ground coordinate system according to an embodiment of the present invention;

FIG. 5 is a schematic structural diagram of a double-pulse middle guidance law device for short-range interception according to an embodiment of the present invention;

fig. 6 is a schematic structural diagram of a computer device 600 according to an embodiment of the present application.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.

The embodiment of the invention provides a double-pulse guidance method and a double-pulse guidance device for short-range interception, which are described by the embodiment below.

Fig. 1 shows a flow diagram of a double-pulse guidance method for short-range interception according to an embodiment of the present invention. As shown in fig. 1, the method is a short-range interception double-pulse guidance method based on gravity difference fitting, and comprises the following steps:

101, establishing a kinetic equation of the interception missile and the target missile in the gliding section under a local ground coordinate system, and establishing a missile-target relative movement speed differential equation under a sight line coordinate system based on the kinetic equation and a coordinate transformation matrix of the sight line coordinate system and the local ground coordinate system;

in the embodiment of the present invention, as an optional embodiment, establishing a kinetic equation of the intercepted missile and the target missile in the glide section under the local ground coordinate system includes:

a11, respectively acquiring the geocentric distance vectors of an interception missile and a target missile according to the geocentric distance of the origin of a local ground coordinate system of a sliding section and the position vectors of the interception missile and the target missile under the local ground coordinate system;

a12, determining gravity acceleration vectors of the intercepting missile and the target missile under a local ground coordinate system respectively based on the earth center distance vector and the earth center gravity constant;

and A13, acquiring kinetic equations of the intercepting missile and the target missile respectively in a local ground coordinate system based on the gravity acceleration vector.

In the embodiment of the invention, in the gliding section, only the influence of gravity acceleration can be considered, so that the kinetic equation of the interception missile-target missile in the local ground coordinate system can be described as follows:

in the formula,

r_Mdand r_TdRespectively are position vectors of the interception missile and the target missile under a local ground coordinate system;

and

derivatives (differentials) of the position vectors of the interceptor missile and the target missile, respectively;

V_Mdand V_TdRespectively are velocity vectors of the interception missile and the target missile under a local ground coordinate system;

and

derivatives of velocity vectors of the interception missile and the target missile respectively;

g_Mdand g_TdThe gravity acceleration vectors of the interception missile and the target missile under a local ground coordinate system are respectively. The expression is as follows:

in the formula,

mu is a gravitational constant;

and

the earth center distance vectors of the interception missile and the target missile are respectively. The expression is as follows:

in the formula:

r_M0is the origin O of the local ground coordinate system_dThe distance between the earth and the center.

In the embodiment of the present invention, as an optional embodiment, a differential equation of the relative movement velocity of the bullet under the sight line coordinate system is constructed based on a kinetic equation and a coordinate transformation matrix of the sight line coordinate system and a local ground coordinate system, and includes:

a21, acquiring a sight elevation angle and a sight declination expression of a sight coordinate system based on the components of the position vectors in the kinetic equation and the relative positions of the interception missile and the target missile;

a22, constructing a coordinate transformation matrix of a sight line coordinate system and a local ground coordinate system according to the sight line elevation angle and the sight line deflection angle expression;

a23, acquiring velocity component equations of the interception missile and the target missile respectively in a sight line coordinate system based on the coordinate transformation matrix, the velocity vector of the interception missile in the kinetic equation and the velocity vector of the target missile in the kinetic equation;

a24, constructing a bullet relative motion velocity equation under a sight coordinate system according to the sight elevation angle and sight declination expression, the relative position between an interception bullet and a target missile and respective velocity component equations;

and A25, carrying out differential operation on the relative movement velocity equation of the bullet, and constructing the differential equation of the relative movement velocity of the bullet under the sight line coordinate system.

Fig. 2 is a schematic diagram illustrating a relationship between a line-of-sight coordinate system and a local ground coordinate system according to an embodiment of the present invention. As shown in FIG. 2, in the embodiment of the present invention, a line-of-sight coordinate system O is defined_L-x_Ly_Lz_LSetting the origin of coordinates O_LCoincident with the current position of the interceptor projectile, x_LThe axis pointing in the direction of the line of sight, y_LThe axis being perpendicular to x in a vertical plane_LAxis, z_LAxis and x_LAxis and y_LThe axes constitute a right-hand coordinate system. Wherein, q, lambda are sight elevation angle and sight declination angle respectively, and the expression of its relative position with the elastic eyes is:

λ＝sin^-1[(r_Tyd-r_Myd)/r]

q＝tan^-1[(r_Tzd-r_Mzd)/(r_Txd-r_Mxd)] (4)

in the formula:

r_Mxd、r_Mydand r_MzdRespectively are components of a position vector of the interception bomb under a local ground coordinate system;

r_Txd、r_Tydand r_TzdRespectively are components of a position vector of the target missile under a local ground coordinate system;

and r is the relative distance between the interception missile and the target missile.

In the embodiment of the invention, according to the relative position relationship of the two coordinate systems, the coordinate transformation matrix L from the local ground coordinate system to the sight line coordinate system_LdComprises the following steps:

by using the coordinate transformation matrix, velocity component equations of the interception missile and the target missile in the sight line coordinate system respectively can be obtained, namely, the component V of the velocity vector of the interception missile in the sight line coordinate system_MxL、V_MyL、V_MzLAnd the component V of the velocity vector of the target missile_TxL、V_TyL、V_TzLRespectively as follows:

in the embodiment of the invention, under the sight line coordinate system, the equation of relative motion of the bullet and the target can be expressed as follows:

in the formula, V_r、V_λ、V_qRespectively, are the components of the relative velocity vector of the bullet in the sight line coordinate system.

The equation of the relative movement velocity of the bullet in the sight line coordinate system can be expressed as:

the time derivation of the above equation can be obtained:

substituting the formula (8) and the formula (1) into the formulae (10) - (12), and performing a series of algebraic operations to obtain a differential equation of the relative movement velocity of the projectile at the sliding stage, namely V_r，V_λAnd V_qThe differential equations of (a) are:

in the formula:

in the formula,

Δg_r、Δg_λ、Δg_qthree projection components of the bullet gravity acceleration vector difference under a sight line coordinate system are respectively included;

g_Mx、g_Myand g_MzRespectively is the gravity acceleration vector g borne by the interception bullet_MdProjection components under a local ground coordinate system;

g_Tx、g_Tyand g_TzRespectively the gravity acceleration vector g borne by the target missile_TdProjection components in the local ground coordinate system.

102, establishing a dynamic equation of a boosting section, and predicting a terminal position vector and a speed vector of the boosting section;

in the embodiment of the present invention, as an optional embodiment, establishing a dynamic equation of a boosting section, and predicting a terminal position vector and a velocity vector of the boosting section includes:

b11, acquiring the orbit inclination angle and the ascent intersection right ascension of the orbit plane based on the angular momentum of the interception bullet in the earth center inertial coordinate system;

b12, establishing a boosting section dynamic model based on the thrust of the interceptor projectile, the initial mass, the mass flow and the operation parameters in the plane of the track;

and B13, determining an end position vector and a velocity vector of the ending moment of the boosting section of the interceptor bomb based on the dynamic model of the boosting section.

In the embodiment of the invention, as the double-pulse engine for intercepting the bomb is generally used in the third stage or the second stage, the altitude of the intercepting bomb is higher and the air density is lower, so that the influence of aerodynamic force can be ignored.

In the embodiment of the invention, if the intercepting bullet is in a standard control state, namely the thrust direction is the same as the current velocity vector direction, the track plane of the intercepting bullet cannot be changed at the moment. The orbital plane can be defined by the orbital inclination and the ascension intersection declination:

i_M＝cos^-1(H_Mz0/H_M0) (15)

Ω_M＝tan^-1(-H_Mx0/H_My0) (16)

in the formula,

i_Mfor track inclination, omega_MIs the ascending right ascension, H_Mx0、H_My0And H_Mz0For intercepting the projected component of the angular momentum vector of the projectile in the earth's center inertial frame, H_M0The angular momentum of the interception bullet in the earth center inertial coordinate system is shown.

Fig. 3 shows a schematic view of the operation parameters of the interceptor projectile according to the embodiment of the present invention. As shown in fig. 3, in the embodiment of the present invention, in the track plane, the operation parameters of the interceptor projectile include: the method comprises the following steps of establishing a boosting section dynamic model as follows, wherein the boosting section dynamic model comprises the following steps of intercepting bullet thrust, initial mass of the intercepting bullet, mass flow of the intercepting bullet, working time of an intercepting bullet engine, trajectory inclination angle of the intercepting bullet, position vector of the intercepting bullet in a track plane and included angle between the position vector of the intercepting bullet and a connecting line from the ground center to a lifting intersection point:

in the formula,

V_Mthe speed of the interceptor bomb in the boosting section is determined;

p is the thrust of the intercepting bullet;

m₀the initial mass of the interception bullet;

q_mmass flow of the interceptor projectile;

t is the working time of the intercepting bullet engine;

g_Mthe gravity acceleration borne by the interception bullet;

γ_Mthe angle of inclination of the trajectory of the intercepted projectile;

r_Mthe ground center distance for intercepting the bomb;

θ_Mthe included angle between the position vector of the intercepting bullet and the connecting line from the earth center to the ascending intersection point.

In the embodiment of the present invention, as an optional embodiment, determining an end position vector and a velocity vector of an interception bullet boosting segment ending time based on a boosting segment dynamics model includes:

simplifying the derivative of the speed of the intercepting bomb in the boosting section dynamic model to obtain a speed simplified derivative;

In the embodiment of the invention, the boosting period is generally short, so that the change of the axial component of gravity is small and can be ignored. In this way, the derivative of the velocity of the interceptor projectile in the boost section can be simplified to a velocity-simplified derivative:

in the formula,

g_M0and gamma_M0The gravity acceleration and the trajectory inclination angle at the current moment are respectively.

Integrating the above formula to obtain a velocity expression at the end time of the boosting section of the interception bomb:

V_Mbo＝V_M0-V_e[ln(1-t_bo/T)+K₁t_bo/T] (22)

in the formula,

V_Mbothe speed of the boosting section ending moment of the interceptor bomb;

V_M0the speed of the interception bullet at the current moment;

t_bothe remaining working time of the main engine is used for intercepting bullets;

V_et and K₁Are constants, and the expressions are respectively:

V_e＝P/q_m

in the embodiment of the present invention, the trajectory inclination angle of the intercepted projectile at the current moment is required to be obtained, so as to be an optional embodiment, the velocity simplified derivative is integrated to obtain the velocity of the intercepted projectile at the boosting section ending moment, and the method includes:

constructing an intermediate variable representing a trajectory inclination angle of a boosting section, and acquiring a derivative of the intermediate variable according to an intercepting projectile trajectory inclination angle equation in a dynamic model of the boosting section;

and acquiring a velocity vector of the intercepting bullet boosting section at the ending moment based on the acquired boosting speed integral term value and the terminal trajectory inclination angle of the boosting section.

In the embodiment of the invention, an intermediate variable χ is defined_MComprises the following steps:

χ_M＝ln{(1+sinγ_M)/(1-sinγ_M)} (24)

by substituting equation (24) for equation (18) and neglecting the effect of the change in the center distance of the boost section, the derivative of the intermediate variable can be obtained:

the integral of the above formula can be used to obtain the end time χ of the boosting section_MThe values of (A) are:

in the formula,

χ_M0is x_MAn initial value of (d);

f_χ1(t_bo)、f_χ2(t_bo) Boost speed V for catching bomb_MThe related boosting speed integral terms are respectively:

χ_M0＝ln{(1+sinγ_M0)/(1-sinγ_M0)}

by equation (24), the terminal ballistic inclination angle of the boost section can be expressed as:

γ_Mbo＝sin^-1[(e^χMbo-1)/(e^χMbo+1)] (28)

in this embodiment of the present invention, as an optional embodiment, obtaining a boost speed integral term value includes:

calculating a boosting speed integral term according to a speed equation of the ending moment of the boosting section of the interceptor bomb to obtain a boosting speed expression;

and solving the boosting speed expression by using a Gauss-Legendre integral formula of N nodes to obtain a boosting speed integral term value.

In the embodiment of the present invention, formula (22) is substituted for formula (27), and a boost speed expression can be obtained:

in the formula,

the remaining operating time of the engine is dimensionless;

is the current velocity of the non-dimensionalized missile.

In the embodiment of the present invention, a gaussian-legendre integral formula of N nodes is used to solve equation (30), so as to obtain:

in the formula,

ω_iis the ith integral weight;

is the dimensionless time at the ith gaussian node. As an alternative, take N-9.

In the embodiment of the invention, the orbit inclination angle and the ascension point right ascension are calculated by intercepting the missile angular momentum, and then the missile position vector magnitude of the missile boosting section terminal point and the analytical formula of the included angle between the missile position vector and the connecting line from the geocenter to the ascension point are obtained by algebraic derivation and Gauss-Legendre integral.

In this embodiment, as another optional embodiment, establishing a dynamical equation of the boosting section, and predicting a position vector and a velocity vector of an end point of the boosting section includes:

b21, fitting the interception bullet trajectory inclination angle based on a derivative equation of the interception bullet trajectory inclination angle in the boosting section dynamic model;

b22, acquiring an end point position equation of the boosting section of the interceptor projectile and an included angle equation of a connecting line between an end point position vector and the earth center to the rising intersection point based on the fitted angle of inclination of the trajectory of the interceptor projectile;

and B23, determining the end point position vector and the velocity vector of the ending moment of the boosting section of the intercepting bullet based on the track inclination angle, the ascent intersection point right ascension, the end point velocity of the boosting section of the intercepting bullet, the end point trajectory inclination angle of the boosting section, the end point position equation and the included angle equation of the end point position vector and the connecting line from the geocenter to the ascent intersection point.

In the embodiment of the present invention, it is difficult to directly obtain r in the formula (19) and the formula (20) because the trigonometric function including the ballistic inclination angle_MAnd theta_MThe analytical solution of (2). In the embodiment of the invention, considering that the boosting section has short time, therefore, the change of the trajectory inclination angle in the boosting section is small, the fitting can be respectively carried out on the sine function and the cosine function of the trajectory inclination angle in the form of a quadratic function taking dimensionless time as an independent variable, so as to obtain the fitted intercepting bullet trajectory inclination angle, and the fitting formula is as follows:

by end point conditions one can solve:

b₁＝T(V_M0/r_M0-g_M0/V_M0)cos²γ_M0

c₁＝sinγ_M0

c₂＝cosγ_M0

the formula (33) is substituted for the formula (19) and the formula (20), and the integration is carried out to obtain the end position r of the boosting section of the interceptor projectile_MboAnd the included angle theta between the vector of the end point position of the intercepting bomb and the connecting line from the geocenter to the ascending intersection point_MboRespectively as follows:

in the formula, r_M0Intercept the bullet ground center distance r at the initial moment_M,aveThe mean geocentric distance is the boost segment.

From equations (15), (16), (22), (28), (34) and (35), the end position vector and the velocity vector at the end time of the interceptor projectile boost section can be determined.

103, acquiring shutdown point parameters meeting the zero control interception triangle at the taxiing section based on a strategy of the zero control interception triangle according to an end point position vector and a speed vector of the ending moment of the interception bullet boosting section, wherein the shutdown point parameters comprise an interception bullet speed inclination angle and a speed deflection angle;

in an embodiment of the present invention, as an optional embodiment, obtaining a shutdown point parameter that satisfies a zero control interception triangle at a taxiing stage according to an end point position vector and a speed vector of an interception bullet boosting stage end time based on a policy of the zero control interception triangle, includes:

c11, applying the condition that the relative speed of the bullets in the direction perpendicular to the sight line at the interception moment is zero to a differential equation of the relative movement speed of the bullets at the sliding stage to obtain an interception bullet speed inclination angle and a speed deflection angle at the shutdown moment of the interception bullet;

in the embodiment of the present invention, the shutdown point parameters include: the expected shutdown speed dip angle and the speed drift angle of the interceptor projectile. In order to improve the probability that an interception missile hits a target missile and form a zero-control interception triangle, the relative speed of the missile eyes in the vertical sight direction needs to be zero at the interception moment, namely:

V_λ(t_f) 0 and V_q(t_f)＝0

Wherein, t_fIs the intercept time.

In the embodiment of the present invention, formula (13) is V_r，V_λAnd V_qEquation of dynamics of (1) V_λ(t_f) 0 and V_q(t_f) Applying the boundary condition of 0 to equation (13) to solve the kinetic equation, V can be obtained_λAnd V_qCalculating the shutdown time V of the interception bomb according to the expression_λAnd V_qThe value of (2) is the shutdown point condition for forming the zero control interception triangle.

In the embodiment of the invention, as an optional embodiment, the condition that the relative speed of the bullet in the direction perpendicular to the sight line at the interception moment is zero is applied to a differential equation of the relative movement speed of the bullet at the sliding stage to obtain the relative speed value of the bullet at the shutdown moment of the interception bullet; the method comprises the following steps:

c111, fitting the difference of the gravitational acceleration of the bullet in the differential equation of the relative movement velocity of the bullet into a function related to the residual flight time;

in the examples of the present invention, as shown in formula (14), Δ g_r，Δg_λAnd Δ g_qCoupled with other variables, makes equation (13) difficult to solve analytically. Therefore, in the embodiment of the invention, the gravity acceleration difference Δ g is used_r，Δg_λAnd Δ g_qFitted to relate to the remaining time of flight t_goAs a function of (c). In order to ensure the fitting accuracy, as an alternative embodiment, a second-order polynomial is used for fitting. Due to the interception moment, i.e. the remaining time of flight t_goWhen 0, the intercept missile equals the target missile acceleration of gravity, and therefore Δ g_r，Δg_λAnd Δ g_qCan be approximated as follows with respect to t_goSecond order polynomial (function):

in the formula,

k_r1、k_r2、k_λ1、k_λ2、k_q1and k_q2Are fitting coefficients.

In the embodiment of the invention, the fitting coefficient can be obtained by calculating the bullet gravity difference and the derivative value thereof at the shutdown time of the intercepting bullet, and the specific expression is as follows:

in the formula,

t_gobothe remaining variables with subscript "bo" represent the value of the variable at the moment of shutdown of the interceptor projectile for the remaining flight time at the moment of shutdown of the interceptor projectile.

C112, deriving a function related to the residual flight time based on the relative motion equation of the bullet and the acceleration difference of the bullet gravity to obtain a differential equation of the acceleration difference of the bullet gravity;

in the examples of the present invention, Δ g in the formula (14)_r、Δg_λAnd Δ g_qRespectively deriving the flight time, and substituting the formula (8) and the formula (14) into the derived formula to obtain a differential equation of the difference of the gravitational acceleration of the bullet eyes, namely

And

the expression of (a) is:

c113, simplifying the differential equation of the relative movement velocity of the bullet eyes to obtain a differential approximate equation of the relative movement velocity of the bullet eyes;

in the embodiment of the present invention, as for the formula (13),

v shown by the formula (13)_rThe obtained differential approximate equation of the relative movement speed of the bullet and the bullet is as follows:

c114, carrying out analytic integration on the projectile relative motion velocity differential approximate equation to obtain a projectile relative motion analytic equation related to the residual flight time;

in the examples of the present invention, V_r,bo、r_boThe relative speed V of the bullet in the visual line direction at the moment of shutdown_rAnd the relative distance r, in turn, are as defined in formula (39) and

performing analytical integration, and considering boundary condition V_r(t_gobo)＝V_r,boAnd r (t)_gobo)＝r_boObtaining V_rAnd r is with respect to t_goThe analytic equation of the relative movement of the bullet eyes is as follows:

in the formula,

c_r0、c_r1is a constant coefficient expressed by

C115, obtaining an analytic expression of the line of sight declination angle speed of the zero-control intercepting triangle on the basis of a boundary condition that the line of sight angular speed of the bullet is zero when the residual flight time is zero and an analytic equation of relative motion of the bullet and the bullet about the residual flight time;

in the embodiment of the invention, in the process of intercepting outside the atmosphere, the component of the relative speed of the missile is large along the sight line direction, and is generallySeveral kilometers per second, while the two components perpendicular to the line of sight are typically only one or two hundred or even tens of meters per second, and thus V_r＞＞V_λAnd V_r＞＞V_q. Thus, as shown in formula (13)

And

the second term in the expression of (a) is small, negligible,

and

can be approximated as:

after algebraic sorting, the following can be obtained:

in the formula,

by integrating equation (43), V can be obtained_λAnd V_qWith respect to the remaining time of flight t_goThe analytic equation of the bullet relative speed is as follows:

in the formula,

c_λ、c_qis an integration constant.

At the interception time, the relative projectile distance is 0, that is, r (0) is 0, and the expression of the relative projectile distance r in equation (40) is substituted to obtain:

considering boundary conditions, in order to realize the interception of the target, when t_goWhen equal to 0, V_λ0 and V_qWhen the value is 0, V satisfying the zero control interception triangle can be obtained_λAnd V_qThe analytic expression of (2), namely the analytic expression of the expected bullet relative speed is as follows:

in the formula, the upper right subscript des represents the expected value of the corresponding variable.

Thus, the condition of forming the zero control interception triangle is obtained.

C116, obtaining a value of the residual flight time based on the fitting coefficient of the function fitted to the residual flight time and the shutdown time;

in the embodiment of the invention, in the process of solving the formula (48), the remaining flight time t at the shutdown moment is required_goboThus, by substituting formula (37) for formula (47):

in the formula (50), except t_goboBesides, other variables can be calculated according to the predicted value of the bullet eye state quantity at the shutdown pointThus, t can be estimated using equation (50)_gobo。

Formula (50) relates to t_goboThe equation of a single element and a cubic equation of a single element can be used for solving by a root equation or an immobile point iteration method.

And C117, acquiring an expected value of the relative speed value of the bullet at the vertical sight at the shutdown moment based on the analytic expression of the relative speed of the bullet of the zero control interception triangle and the analytic expression of the expected relative speed of the bullet.

In the embodiment of the invention, in order to realize the interception of the target missile by the uncontrollable sliding of the intercepted missile after the shutdown, the relative speed of the missile at the shutdown time needs to be ensured to meet the zero control interception triangle at the sliding section. According to the conditions for forming the "zero control interception triangle" shown in the equations (48) and (49), the expected values of the bullet relative velocity components of the vertical sight line at the time of shutdown are respectively:

and C12, adjusting the speed direction of the intercepting bullet to enable the shutdown speed to meet the expected value of the relative speed value of the bullet eyes.

In the embodiment of the invention, the thrust stopping device is not arranged on the intercepting bullet, and the shutdown speed is difficult to adjust, so that the shutdown speed meets the expected value of the relative speed value of the bullet eyes by adjusting the speed direction.

In the embodiment of the invention, the direction of the intercepting bullet speed comprises the following steps: the method for acquiring the speed direction of the interception bullet by using the expected shutdown speed inclination angle and the speed deflection angle of the interception bullet comprises the following steps:

acquiring a velocity component, a velocity dip angle and a dip angle expression of a velocity drift angle of an interception bullet velocity vector under a local ground coordinate system;

and obtaining the expected shutdown speed inclination angle and the speed deflection angle of the interception bullet based on the expression of the expected shutdown speed inclination angle and the speed deflection angle of the interception bullet.

Fig. 4 shows a three-dimensional interception schematic under a local ground coordinate system provided by an embodiment of the present invention. The components of the velocity vector of the interceptor projectile in the local ground coordinate system may be expressed as the following expressions relating to the velocity dip and the velocity slip:

in the formula,

in order to be the speed inclination angle,

is the velocity declination angle, V_MIs the velocity of the interceptor projectile.

Replacing formula (52) with formula (9), and intercepting bomb expecting shutdown speed dip angle

And angle of speed declination

Satisfying the expression of the expected shutdown speed inclination angle and the speed deflection angle of the interceptor projectile:

in the formula: v_λT,bo、V_qT,boThe component of the velocity vector of the target at the moment of the shutdown point in the direction perpendicular to the line of sight, λ_bo、q_boWhich are the elevation angle and declination angle of the sight line at the moment of shutdown.

In the initial guidance phase, the interceptor missile will aim the shot at the predicted hit point, and therefore, in the intermediate guidance phase,

smaller, can be approximately considered

From the equation (53), the expected shutdown speed inclination angle of the interception bullet can be obtained

And angle of speed declination

The values of (A) are:

in the formula: v_MboThe missile speed at the moment of shutdown point.

104, deducing the optimal ignition time of the second pulse of the interception bomb based on a preset performance index function of the ignition time of the second pulse of the interception bomb according to the shutdown point parameter, the position vector analytic expression and the boundary condition;

in the embodiment of the present invention, as an optional embodiment, deriving the optimal ignition time of the second pulse of the interceptor projectile according to the shutdown point parameter, the position vector analytic expression and the boundary condition includes:

d41, acquiring a differential equation of the relative distance and the relative speed of the projectile at the second pulse ignition moment of the intercepted projectile based on the position vector analytic expression and a preset boundary condition;

in the embodiment of the invention, on the premise that the second pulse of the intercepting bullet does not work, the remaining flight time at the end moment of the first pulse is obtained, and on the premise that the pulse interval time is known, the bullet relative distance, the relative speed and the pulse interval time derivative of the interception bullet at the second pulse ignition moment are obtained through derivation, so that the bullet relative distance and the relative speed at the second pulse ignition moment of the intercepting bullet are obtained. As an optional embodiment, the obtaining of a differential equation of the relative distance and the relative speed of the projectile at the second pulse ignition moment of the interceptive projectile based on the position vector analytic expression and the preset boundary condition includes:

d411, acquiring the remaining flight time of the first pulse end moment when the second pulse of the interception bullet does not work based on the position vector of the first pulse end moment of the interception bullet, the projection of the relative speed of the bullet eyes along the sight line direction and the projection of the gravity acceleration difference of the bullet eyes along the sight line direction;

in the embodiment of the present invention, similar to equation (50), assuming that when the second pulse of the interception bullet does not work, the remaining flight time of the end time of the first pulse is:

in the formula, t_go0The remaining time of flight at the end of the first pulse, r_bo1、V_rbo1、Δg_rbo1The value of the position vector of the first pulse ending moment of the intercepting bullet, the projection of the relative speed of the bullet eyes along the sight line direction and the projection of the gravity acceleration difference of the bullet eyes along the sight line direction can be calculated according to the predicted value of the state quantity of the bullet eyes at the shutdown moment of the first pulse. Solving the above formula according to a root-solving formula of a unitary cubic equation or an immobile point iteration method to obtain t_go0。

D412, acquiring an analytic expression of the relative speed and the relative distance of the bullet eyes in the pulse interval section along with the change of time based on the position vector analytic expression and a preset boundary condition;

in the embodiment of the invention, the boundary condition V is combined according to the formula (40)_r(t_go0)＝V_rbo1And r (t)_go0)＝r_bo1Obtaining the relative speed V of the bullet in the pulse interval section_r,interAnd relative distance r of bullet eyes_interThe time-varying analytical expression of (a) is:

c_r0,interand c_r1,interThe specific expression is as follows:

d413, acquiring a position vector and a relative velocity vector of the second pulse ignition moment based on an analytic expression that the relative speed and the relative distance of the bullet in the pulse interval section change along with time;

in the embodiment of the invention, V at the time of second pulse ignition can be obtained_rAnd r, respectively, is V_rig2And r_ig2Expressed as:

wherein, t_goig2The remaining time of flight of the second pulse ignition instant, which is separated from the pulse interval time t_interThe relationship of (1) is:

t_goig2＝t_go0-t_inter (59)

d414, obtaining an analytic expression of the relative speed of the bullet eyes in the vertical sight direction in the pulse interval section according to the analytic equation of the relative motion of the bullet eyes;

in the embodiment of the invention, the bullet relative speed V in the vertical sight line direction in the pulse interval section can be obtained by the formula (45)_λ,interThe analytical expression of (a) is:

wherein the constant value coefficient c_λ,interThe state quantity at the first pulse shutdown time is calculated, and the specific expression is as follows:

and D415, acquiring a bullet relative speed differential equation during the ignition of the second pulse based on an analytic expression of the bullet relative speed in the vertical sight direction in the pulse interval section.

In the embodiment of the present invention, V at the time of second pulse ignition can be obtained from the formula (60)_λValue V of_λig2Comprises the following steps:

similarly, the second pulse ignition time V can be obtained_qValue V of_qig2Comprises the following steps:

and (3) solving the derivation of the bullet relative distance and the relative speed equation at the second pulse ignition moment to obtain:

in the formula,

Δg_rig2、Δg_λig2、Δg_qig2the difference between the elastic eye gravity and the second pulse ignition time is obtained from equation (36):

d42, acquiring an analytic expression of the bullet relative speed and the pulse interval time derivative in the second pulse working stage according to the bullet relative speed differential equation and the boundary condition of the ignition moment;

in the embodiment of the invention, by establishing a differential equation of the bullet relative speed containing thrust and fitting the interception axial acceleration and the bullet gravity difference related terms into a function related to flight time, the analytic expressions of the bullet relative distance, the sight inclination angle and the sight declination angle can be obtained, and further the bullet relative speed in the direction vertical to the sight at the second pulse shutdown time and the derivative equation of the bullet relative speed to the pulse interval time can be derived.

In the embodiment of the invention, the component a of the axial acceleration of the interceptor projectile in the sight line system at zero attack angle and zero sideslip angle_MxL、a_MyL、a_MzLRespectively as follows:

in the formula, a_MThe axial acceleration of the interceptor projectile is large or small.

In the embodiment of the present invention, as an optional embodiment, obtaining an analytic expression of the projectile relative velocity and the pulse interval time derivative at the second pulse working stage according to the projectile relative velocity differential equation and the boundary condition of the ignition time includes:

d421, acquiring a differential equation of the relative speed of the bullet in the direction perpendicular to the sight line of the boosting section of the intercepting bullet according to the differential equation of the relative speed of motion of the bullet and the component of the axial acceleration of the intercepting bullet in the sight line;

in the embodiment of the invention, by combining the formula (13), the differential equation of the relative speed of the bullet eyes in the direction perpendicular to the visual line of the boosting section of the intercepting bullet can be obtained as follows:

d422, fitting the interception axial acceleration and the bullet gravity difference into a function related to flight time, and simplifying a differential equation of the bullet relative speed of the interception bullet boosting section in the direction perpendicular to the sight line based on the fitted function to obtain a simplified differential equation of the bullet relative speed of the interception bullet boosting section in the direction perpendicular to the sight line;

in the embodiment of the present invention, V is similar to the formula (42)_r＞＞V_λAnd V_r＞＞V_qNeglecting small amounts

And V_λV_qtanλAnd fitting the intercept axial acceleration and the bullet eye gravity difference related terms to a function related to time of flight, equation (67) can be approximated as:

wherein Q is_λ(t) and Q_q(t) are fitting coefficients of the bullet gravity difference related terms respectively, and expressions thereof are respectively:

d423, analyzing and integrating the simplified differential equation of the bullet relative speed of the interception bullet boosting section in the direction vertical to the sight line by combining the boundary condition of the ignition time to obtain a bullet relative speed equation in the direction vertical to the sight line at the second pulse shutdown time;

in the embodiment of the present invention, equation (68) is analyzed and integrated, and combined with the boundary condition of the ignition timing, the following can be obtained:

in the formula, V_λbo2、V_qbo2The relative speed of the second pulse in the direction perpendicular to the visual line at the time of shutdown, delta t_burn2The working time of the second pulse is;

r_ig2，V_λig2and V_qig2Is represented by the formulae (58), (62) and (63);

r_bo2the relative position of the bullet eyes at the second pulse working end moment of the intercepting bullet;

t_ig2the second pulse firing time.

In the embodiment of the invention, in order to obtain a specific expression of the integral term in the formula (70), r and Q need to be derived_λAnd Q_qFitting formula with respect to time of flight t.

Because the interception bullet has a section of longer uncontrolled gliding section just can realize the interception to the target guided missile after second pulse shuts down, consequently, to second pulse working segment, bullet mesh relative distance is great and because boosting section operating time is short, and the change of bullet mesh relative distance is not big, can guarantee sufficient fitting accuracy with bullet mesh relative distance fitting for the linear function about t, and specific expression is:

wherein Δ t is t-t_igThe working time of the boosting section is; Δ V_r,burn2The change of the relative speed of the bullet eyes caused by the acceleration of the interception bullet during the second pulse working period; v_rig2The bullet relative speed of the second pulse ignition moment along the sight line direction can be calculated by the formula (58);

is the average relative speed of the boost segment along the line of sight.

Wherein, is Δ V_r,burn2Can be approximated by:

in the formula,

λ_ig2、q_ig2the trajectory inclination angle, the sight elevation angle and the sight declination angle of the interception bullet at the second pulse ignition moment are respectively;

ΔV_Min order to intercept the second pulse segment speed increment of the bomb, the expression is specifically as follows:

in the formula, m₂₀For intercepting the second pulseInitial mass of the punching section;

P₂and q is_m2Respectively the thrust and the mass flow of the second pulse of the interception bullet.

By rewriting formula (71), the following can be obtained:

r＝a_r1(1-Δt/T₂)+a_r0 (74)

in the formula, T₂The second pulse working time of the interception bomb has no dimensional factor a_r1、a_r0The specific expressions are as follows:

T₂＝m₂₀/q_m2

in the second pulse working section, the relative distance of the bullet eyes is larger, so that the change of the visual angle caused by the relative speed of the bullet eyes in the vertical visual line direction is small, the change of the gravity difference of the bullet eyes is small, and lambda, q and delta g can be ignored_λ、Δg_qChange of (2) to Q_λAnd Q_qInfluence. Then λ, q and Δ g_λ、Δg_qCan be approximately expressed as:

in the formula: the lower corner mark "bo 1" indicates the corresponding state of the first pulse end timing of the interceptor projectile, and the lower corner mark "ig 2" indicates the corresponding state of the second pulse firing timing of the interceptor projectile.

Because the boosting section has short working time and the intercepting bomb only turns under the action of gravity at zero attack angle and zero sideslip angle, the speed inclination angle and the time interval can be approximate to the following linear function:

in the formula,

the average change rate of the speed inclination angle in the second pulse working stage is shown, and delta t is a time interval;

the speed inclination angle of the interception bullet at the second pulse ignition moment is equal to the speed inclination angle of the first pulse shutdown

And the pulse interval time t_interIt is related.

In the embodiment of the invention, the pulse interval time is generally not long, so that the change of the gravity acceleration and the speed can be ignored, and according to the formulas (24) to (28), the differential equation and the analytic expression of the ballistic inclination angle of the second pulse ignition moment of the interception bullet can be respectively as follows:

in the formula, V_Mbo1The speed of the interception bullet at the moment when the first pulse works is finished;

χ_Mbo1、χ_Mig2the intermediate variables of the interception bullet at the working end moment of the first pulse and the ignition moment of the second pulse are related to the trajectory inclination angle respectively.

Due to zero attack angle and zero sideslip angle during flight

Is always 0. Thus, Q_λAnd Q_qCan be approximated as:

and then combining the expression a of the axial acceleration of the intercepting bullet_M＝P₂/(m₂₀-q_m2Δt)，Q_λAnd Q_qCan be expressed as a fit equation as follows:

wherein, a_λ1、a_λ0、a_q1、a_q0All are proportionality coefficients, and the expression is as follows:

in the formula, V_e2The second pulse speed of the interceptor projectile has no dimensional factor.

By combining the equations (74) and (82), the approximate value of the integral term in the equation (70) can be obtained

By substituting the above equation into equation (70), the equation of the bullet-eye relative velocity in the direction perpendicular to the line of sight at the time of second pulse shutdown is:

from formula (71):

and D424, acquiring a derivative equation of the bullet relative velocity in the direction perpendicular to the line of sight at the second pulse shutdown time.

In the embodiment of the invention, through the derivation, the bullet relative speed V perpendicular to the sight line direction at the second pulse shutdown time is obtained_λbo2And V_qbo2To solve the optimal pulse interval, it is necessary to derive the pair t_interThe derivative of (c). Because the line-of-sight angle of the bullet at the second pulse ignition moment and the change of the gravity difference of the bullet are very small along with the change of the ignition moment, t is ignored in the solving process for simplifying the operation_interAngle of line of sight lambda_ig2And q is_ig2And a difference in the elastic eye gravity Δ g_λig2And Δ g_qig2The influence of (c). The derivation of equations (75) and (83) can be:

wherein dr is_ig2/dt_interAnd dV_rig2/dt_interIs represented by formula (64).

By taking the derivatives of equations (72) and (79), the following can be obtained:

in the formula, g_Mig2The gravity acceleration at the moment of igniting the second pulse of the interceptor projectile is obtained.

In conclusion, V can be obtained_λbo2And V_qbo2For t_interThe optimal pulse interval time derivative equation:

in the formula, x_λ1～χ_λ3、χ_q1～χ_q3The formula is a proportionality coefficient:

d43, solving the relation between the expected relative speed of the intercepted projectile at the second pulse shutdown time and the pulse interval time, and acquiring an equation of the expected relative speed of the projectile in the direction perpendicular to the sight;

in the embodiment of the invention, the remaining flight time of the second pulse shutdown is corrected, and then in step 101, the bullet relative speed in the vertical sight direction expected to be reached by the second pulse shutdown time of the interception bullet and the derivative of the bullet relative speed to the pulse interval time can be obtained. As an optional embodiment, solving a relationship between the expected relative speed of the interception bullet at the second pulse shutdown time and the pulse interval time to obtain an equation of the expected relative speed of the bullet in the vertical line of sight direction includes:

d431, acquiring a relation equation of the remaining flight time and the pulse interval time when the second pulse is shut down according to a state equation which is satisfied by the remaining flight time when the second pulse does not work and the first pulse is shut down;

in the embodiment of the invention, by the formula (47), when the second pulse does not work, the remaining flight time t when the first pulse is shut down_go0Satisfies the following conditions:

in practical application, the bullet interception speed after the second pulse ignition is increased, so that the relative speed V of the bullet eyes is caused_rA large variation occurs. The actual remaining time of flight at shutdown of the first pulse is then less than t_go0In (1). Neglecting the gravity difference to the bullet relative speed V in the pulse interval section and the second pulse working section_rThe influence of (c) can be given by:

the remaining flight time t at the time of the second pulse shutdown can be obtained from equations (91) and (92)_gobo2With time t between pulses_interThe relational equation of (A) is as follows:

in the formula,

for the velocity ratio, the above formula is given to t_interThe derivation can be:

and D432, acquiring a bullet relative velocity equation in the vertical sight direction expected to be reached by the second pulse shutdown time according to the expected value equation of the bullet relative velocity component of the vertical sight at the shutdown time.

In the embodiment of the present invention, the bullet relative speed in the vertical line of sight direction expected to be reached at the second pulse shutdown time can be obtained from the formula (51)

The equation of (a) is:

the above formula is to t_interThe derivation can be:

d44, solving the optimal ignition time of the second pulse of the interception bullet by using a variational method based on a bullet relative speed equation of the second pulse ignition time of the interception bullet, an equation of the bullet relative speed and a time derivative of a pulse interval in the second pulse working stage, and a bullet expected relative speed equation in the vertical sight direction.

In the embodiment of the invention, according to the performance index function of the ignition time of the second pulse of the interception bomb and the property of the maximum value of the performance index function, the pulse interval time is derived, and the optimal pulse interval time can be obtained by solving the equation with the derivative of 0, so that the optimal ignition time of the second pulse of the interception bomb is obtained.

In the embodiment of the invention, the aim of optimizing the ignition time is to minimize the performance functional of the boosting section, namely the sum of the square of the attack angle and the sideslip angle, and the optimal ignition time is the ignition time of the 'zero control interception triangle' of the gliding section which can meet the requirement of zero attack angle flight after the boosting section is ignited.

In the embodiment of the invention, the influence of the ignition time of the second pulse of the interception bullet on the zero control interception triangle of the longitudinal plane gliding section is larger, namely along with the change of the ignition time of the second pulse of the interception bullet, the change of the expected value and the actual value of the speed component of the bullet eyes is larger along the direction vertical to the visual line of the shutdown time of the second pulse of the interception bullet, so that the ignition time of the second pulse with the expected value and the actual value equal to each other is the optimal ignition time.

In the embodiment of the invention, the optimal ignition time of the second pulse of the interception bullet is the pulse interval time which enables the performance index function to be minimum.

In the embodiment of the invention, the performance index function J of the second pulse ignition time of the interception bomb is as follows:

second pulse ignition time t of interception bomb_ig2Time t from pulse interval_interAnd the two pulses are in one-to-one correspondence, so that the optimal moment for solving the second pulse ignition of the interception bomb can be equivalent to the optimal pulse interval time for solving the interception bomb. The pulse interval time t for minimizing the target function according to the property of the function maximum_interI.e. the optimum pulse interval time, should satisfy:

substituting and sorting the formula (95), the formula (96), the formula (85) and the formula (89) to obtain the optimal pulse interval time

The following equations need to be satisfied simultaneously:

equation (100) is a constraint equation for the time length of the pulse interval segment and the glide segment after shutdown. Wherein,

and

minimum and maximum values of the pulse interval time, respectively;

and

respectively is the minimum value and the maximum value of the gliding section time after the shut-off of the interception bomb.

The formula (93) shows the residual flight time t after the second pulse of the interception bomb is shut down_gobo2And the pulse interval t_interIs a function of (A), wherein V_r,bo1，t_go0And Δ t_burn2Is and t_interThe variables that are not related to each other are,

although it does notAnd t_interRelated but much less than 1, therefore, t_gobo2Will follow t_interIs increased and decreased. Can be solved by the formula (93)

And

corresponding pulse interval time

And

considering the constraints in equation (100) together, t can be obtained_interIt should satisfy:

in the formula,

and

respectively, a minimum value and a maximum value of the pulse interval time.

The objective function J shown in the formula (97) is in the form of an approximate quadratic function with t_interSince the increase of (1) is first decreased and then increased, and only one extreme point exists, that is, only one root exists in the formula (99), the design is as follows

The calculating method of (2):

(1) if it is not

Description of the invention

Is rooted in

In between, then select

Calculated by the following secant method

The value of (c):

(2) if it is not

Description of the invention

Is rooted in

Otherwise, select

Is composed of

And

to a value that makes the objective function J smaller.

And 105, acquiring a double-pulse optimal guidance instruction based on the predicted values and the expected values of the velocity dip angle and the velocity drift angle at the shutdown time of the interceptor projectile and the second-pulse optimal ignition time of the interceptor projectile.

In the embodiment of the present invention, as an optional embodiment, the obtaining of the double-pulse optimal guidance instruction based on the predicted values and the expected values of the velocity inclination angle and the velocity drift angle at the shutdown time of the interceptor projectile and the second-pulse optimal ignition time of the interceptor projectile includes:

e51, solving a first pulse optimal guidance instruction, wherein the first pulse optimal guidance instruction comprises optimal values of an attack angle and a sideslip angle;

in the embodiment of the invention, when the first pulse of the interceptor projectile works, the boosting section is divided into the first pulse working section, the pulse spacing section and the second pulse working section, the perturbation equation of the trajectory velocity inclination angle and the trajectory velocity deflection angle is established, the performance functional is selected, the function of the covariance variable and the control variable can be solved according to a first-order necessary condition, and the approximate solution of the guidance coefficient is solved through the Gauss-Legendre integral formula, so that the optimal values of the attack angle and the sideslip angle are obtained.

In the embodiment of the present invention, solving the first pulse optimal guidance instruction includes:

e511, acquiring perturbation equations of the velocity dip angle and the velocity drift angle of the interception bomb in the first pulse working section, the pulse interval section and the second pulse working section respectively;

in the embodiment of the invention, when the first pulse optimal guidance instruction is solved, due to the change of the thrust, the solved optimal control problem is divided into three sections, namely a first pulse working section, a pulse interval section and a second pulse working section, wherein the kinetic equations of the sections are different. Wherein, the perturbation equations of the velocity dip angle and the velocity drift angle of each section are respectively as follows:

in the formula,

and

the shooting quantities are respectively a speed inclination angle and a speed deflection angle;

alpha and beta are respectively an intercepting bullet attack angle and a sideslip angle;

P₁、P₂respectively a first pulse thrust and a second pulse thrust of the interception bomb;

and

respectively the derivative of the interception elastic lifting force coefficient to an attack angle and the derivative of the lateral force coefficient to a sideslip angle;

q is dynamic pressure;

S_refis the aerodynamic reference area;

t₀＝0，t₁＝t_bo1，t₂＝t_bo1+t_interand t₃＝t_bo1+t_inter+t_bo2The start and end times of each segment.

At the segmentation point t₁And t₂The following boundary conditions need to be satisfied:

in order to achieve the desired speed direction at the time of shutdown of the second pulse, the following end point constraint needs to be satisfied:

in the formula,

and

and respectively predicting values of a speed inclination angle and a speed deflection angle at the shutdown time of the interceptor projectile.

E512, selecting a performance functional for a perturbation equation of the velocity dip angle and the velocity drift angle;

in the embodiment of the invention, in order to provide stable control input, the weighted square sum of the attack angle and the sideslip angle is selected as a performance functional, and the expression is as follows:

wherein the weight term (t) of the remaining combustion time₁-t)ⁿAnd (t)₃-t)ⁿThe method is used for shaping the attack angle and the sideslip angle curve. In the present embodiment, if n > 0 is chosen, the end point values of the angle of attack and the angle of sideslip will converge to zero.

E513, acquiring a Hamiltonian of the optimal control problem based on the perturbation equation of the velocity inclination angle and the velocity drift angle and the performance functional;

from equations (103) and (106), the Hamiltonian H of the optimal control problem can be obtained as:

wherein,

and

is a covariate. According to the first-order necessary condition, the differential equation of the obtained covariate is as follows:

as can be seen from the above formula, the covariates are all invariant with time at each stage. Meanwhile, since the continuous condition at the segmentation point shown in equation (104) needs to be satisfied, the covariates need to satisfy the following boundary conditions at the segmentation point:

e514, obtaining an optimal attack angle and sideslip angle equation according to the Hamiltonian of the optimal control problem;

in the embodiment of the invention, the covariates

And

all equal in three segments. According to the first-order necessary conditions, the equation of the optimal attack angle and sideslip angle can be obtained as follows:

e515, acquiring an expression of a speed inclination angle deviation value and a speed deflection angle deviation value at the second pulse shutdown time based on the optimal attack angle and sideslip angle equation and a perturbation equation of the speed inclination angle and the speed deflection angle;

in the embodiment of the present invention, the above equation (110) is substituted for the equation (103) and integrated, and the expressions of the speed inclination deviation value and the speed deflection deviation value at the second pulse shutdown time are obtained as follows:

e516, acquiring a covariance quantity equation based on the expression of the speed inclination angle deviation value and the speed deflection angle deviation value at the second pulse shutdown time and a preset terminal point constraint equation;

in the embodiment of the present invention, the end point constraint equation shown in formula (105) is combined to obtain a covariance equation:

in the formula,

and

for intermediate variables, the expression is:

in the formula, m₀、V_M0And

the current moment mass, the speed and the speed inclination angle of the interception bullet are respectively.

And E517, acquiring optimal values of the attack angle and the sideslip angle based on the covariance equation and the optimal attack angle and sideslip angle equation.

In the embodiment of the present invention, equation (112) is substituted for equation (110), and the optimal values of the attack angle and the sideslip angle can be obtained as follows:

in the formula, N_p1And N_p2The specific expression of the guidance coefficient is as follows:

as can be seen from the above formula, the guidance coefficient is not constant and changes with the flight time. Because the expression of the optimal guidance coefficient is too complex, an analytic solution is difficult to solve. Recording:

the variable values in the above formula can be obtained by predicting the terminal position and the velocity vector of the boosting section in step 102, so that the guidance coefficient N can be obtained by a Gauss-Legendre integral formula_p1And N_p2Approximate solution of (a):

wherein,

and

respectively being the ith Gaussian integral node x_iCorresponding first and second pulse on times;

ω_iis the ith Gaussian integral weight coefficient;

η₁and eta₂The coefficient is a constant coefficient, and the specific expression is as follows:

and E52, solving a second pulse optimal guidance instruction, wherein the second pulse optimal guidance instruction comprises optimal values of an attack angle and a sideslip angle.

In the embodiment of the invention, the flow of solving the second pulse optimal guidance instruction of the intercepted projectile is similar to the flow of solving the first pulse optimal guidance instruction of the intercepted projectile, and the difference is that in the second pulse stage of the intercepted projectile, the perturbation equation of the trajectory velocity inclination angle and the trajectory velocity deflection angle does not need to be segmented.

In the embodiment of the present invention, as an optional embodiment, a second pulse optimal guidance instruction is solved, where the second pulse optimal guidance instruction includes optimal values of an attack angle and a sideslip angle, and includes:

e521, acquiring a perturbation equation of a trajectory inclination angle and a trajectory deflection angle of the intercepted projectile in a second pulse stage;

e522, acquiring a Hamiltonian of an optimal control problem according to a preset performance functional and perturbation equations of a trajectory inclination angle and a trajectory deflection angle of the intercepted projectile in a second pulse stage;

e523, acquiring expressions of a speed inclination angle deviation value and a speed deviation angle deviation value at the shutdown time based on a Hamilton function and a perturbation equation of a trajectory inclination angle and a trajectory deviation angle of the intercepted projectile at the second pulse stage;

and E524, acquiring optimal values of the attack angle and the sideslip angle according to the speed inclination angle deviation value at the shutdown time, the expression of the speed deviation angle deviation value and the preset constraint condition.

In the embodiment of the invention, the perturbation equation of the trajectory inclination angle and the trajectory deflection angle of the intercepted projectile in the second pulse stage is as follows:

the end point constraints that need to be satisfied are:

to provide a stable control input, the following weighted square sum of the angle of attack and the angle of sideslip was chosen as the performance functional:

weight term (t) of remaining combustion time in the same way as the derivation of the first pulse optimal guidance command_bo2-t)ⁿThe method is used for shaping the attack angle and the sideslip angle curve. If n > 0 is chosen, the end values of the angle of attack and sideslip angle will converge to zero.

From equations (119) and (121), the Hamiltonian of the optimal control problem is:

in the formula of lambda₁And λ₂Are all covariates. According to the first order requirements, there are:

the above formula is substituted into formula (119), and integration is performed, so that the expressions of the speed inclination angle deviation value and the speed deviation angle deviation value at the shutdown time are obtained as follows:

in combination with the end point constraint shown in equation (120), the value of the covariance matrix can be found as:

in the formula, theta₁And Θ₂Is an intermediate variable, and the expression is:

by substituting equation (126) for equation (124), the optimum values for the angle of attack and sideslip angle can be found as:

wherein N is_p1And N_p2The specific expression of (A) is as follows:

as can be seen from the above formula, the guidance coefficient is not constant and changes along with the flight time, and the approximate solution is obtained through the Gaussian-Legendre integral formula. Recording:

the values of the variables in the above equation are similarly predicted from the position of the end of the boost phase and the velocity vector in step 102. Then a guidance factor N can be obtained_p1And N_p2The specific values of (A) are:

wherein,

is the ith Gaussian integral node x_iA corresponding time of flight;

ω_ithe weighting coefficient is integrated for the ith Gaussian.

So far, the optimal guidance instruction of two pulses of the double-pulse interception bomb is derived.

The short-range interception dipulse optimal intermediate guidance method based on gravity difference fitting provided by the embodiment of the invention is based on the working characteristics of an interception bullet dipulse solid rocket engine, uses the interception outside the atmosphere as a background, aims at reducing the calculated amount, and fits the gravity difference borne by a bullet to a quadratic polynomial of the residual flight time, thereby analyzing and solving a guidance instruction. In order to obtain the position and the speed of the engine at the shutdown time of the boosting section, the embodiment of the invention provides an analytic method for predicting the terminal position and the speed of the boosting section outside the atmosphere, and the high-precision prediction of the position and the speed of the shutdown time of the boosting section in a three-dimensional space can be realized on the premise of less calculation amount. Furthermore, the embodiment of the invention deduces the optimal guidance law according to the first-order necessary conditions in the optimal control theory, can meet the optimality of guidance instructions, and enables the attack angle and the sideslip angle of the intercepted missile to be kept in a smaller magnitude in the boosting stage, thereby reducing the requirements on the control system of the intercepted missile and improving the interception capability and reliability of the intercepted missile.

Fig. 5 shows a schematic structural diagram of a double-pulse medium guidance law device for short-range interception according to an embodiment of the present invention. As shown in fig. 5, the apparatus includes:

the differential equation building module 501 is used for building a kinetic equation of the interception missile and the target missile in the glide section under the local ground coordinate system, and building a differential equation of the relative movement speed of the missile and the target missile under the line of sight coordinate system based on the kinetic equation and a coordinate transformation matrix of the line of sight coordinate system and the local ground coordinate system;

in this embodiment of the present invention, as an optional embodiment, the differential equation constructing module 501 includes:

a geocentric distance vector acquiring unit (not shown in the figure) for acquiring geocentric distance vectors of the interception missile and the target missile respectively according to the geocentric distance of the origin of the local ground coordinate system of the sliding section and the position vectors of the interception missile and the target missile under the local ground coordinate system;

the gravity acceleration vector acquisition unit is used for determining the gravity acceleration vectors of the interception missile and the target missile under a local ground coordinate system respectively based on the earth-center distance vector and the earth-center gravity constant;

the dynamic equation building unit is used for acquiring dynamic equations of the intercepting missile and the target missile in a local ground coordinate system respectively based on the gravity acceleration vector;

the sight elevation and sight declination expression acquisition unit is used for acquiring a sight elevation and sight declination expression of a sight coordinate system based on the component of a position vector in a kinetic equation and the relative position of a missile target between an interception missile and a target missile;

the coordinate transformation matrix acquisition unit is used for constructing a coordinate transformation matrix of a sight line coordinate system and a local ground coordinate system according to the sight line elevation angle and the sight line deflection angle expression;

the speed component equation acquisition unit is used for acquiring speed component equations of the interception missile and the target missile respectively in a sight line coordinate system based on the coordinate transformation matrix, the speed vector of the interception missile in the kinetic equation and the speed vector of the target missile in the kinetic equation;

the relative motion velocity equation building unit is used for building a bullet and target relative motion velocity equation under a sight coordinate system according to the sight elevation angle and sight deflection angle expression, the relative position between the intercepting bullet and the target missile and respective velocity component equations;

and the speed differential equation building unit is used for carrying out differential operation on the relative movement speed equation of the bullet and building the relative movement speed differential equation of the bullet under the sight coordinate system.

The prediction module 502 is used for establishing a boosting section dynamic equation and predicting a terminal position vector and a speed vector of a boosting section;

in this embodiment of the present invention, as an optional embodiment, the prediction module 502 includes:

the inclination angle acquisition unit is used for acquiring an orbit inclination angle and a rising intersection right ascension of an orbit plane based on the angular momentum of the interception missile under the earth center inertial coordinate system;

the model building unit is used for building a boosting section dynamic model based on a projectile relative motion velocity differential equation, an interception projectile operation parameter and an interception projectile velocity in a track plane;

and the vector determining unit is used for determining an end point position vector and a speed vector of the ending moment of the boosting section of the intercepting bomb based on the dynamic model of the boosting section.

In the embodiment of the present invention, as an optional embodiment, the integrating the simplified speed derivative to obtain the speed of the ending time of the boosting section of the interceptor projectile includes:

and acquiring the speed of the intercepting bullet boosting section at the ending moment based on the acquired boosting speed integral term value and the terminal trajectory inclination angle of the boosting section.

In this embodiment, as another optional embodiment, the predicting module 502 includes:

the fitting unit is used for fitting the intercepting bullet trajectory inclination angle based on a derivative equation of the intercepting bullet trajectory inclination angle in the boosting section dynamic model;

the included angle equation acquisition unit is used for acquiring an end point position equation of the boosting section of the intercepted projectile and an included angle equation of a connecting line between an end point position vector and the geocenter and a rising intersection point based on the fitted angle of the trajectory inclination of the intercepted projectile;

and the vector acquisition unit is used for determining an end point position vector and a velocity vector of the ending moment of the booster section of the intercepted projectile based on the track inclination angle, the ascent intersection point right ascension, the end point velocity of the booster section of the intercepted projectile, the end point trajectory inclination angle of the booster section, an end point position equation and an included angle equation of the end point position vector and a connecting line from the geocenter to the ascent intersection point.

A shutdown point parameter obtaining module 503, configured to obtain a shutdown point parameter that satisfies a zero control interception triangle in a taxiing segment based on a zero control interception triangle policy according to an end point position vector and a velocity vector of an intercepted missile boosting segment ending time, where the shutdown point parameter includes an intercepted missile velocity inclination angle and a velocity deflection angle;

in this embodiment of the present invention, as an optional embodiment, the shutdown point parameter obtaining module 503 includes:

the sight deviation angular velocity value acquisition unit is used for applying the condition that the relative speed of the bullet eyes in the direction perpendicular to the sight at the interception moment is zero to a differential equation of the relative movement velocity of the bullet eyes at the sliding stage to obtain a bullet eye deviation angular velocity value at the shutdown moment of the interception bullet;

and the adjusting unit is used for adjusting the speed direction of the intercepting bullet to enable the shutdown speed to meet the expected value of the bullet sight declination speed value.

A derivation module 504, configured to derive an optimal ignition time of the second pulse of the interception bullet based on a preset performance index function of the ignition time of the second pulse of the interception bullet according to the shutdown point parameter, the position vector analytic expression, and the boundary condition;

in this embodiment of the present invention, as an optional embodiment, the derivation module 504 includes:

the sight line declination angular velocity equation acquisition unit is used for acquiring a bullet eye sight line declination angular velocity equation of the interception bullet at the second pulse ignition moment based on the position vector analytic expression and a preset second boundary condition;

the derivative equation obtaining unit is used for obtaining an analytic expression of the projectile relative speed and the pulse interval time derivative in the second pulse working stage according to the projectile relative speed differential equation and the boundary condition of the ignition moment, and solving an optimal pulse interval time derivative equation based on the analytic expression;

the bullet relative velocity equation acquisition unit is used for solving the relation between the expected bullet relative velocity at the second pulse shutdown time of the intercepting bullet and the pulse interval time to acquire a bullet relative velocity equation in the direction perpendicular to the sight line;

and the optimal ignition time acquisition unit is used for solving the optimal ignition time of the second pulse of the interception bullet by using a variational method based on a bullet eye line deflection angular velocity equation, an optimal pulse interval time derivative equation and a bullet eye relative velocity equation in the direction perpendicular to the line of sight at the ignition time of the second pulse of the interception bullet.

And the optimal instruction acquisition module 505 is configured to acquire a double-pulse optimal guidance instruction based on the predicted values and the expected values of the speed inclination and the speed drift angle at the shutdown time of the interception bullet and the second-pulse optimal ignition time of the interception bullet.

In this embodiment of the present invention, as an optional embodiment, the optimal instruction obtaining module 505 includes:

the device comprises a first pulse optimal guidance instruction acquisition unit, a first control unit and a second control unit, wherein the first pulse optimal guidance instruction acquisition unit is used for solving a first pulse optimal guidance instruction which comprises optimal values of an attack angle and a sideslip angle;

and the second pulse optimal guidance instruction acquisition unit is used for solving a second pulse optimal guidance instruction, and the second pulse optimal guidance instruction comprises optimal values of an attack angle and a sideslip angle.

As shown in fig. 6, an embodiment of the present application provides a computer device 600 for executing the double-pulse guidance method for short-range interception in fig. 1, the device includes a memory 601, a processor 602 connected to the memory 601 through a bus, and a computer program stored in the memory 601 and running on the processor 602, wherein the processor 602 implements the steps of the double-pulse guidance method for short-range interception when executing the computer program.

Specifically, the memory 601 and the processor 602 can be general-purpose memories and processors, which are not specifically limited herein, and the double pulse mid-guidance method for short-range interception described above can be performed when the processor 602 executes a computer program stored in the memory 601.

Corresponding to the double-pulse mid-guidance method for short-range interception in fig. 1, the present application also provides a computer readable storage medium having a computer program stored thereon, where the computer program is executed by a processor to perform the steps of the double-pulse mid-guidance method for short-range interception.

In particular, the storage medium can be a general-purpose storage medium, such as a removable disk, a hard disk, etc., on which a computer program can be executed to perform the above-described double-pulse mid-guidance method for short-range interception.

In the embodiments provided in the present application, it should be understood that the disclosed system and method may be implemented in other ways. The above-described system embodiments are merely illustrative, and for example, the division of the units is only one logical functional division, and there may be other divisions in actual implementation, and for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection of systems or units through some communication interfaces, and may be in an electrical, mechanical or other form.

The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.

In addition, functional units in the embodiments provided in the present application may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit.

The functions may be stored in a computer-readable storage medium if they are implemented in the form of software functional units and sold or used as separate products. Based on such understanding, the technical solutions of the present application or portions thereof that substantially contribute to the prior art may be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the methods described in the embodiments of the present application. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.

It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined or explained in subsequent figures, and moreover, the terms "first," "second," "third," etc. are used merely to distinguish one description from another, and are not to be construed as indicating or implying relative importance.

Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present application, and are used to illustrate the technical solutions of the present application, but not to limit the technical solutions, and the scope of the present application is not limited to the above-mentioned embodiments, although the present application is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope disclosed in the present application; such modifications, changes or substitutions do not depart from the spirit and scope of the present disclosure, which should be construed in light of the above teachings. Are intended to be covered by the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims

1. A double-pulse mid-guidance method for short-range interception, comprising:

deducing the optimal ignition time of the second pulse of the interception bullet based on a preset performance index function of the ignition time of the second pulse of the interception bullet according to the shutdown point parameter, the position vector analytical formula and the boundary condition;

2. The method of claim 1, wherein the establishing of the kinetic equations of the intercepted missile and the target missile in the taxiing section under the local ground coordinate system comprises:

determining gravity acceleration vectors of the intercepting missile and the target missile under a local ground coordinate system respectively based on the geocentric distance vector and the geocentric gravity constant;

3. The method of claim 2, wherein constructing the differential equation of the projectile relative motion velocity in the line of sight coordinate system based on the kinetic equation and a coordinate transformation matrix of the line of sight coordinate system and the local ground coordinate system comprises:

acquiring velocity component equations of the intercepting missile and the target missile respectively under a sight line coordinate system based on the coordinate transformation matrix, the velocity vector of the intercepting missile in the kinetic equation and the velocity vector of the target missile in the kinetic equation;

4. The method of claim 1, wherein establishing a boost segment dynamics equation and predicting a position vector and a velocity vector of an end point of a boost segment comprises:

acquiring an orbit inclination angle and a rising intersection right ascension of an orbit plane based on the angular momentum of the intercepting projectile under the earth center inertial coordinate system;

and determining an end point position vector and a velocity vector of the ending moment of the boosting section of the intercepting bomb based on the dynamic model of the boosting section.

5. The method of claim 4, wherein determining an end position vector and a velocity vector of the projectile boost segment end time based on the boost segment dynamics model comprises:

and integrating the simplified speed derivative to obtain the speed of the ending moment of the boosting section of the intercepting bomb.

6. The method of claim 5, wherein the integrating the simplified derivative of the velocity vector to obtain the velocity vector at the end of the interceptor bomb boost segment comprises:

7. The method of claim 1, wherein establishing a boost section dynamics equation and predicting an end position vector and a velocity vector of a boost section comprises:

8. A double-pulse mesoguidance law device for short-range interception, comprising:

9. A computer device, comprising: a processor, a memory and a bus, the memory storing machine readable instructions executable by the processor, the processor and the memory communicating over the bus when a computer device is running, the machine readable instructions when executed by the processor performing the steps of the double pulse mid-guidance method for short range interception according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that a computer program is stored on the computer-readable storage medium, which computer program, when being executed by a processor, performs the steps of the double pulse mid-guidance method for short-range interception according to one of claims 1 to 7.