CN111191359A

CN111191359A - Method for constructing air-defense missile space killer area model and calculating shooting data based on small amount of actual data

Info

Publication number: CN111191359A
Application number: CN201911351195.3A
Authority: CN
Inventors: 黄隽; 刘方; 彭英武; 邹强; 李晓宝; 肖金石; 薛冰
Original assignee: Naval University of Engineering PLA
Current assignee: Naval University of Engineering PLA
Priority date: 2019-12-24
Filing date: 2019-12-24
Publication date: 2020-05-22
Anticipated expiration: 2039-12-24
Also published as: CN111191359B

Abstract

The invention discloses a method for constructing an air-defense missile space killer zone model and calculating shooting data elements based on a small amount of actual data, which mainly comprises the following steps of: 1) acquiring air defense missile data; 2) establishing a space killer area model based on the air defense missile data; 3) and resolving the space killing area model to obtain shooting data. According to the invention, a killing area model is constructed by adopting polynomial fitting and linear fitting methods and mapping matrix algorithms of curved edge polygons, planar polygons and spatial polygons according to an analytic geometric mathematical model of a killing area and a small amount of public actual data, and the defects of blindness and low efficiency in the construction of the traditional spatial killing area are overcome.

Description

Method for constructing air-defense missile space killer area model and calculating shooting data based on small amount of actual data

Technical Field

The invention relates to the field of missile weapon system application, in particular to an air-defense missile space killer area model construction and shooting data resolving method based on a small amount of actual data.

Background

The killing zone (killing zone) refers to a space area (a space range for killing a typical target with a given probability) for killing a specified aerial target by the air defense missile weapon system, and is an important operational comprehensive performance index of the air defense missile weapon system. The space shape of the air defense missile weapon system killing area is complex and comprises indexes such as a far boundary, a near boundary, a high boundary, a low boundary, a maximum airway shortcut, a maximum airway angle, a maximum altitude angle and the like. The general outline of the killing area is represented by a data table and a graph, most of the general outlines do not provide a mathematical model of the boundary of the killing area, and the space killing area is usually represented by two plane graphs of a vertical plane killing area and a horizontal plane killing area in engineering. The vertical plane killing area is a graph obtained after the vertical plane cuts the space killing area, the horizontal plane killing area is obtained after the horizontal plane cuts the space killing area, obviously, the two plane killing areas are infinite, and in practical application, only typical situations such as a zero-route shortcut vertical plane killing area and a horizontal plane killing area with a typical height are generally analyzed. The key technology of modeling the killing area is generally divided into four basic method types of a mathematical modeling method, a simulation method, a fitting method and a table look-up method, or a method combining the basic types. The existing mathematical model is not derived from theory, but seven space killing area expressions, five vertical killing area expressions with zero route shortcut and four horizontal killing area expressions with a certain height are formed by adopting a numerical fitting method according to actual shooting and simulation experiment data, so that the change rule of the boundary of the killing area can be theoretically explained, the internal relation and essence between discrete experiment data can be well reflected, and the method is very valuable for researching the air-defense missile shooting theory. However, due to the simple and clear characteristic of a single-part expression of the existing mathematical model of the space killing area, the research on the complex relationship correspondingly generated by the coupling interface between the boundary surfaces is less, and a high-precision and totally-enclosed space killing area engineering model constructed based on the mathematical model and actual data is rare. The simulation calculation method needs to construct and solve a missile simulation differential trajectory equation set consisting of a mass equation, a kinetic equation, a kinematic equation, a guidance equation and a control equation, carry out an interception simulation experiment to obtain interception encounter point data of the air-defense missile, obtain a miss distance range or an equal overload envelope, and then correct to obtain a calculated theoretical kill area. The numerical fitting method has the problems that the function is difficult to determine and the segmentation range of the function is difficult to master; the form of the fitting function is various. For the one-dimensional fitting problem of data, nodes can be smoothly connected through segmentation processing, and fitting errors can be made to be small at will. But for multi-dimensional problems, it is very difficult to process if segmentation is performed, because a curved surface or a curve, or even a higher dimensional situation, will appear at the multi-dimensional problem segmentation. For the occurrence of high dimensional situations, fitting the segmentation is not well handled. The table lookup interpolation method has higher requirements on calculation and storage and is less used in engineering application. A large amount of data of missile launching area envelope can be effectively utilized through BP artificial neural network solution, and integral data fitting is realized; for the case of large data volume or complex input and output relation, a deep neural network architecture and a deep learning method under a large data environment are adopted, and a deep belief network is introduced, so that the fitting performance can be improved, and higher precision can be achieved. However, the uncertainty of local convergence of the method is still little applied in engineering, and fitting data mainly comes from analog simulation data and is not suitable for fitting of a small amount of actual data. A method for generating a space killing area in a plane killing area needs a spline function and a piecewise interpolation method to process data to obtain the boundary of a vertical killing area, the vertical killing area is rotated to be combined with a horizontal killing area which is translated, then the space killing area is obtained by correcting a near interface, a side interface, a low interface and the like, or a discrete cluster of vertical killing areas distributed on an equidistant airway shortcut is used for representing. The method is complicated, the change of the characteristic points is complicated, the difficulty of generating a smooth space killing area by fitting a cluster of vertical killing areas is high, the occupied data space is large, the real-time performance is weak, and the calculation of the firing data of any application route shortcut and the formation of the horizontal killing area are inconvenient. The traditional analysis method of the killing area needs a large amount of actual data, but in most cases, enough actual data cannot be obtained, particularly for some introduced or newer models. The method is based on a small amount of actual data, and adopts a method of combining a mathematical model and numerical fitting to construct an air-defense missile killing area Matalab model, so that the efficiency is improved, and the engineering operability is enhanced. Therefore, the research on modeling of the air defense missile killer area has important significance for air defense combat simulation.

Disclosure of Invention

The present invention is directed to solving the problems of the prior art.

The technical scheme adopted for achieving the purpose of the invention is that the method for constructing the air-defense missile space-killing area model and calculating shooting data base based on a small amount of actual data mainly comprises the following steps:

1) and acquiring air defense missile data.

Further, the air defense missile data comprise a high bound H of a killing area_maxAnd a low boundary H of the killing area_minAnd killing zone far boundary S_syNear boundary S of killing zone_sjMaximum height angle epsilon of killing area_maxMaximum route angle q of killer area_maxMaximum airway shortcut P_maxTime t of encounter of air defense missile and target_{D practice}And encounter point slope distance D_{s actual}。

2) And establishing a space killing area model based on the air defense missile data.

The method mainly comprises the following steps of:

2.1) establishing a killer area analytic geometric mathematical model based on the killer area boundary parameters.

2.2) inputting the air defense missile data into the analytic geometric mathematical model of the killing area to obtain the engineering model of the closed killing area.

The closed killing area engineering model comprises a killing area low-near interface, a killing area high-near interface, a killing area far interface, a killing area high interface, a killing area low interface, a killing area positive side interface, a killing area negative side interface, a killing area upper front positive interface, a killing area upper front negative interface, a killing area lower front positive interface and a killing area lower front negative interface.

a) The method mainly comprises the following steps of determining the DGG 'D' of the low and near interface of the killing area:

1) establishing a low-near-field spherical equation, namely:

wherein P is the air route shortcut. H is the target height. And q is the target route angle. H_minIs the low boundary of the killing area. D_sjminThe minimum near-bound slant distance is a killing area. S_scjIs the near boundary of the killing area. Epsilon_maxThe maximum elevation angle of the killing area. q. q.s_maxThe maximum route angle of the killing area. And S is a killing area interface. H_JIs the near-boundary height of the killing area.

2) Correcting the initial low and near sphere by using the find function to obtain a matrix set (S)_scj，P，H)_DGG′D′。

3) Using surf (S)_scj，P，H)_DGG′D′The function forms the killing zone low-near interface DGG 'D'.

b) The main steps for determining the high-near interface BDD 'B' of the killing area are as follows:

1) establishing a high-near cone equation, namely:

in the formula, H_maxIs the high boundary of the killing area. S_sjIs a near boundary of the killing area.

2) Correcting the initial high and near boundary conical surface by using the find function to obtain a matrix group (S)_sj，P，H)_BDD′B′。

3) Invoking surf (S)_sj，P，H)_BDD′B′The function forms the killing zone high-near interface BDD 'B'.

c) The main steps for determining the far boundary EHH 'E' of the kill zone are as follows:

1) establishing a far-bound surface equation, namely:

in the formula, a, b and c are curved surface equation coefficients. S_syIndicating a far boundary of the kill zone.

2) The data (H) of m groups of air defense missiles_j，S_syj) Input into p ═ polyfit (H, S)_syR) function, and fitting out far boundary of killing area by polynomial fitting method

The non-linear function expression of (2). r is the fitting order. r is less than m. p is a vector formed by polynomial coefficients of the function F. j is 1, …, m. (H)_j，S_syj) And representing the jth air defense missile data.

3) In the interpolation interval [ H_min，H_max]Uniformly taking n points and substituting into the far boundary of the killing area

In the function, a bus (H) of the far boundary of the killing area is linearly fitted_i，S_syi). Bus bar (H)_i，S_syi) Around the OH axis of the coordinate system within + -q_maxRotating within the range to obtain an initial far-bound curved surface. i is 1, …, n. (H)_i，S_syi) And representing the air defense missile data corresponding to the ith point.

4) Correcting the initial far-bound surface by using a find function to obtain a matrix group(s)_sy，P，H)_EHH′E′。

5) Using surf (S)_sy，P，H)_EHH′E′The function forms a far interface EHH 'E' of the kill zone.

d) The main steps for determining the high interface HABB ' A ' H ' of the killing area are as follows:

1) establishing a high-boundary plane equation, namely:

2) correcting the initial high-boundary plane equation by using a find function to obtain a matrix set (S, P, H)_{HABB′A′H′}。

3) Using surf (S, P, H)_{HABB′A′H′}The function forms the killer high interface HABB ' A ' H '.

e) The main steps for determining the killing area low interface GFF 'G' are as follows:

1) establishing a low-boundary plane equation, namely:

2) correcting the initial high-boundary plane equation by using a find function to obtain a matrix set (S, P, H)_GFF′G′。

3) Using surf (S, P, H)_GFF′G′The function forms the killer region low interface GFF 'G'.

f) The main steps for determining the interface on the front side of the killing area are as follows:

1) curve of distance bound

Straight line

And a straight line

And (3) stretching into a curved polygon HAE, namely the equation:

in the formula, H (,) represents the coordinates of H (,) in the formula.

Determining a characteristic point E of a curved-edge polygon HAE, wherein the method comprises the following steps: in the interpolation interval [ H_min，H_max]Uniformly taking n points in the inner part of the sample,and substituted into the far boundary of the killing area

In the function, a function is obtained

Substituting n points into function in sequence

In (1) obtaining

The k point corresponding to the time so as to obtain the coordinate of the E point

H_kThe height corresponding to the k-th point.

2) Respectively mapping the curved-edge polygons HAE into (n-k +1) -dimensional matrixes S_HAEA (n-k +1) -dimensional matrix P_HAEAnd (n-k +1) -dimensional matrix H_HAEObtaining a matrix set (S)_HAE，P_HAE，H_HAE)。

3) Invoking surf (S)_HAE，P_HAE，H_HAE) The function establishes the killing zone positive side interface.

g) The main steps for determining the negative side interface of the killing area are as follows:

1) curve of distance bound

Straight line

And a straight line

And (3) stretching into a curved polygon H ' A ' E ', namely the equation:

2) polygonal with curved edgeH ' A ' E ' are respectively mapped into (n-k +1) -dimensional matrixes S_H′A′E′A (n-k +1) -dimensional matrix P_H′A′E′And (n-k +1) -dimensional matrix H_H′A′E′Obtaining a matrix set (S)_H′A′E′，P_H′A′E′，H_H′A′E′)。

3) Invoking surf (S)_H′A′E′，P_H′A′E′，H_H′A′E′) The function establishes the kill zone negative side interface.

h) The main steps for determining the front positive interface on the killing area are as follows:

1) plane of maximum route angle

The high interface of the killing area, the positive side interface of the killing area and the high-near interface of the killing area are stretched into a plane polygon ABCD, namely:

2) mapping a planar polygonal ABCD surface to an n-dimensional matrix S_ABCDN-dimensional matrix P_ABCDAnd n-dimensional matrix H_ABCDObtaining a matrix set (S)_ABCD，P_ABCD，H_ABCD)。

3) Invoking surf (S)_ABCD，P_ABCD，H_ABCD) The function yields the front positive interface on the kill zone.

i) The main steps for determining the front negative interface on the killing area are as follows:

1) plane of maximum route angle

The high boundary of the killing area, the negative side boundary of the killing area and the high-near boundary of the killing area are stretched into a plane polygon A 'B' C 'D', namely:

2) mapping a planar polygon A 'B' C 'D' surface to an n-dimensional matrix S_{A′B′C′D′}、nDimension matrix P_{A′B′C′D′}And n-dimensional matrix H_{A′B′C′D′}Obtaining a matrix set (S)_{A′B′C′D′}，P_{A′B′C′D}，H_{A′B′C′D′})。

3) Invoking surf (S)_{A′B′C′D′}，P_{A′B′C′D′}，H_{A′B′C′D′}) The function yields the front negative interface on the kill zone.

j) The main steps for determining the front positive interface under the killing area are as follows:

1) plane of maximum route angle

The low boundary of the killing area, the positive boundary of the killing area and the low-near boundary of the killing area are expanded into a spatial polygon CEFGD, namely:

in the formula, the point F is the starting point of the far field.

2) Mapping spatial polygons CEFGD into a n x 3 n-dimensional matrix S_CEFGDN x 3n dimensional matrix P_CEFGDAnd n x 3n dimensional matrix H_CEFGDObtaining a matrix set (S)_CEFGD，P_CEFGD，H_CEFGD)。

3) Invoking surf (S)_CEFGD，P_CEFGD，H_CEFGD) The function yields the front positive interface under the kill zone.

k) The main steps for determining the front negative interface under the killing area are as follows:

1) plane of maximum route angle

The low interface, the front side interface and the low-near interface are flared into a spatial polygon C ' E ' F ' G ' D ', namely:

in the formula, the F' point is the starting point of the far boundary.

2) Will spaceThe polygon C ' E ' F ' G ' D ' is mapped to a matrix S of dimensions n x 3n_{CE′F′G′D′}N x 3n dimensional matrix P_{C′E′F′G′D′}And n x 3n dimensional matrix H_{C′E′F′G′D′}Obtaining a matrix set (S)_{C′E′F′G′D′}，P_{C′E′F′G′D′}，H_{C′E′F′G′D′})。

3) Invoking surf (S)_{C′E′F′G′D′}，P_{C′E′F′G′D′}，H_{C′E′F′G′D′}) The function yields the front negative interface under the kill zone.

3) And resolving the space killing area model to obtain shooting data.

The main steps of solving the space killing area model are as follows:

3.1) establishing a space transmitting area model based on the space killing area model. And inputting the air defense missile data into a space launching area model to obtain space launching area parameters.

The main steps for obtaining the parameters of the space transmitting area are as follows:

3.1.1) establishing a space transmitting area model, namely:

S_f＝S_s+V_t·t_D(12)

in the formula, V_tIs the target speed. t is t_DThe time of the air defense missile encountering the target. D_fTo encounter the point skew. S_fIs an emitter interface.

Time t of air defense missile encountering with target_DAs follows:

3.1.2) time t of encountering air defense missile with target_{D practice}And encounter point slope distance D_{s actual}Input into the formula (14) to obtain the time calculation coefficient b₁Time calculation coefficient b₂Time calculation coefficient b₃And calculating the time t of the air-defense missile encountering the target_D。

3.1.3) time t of encountering air defense missile with target_DAnd inputting the parameters into a space transmitting area model to obtain space transmitting area parameters.

And 3.2) resolving the space killing area model to obtain a horizontal killing area and a transmitting area under the target height.

The steps of resolving the space killing area model to obtain a horizontal killing area and a transmitting area under the target height are as follows:

3.2.1) determining the height interval Δ H of the cutting horizontal killing zone of the space killing zone.

3.2.2) to interpolate the interval [ H ]_min，H_max]Within the range of any height H as a reference and in the height interval

And internally intercepting the horizontal killing area and the transmitting area.

3.2.3) the encounter point and emission point Data of the horizontal killer region, horizontal emitter region at height H are extracted using Malab's Data Cursor function.

And 3.3) resolving the space killing area model to obtain a vertical killing area and a transmitting area under the short-cut of the route where the target is located.

The steps of resolving the space killing area model to obtain a vertical killing area and a transmitting area under the route shortcut where the target is located are as follows:

3.3.1) determining the air route shortcut interval delta P of the space killing area launching area cutting vertical killing area launching area.

3.3.2) short-cut range of air route [ -P ]_max，P_max]Taking any route shortcut P in the range as a reference, and taking the route shortcut P as a reference

And internally intercepting a vertical killing area and a transmitting area on the short-cut of the navigation path.

3.3.3) extracting the encounter point and the emission point Data of the vertical killing area and the vertical emission area on the airway shortcut P by utilizing the Data Cursor function of Malab.

3.4) extracting the encountering points and the transmitting points Data in the horizontal killing area, the horizontal transmitting area, the vertical killing area and the vertical transmitting area by using a Data Cursor function to obtain the transmitting time t_{When the emission is left}And time t of target flying out of emitting area_{Time of flight}And completing shooting data element calculation. The firing data includes encounter point slope, encounter point height, shot time, time-to-flight, shot distance and shot distance.

The emission remains as follows:

where s denotes the s-coordinate of the target in the firing coordinate system O-SPH. D_FYIs the far bound slant distance of the emitting area. D_FJThe near-bound slant range of the emitting area. S_fyFar bound the emission area. S_fjThe emission region is near-bound. t is t₀The time the target is at the current location.

In a shooting coordinate system O-SPH, the air defense missile system guidance radar or the launching device is taken as the origin of coordinates. The OS axis is in the horizontal plane passing through the O point and is directed to be parallel to and opposite to the horizontal projection line of the target route. The OH axis is vertical to the horizontal plane and points to the sky. The OP axis is determined according to the right hand rule.

The target departure launch time is as follows:

t_{time of flight}＝t_FJ-t_FY(16)

Wherein the time t when the target reaches the near boundary of the emission region_FJAs follows:

in the formula, v is a target speed.

It is worth explaining that the construction method of the killing area model has strong data requirement, large calculation amount and low efficiency, so that the construction method of the killing area model overcomes the defects of blindness and low efficiency of the construction method of the killing area model based on a high-precision and totally-enclosed space killing area engineering model constructed on the basis of a mathematical model and actual data aiming at the complex relation correspondingly generated by the coupling interfaces between the boundary surfaces.

The technical effect of the present invention is undoubted. Compared with the prior art, the invention has the advantages that: 1) according to the analytic geometric mathematical model of the killing area and a small amount of public actual data, a killing area model is constructed by adopting a polynomial fitting method, a linear fitting method and a mapping matrix algorithm of a curved polygon, a planar polygon and a space polygon, so that the defects of blindness and low efficiency in the construction of the traditional space killing area are overcome. 2) According to the time and the actual data of the slant range, the space killing area is used for solving the space transmitting area, a small amount of actual data information and characteristics are fully utilized, and the efficiency and the precision of data fitting of the space transmitting area are improved. 3) The constructed space killing area contains the information of all plane killing areas, the horizontal killing area and the launching area can be easily solved, and compared with a simulation calculation method, a BP neural network and a deep learning method, the method has the advantages of higher efficiency and stronger engineering operability. 4) The Data Cursor technology is used for extracting encounter point and launch point Data to complete shooting Data solution, and compared with a traditional method for iteratively solving the midpoint by using a nonlinear equation, the method is high in searching efficiency, high in speed and high in solving precision.

Drawings

FIG. 1 shows a Matlab model construction step of an air defense missile space killer area;

FIG. 2 is a schematic view of an air defense missile system space killing zone;

FIG. 3 is a low-near interface, a high-near interface, a far interface and a high interface of a space killing zone;

FIG. 4 is a front side interface of the kill zone;

FIG. 5 is the upper front face of the kill zone;

FIG. 6 is the lower front face of the kill zone;

FIG. 7 is a process of shot data calculation;

fig. 8 is a horizontal transmitting region model of H ═ 14 km;

fig. 9 is a horizontal kill zone model with H ═ 14 km;

fig. 10 is a vertical kill zone model with P-0;

fig. 11 is a vertical emitter model with P-0;

FIG. 12 is time-slope data for a type of air defense missile;

FIG. 13 is a model of the firing zone of an anti-subsonic missile killer zone;

fig. 14 shows a horizontal emitter model with H ═ 15 km.

Detailed Description

The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.

Example 1:

referring to fig. 1 to 7, a method for constructing an air-defense missile space-kill zone model and calculating shooting data base based on a small amount of actual data mainly comprises the following steps:

1) and acquiring air defense missile data.

The air defense missile data comprises a high bound H of a killing area_maxAnd a low boundary H of the killing area_minAnd killing zone far boundary S_syNear boundary S of killing zone_sjMaximum height angle epsilon of killing area_maxMaximum route angle q of killer area_maxMaximum airway shortcut P_maxTime t of encounter of air defense missile and target_{D practice}And encounter point slope distance D_{s actual}。

The method mainly comprises the following steps of:

Establishing a shooting parameter rectangular coordinate system O _ SPH (namely O _ XYZ) by taking the air-defense missile system guided radar or the transmitting device as a coordinate origin, wherein an OS axis is parallel to and opposite to a horizontal projection line of a target route in a horizontal plane passing through an O point; the OH axis is vertical to the horizontal plane and points to the sky; the OP axis is determined in a right-hand system. As shown in fig. 2, assuming that the target flies linearly, after obtaining the target height H, the airway shortcut P and the target airway angle (course angle) q, the HABB ' a ' H ' is a high interface of the killing area, typically a part of a horizontal sector; GFF 'G' is a killer zone low interface, typically a portion of a horizontal sector; EHH 'E' is the far interface of the killing area, which is generally a curved surface; BDD 'B' is a high-near interface of a killing area, and is typically a part of a conical surface, and the top of the conical surface is at a point 0; DGG 'D' is a low-near interface of a killing area, and is typically a part of a spherical surface, and the center of the spherical surface is at a point O; HAE and H ' A ' E ' are two side near interfaces of a killing area, and the front side surface respectively has an included angle of +/-q between two vertical planes passing through the O point and having zero short-cut with an airway_maxIn the vertical plane, the shortcuts of the positive side surface and the negative side surface of the air route are plus or minus P respectively_maxThe vertical plane of (a).

1) establishing a low-near-field spherical equation, namely:

wherein P is the air route shortcut. H is the target height. And q is the target route angle. H_minIs the low boundary of the killing area. D_sjminThe minimum near-bound slant distance is a killing area. S_scjIs the near boundary of the killing area. Epsilon_maxThe maximum elevation angle of the killing area. q. q.s_maxThe maximum route angle of the killing area. And S is a killing area interface. D_maxThe far-range slant distance is a killing area.

2) Correcting the initial low and near sphere by using the find function to obtain a matrix set (S)_scj，P，H)DGG′D′。

3) Using surf (S)_scj，P，H)_DGG′D′Function forming killer regionLow proximity interface D_GG′D′。

1) establishing a high-near cone equation, namely:

in the formula, H_maxIs the high boundary of the killing area. S_sjIs a near boundary of the killing area. The initial interface equation is in parentheses, and the reserved part of the interface equation to be corrected is in parentheses (the interface equations are the same way below).

2) Correcting the initial high and near boundary conical surface by using the find function to obtain a matrix group (S)_sj，P，H)BDD′B′。

1) establishing a far-bound surface equation, namely:

The non-linear function expression of (2). r is the fitting order. r is less than m. p is a vector formed by polynomial coefficients of the function F. j is 1, …, m. r is 2.

In the function, a bus (H) of the far boundary of the killing area is linearly fitted_i，S_syi). Bus bar (H)_i，S_syi) Around the OH axis of the coordinate system within + -q_maxRotating within the range to obtain an initial far-bound curved surface. i is 1, …, n.

4) Correcting the initial far-bound surface by using a find function to obtain a matrix group (S)_sy，P，H)_EHH′E′。

1) establishing a high-boundary plane equation, namely:

2) correcting the initial high-boundary plane equation by using a find function to obtain a matrix set (S, P, H)_{HABB′A′H′}

1) establishing a low-boundary plane equation, namely:

the upper and lower boundaries of the killing area are Z ═ H_max、Z＝H_minIs limited by the maximum way shortcut, the maximum way angle, the maximum altitude angle, the far bound and the near bound.

2) Correcting the initial high-boundary plane equation by using a find function to obtain a matrix set (S, P, H)_GFF′G′

1) curve of distance bound

Straight line

And a straight line

And (3) stretching into a curved polygon HAE, namely the equation:

determining a characteristic point E of a curved-edge polygon HAE, wherein the method comprises the following steps: the boundary curve function of the killing area is processed by using a linear interpolation method, an interpolation interval is divided into a plurality of small intervals, and a linear interpolation function is constructed in each small interval so as to achieve the purposes of properly reducing the length of the interpolation interval and improving the interpolation precision. In geometric sense, piecewise linear interpolation is to use polygonal line approximation to replace curve

In the interpolation interval [ H_min，H_max]Uniformly taking n points and substituting into the far boundary of the killing area

In the function, a function is obtained

Substituting n points into function in sequence

In (1) obtaining

H_kThe height corresponding to the k-th point.

The algorithm is as follows:

I) using round () function pair S_syi(i ═ k, k +1, …, n) for quantization

qi＝round((Ssyi-min(Ssyi))/((max(Ssyi)-min(Ssyi))/(k-1))+1；

II) Linear interpolation function line () pair S_HAEAssigning values to the 1-qi columns of the ith row;

S_HAE(i，1：qi)＝linspace(min(x6)，Ssyi，qi))；

III) reacting S_HAEThe remaining (n-k +1-qi) portion of the ith row of (a) is set to a non-integer Nan;

IV)

becoming the ith row vector;

V)P_maxbecomes a matrix H_HAE。

The key to applying piecewise interpolation is the problem of proper selection of interpolation points. The principle of selecting interpolation nodes in theory is to select interpolation nodes near the interpolation points as much as possible, and the more interpolation nodes, the higher the interpolation precision. However, for the air-defense missile killing area, the selection of interpolation nodes and the determination of the number of the nodes need to consider the operational background of the air-defense missile killing area, and certain mathematical calculation processing is performed on the graph of the killing area by combining the shooting command requirements. After a plane killing area is approximately processed by using a piecewise linear interpolation method, the original irregular killing area is replaced by a polygon formed by linear piecewise functions with a certain form, so that a part of a killing airspace is lost.

In order to minimize the damage airspace loss of the damage with high probability, the approximate polygon should cover the original damage area as much as possible. Obviously, the more interpolation nodes, the more coverage of the approximation polygon and the original killing area, and the higher the approximation precision. However, for the killing area used by the air defense missile shooting command, increasing the interpolation node to improve the approximation precision sometimes does not have great significance. Therefore, determining the number and distribution of interpolation nodes is a core problem of the planar killer area processing. On the premise of taking mathematical calculation analysis as a tool, the actual needs of tactical application of the method are fully considered. Under the precision of meeting certain combat requirements, the workload is simplified as much as possible, and no meaningless work is done.

After the above treatment, the killer area patterns with different shapes are all approximated to regular closed polygons. Thus, the killing area of any one boundary plane is represented as a set of coordinates of points, i.e., a row of points consisting of the vertices of the polygon of the killing area.

1) curve of distance bound

Straight line

And a straight line

And (3) stretching into a curved polygon H ' A ' E ', namely the equation:

2) respectively mapping the curved edge polygons H ' A ' E ' into (n-k +1) dimensional matrixes S_H′A′E′A (n-k +1) -dimensional matrix P_H′A′E′And (n-k +1) -dimensional matrix H_H′A′E′Obtaining a matrix set (S)_H′A′E′，P_H′A′E′，H_H′A′E′)。

1) plane of maximum route angle

The algorithm is as follows:

I)S_ABCD1 st line A to B, S_ABCDN-dimensional linear interpolation of S coordinates of the n-th line C to D;

II)S_ABCDi-2 to (n-1) actions

S_ABCD(：，i)＝linspace(S_ABCD(1，i)，S_ABCD(1000，i)，n)；

III)P_ABCD1 st line A to B, P_ABCDThe nth behavior of C to D is an n-dimensional linear interpolation of the P coordinates;

IV)P_ABCDi-2 to (n-1) actions

P_ABCD(：，i)＝linspace(P_ABCD(1，i)，P_ABCD(1000，i)，n)；

V)H_ABCD1 st line A to B, H_ABCDThe nth behavior of C to D is an n-dimensional linear interpolation of the P coordinates;

VI)H_ABCDi-2 to (n-1) actions

H_ABCD(：，i)＝linspace(H_ABCD(1，i)，H_ABCD(1000，i)，n)。

1) plane of maximum route angle

2) mapping a planar polygon A 'B' C 'D' surface to an n-dimensional matrix S_{A′B′C′D′}N-dimensional matrix P_{A′B′C′D′}And n-dimensional matrix H_{A′B′C′D′}Obtaining a matrix set (S)_{A′B′C′D′}，P_{A′B′C′D′}，H_{A′B′C′D′})。

1) plane of maximum route angle

in the formula, the point F is the starting point of the far field.

The find function and the surf function are stored in Matlab.

The algorithm is as follows:

I) obtaining matrix groups (S) according to the algorithm of h) respectively_CEF，P_CEF，H_CEF)、(S_CDF，P_CDF，H_CDF) And (S)_DFG，P_DFG，H_DFG)；

II) constructing a new set S of matrices_CEFGD＝[S_CEF，S_CDF，S_DFG]，

P_CEFGD＝[P_CEF，P_CDF，P_DFG]And H_CEFGD＝[H_CEF，H_CDF，H_DFG]。

1) plane of maximum route angle

in the formula, the F' point is the starting point of the far boundary.

2) Mapping the spatial polygon C ' E ' F ' G ' D ' into a n-x 3 n-dimensional matrix S_{C′E′F′G′D′}N x 3n dimensional matrix P_{C′E′F′G′D′}And n x 3n dimensional matrix H_{C′E′F′G′D′}Obtaining a matrix set (S)_{C′E′F′G′D′}， P_{C′E′F′G′D′}，H_{C′E′F′G′D′)}。

3) Invoking surf (S)_{C′E′F′G′D′}，P_{C′E′F′G′D}′，H_{C′E′F′G′D′}) Function to obtain the lower front negative bound of the killing areaAnd (5) kneading.

3) And resolving the space killing area model to obtain shooting data.

The main steps of solving the space killing area model are as follows:

As shown in fig. 8, according to the target height, the horizontal killing area and the emitting area at the height are solved by the space killing area and the emitting area. And shearing the air defense missile space killing area with the closed surface and the launching area to obtain the horizontal killing area. The horizontal kill zone is the cross-section resulting from cutting the kill zone at a given height level. The horizontal killing area and the launching area can more visually observe the position relation among the target, the killing area and the launching area, and the shooting data can be more easily solved.

To make the kill zone model take effect better in the computer, and provide real-time support for shoot command decisions, [ H ] can be used_min，H_max]A horizontal kill zone of any height within the range. Because the horizontal killing area and the far boundary and the near boundary of the launching area of most air-defense missile weapons are circular arc-shaped, the horizontal killing area and the launching area models with different heights can be conveniently generated by the space killing area model and the launching area model.

3.1.1) establishing a space transmitting area model, namely:

Time t of air defense missile encountering with target_DAs follows:

As shown in fig. 10 and 11, according to the target route shortcut, the vertical killing area and the launching area under the route shortcut are solved by the space killing area and the launching area. And shearing the air defense missile space killing area and the launching area with the closed surfaces to obtain a vertical killing area and a launching area. The vertical kill zone and launch zone are cross sections obtained by cutting the space kill zone and launch zone from a given airway shortcut vertical plane. The vertical killing area and the launching area can more intuitively observe the position relation between the maneuvering target in the vertical plane and the killing area and the launching area, and the shooting data can be solved more easily.

For the killing area and transmitting area model to take effect in computer and providing real-time support for shooting command decision, the [ -P ] can be used_max，P_max]Vertical kill areas and launch areas of any route shortcut within the range. As the vertical killing area and the far boundary and the near boundary of the launching area of most air-defense missile weapons are all polygonal closed by the multi-section broken lines, the vertical killing area and the launching area models of different air routes and shortcuts can be conveniently generated by the space killing area and the launching area models.

3.4) extracting the encountering points and the transmitting points Data in the horizontal killing area, the horizontal transmitting area, the vertical killing area and the vertical transmitting area by using the Data Cursor function of Malab to obtain the transmitting residual time t_{When the emission is left}And time t of target flying out of emitting area_{Time of flight}And completing shooting data element calculation. The firing data includes encounter point slope, encounter point height, shot time, time-to-flight, shot distance and shot distance.

The emission remains as follows:

The target departure launch time is as follows:

t_{time of flight}＝t_FJ-t_FY(16)

in the formula, v is a target speed.

Example 2:

a method for constructing an air-defense missile space killer zone model and calculating shooting data elements based on a small amount of actual data mainly comprises the following steps:

1) constructing a Matlab model of a space killing area: according to the analytic geometrical mathematical model of the killing area, inputting a small amount of public actual data, and constructing a closed killing area engineering model by adopting a polynomial fitting method, a linear fitting method and a mapping matrix algorithm of a curved polygon, a planar polygon and a spatial polygon according to the sequence from a low-near interface, a high-near interface, a far interface, a high-low interface, a positive-negative side interface from the top to the bottom.

2) Solving shooting data elements by using a killing area model: solving shooting data elements by using a killing area model, and solving a space launching area by using a space killing area according to time and slope distance actual data; according to the target height, solving a horizontal killing area and a transmitting area under the height by the space killing area; according to the route shortcut where the target is located, solving a vertical killing area and a launching area under the route shortcut by a space killing area; and (4) extracting encounter point and emission point Data in the horizontal killing area and the vertical killing area by using a Data Cursor technology to complete shooting Data resolution.

Example 3:

an experiment for verifying a method for constructing an air-defense missile space killer zone model and calculating shooting data based on a small amount of actual data mainly comprises the following steps:

1) acquiring actual data: the actual data of the parameters of the air defense missile killer zone of a certain type are shown in the table 1, and the actual data of time and slope distance are shown in the figure 12.

TABLE 1 practical data table of parameters of air defense missile killer zone

2) Killer and emitter model construction for typical targets

A certain missile weapon system intercepts a horizontal uniform-speed flying anti-ship missile target with V less than or equal to 300m/s, and the calculation results of a killing area and a launching area are shown in figure 13.

2.1) killing zone

a) Low proximity interface

Killing zone low near-bound DGG 'D' equation:

b) high and near interface

Killer zone high-near boundary BDD 'B' equation:

c) remote interface

Killing zone remote boundary EHH 'E' equation:

d) high low interface

① killer zone high interface HABB ' a ' H ' equation:

② killer zone low interface GFF 'G' equation:

e) positive and negative side interface

① front side interface

Curved-edge polygon HAE equation:

② negative side interface

Curved polygon H ' A ' E ' equation:

f) front positive and negative surfaces

① front upper surface

Trapezoidal ABCD equation:

② negative front

Trapezoidal A 'B' C 'D' equation:

g) lower front positive and negative surface

① lower front face

Spatial polygon CEFGD equation:

② lower front negative

The spatial polygon C ' E ' F ' G ' D ' equation:

2.2) emission area

21 sets of data (t) were extracted from table 1 available Excel_{D practice}，D_{Actual fact of killing}) Fitting t by a polyfit () function_DHeel D_{Killing and killing}By a polynomial of the functional relationship (b), b can be obtained₁，b₂，b₃；

Substituting into the desired space killing area (S)_{Killing and killing}，P_{Killing and killing}，H_{Killing and killing}) Obtaining parameters of the killing area

Corresponding t_DFrom (12) the spatial emission region (S) can be derived_Launching，P_Launching，H_Launching) The model is shown in fig. 13.

3) Data resolution for typical target shooting

3.1) shooting data element calculation of horizontal equal-height straight line flight target

Assuming that the position where the target M is precisely steered is (120, 20, 14), the target flies at 300M/s along the OP axis at the same level. At this time, the horizontal transmitting area H-14 km shown in FIG. 8 and the horizontal killing area shown in FIG. 9 are intercepted. The intersection points of the target and the far and near boundaries of the emitting area are A, B respectively, and the intersection points of the target and the far and near boundaries of the killing area are C, D respectively. Matlab can solve for the A, B, C, D coordinates and solve for the shot data.

a) When emission is left:

b) flying-out time:

t_{time of flight}＝t_FJ-t_FY＝266.50s

Table 2 shows the data of the shots at different heights when the shortcut of the flight path is 20 km.

TABLE 2 data of shots at different heights

H(km)	S_fy(km)	S_fj(km)	T_{When the emission is left}(s)	T_{Time of flight}(s)
					10	93.57	19.8	88.1	245.9
11	95.71	20.2	80.97	251.70
					12	98.57	20.5	71.43	260.24
13	100.0	21.0	66.67	263.33
					14	100.4	20.45	65.33	266.50
15	100.2	21.25	66	263.17
					16	99.7	21.6	67.67	260.33
17	97.86	22.0	73.8	252.87
					18	95.71	22.3	80.97	244.70

4) Data resolution of horizontal serpentine maneuvering flight target

Assuming that the position where the target M is precisely steered is (120, 0, 15), the target level maneuvers. The truncated H-15 km horizontal transmission area is shown in fig. 14. The intersection points of the target and the far and near boundaries of the emitting area are A, B respectively, and coordinates A (102.8, 3.311, 14.86) and B (13.86, -3.094,14.99) can be obtained by adopting Matlab's DataCursor technology. Although the target adopts horizontal maneuvering flight, the flight speed component of the target along the S axis is 300m/S, so the shooting data of the horizontal maneuvering target is solved in a transmitting area corresponding to a killing area of a high-straight-line flight target with the height of H being 15km horizontally. Then S_fy＝102.8km，S_fj＝13.86km， T_{When the emission is left}＝57.33s，T_{Time of flight}＝296.47s。

5) Serpentine maneuvering flight target data element calculation in vertical plane

Assuming that the flying velocity component of the target along the S axis is constant, the position of the target which is accurately guided is (120, 0, 10), and the target flies in a snake-shaped maneuvering plane in the vertical plane. The vertical emission region with cut P-0 is shown in fig. 11.

The intersection points of the target and the far and near boundaries of the emitting region are A, B respectively, and coordinates A (99.88, 0, 11.36) and B (7.391, 0, 14.44) can be obtained by adopting the Data Cursor technology of Matlab. Although the target adopts vertical maneuvering flight, the flight speed component of the target along the S axis is 300m/S, so the shooting data of the vertical maneuvering target is solved in a transmitting area corresponding to a killing area of a high-straight-line flight target with the H-0 km horizontal height. Then S_fy＝99.88km， S_fj＝7.39km，T_{When the emission is left}＝67.07s，T_{Time of flight}＝308.30s。

Claims

1. A method for constructing an air-defense missile space-killing area model and calculating shooting data elements based on a small amount of actual data is characterized by mainly comprising the following steps of:

1) and acquiring the air defense missile data.

2) Establishing a space killer area model based on the air defense missile data;

3) and resolving the space killing area model to obtain shooting data.

2. The method for constructing model of air-defense missile space-kill zone and solving shooting data base on the basis of a small amount of actual data according to claim 1, wherein the air-defense missile data comprises a high bound H of the kill zone_maxAnd a low boundary H of the killing area_minAnd killing zone far boundary S_syNear boundary S of killing zone_sjMaximum height angle epsilon of killing area_maxMaximum route angle q of killer area_maxMaximum airway shortcut P_maxTime t of encounter of air defense missile and target_{D practice}And encounter point slope distance D_{s actual}。

3. The method for constructing the air-defense missile space-killing area model and shooting data element calculation based on the small amount of actual data according to claim 1, wherein the method for establishing the space-killing area model mainly comprises the following steps:

1) establishing a killer area analytic geometric mathematical model based on the killer area boundary parameters;

2) and inputting the air defense missile data into the analytic geometric mathematical model of the killing area to obtain the engineering model of the closed killing area.

4. The method for constructing the air-defense missile space-killer zone model and calculating shooting data elements based on the small amount of actual data according to claim 3, wherein the method comprises the following steps: the closed killing area engineering model comprises a killing area low-near interface, a killing area high-near interface, a killing area far interface, a killing area high interface, a killing area low interface, a killing area positive side interface, a killing area negative side interface, a killing area upper front positive interface, a killing area upper front negative interface, a killing area lower front positive interface and a killing area lower front negative interface;

1) establishing a low-near-field spherical equation, namely:

in the formula, P is an air route shortcut; h is the target height; q is a target route angle; h_minIs the low boundary of the killing area; d_sjminMinimum near-bound skew distance for a killing area; s_scjIs a near boundary of a killing area; epsilon_maxThe maximum height angle of the killing area; q. q.s_maxThe maximum route angle is a killer area; s is a killing area interface;

2) correcting the initial low and near sphere by using the find function to obtain a matrix set (S)_scj，P，H)_DGG′D′；

3) Using surf (S)_scj，P，H)_DGG′D′Forming a killing area low and near interface DGG 'D' by a function;

1) establishing a high-near cone equation, namely:

in the formula, H_maxIs the high boundary of the killing area; s_sjIs a near boundary of a killing area;

2) correcting the initial high and near boundary conical surface by using the find function to obtain a matrix group (S)_sj，P，H)_BDD′B′；

3) Invoking surf (S)_sj，P，H)_BDD′B′A function forming killing area high-near interface BDD 'B';

1) establishing a far-bound surface equation, namely:

in the formula, a, b and c are curved surface equation coefficients;S_syrepresenting the far boundary of a killing area;

A non-linear function expression of (a); r is the fitting order; r is less than m; p is a vector formed by polynomial coefficients of the function F; j is 1, …, m;

In the function, a bus (H) of the far boundary of the killing area is linearly fitted_i，S_syi) (ii) a Bus bar (H)_i，S_syi) Around the OH axis of the coordinate system within + -q_maxRotating within the range to obtain an initial far-bound curved surface; 1, …, n;

4) correcting the initial far-bound surface by using a find function to obtain a matrix group (S)_sy，P，H)_EHH′E′；

5) Using surf (S)_sy，P，H)_EHH′E′Function form kill zone remote interface EHH 'E';

1) establishing a high-boundary plane equation, namely:

2) correcting the initial high-boundary plane equation by using a find function to obtain a matrix set (S, P, H)_{HABB′A′H′}；

3) Using surf (S, P, H)_{HABB′A′H′}Function-forming killer region high interface HABB ' a ' H ':

1) establishing a low-boundary plane equation, namely:

2) correcting the initial high-boundary plane equation by using a find function to obtain a matrix set (S, P, H)_GFF′G′；

3) Using surf (S, P, H)_GFF′G′Forming a killing area low interface GFF 'G' by a function;

1) curve of distance bound

Straight line

And a straight line

And (3) stretching into a curved polygon HAE, namely the equation:

determining a characteristic point E of a curved-edge polygon HAE, wherein the method comprises the following steps: in the interpolation interval [ H_min，H_max]Uniformly taking n points and substituting into the far boundary of the killing area

In the function, a function is obtained

Substituting n points into function in sequence

In (1) obtaining

H_kThe height corresponding to the k point;

2) respectively mapping the curved-edge polygons HAE into (n-k +1) -dimensional matrixes S_HAEA (n-k +1) -dimensional matrix P_HAEAnd (n-k +1) -dimensional matrix H_HAEObtaining a matrix set (S)_HAE，P_HAE，H_HAE)；

3) Invoking surf (S)_HAE，P_HAE，H_HAE) Establishing a front side interface of a killing area by a function;

1) curve of distance bound

Straight line

And a straight line

And (3) stretching into a curved polygon H ' A ' E ', namely the equation:

2) respectively mapping the curved edge polygons H ' A ' E ' into (n-k +1) dimensional matrixes S_H′A′E′A (n-k +1) -dimensional matrix P_H′A′E′And (n-k +1) -dimensional matrix H_H′A′E′Obtaining a matrix set (S)_H′A′E′，P_H′A′E′，H_H′A′E′)；

3) Invoking surf (S)_H′A′E′，P_H′A′E′，H_H′A′E′) Establishing a negative side interface of a killing area by a function;

1) plane of maximum route angle

2) mapping a planar polygonal ABCD surface to an n-dimensional matrix S_ABCDN-dimensional matrix P_ABCDAnd n-dimensional matrix H_ABCDObtaining a matrix set (S)_ABCD，P_ABCD，H_ABCD)；

3) Invoking surf (S)_ABCD，P_ABCD，H_ABCD) Obtaining a front positive interface on the killing area by the function;

1) plane of maximum route angle

2) mapping a planar polygon A 'B' C 'D' surface to an n-dimensional matrix S_{A′B′C′D′}N-dimensional matrix P_{A′B′C′D′}And n-dimensional matrix H_{A′B′C′D′}Obtaining a matrix set (S)_{A′B′C′D′}，P_{A′B′C′D′}，H_{A′B′C′D′})；

3) Invoking surf (S)_{A′B′C′D′}，P_{A′B′C′D′}，H_{A′B′C′D′}) Obtaining a front negative interface on the killing area by the function;

1) plane of maximum route angle

wherein point F is the starting point of the far field;

2) mapping spatial polygons CEFGD into a n x 3 n-dimensional matrix S_CEFGDN x 3n dimensional matrix P_CEFGDAnd n x 3n dimensional matrix H_CEFGDObtaining a matrix set (S)_CEFGD，P_CEFGD，H_CEFGD)；

3) Invoking surf (S)_CEFGD，P_CEFGD，H_CEFGD) Obtaining a front interface under the killing area by the function;

1) plane of maximum route angle

wherein, the F' point is the starting point of the far boundary;

2) mapping the spatial polygon C ' E ' F ' G ' D ' into a n-x 3 n-dimensional matrix S_{C′E′F′G′D′}N x 3n dimensional matrix P_{C′E′F′G′D′}And n x 3n dimensional matrix H_{C′E′F′G′D′}Obtaining a matrix set (S)_{C′E′F′G′D′}，P_{C′E′F′G′D′}，H_{C′E′F′G′D′})；

5. The method for constructing the air-defense missile space-killing area model and calculating shooting data base based on the small amount of actual data according to claim 1, wherein the method for calculating the space-killing area model mainly comprises the following steps:

1) establishing a space transmitting area model based on the space killing area model; inputting the air defense missile data into a space launching area model to obtain space launching area parameters;

2) resolving the space killing area model to obtain a horizontal killing area and a transmitting area under the target height;

3) resolving the space killing area model to obtain a vertical killing area and a transmitting area under the short-cut of the route where the target is located;

4) data Cursor function is used for extracting encounter point and emission point Data in a horizontal killing area, a horizontal emission area, a vertical killing area and a vertical emission area to obtain emission residual time t_{When the emission is left}And time t of target flying out of emitting area_{Time of flight}And completing shooting data element calculation.

6. The method for constructing the air-defense missile space-killer zone model and shooting data solution based on the small amount of actual data according to claim 1 or 5, wherein the method comprises the following steps: the firing data includes encounter point slope, encounter point height, shot time, time-to-flight, shot distance and shot distance.

7. The method for constructing the air-defense missile space-kill-zone model and calculating shooting data elements based on the small amount of actual data according to claim 1, wherein the method for obtaining the parameters of the space launching zone comprises the following main steps:

1) establishing a space transmitting area model, namely:

S_f＝S_s+V_t·t_D(12)

in the formula, V_tIs the target speed; t is t_DThe time of encountering the air defense missile with the target; d_fIs the encounter point slope distance; s_fIs an emitter region interface;

time t of air defense missile encountering with target_DAs follows:

2) time t for encountering air defense missile with target_{D practice}And encounter point slope distance D_{s actual}Input into equation (14) to obtain time calculation coefficient b₁Time calculation coefficient b₂Time calculation coefficient b₃And calculating the time t of the air-defense missile encountering the target_D；

3) Time t for encountering air defense missile with target_DAnd inputting the parameters into a space transmitting area model to obtain space transmitting area parameters.

8. The method for constructing the air-defense missile space-killing area model and shooting data element calculation based on the small amount of actual data according to claim 1, wherein the step of calculating the space-killing area model to obtain the horizontal killing area and the launching area under the target height comprises the following steps:

1) determining the height interval delta H of a cutting horizontal killing area of the space killing area;

2) by interpolation interval [ H_min，H_max]Within the range of any height H as a reference and in the height interval

Internally intercepting a horizontal killing area and a transmitting area;

3) and extracting encounter point and emission point Data of the horizontal killing area and the horizontal emission area on the height H by using a Data Cursor function of Malab.

9. The method for constructing the air-defense missile space-killing-area model and calculating shooting data base based on the small amount of actual data according to claim 1, wherein the step of calculating the space-killing-area model to obtain the vertical killing area and the launching area under the route shortcut where the target is located is as follows:

1) determining an airway shortcut interval delta P for cutting the emitting area of the vertical killing area by the emitting area of the space killing area;

2) taking a short-cut range of the air route [ -P [ ]_max，P_max]Taking any route shortcut P in the range as a reference, and taking the route shortcut P as a reference

Internally intercepting a vertical killing area and a transmitting area on the route shortcut;

3) and extracting encounter points and emission point Data of the vertical killing area and the vertical emission area on the airway shortcut P by using a Data Cursor function of Malab.

10. The method for constructing the air-defense missile space-killer zone model and calculating shooting data elements based on the small amount of actual data according to claim 1, wherein the firing residue is as follows:

wherein s represents the s coordinate of the target in the shooting coordinate system O-SPH; d_FYA far-bound slant range of the emitting area; d_FJThe near-boundary slant distance of the emission region; s_fyA far boundary of the emission region; s_fjIs the near boundary of the emission region; t is t₀Time of the target at the current position;

the target departure launch time is as follows:

t_{time of flight}＝t_FJ-t_FY(16)

in the formula, v is a target speed.