CN111191359B - Method for constructing space killer zone model of air-defense missile and calculating shooting data - Google Patents

Method for constructing space killer zone model of air-defense missile and calculating shooting data Download PDF

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CN111191359B
CN111191359B CN201911351195.3A CN201911351195A CN111191359B CN 111191359 B CN111191359 B CN 111191359B CN 201911351195 A CN201911351195 A CN 201911351195A CN 111191359 B CN111191359 B CN 111191359B
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killing
killing area
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黄隽
刘方
彭英武
邹强
李晓宝
肖金石
薛冰
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Naval University of Engineering PLA
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Abstract

The invention discloses a method for constructing an air-defense missile space killer zone model and calculating shooting data elements, which mainly comprises the following steps: 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 space killer zone model of air-defense missile and calculating shooting 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 areamaxAnd a low boundary H of the killing areaminAnd killing zone far boundary SsyNear boundary S of killing zonesjMaximum height angle epsilon of killing areamaxMaximum route angle q of killer areamaxMaximum airway shortcut PmaxTime t of encounter of air defense missile and targetD practiceAnd encounter point slope distance Ds 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:
Figure GDA0002908919370000021
wherein P is the air route shortcut. H is the target height. And q is the target route angle. HminIs the low boundary of the killing area. DsjminThe minimum near-bound slant distance is a killing area. SscjIs the near boundary of the killing area. EpsilonmaxThe maximum elevation angle of the killing area. q. q.smaxThe maximum route angle of the killing area. And S is a killing area interface. HJIs 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:
Figure GDA0002908919370000031
in the formula, HmaxIs the high boundary of the killing area. SsjIs 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:
Figure GDA0002908919370000032
in the formula, a, b and c are curved surface equation coefficients. SsyIndicating a far boundary of the kill zone.
2) The data (H) of m groups of air defense missilesj,Ssyj) Input into p ═ polyfit (H, S)syR) function, and fitting out far boundary of killing area by polynomial fitting method
Figure GDA0002908919370000033
The non-linear function expression of (2). r is the fitting order. r is<And m is selected. p is a vector formed by polynomial coefficients of the function F. j is 1, …, m. (H)j,Ssyj) And representing the jth air defense missile data.
3) In the interpolation interval [ Hmin,Hmax]Uniformly taking n points and substituting into the far boundary of the killing area
Figure GDA0002908919370000034
In the function, a bus (H) of the far boundary of the killing area is linearly fittedi,Ssyi). Bus bar (H)i,Ssyi) Around the OH axis of the coordinate system within + -qmaxRotating within the range to obtain an initial far-bound curved surface. i is 1, …, n. (H)i,Ssyi) 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:
Figure GDA0002908919370000041
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:
Figure GDA0002908919370000042
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
Figure GDA0002908919370000043
Straight line
Figure GDA0002908919370000044
And a straight line
Figure GDA0002908919370000045
And (3) stretching into a curved polygon HAE, namely the equation:
Figure GDA0002908919370000046
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 [ Hmin,Hmax]Uniformly taking n points and substituting into the far boundary of the killing area
Figure GDA0002908919370000047
In the function, a function is obtained
Figure GDA0002908919370000048
Substituting n points into function in sequence
Figure GDA0002908919370000049
In (1) obtaining
Figure GDA0002908919370000051
The k point corresponding to the time so as to obtain the coordinate of the E point
Figure GDA0002908919370000052
HkThe height corresponding to the k-th point.
2) Respectively mapping the curved-edge polygons HAE into (n-k +1) -dimensional matrixes SHAEA (n-k +1) -dimensional matrix PHAEAnd (n-k +1) -dimensional matrix HHAEObtaining a matrix set (S)HAE,PHAE,HHAE)。
3) Invoking surf (S)HAE,PHAE,HHAE) 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
Figure GDA0002908919370000053
Straight line
Figure GDA0002908919370000054
And a straight line
Figure GDA0002908919370000055
And (3) stretching into a curved polygon H ' A ' E ', namely the equation:
Figure GDA0002908919370000056
2) respectively mapping the curved edge polygons H ' A ' E ' into (n-k +1) dimensional matrixes SH′A′E′A (n-k +1) -dimensional matrix PH′A′E′And (n-k +1) -dimensional matrix HH′A′E′Obtaining a matrix set (S)H′A′E′,PH′A′E′,HH′A′E′)。
3) Invoking surf (S)H′A′E′,PH′A′E′,HH′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
Figure GDA0002908919370000057
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:
Figure GDA0002908919370000058
2) mapping a planar polygonal ABCD surface to an n-dimensional matrix SABCDN-dimensional matrix PABCDAnd n-dimensional matrix HABCDObtaining a matrix set (S)ABCD,PABCD,HABCD)。
3) Invoking surf (S)ABCD,PABCD,HABCD) 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
Figure GDA0002908919370000061
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:
Figure GDA0002908919370000062
2) mapping a planar polygon A 'B' C 'D' surface to an n-dimensional matrix SA′B′C′D′N-dimensional matrix PA′B′C′D′And n-dimensional matrix HA′B′C′D′Obtaining a matrix set (S)A′B′C′D′,PA′B′C′D′,HA′B′C′D′)。
3) Invoking surf (S)A′B′C′D′,PA′B′C′D′,HA′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) will be provided withMaximum angle plane of flight path
Figure GDA0002908919370000063
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:
Figure GDA0002908919370000064
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 SCEFGDN x 3n dimensional matrix PCEFGDAnd n x 3n dimensional matrix HCEFGDObtaining a matrix set (S)CEFGD,PCEFGD,HCEFGD)。
3) Invoking surf (S)CEFGD,PCEFGD,HCEFGD) 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
Figure GDA0002908919370000065
The low interface, the front side interface and the low-near interface are flared into a spatial polygon C ' E ' F ' G ' D ', namely:
Figure GDA0002908919370000071
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 SC′E′F′G′D′N x 3n dimensional matrix PC′E′F′G′D′And n x 3n dimensional matrix HC′E′F′G′D′Obtaining a matrix set (S)C′E′F′G′D′,PC′E′F′G′D′,HC′E′F′G′D′)。
3) Invoking surf (S)C′E′F′G′D′,PC′E′F′G′D′,HC′E′F′G′D′) Function obtaining killerThe lower front negative interface of the lesion.
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:
Sf＝Ss+Vt·tD (12)
Figure GDA0002908919370000072
in the formula, VtIs the target speed. t is tDThe time of the air defense missile encountering the target. DfTo encounter the point skew. SfIs an emitter interface.
Time t of air defense missile encountering with targetDAs follows:
Figure GDA0002908919370000073
3.1.2) time t of encountering air defense missile with targetD practiceAnd encounter point slope distance Ds actualInput 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 targetD。
3.1.3) time t of encountering air defense missile with targetDAnd 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,Hmax]Within the range of any height H as a reference and in the height interval
Figure GDA0002908919370000081
Figure GDA0002908919370000082
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,Pmax]Taking any route shortcut P in the range as a reference, and taking the route shortcut P as a reference
Figure GDA0002908919370000083
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 tWhen the emission is leftAnd time t of target flying out of emitting areaTime of flightAnd completing shooting data element calculation. The shooting data includes a wordMeeting point slope distance, meeting point height, shot time, departure time, far boundary of the launch region and near boundary of the launch region.
The emission remains as follows:
Figure GDA0002908919370000084
where s denotes the s-coordinate of the target in the firing coordinate system O-SPH. DFYIs the far bound slant distance of the emitting area. DFJThe near-bound slant range of the emitting area. SfyFar bound the emission area. SfjThe 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:
ttime of flight＝tFJ-tFY (16)
Wherein the time t when the target reaches the near boundary of the emission regionFJAs follows:
Figure GDA0002908919370000085
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 areamaxAnd a low boundary H of the killing areaminAnd killing zone far boundary SsyNear boundary S of killing zonesjMaximum height angle epsilon of killing areamaxMaximum route angle q of killer areamaxMaximum airway shortcut PmaxTime t of encounter of air defense missile and targetD practiceAnd encounter point slope distance Ds 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.
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; o isThe H 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 airwaymaxIn the vertical plane, the shortcuts of the positive side surface and the negative side surface of the air route are plus or minus P respectivelymaxThe vertical plane of (a).
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:
Figure GDA0002908919370000101
wherein P is the air route shortcut. H is the target height. And q is the target route angle. HminIs the low boundary of the killing area. DsjminThe minimum near-bound slant distance is a killing area. SscjIs the near boundary of the killing area. EpsilonmaxThe maximum elevation angle of the killing area. q. q.smaxThe maximum route angle of the killing area. And S is a killing area interface. DmaxThe 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′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:
Figure GDA0002908919370000111
in the formula, HmaxIs the high boundary of the killing area. SsjIs 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′。
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:
Figure GDA0002908919370000112
in the formula, a, b and c are curved surface equation coefficients. SsyIndicating a far boundary of the kill zone.
2) The data (H) of m groups of air defense missilesj,Ssyj) Input into p ═ polyfit (H, S)syR) function, and fitting out far boundary of killing area by polynomial fitting method
Figure GDA0002908919370000113
The non-linear function expression of (2). r is the fitting order. r is<And m is selected. p is a vector formed by polynomial coefficients of the function F. j is 1, …, m. r is 2.
3) In the interpolation interval [ Hmin,Hmax]Uniformly taking n points and substituting into the far boundary of the killing area
Figure GDA0002908919370000114
In the function, a bus (H) of the far boundary of the killing area is linearly fittedi,Ssyi). Bus bar (H)i,Ssyi) Around the OH axis of the coordinate system within + -qmaxRotating within the range to obtain an initial far-bound curved surface. i ═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′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:
Figure GDA0002908919370000115
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:
Figure GDA0002908919370000121
the upper and lower boundaries of the killing area are Z ═ Hmax、Z＝HminIs 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′。
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
Figure GDA0002908919370000122
Straight line
Figure GDA0002908919370000123
And a straight line
Figure GDA0002908919370000124
And (3) stretching into a curved polygon HAE, namely the equation:
Figure GDA0002908919370000125
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
Figure GDA0002908919370000126
In the interpolation interval [ Hmin,Hmax]Uniformly taking n points and substituting into the far boundary of the killing area
Figure GDA0002908919370000127
In the function, a function is obtained
Figure GDA0002908919370000128
Substituting n points into function in sequence
Figure GDA0002908919370000129
In (1) obtaining
Figure GDA00029089193700001210
The k point corresponding to the time so as to obtain the coordinate of the E point
Figure GDA00029089193700001211
HkThe height corresponding to the k-th point.
2) Respectively mapping the curved-edge polygons HAE into (n-k +1) -dimensional matrixes SHAEA (n-k +1) -dimensional matrix PHAEAnd (n-k)+1) dimensional matrix HHAEObtaining a matrix set (S)HAE,PHAE,HHAE)。
3) Invoking surf (S)HAE,PHAE,HHAE) The function establishes the killing zone positive side interface.
The algorithm is as follows:
I) using round () function pair Ssyi(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 SHAEAssigning values to the 1-qi columns of the ith row;
SHAE(i,1:qi)＝linspace(min(x6),Ssyi,qi))；
III) reacting SHAEThe remaining (n-k +1-qi) portion of the ith row of (a) is set to a non-integer Nan;
IV)Hi(i ═ k, k +1, …, n) becomes the ith row vector;
V)Pmaxbecomes a matrix SHAE。
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.
g) The main steps for determining the negative side interface of the killing area are as follows:
1) curve of distance bound
Figure GDA0002908919370000131
Straight line
Figure GDA0002908919370000132
And a straight line
Figure GDA0002908919370000133
And (3) stretching into a curved polygon H ' A ' E ', namely the equation:
Figure GDA0002908919370000141
2) respectively mapping the curved edge polygons H ' A ' E ' into (n-k +1) dimensional matrixes SH′A′E′A (n-k +1) -dimensional matrix PH′A′E′And (n-k +1) -dimensional matrix HH′A′E′Obtaining a matrix set (S)H′A′E′,PH′A′E′,HH′A′E′)。
3) Invoking surf (S)H′A′E′,PH′A′E′,HH′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
Figure GDA0002908919370000142
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:
Figure GDA0002908919370000143
2) mapping a planar polygonal ABCD surface to an n-dimensional matrix SABCDN-dimensional matrix PABCDAnd n-dimensional matrix HABCDObtaining a matrix set (S)ABCD,PABCD,HABCD)。
3) Invoking surf (S)ABCD,PABCD,HABCD) The function yields the front positive interface on the kill zone.
The algorithm is as follows:
I)SABCD1 st line A to B, SABCDN-dimensional linear interpolation of S coordinates of the n-th line C to D;
II)SABCDi-2 to (n-1) actions
SABCD(:,i)＝linspace(SABCD(1,i),SABCD(1000,i),n)；
III)PABCD1 st line A to B, PABCDThe nth behavior of C to D is an n-dimensional linear interpolation of the P coordinates;
IV)PABCDi-2 to (n-1) actions
PABCD(:,i)＝linspace(PABCD(1,i),PABCD(1000,i),n)；
V)HABCD1 st line A to B, HABCDThe nth behavior of C to D is an n-dimensional linear interpolation of the P coordinates;
VI)HABCDi-2 to (n-1) actions
HABCD(:,i)＝linspace(HABCD(1,i),HABCD(1000,i),n)。
i) The main steps for determining the front negative interface on the killing area are as follows:
1) plane of maximum route angle
Figure GDA0002908919370000151
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:
Figure GDA0002908919370000152
2) mapping a planar polygon A 'B' C 'D' surface to an n-dimensional matrix SA′B′C′D′N-dimensional matrix PA′B′C′D′And n-dimensional matrix HA′B′C′D′Obtaining a matrix set (S)A′B′C′D′,PA′B′C′D′,HA′B′C′D′)。
3) Invoking surf (S)A′B′C′D′,PA′B′C′D′,HA′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
Figure GDA0002908919370000153
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:
Figure GDA0002908919370000154
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 SCEFGDN x 3n dimensional matrix PCEFGDAnd n x 3n dimensional matrix HCEFGDObtaining a matrix set (S)CEFGD,PCEFGD,HCEFGD)。
3) Invoking surf (S)CEFGD,PCEFGD,HCEFGD) The function yields the front positive interface under the kill zone.
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) respectivelyCEF,PCEF,HCEF)、(SCDF,PCDF,HCDF)/(SDFG,PDFG,HDFG)；
II) constructing a new set S of matricesCEFGD＝[SCEF,SCDF,SDFG]，PCEFGD＝[PCEF,PCDF,PDFG]，HCEFGD＝[HCEF,HCDF,HDFG]。
k) The main steps for determining the front negative interface under the killing area are as follows:
1) plane of maximum route angle
Figure GDA0002908919370000161
The low interface, the front side interface and the low-near interface are flared into a spatial polygon C ' E ' F ' G ' D ', namely:
Figure GDA0002908919370000162
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 SC′E′F′G′D′N x 3n dimensional matrix PC′E′F′G′D′And n x 3n dimensional matrix HC′E′F′G′D′Obtaining a matrix set (S)C′E′F′G′D′,PC′E′F′G′D′,HC′E′F′G′D′)。
3) Invoking surf (S)C′E′F′G′D′,PC′E′F′G′D′,HC′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.
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 usedmin,Hmax]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.
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:
Sf＝Ss+Vt·tD (12)
Figure GDA0002908919370000171
in the formula, VtIs the target speed. t is tDThe time of the air defense missile encountering the target. DfTo encounter the point skew. SfIs an emitter interface.
Time t of air defense missile encountering with targetDAs follows:
Figure GDA0002908919370000172
3.1.2) time t of encountering air defense missile with targetD practiceAnd encounter point slope distance Ds actualInput into equation (14) to obtain time calculation coefficient b1When in useInter-calculating coefficient b2Time calculation coefficient b3And calculating the time t of the air-defense missile encountering the targetD。
3.1.3) time t of encountering air defense missile with targetDAnd 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.
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 usedmax,Pmax]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.
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,Hmax]Within the range of any height H as a reference and in the height interval
Figure GDA0002908919370000173
Figure GDA0002908919370000174
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,Pmax]Taking any route shortcut P in the range as a reference, and taking the route shortcut P as a reference
Figure GDA0002908919370000181
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 the Data Cursor function of Malab to obtain the transmitting residual time tWhen the emission is leftAnd time t of target flying out of emitting areaTime of flightAnd 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:
Figure GDA0002908919370000182
where s denotes the s-coordinate of the target in the firing coordinate system O-SPH. DFYIs the far bound slant distance of the emitting area. DFJThe near-bound slant range of the emitting area. SfyFar bound the emission area. SfjThe 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:
ttime of flight＝tFJ-tFY (16)
Wherein the time t when the target reaches the near boundary of the emission regionFJAs follows:
Figure GDA0002908919370000183
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
Figure GDA0002908919370000191
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:
Figure GDA0002908919370000192
b) high and near interface
Killer zone high-near boundary BDD 'B' equation:
Figure GDA0002908919370000193
c) remote interface
Killing zone remote boundary EHH 'E' equation:
Figure GDA0002908919370000201
d) high low interface
Firstly, a killing region high interface HABB ' A ' H ' equation:
Figure GDA0002908919370000202
(ii) killing zone low interface GFF 'G' equation:
Figure GDA0002908919370000203
e) positive and negative side interface
(ii) Positive side interface
Curved-edge polygon HAE equation:
Figure GDA0002908919370000204
negative side interface
Curved polygon H ' A ' E ' equation:
Figure GDA0002908919370000205
f) front positive and negative surfaces
Upper front face
Trapezoidal ABCD equation:
Figure GDA0002908919370000211
top negative
Trapezoidal A 'B' C 'D' equation:
Figure GDA0002908919370000212
g) lower front positive and negative surface
Lower front
Spatial polygon CEFGD equation:
Figure GDA0002908919370000213
front negative
The spatial polygon C ' E ' F ' G ' D ' equation:
Figure GDA0002908919370000221
2.2) emission area
21 sets of data (t) were extracted from table 1 available ExcelD practice，DActual fact of killing) Fitting t by a polyfit () functionDHeel DKilling and killingBy a polynomial of the functional relationship (b), b can be obtained1，b2，b3；
Figure GDA0002908919370000225
Substituting into the desired space killing area (S)Killing and killing,PKilling and killing,HKilling and killing) Obtaining parameters of the killing area
Figure GDA0002908919370000222
Corresponding tDFrom (12) the spatial emission region (S) can be derivedLaunching,PLaunching,HLaunching) 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:
Figure GDA0002908919370000223
Figure GDA0002908919370000224
b) flying-out time:
ttime of flight＝tFJ-tFY＝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) Sfy(km) Sfj(km) TWhen the emission is left(s) TTime 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 region 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 the Data Cursor technology of Matlab. 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 Sfy＝102.8km，Sfj＝13.86km，TWhen the emission is left＝57.33s，TTime 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 Sfy＝99.88km，Sfj＝7.39km，TWhen the emission is left＝67.07s，TTime of flight＝308.30s。

Claims (8)

1. The method for constructing the air-defense missile space killer zone model and calculating shooting data elements is characterized by comprising the following steps of:
1) acquiring air defense missile data;
2) establishing a space killer area model based on the air defense missile data;
the steps for establishing the space killing area model are as follows:
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 a killer area analytic geometric mathematical model to obtain a closed killer area engineering model;
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 steps for determining the DGG 'D' of the low and near interface of the killing area are as follows:
1) establishing a low-near-field spherical equation, namely:
Figure FDA0002898216850000011
in the formula, P is an air route shortcut; h is the target height; q is a target route angle; hminIs the low boundary of the killing area; dsjminMinimum near-bound skew distance for a killing area; sscjIs a near boundary of a killing area; epsilonmaxThe maximum height angle of the killing area; q. q.smaxThe maximum route angle is a killer area; s is a killing area interface;
2) correcting the 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;
b) the steps for determining the high-near interface BDD 'B' of the killing area are as follows:
1) establishing a high-near cone equation, namely:
Figure FDA0002898216850000012
in the formula, HmaxIs the high boundary of the killing area; ssjIs a near boundary of a killing area;
2) correcting the high and near cone 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';
c) the steps for determining the far boundary EHH 'E' of the kill zone are as follows:
1) establishing a far-bound surface equation, namely:
Figure FDA0002898216850000021
in the formula, a, b and c are curved surface equation coefficients; ssyRepresenting the far boundary of a killing area; pmaxRepresenting a maximum airway shortcut;
2) the data (H) of m groups of air defense missilesj,Ssyj) Input into p ═ polyfit (H, S)syR) function, and fitting out far boundary of killing area by polynomial fitting method
Figure FDA0002898216850000022
A non-linear function expression of (a); r is the fitting order; r is<m; p is a vector formed by polynomial coefficients of the function F; j is 1, …, m;
3) in the interpolation interval [ Hmin,Hmax]Uniformly taking n points and substituting into the far boundary of the killing area
Figure FDA0002898216850000023
In the function, a bus (H) of the far boundary of the killing area is linearly fittedi,Ssyi) (ii) a Bus bar (H)i,Ssyi) Around the OH axis of the coordinate system within + -qmaxRotating within the range to obtain a far curved surface; 1, …, n; in a shooting coordinate system O-SPH, an air defense missile system guidance radar or a launching device is taken as an origin of coordinates; the OS axis is in the horizontal plane passing through the O point and points 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; determining the OP axis according to the right-hand rule;
4) correcting the 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';
d) the steps for determining the high interface HABB ' A ' H ' of the killing area are as follows:
1) establishing a high-boundary plane equation, namely:
Figure FDA0002898216850000024
2) correcting the high boundary plane equation by using find function to obtain a matrix set (S, P, H)HABB′A′H′；
3) Using surf (S, P, H)HABB′A′H′Forming a killing area high interface HABB ' A ' H ' by a function;
e) the procedure for determining the kill zone low interface GFF 'G' is as follows:
1) establishing a low-boundary plane equation, namely:
Figure FDA0002898216850000031
2) correcting the low boundary plane equation by using the 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;
f) the steps for determining the boundary surface of the front side of the killing area are as follows:
1) curve of distance bound
Figure FDA0002898216850000032
Straight line
Figure FDA0002898216850000033
And a straight line
Figure FDA0002898216850000034
And (3) stretching into a curved polygon HAE, namely the equation:
Figure FDA0002898216850000035
determining a characteristic point E of a curved-edge polygon HAE, wherein the method comprises the following steps: in the interpolation interval [ Hmin,Hmax]Uniformly taking n points and substituting into the far boundary of the killing area
Figure FDA0002898216850000036
In the function, a function is obtained
Figure FDA0002898216850000037
Substituting n points into function in sequence
Figure FDA0002898216850000038
In (1) obtaining
Figure FDA0002898216850000039
The k point corresponding to the time so as to obtain the coordinate of the E point
Figure FDA00028982168500000310
HkThe height corresponding to the k point;
2) respectively mapping the curved-edge polygons HAE into (n-k +1) -dimensional matrixes SHAEA (n-k +1) -dimensional matrix PHAEAnd (n-k +1) -dimensional matrix HHAEObtaining a matrix set (S)HAE,PHAE,HHAE)；
3) Invoking surf (S)HAE,PHAE,HHAE) Function establishing methodA lesion front side interface;
g) the steps for determining the negative side interface of the killing area are as follows:
1) curve of distance bound
Figure FDA00028982168500000311
Straight line
Figure FDA00028982168500000312
And a straight line
Figure FDA00028982168500000313
And (3) stretching into a curved polygon H ' A ' E ', namely the equation:
Figure FDA0002898216850000041
2) respectively mapping the curved edge polygons H ' A ' E ' into (n-k +1) dimensional matrixes SH′A′E′A (n-k +1) -dimensional matrix PH′A′E′And (n-k +1) -dimensional matrix HH′A′E′Obtaining a matrix set (S)H′A′E′,PH′A′E′,HH′A′E′)；
3) Invoking surf (S)H′A′E′,PH′A′E′,HH′A′E′) Establishing a negative side interface of a killing area by a function;
h) the steps for determining the front positive interface on the killing area are as follows:
1) plane of maximum route angle
Figure FDA0002898216850000042
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:
Figure FDA0002898216850000043
2) mapping a planar polygonal ABCD surface to an n-dimensional matrix SABCDN-dimensional matrix PABCDAnd n-dimensional matrix HABCDObtaining a matrix set (S)ABCD,PABCD,HABCD)；
3) Invoking surf (S)ABCD,PABCD,HABCD) Obtaining a front positive interface on the killing area by the function;
i) the steps for determining the front negative interface on the killing area are as follows:
1) plane of maximum route angle
Figure FDA0002898216850000045
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:
Figure FDA0002898216850000044
2) mapping a planar polygon A 'B' C 'D' surface to an n-dimensional matrix SA′B′C′D′N-dimensional matrix PA′B′C′D′And n-dimensional matrix HA′B′C′D′Obtaining a matrix set (S)A′B′C′D′,PA′B′C′D′,HA′B′C′D′)；
3) Invoking surf (S)A′B′C′D′,PA′B′C′D′,HA′B′C′D′) Obtaining a front negative interface on the killing area by the function;
j) the steps for determining the front positive interface under the killing area are as follows:
1) plane of maximum route angle
Figure FDA0002898216850000051
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:
Figure FDA0002898216850000052
wherein point F is the starting point of the far field;
2) will spacePolygonal CEFGD mapping to n x 3n dimensional matrix SCEFGDN x 3n dimensional matrix PCEFGDAnd n x 3n dimensional matrix HCEFGDObtaining a matrix set (S)CEFGD,PCEFGD,HCEFGD)；
3) Invoking surf (S)CEFGD,PCEFGD,HCEFGD) Obtaining a front interface under the killing area by the function;
k) the steps for determining the front negative interface under the killing area are as follows:
1) plane of maximum route angle
Figure FDA0002898216850000053
The low interface, the front side interface and the low-near interface are flared into a spatial polygon C ' E ' F ' G ' D ', namely:
Figure FDA0002898216850000054
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 SC′E′F′G′D′N x 3n dimensional matrix PC′E′F′G′D′And n x 3n dimensional matrix HC′E′F′G′D′Obtaining a matrix set (S)C′E′F′G′D′,PC′E′F′G′D′,HC′E′F′G′D′)；
3) Invoking surf (S)C′E′F′G′D′,PC′E′F′G′D′,HC′E′F′G′D′) Obtaining a front negative interface under the killing area by the function;
3) and resolving the space killing area model to obtain shooting data.
2. The airdefense missile space-killing area model building and shooting data solving method according to claim 1, wherein the airdefense missile data comprises a killing area high bound HmaxAnd a low boundary H of the killing areaminAnd killing zone far boundary SsyNear boundary S of killing zonesjMaximum height angle epsilon of killing areamaxMaximum route angle of killing areaqmaxMaximum airway shortcut PmaxTime t of encounter of air defense missile and targetD practiceAnd encounter point slope distance Ds actual。
3. The airdefense missile space-killing-zone model building and shooting data solving method according to claim 1, wherein the step of solving the space-killing-zone model is as follows:
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 tWhen the emission is leftAnd time t of target flying out of emitting areaTime of flightAnd completing shooting data element calculation.
4. The airdefense missile space-killing zone model building and shooting data element solving method as claimed in claim 1 or 3, 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.
5. The air-defense missile space-kill zone model construction and shooting data element calculation method according to claim 3, characterized in that the step of obtaining space launching zone parameters is as follows:
1) establishing a space transmitting area model, namely:
Sf＝Ss+Vt·tD (12)
Figure FDA0002898216850000061
in the formula, VtIs the target speed; t is tDThe time of encountering the air defense missile with the target; dfIs the encounter point slope distance; sfIs an emitter region interface;
time t of air defense missile encountering with targetDAs follows:
Figure FDA0002898216850000062
2) time t for encountering air defense missile with targetD practiceAnd encounter point slope distance Ds actualInput 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 targetD；
3) Time t for encountering air defense missile with targetDAnd inputting the parameters into a space transmitting area model to obtain space transmitting area parameters.
6. The airdefense missile space-killing-zone model building and shooting data solving method according to claim 1, characterized in that the steps of solving the space-killing-zone model to obtain a horizontal killing zone and a launching zone at a target height are as follows:
1) determining the height interval delta H of a cutting horizontal killing area of the space killing area;
2) by interpolation interval [ Hmin,Hmax]Within the range of any height H as a reference and in the height interval
Figure FDA0002898216850000063
Figure FDA0002898216850000071
Internally intercepting a horizontal killing area and a transmitting area; hmaxIs the high boundary of the killing area; hminIs the low boundary of the killing 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.
7. The airdefense missile space-killing-zone model building and shooting data solving method according to claim 1, characterized in that the steps of solving the space-killing-zone model to obtain a vertical killing zone and a launching zone under the route shortcut where the target is located are 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,Pmax]Taking any route shortcut P in the range as a reference, and taking the route shortcut P as a reference
Figure FDA0002898216850000072
Internally intercepting a vertical killing area and a transmitting area on the route shortcut; pmaxIs the maximum airway 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.
8. The air-defense missile space-killing area model building and shooting data element solving method according to claim 1, wherein the firing residue is as follows:
Figure FDA0002898216850000073
wherein s represents the s coordinate of the target in the shooting coordinate system O-SPH; dFYA far-bound slant range of the emitting area; dFJThe near-boundary slant distance of the emission region; sfyA far boundary of the emission region; sfjIs the near boundary of the emission region; p is an airway shortcut; h is the height;
the target departure launch time is as follows:
ttime of flight＝tFJ-tFY (16)
Wherein the target arrives at the hairTime t of near bound of shotFJAs follows:
Figure FDA0002898216850000074
in the formula, v is a target speed.
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