CN112417653A - Method for establishing ship-air missile interception model - Google Patents

Method for establishing ship-air missile interception model Download PDF

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CN112417653A
CN112417653A CN202011207742.3A CN202011207742A CN112417653A CN 112417653 A CN112417653 A CN 112417653A CN 202011207742 A CN202011207742 A CN 202011207742A CN 112417653 A CN112417653 A CN 112417653A
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missile
ship
air
naval
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刘方
黄隽
肖玉杰
肖金石
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Naval University of Engineering PLA
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Naval University of Engineering PLA
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Abstract

The invention discloses a ship-air missile interception model establishing method, which comprises the steps of firstly carrying out interception analysis on anti-ship missiles, then carrying out calculation on the killing probability of ship-air missiles and the launching area of the ship-air missiles, then carrying out calculation on the states of a firepower channel and a launching cradle of a ship-air missile weapon system, calculating a ship-air missile service model and calculating the flight trajectory of the ship-air missiles; and finally, evaluating the target hit of the ship-air missile, and calculating the penetration probability of the anti-ship missile on the ship-air missile. The invention finds out main links on the basis of comprehensive analysis, determines evaluation indexes, and establishes a scientific and reasonable ship-air missile interception model, so that the combat effectiveness evaluation method is scientific and systematized. Provides theoretical guidance for the improvement of the ship-air missile weapon system.

Description

Method for establishing ship-air missile interception model
Technical Field
The invention relates to the field of missile weapon system application, in particular to a ship-based air-borne missile interception model establishing method.
Background
The purpose of establishing the ship-air missile interception model is to research the process of fighting and confronting ship-air missiles and anti-ship missiles, and analyze the interception combat effect of the ship-air missiles on the anti-ship missiles and the penetration prevention capability of the anti-ship missiles in the confronting mode. The methods generally adopted for evaluating the combat effectiveness include an analytic method, an index method, a statistical test method, a combat simulation method, an expert evaluation method, a multi-index comprehensive evaluation method and the like.
The analytical method calculates the index value according to an analytical expression for describing the functional relationship between the efficiency index and the given condition, wherein the analytical expression can be established according to a military operational research theory and can also be solved by utilizing an efficiency equation established by a mathematical method. At present, analysis methods for performance evaluation are classified into 9 types, such as an ADC method, an SEA method, a structure evaluation method, an experience hypothesis method, a quantitative scale evaluation method, a stage probability method, a degree analysis method, a fuzzy evaluation method, and an information entropy evaluation method. The analytical method has the advantages of concise and clear formula, easy understanding and simple calculation; the disadvantages are that the consideration is less, and the analytic formula itself is not easy to obtain.
The actual fact of the combat simulation method is that a combat environment is established by a computer, various combat environments and use conditions are given, a combat simulation test is carried out, data about combat progress and results are obtained, and an effectiveness index evaluation value is given after statistical processing. The simulation method is easy to implement, but the evaluation values of various performance indexes are not accurate enough.
Statistical method in the stipulated and accurate simulation environment, carry on the statistical analysis to the system with influence of random factor, through practice, exercise, test obtain a large amount of statistical data in order to assess the method of the performance index. Common statistical methods are parameter estimation, hypothesis testing, regression analysis, correlation analysis, and the like. The statistical method can obtain the evaluation value of the performance index, and can analyze the influence of factors such as combat rules, weapon system performance and the like on the performance index, and the result is more accurate. However, statistical methods require a large amount of weaponry as the material basis for testing, which cannot be implemented until weapons are developed, and the tests are expensive and have long storage times.
The three methods have respective advantages and disadvantages, the simulation method is simple and feasible, but the evaluation value is not accurate enough; the statistical method is costly and time-consuming, so the analytical method is mostly adopted in the battle effectiveness evaluation.
An air-borne missile interception model established by the existing anti-ship missile penetration capability assessment is too simple and lacks antagonism; and the naval-aircraft missile combat effectiveness analysis model is directly used for the anti-ship missile penetration capacity evaluation and is too complicated. Therefore, the research of a reasonable ship-air missile interception model has important significance for the anti-ship missile penetration capability assessment.
Disclosure of Invention
The invention aims to provide a ship-air missile interception model establishing method, integrates the advantages of various models and provides a model with high interception success probability.
In order to solve the technical problems, the invention adopts the technical scheme that:
a warship-air missile weapon system combat effectiveness evaluation method is characterized by comprising the following steps:
1. interception analysis of ship-air missile on anti-ship missile
Assuming that the anti-ship missile flies linearly, a schematic diagram is drawn on a plane where a target ship position and an anti-ship missile flight route are located.
The necessary condition that the ship-air missile system can intercept an incoming anti-ship missile is that the interception point of the ship-air missile on the anti-ship missile must be in the interception area of the ship-air missile, and the requirements are met:
tmy≤tmf1+tmb+tmaformula (1)
tmj≥tmfnOr tmj≥tmfn+tmb+tmaFormula (2)
The formula (1) is a condition to be met by the interception point at a far point of a ship-borne missile defense area.
The formula (2) is a condition which is far from the near point of the interception point of the naval missile.
2. Calculation of ship-air missile killing probability
The single-shot killing probability model of the ship-air missile is as follows:
Figure BDA0002757611120000011
in the formula:
LR is the missile kill radius.
CEP is the circular probability deviation, which can be a function of distance and signal-to-noise ratio S/N in the absence of interference. The expression is as follows:
Figure BDA0002757611120000021
in the formula:
r is the distance when transmitting;
N/S is the inverse of the signal-to-noise ratio.
The killing probability of the ship-air missile in each air firing is as follows:
Pkm＝Rm·Dm·Cm·[1-(1-a·r·ω)s]formula (5)
In equation (5):
Rmguiding the normal working probability of the radar for interception;
Dmdetecting the probability for the target;
Cmthe probability of transmission and conversion of the detection information is obtained;
a is the reliable launching probability of the ship-air missile;
r is the missile reliable flight probability;
omega is the single-shot killing probability of each ship-borne missile to the target;
and S is the number of the air-borne missiles which are fired at each time.
3. Calculation of launching area of naval-aircraft missile
(1) Defining a coordinate system
The system comprises an air-borne missile launching coordinate system and a fleet central coordinate system.
(2) Distance calculation from anti-ship missile to ship-to-aircraft missile
Firstly, calculating position coordinates of a launching ship expressed by longitude and latitude and height according to the relative position of an air-borne missile launching ship in a fleet; and converting the coordinates of the anti-ship missile and the coordinates of the launching ship into coordinates under a fleet central coordinate system, and respectively recording the coordinates as (x)b,yb,zb) And (x)h,yh,zh). The distance from the anti-ship missile to the launching ship of the ship-borne missile is
Figure BDA0002757611120000022
(3) Calculation of stable tracking time of anti-ship missile by using ship-based irradiation radar
The judgment criteria of the radar for stably tracking the target are as follows: the target signal is acquired at least 4 times in 5 consecutive scan periods.
(4) Calculation of response time of ship-air missile system
Response time T of naval air-borne missile systemRThe method is the time required from the beginning of identifying an anti-ship missile by a ship-based detection radar to the completion of launcher distribution and interception decision and finally launching the ship-based missile off the launcher. The calculation is as follows:
TR＝TD+TA+TEformula (7)
In the formula:
TDcompleting the stable tracking time of the anti-ship missile for the ship-air missile radar system;
TAcompleting interception decision time for the naval missile combat command system in a centralized or autonomous mode;
TEthe time of firing data is resolved for fire control.
(5) Calculation of launching area of naval-aircraft missile
1) Transmissible far field
Naval air guided missile can launch far range R1Comprises the following steps:
Figure BDA0002757611120000031
in a special case, when P is 0:
R1＝r1-Vfj·TRformula (9)
2) Need to transmit far field
Suppose that the vessel-air missile is in b1The point meets the anti-ship missile, and the corresponding launching point a'1Calculating the remote range R required to be launched by the ship-air missile according to the distance R2Comprises the following steps:
Figure BDA0002757611120000032
in the formula:
in a special case, when P is 0:
Figure BDA0002757611120000033
3) far field of emission
Naval air guided missile launching distance fmaxShould be R1、R2The smaller of these:
fmax＝min(R1,R2) Formula (12)
4) Emission near bound
Launching near field f of naval air missileminAccording to the killing proximity r3And determining, wherein the calculation formula is as follows:
Figure BDA0002757611120000034
in a special case, when P is 0:
Figure BDA0002757611120000035
4. calculation of states of fire channel and launcher of naval-aircraft missile weapon system
(1) No. k firepower channel state of naval air-borne missile weapon system
Figure BDA0002757611120000036
In the formula:
M_statekfor the k fire channel state, "1" ready, "0" not ready;
t is the current time estimated by the system;
Figure BDA0002757611120000038
the time when the target instruction is received for the k-th fire channel;
Figure BDA0002757611120000039
the time required for the k-th fire channel to be ready (corresponding to the reaction time of the system).
(2) Number L launcher preparation state of naval vessel guided missile weapon system
Figure BDA0002757611120000037
In the formula:
L_stateLfor the launcher status No. L, "1" ready, "0" not ready;
Figure BDA0002757611120000045
the moment when the No. L launcher launches the naval vessel-air missile finally;
Figure BDA0002757611120000046
the transmission interval (corresponding to the transmission frame retransmission time) is transmitted again for the L-th transmission frame.
5. Calculation of service model of anti-ship missile queuing-waiting aircraft-borne missiles
(1) Interception condition for launching ship-air missile
When the anti-ship missile is positioned above a launching area, whether the anti-ship missile launches an air-borne missile to intercept needs to meet two conditions:
1) preparing a fire channel of the naval-aircraft missile weapon system;
2) and preparing a launching cradle of the ship-based missile weapon system.
Namely, it is
Figure BDA0002757611120000041
In the formula:
Flag_serveri,kthe sign of whether the ith anti-ship missile is served by the kth ship and aircraft missile is that '1' can be served and '0' cannot be served;
Flag_HLk,ithe method is characterized in that a mark indicating whether an air defense fire channel aiming at the i-th anti-ship missile on the k-th ship is ready or not is provided, wherein 1 is ready and 0 is not ready;
Flag_FSkand indicating whether the k-th ship launching system is ready, wherein '1' is ready and '0' is not ready.
(2) Aircraft-based missile service determination
When the anti-ship missile is in the launching area and is judged to be Flag _ serveri,kWhen the value is still 0, the anti-ship missile is in a waiting state, and Flag _ wait is seti,kWaiting for the total number of k-th vessel air-borne missile services (with the set variable sum _ wait) 1i,k) Add 1, and sum _ waiti,kIs given to Number _ waiti,kVariable Number _ waiti,kThe meaning of (1) is the serial number of the No. i anti-ship missile waiting for the No. k naval vessel air-borne missile service.
When the anti-ship missile is in the launching area, the Flag _ server is judgedi,kIs 1 and Flag _ waiti,kWhen 1, the Number _ wait is determined according to the first come first serve principlei,kWhether the value of (d) is 1: if the number of the missile is 1, launching an aircraft missile to intercept the anti-aircraft missile, and enabling a variable sum _ waiti,kAnd Number _ waiti,kAnd the sequence numbers of other anti-ship missiles waiting for the service of the k-th naval vessel air-borne missile are respectively reduced by 1; if not, launching the ship-to-ship missile to not intercept the anti-ship missile.
When the anti-ship missile is in the launching area, the Flag _ server is judgedi,kIs 1 and Flag _ waiti,kAnd when the value is 0, launching the ship-to-ship missile to intercept the anti-ship missile.
6. Calculation of flight trajectory of ship-air missile
The guidance and guidance section of the ship-based air missile adopts a proportional guidance mode, namely the following formula is satisfied:
Figure BDA0002757611120000042
in the formula:
k is a proportionality constant and is generally 3-5;
Figure BDA0002757611120000043
the change rate of the deviation angle of the ship-air missile trajectory is obtained;
Figure BDA0002757611120000044
is the angular velocity of rotation of the target line of sight.
The distance from the ship-based air missile to the target is as follows:
Figure BDA0002757611120000051
the trajectory simulation of the ship-air missile can be simplified and processed according to the proportion guidance, and the motion equation of the ship-air missile in the plane is expressed as follows:
Figure BDA0002757611120000052
the course and time of the air-borne missile encountering the anti-ship missile can be expressed as:
Figure BDA0002757611120000053
in the formula:
Ffjthe direction of the anti-ship missile;
Vfjthe speed of the anti-ship missile;
Vjkthe velocity of the vessel-based air-borne missile;
Qfjattack the bulwark angle of the target naval vessel for the anti-ship missile;
TT is the time required for the ship-to-ship missile to meet the anti-ship missile;
c is the course of the ship-air missile when meeting the anti-ship missile;
Sign(Qfj) To take a variable QfjjSign value function (return ± 1).
7. Target evaluation of ship-air missile
(1) Judging whether the ship-air missile meets the target or not;
(2) the judgment and the processing of the ship-air missile hit can be expressed by the formula (22):
Figure BDA0002757611120000054
in the formula:
r is a random number uniformly distributed according to 0-1;
Pkmthe attack probability of the k-th interception of the ship-based missile by the ship-based missile under the condition of no impact interference is obtained.
8. Probability of sudden defense of anti-ship missile to ship-borne missile
The penetration probability of the anti-ship missile to the ship-borne missile can be calculated by adopting a Monte Carlo simulation method.
Figure BDA0002757611120000061
In the formula:
PJD_iis the i-th penetration probability, PJDIs the penetration probability.
Aiming at the problems that an existing naval-aircraft missile interception model established by anti-naval missile penetration capability evaluation is too simple and lacks antagonism, and an analysis model of naval-aircraft missile operational effectiveness is directly used for anti-naval missile penetration capability evaluation and is too complicated, the naval-aircraft missile interception model suitable for anti-naval missile penetration capability evaluation is established, and naval-aircraft missile target-hitting evaluation is carried out through interception analysis of anti-naval missiles, naval-aircraft missile killing probability, naval-aircraft missile launching areas, naval-aircraft missile weapon system fire channels and launching rack states, naval-aircraft missile service models and naval-aircraft missile flight calculation, and naval-aircraft missile target-hitting analysis of the anti-naval missiles to the naval-aircraft missiles under the antagonism condition is realized.
Compared with the prior art, the invention has the advantages that: the traditional analytic modeling method for the ship-air missile interception model has complex links such as processing of killing probability, service probability, launching area and the like, and is not suitable for anti-ship missile penetration capability evaluation. The method finds out main links on the basis of comprehensive analysis, determines evaluation indexes, adopts a method of combining a mathematical analysis model and numerical fitting, and establishes a scientific and reasonable ship-borne missile interception model, so that the anti-ship missile penetration capacity evaluation method is scientific and systematic, the efficiency is high, and the engineering operability is good.
Drawings
FIG. 1 is a schematic diagram of an air-borne missile interception process. SmThe point is the position of the target vessel, AmThe point is that the target naval vessel finds the attacking missile point and distributes time t through the firepower channelmaAnd the response time t of the naval-aircraft missile weapon systemmbThen, launching the naval missile for a flight time tmf1At the interception point Al1Judging whether the anti-ship missile is successfully intercepted or not, tmpJudging whether the interception is successful or not, if the interception is successful, turning fire to attack another anti-ship missile, and if not, continuing to launch the next anti-ship missile for interception until the interception is successful or the anti-ship missile flies out of an air-ship missile weapon system interception area. A. themyThe point is the interception far end of the defense area of the ship-air missile, tmyFor anti-ship missilemFly to AmyTime required for spotting, AfnThe point represents the position of the anti-ship missile when the ship-borne missile is intercepted for the last time, AlnThe point is the last interception point, tmfnFor anti-ship missilefnFly to AlnTime required for spotting, AmjThe point is the interception near end of the defense area of the naval vessel-air missile, tmjFor anti-ship missilefnFly to AmjThe time required for the spot.
FIG. 2 is a schematic diagram of calculation of an air-borne missile launching zone. Anti-ship missile at a0And the point enters the irradiation range of the ship-based radar, and the target is searched for by the sea alarm ring radar at the point. Through the response time T of the naval-aircraft missile weapon systemRFurthest ship-to-air missileCan be at a1Point emission at b1The point meets the anti-ship missile. a is0In order to illuminate the point of maximum line-of-sight of the radar,
Figure BDA0002757611120000062
the maximum action distance of the radar; a is1Is the farthest point, a ', which can be launched by the ship-borne missile'1The aircraft missile needs to launch the farthest point,
Figure BDA0002757611120000063
to emit far range, R2A remote field is required to be transmitted; b1Is the farthest interception point of the ship-borne missile,
Figure BDA0002757611120000064
to kill the distant world; a is2Is the nearest launching point of the ship-based air missile,
Figure BDA0002757611120000065
is the emission near-bound; b2Is the nearest interception point of the ship-borne missile,
Figure BDA0002757611120000066
to kill the near field; p is the anti-ship missile route shortcut; vfjIs the speed of the anti-ship missile, VjkThe ship-to-aircraft missile speed.
FIG. 3 is a Monte Carlo simulation process of anti-ship missile to aircraft missile defense.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and examples, but it should not be construed that the scope of the above-described subject matter is limited to the 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.
The invention discloses a ship-air missile interception model establishing method, which comprises the following steps:
1. interception analysis of ship-air missile on anti-ship missile
Assuming that the anti-ship missile flies linearly, a schematic diagram is drawn on a plane where a target ship position and an anti-ship missile flight route are located.
The necessary condition that the ship-air missile system can intercept an incoming anti-ship missile is that the interception point of the ship-air missile on the anti-ship missile must be in the interception area of the ship-air missile, and the requirements are met:
tmy≤tmf1+tmb+tmaformula (1)
tmj≥tmfnOr tmj≥tmfn+tmb+tmaFormula (2)
The formula (1) is a condition to be met by the interception point at a far point of a ship-borne missile defense area.
The formula (2) is a condition which is far from the near point of the interception point of the naval missile.
2. Calculation of ship-air missile killing probability
The single-shot killing probability model of the ship-air missile is as follows:
Figure BDA0002757611120000071
in the formula:
LR is the missile kill radius.
CEP is the circular probability deviation, which can be a function of distance and signal-to-noise ratio S/N in the absence of interference. The expression is as follows:
Figure BDA0002757611120000072
in the formula:
r is the distance when transmitting;
N/S is the inverse of the signal-to-noise ratio.
The k-th air firing of the ship-air missile has the killing probability of
Pkm＝Rm·Dm·Cm·[1-(1-a·r·ω)s]Formula (5)
In the formula:
Rmguiding the normal working probability of the radar for interception;
Dmdetecting the probability for the target;
Cmthe probability of transmission and conversion of the detection information is obtained;
a is the reliable launching probability of the ship-air missile;
r is the missile reliable flight probability;
omega is the single-shot killing probability of each ship-borne missile to the target;
and S is the number of the flush-launched aircraft missiles.
3. Calculation of launching area of naval-aircraft missile
(1) Defining a coordinate system
Launching a ship-air missile coordinate system: and taking the missile launching point O as the origin of coordinates, taking the vertical upward direction as the y axis, taking the direction perpendicular to the y axis as the x axis, and determining the z axis through a right-hand screw rule. The function of establishing the missile launching coordinate system is to calculate the interception flight process of the missile.
Fleet center coordinate system: taking the geometric center of the fleet as the origin of coordinates and the vertical upward direction as yuAxis pointing in the north direction yuAxis, zuThe axis is determined by the right-hand screw rule. The function of establishing the fleet central coordinate system is to calculate the relative position and distance of the anti-ship missile.
(2) Distance calculation from anti-ship missile to ship-to-aircraft missile
Firstly, calculating position coordinates of a launching ship expressed by longitude and latitude and height according to the relative position of an air-borne missile launching ship in a fleet; and converting the coordinates of the anti-ship missile and the coordinates of the launching ship into coordinates under a fleet central coordinate system, and respectively recording the coordinates as (x)b,yb,zb) And (x)h,yh,zh). The distance from the anti-ship missile to the launching ship of the ship-borne missile is
Figure BDA0002757611120000081
(3) Calculation of stable tracking time of anti-ship missile by using ship-based irradiation radar
The ship-air missile radar system is used for detecting and tracking the anti-ship missiles immediately after the fleet detection radar accurately identifies the target. The judgment criteria of the radar for stably tracking the target are as follows: the target signal is acquired at least 4 times in 5 consecutive scan periods.
(4) Calculation of response time of ship-air missile system
Response time T of naval air-borne missile systemRThe method is the time required from the beginning of identifying an anti-ship missile by a ship-based detection radar to the completion of launcher distribution and interception decision and finally launching the ship-based missile off the launcher.
The ship-air missile weapon system needs to complete the following work within the reaction time: processing the received target information; controlling a tracking device to track the tracking device; commanding (operating) personnel or selecting a target by a weapon system; preparing shooting data; carrying out threat sequencing on the targets; assigning a target to a transmit channel; the seeker tunes or the launcher aligns the launching direction; press a launch button, etc.
The response time of the naval-vessel missile weapon system is a random quantity, is related to the composition of the weapon system, the degree of automation, the delay determined by operators and the like, and is calculated as follows:
TR＝TD+TA+TEformula (7)
In the formula:
TDthe time for stably tracking the anti-ship missile is finished for the ship-to-aircraft missile radar system;
TAcompleting interception decision time for the naval missile combat command system in a centralized or autonomous mode;
TEthe time of firing data is resolved for fire control.
(5) Calculation of launching area of naval-aircraft missile
The launching area of the naval vessel missile is determined by the following processes:
1) the radar irradiates the maximum action distance r by a ship-borne radar1Determined transmissible far field
The far-range R1 which can be launched by the naval vessel missile is as follows:
Figure BDA0002757611120000082
in a special case, when P is 0:
R1＝r1-Vfj·TRformula (9)
2) Need to transmit far field
Suppose that the vessel-air missile is in b1The point meets the anti-ship missile, and the corresponding launching point a'1Calculating the remote range R required to be launched by the ship-air missile according to the distance R2Comprises the following steps:
Figure BDA0002757611120000083
in the formula:
in a special case, when P is 0:
Figure BDA0002757611120000084
3) naval air guided missile launching distance fmax
Naval air guided missile launching distance fmaxShould be R1、R2The smaller of these:
fmax＝min(R1,R2) Formula (12)
4) Launching near field f of naval air missilemin
Launching near field f of naval air missileminAccording to the killing proximity r3And determining, wherein the calculation formula is as follows:
Figure BDA0002757611120000091
in a special case, when P is 0:
Figure BDA0002757611120000092
4. calculation of states of fire channel and launcher of naval-aircraft missile weapon system
(1) No. k firepower channel state of naval air-borne missile weapon system
Figure BDA0002757611120000093
In the formula:
M_statekfor the k fire channel state, "1" ready, "0" not ready;
t is the current time estimated by the system;
Figure BDA0002757611120000096
the time when the target instruction is received for the k-th fire channel;
Figure BDA0002757611120000097
the time required for the k-th fire channel to be ready (corresponding to the reaction time of the system).
(2) Number L launcher preparation state of naval vessel guided missile weapon system
Figure BDA0002757611120000094
In the formula:
L_stateLfor the launcher status No. L, "1" ready, "0" not ready;
Figure BDA0002757611120000098
the moment when the No. L launcher launches the naval vessel-air missile finally;
Figure BDA0002757611120000099
the transmission interval (corresponding to the transmission frame retransmission time) is transmitted again for the L-th transmission frame.
5. Calculation of service model of anti-ship missile queuing-waiting aircraft-borne missiles
(1) Interception condition for launching ship-air missile
When the anti-ship missile is positioned above a launching area, whether the anti-ship missile launches an air-borne missile to intercept needs to meet two conditions:
1) preparing a fire channel of the naval-aircraft missile weapon system;
2) and preparing a launching cradle of the ship-based missile weapon system.
Namely, it is
Figure BDA0002757611120000095
In the formula:
Flag_serveri,kthe sign of whether the ith anti-ship missile is served by the kth ship and aircraft missile is that '1' can be served and '0' cannot be served;
Flag_HLk,ithe method is characterized in that a mark indicating whether an air defense fire channel aiming at the i-th anti-ship missile on the k-th ship is ready or not is provided, wherein 1 is ready and 0 is not ready;
Flag_FSkand indicating whether the k-th ship launching system is ready, wherein '1' is ready and '0' is not ready.
(2) Aircraft-based missile service determination
When the anti-ship missile is in the launching area and is judged to be Flag _ serveri,kWhen the value is still 0, the anti-ship missile is in a waiting state, and Flag _ wait is seti,kWaiting for the total number of k-th vessel air-borne missile services (with the set variable sum _ wait) 1i,k) Add 1, and sum _ waiti,kIs given to Number _ waiti,kVariable Number _ waiti,kThe meaning of (1) is the serial number of the No. i anti-ship missile waiting for the No. k naval vessel air-borne missile service.
When the anti-ship missile is in the launching area, the Flag _ server is judgedi,kIs 1 and Flag _ waiti,kWhen 1, the Number _ wait is determined according to the first come first serve principlei,kWhether the value of (d) is 1: if the number of the missile is 1, launching an aircraft missile to intercept the anti-aircraft missile, and enabling a variable sum _ waiti,kAnd Number _ waiti,kAnd the order of other anti-ship missiles waiting for the service of the k-th ship naval missileThe sequence numbers are respectively reduced by 1; if not, launching the ship-to-ship missile to not intercept the anti-ship missile.
When the anti-ship missile is in the launching area, the Flag _ server is judgedi,kIs 1 and Flag _ waiti,kAnd when the value is 0, launching the ship-to-ship missile to intercept the anti-ship missile.
6. Aircraft-warship missile flight trajectory
The guidance and guidance section of the ship-based air missile adopts a proportional guidance mode, namely the following formula is satisfied:
Figure BDA0002757611120000101
in the formula:
k is a proportionality constant and is generally 3-5;
Figure BDA0002757611120000102
the change rate of the deviation angle of the ship-air missile trajectory is obtained;
Figure BDA0002757611120000103
is the angular velocity of rotation of the target line of sight.
The distance from the ship-based air missile to the target is as follows:
Figure BDA0002757611120000104
the trajectory simulation of the ship-air missile can be simplified and processed according to the proportion guidance, and the motion equation of the ship-air missile in the plane is expressed as follows:
Figure BDA0002757611120000105
then the course and time of the meeting of the ship-air missile and the anti-ship missile can be calculated by the formula (21):
Figure BDA0002757611120000111
in the formula:
Ffjthe direction of the anti-ship missile;
Vfjthe speed of the anti-ship missile;
Vjkthe velocity of the vessel-based air-borne missile;
Qfjattack the bulwark angle of the target naval vessel for the anti-ship missile;
TT is the time required for the ship-to-ship missile to meet the anti-ship missile;
c is the course of the ship-air missile when meeting the anti-ship missile;
Sign(Qfj) To take a variable QfjjSign value function (return ± 1).
7. Target evaluation of ship-air missile
The method for evaluating the target hit of the ship-air missile comprises the following steps:
(1) judging whether the ship-air missile meets the target or not;
(2) the judgment and the processing of the ship-air missile hit can be expressed by the formula (22):
Figure BDA0002757611120000112
in the formula:
r is a random number uniformly distributed according to 0-1;
Pkmthe attack probability of the k-th interception of the ship-based missile by the ship-based missile under the condition of no impact interference is obtained.
8. Anti-ship missile to ship-to-ship missile penetration probability calculation
Penetration probability P of anti-ship missile to ship-borne missileJDThe calculations can be performed using a monte carlo simulation method.
Figure BDA0002757611120000113
In the formula:
PJD_iis the i-th penetration probability, PJDIs the penetration probability.
The above embodiments are merely illustrative of the present invention and are not to be construed as limiting the invention. Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that various combinations, modifications and equivalents may be made without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims (9)

1. A ship-based air-borne missile interception model establishing method is characterized by mainly comprising the following steps:
(1) intercepting and analyzing anti-ship missiles by ship-air missiles;
(2) calculating the damage probability of the ship-air missile;
(3) calculating an aircraft missile launching area;
(4) calculating the states of a fire channel and a launcher of the naval missile weapon system;
(5) the anti-ship missile queues to wait for calculation of the ship-to-air missile service model;
(6) calculating the flight trajectory of the ship-air missile;
(7) evaluating the target hit of the ship-air missile;
(8) and (4) calculating the penetration probability of the anti-ship missile to the ship-to-air missile, and completing the establishment of the ship-to-air missile interception model.
2. The method for establishing the naval-vessel missile interception model according to claim 1, wherein the main steps of naval-vessel missile to anti-naval missile interception analysis are as follows:
assuming that the anti-ship missile flies linearly, a schematic diagram is drawn on a plane where a target ship position and an anti-ship missile flight route are located,
the necessary condition that the ship-air missile system can intercept an incoming anti-ship missile is that the interception point of the ship-air missile on the anti-ship missile must be in the interception area of the ship-air missile, and the requirements are met:
tmy≤tmf1+tmb+tmaformula (1)
tmj≥tmfnOr tmj≥tmfn+tmb+tmaFormula (2)
The formula (1) is a condition which is required to be met by the interception point at a far point of a ship-borne missile defense area;
the formula (2) is a condition which is far from a near point of an interception point in a naval vessel missile interception area to be met;
tmyfor anti-ship missilemFly to AmyTime required for point, tmf1Time to launch an aircraft-borne missile to fly at the intercept point, tmaAssigning time, t, to fire channelmbFor the response time of the naval-aircraft missile weapon system, tmfnThe time required for the anti-ship missile to fly from the position of the anti-ship missile to the last interception point when the anti-ship missile carries out the last interception, AmjThe point is the interception near end of the defense area of the naval vessel-air missile, tmjFor anti-ship missilefnFly to AmjThe time required for the spot.
3. The method for establishing the naval-aircraft missile interception model according to claim 1, wherein the method for calculating the naval-aircraft missile killing probability mainly comprises the following steps:
the single-shot killing probability model of the ship-air missile is as follows:
Figure FDA0002757611110000011
in equation (3):
LR is missile killer radius;
CEP is the circular probability deviation, which can be expressed as a function of distance and signal-to-noise ratio S/N without interference:
Figure FDA0002757611110000012
in equation (4):
r is the distance when transmitting;
N/S is the reciprocal of the signal-to-noise ratio;
the killing probability of the ship-air missile in each air firing is as follows:
Pkm＝Rm·Dm·Cm·[1-(1-a·r·ω)s]formula (5)
In equation (5):
Rmguiding the normal working probability of the radar for interception;
Dmdetecting the probability for the target;
Cmthe probability of transmission and conversion of the detection information is obtained;
a is the reliable launching probability of the ship-air missile;
r is the missile reliable flight probability;
omega is the single-shot killing probability of each ship-borne missile to the target;
and S is the number of the air-borne missiles which are fired at each time.
4. The method for establishing the naval-aircraft missile interception model according to claim 1, wherein the naval-aircraft missile launching area is calculated by the following main steps:
(1) defining a coordinate system
The system comprises an air-borne missile launching coordinate system and a fleet central coordinate system;
(2) distance calculation from anti-ship missile to ship-to-aircraft missile
Firstly, calculating position coordinates of a launching ship expressed by longitude and latitude and height according to the relative position of an air-borne missile launching ship in a fleet; and converting the coordinates of the anti-ship missile and the coordinates of the launching ship into coordinates under a fleet central coordinate system, and respectively recording the coordinates as (x)b,yb,zb) And (x)h,yh,zh) The distance from the anti-ship missile to the launching ship of the ship-based missile is
Figure FDA0002757611110000021
(3) Calculation of stable tracking time of anti-ship missile by using ship-based irradiation radar
The judgment criteria of the radar for stably tracking the target are as follows: obtaining a target signal at least 4 times in 5 consecutive scanning periods;
(4) calculation of response time of ship-air missile system
Response time T of naval air-borne missile systemRThe time required from the beginning of identifying an anti-ship missile by a ship-based detection radar to the completion of launcher distribution and interception decision and finally launching an aircraft missile off-rack is calculated as follows:
TR＝TD+TA+TEformula (7)
In the formula:
TDcompleting the stable tracking time of the anti-ship missile for the ship-air missile radar system;
TAcompleting interception decision time for the naval missile combat command system in a centralized or autonomous mode;
TEresolving the time of firing data for fire control;
(5) calculation of launching area of naval-aircraft missile
1) Transmissible far field
Naval air guided missile can launch far range R1Comprises the following steps:
Figure FDA0002757611110000022
when P is 0:
R1＝r1-Vfj·TRformula (9)
VfjIs the speed of the anti-ship missile, r1The maximum action distance of the radar;
2) need to transmit far field
Suppose that the vessel-air missile is in b1The point meets the anti-ship missile, and the corresponding launching point a'1Calculating the remote range R required to be launched by the ship-air missile according to the distance R2Comprises the following steps:
Figure FDA0002757611110000023
in the formula VjkThe velocity of the vessel-based air-borne missile:
when P is 0:
Figure FDA0002757611110000031
3) far field of emission
Naval air guided missile launching distance fmaxShould be R1、R2The smaller of these:
fmax＝min(R1,R2) Formula (12)
4) Emission near bound
Launching near field f of naval air missileminAccording to the killing proximity r3And determining, wherein the calculation formula is as follows:
Figure FDA0002757611110000032
when P is 0:
Figure FDA0002757611110000033
5. the method for establishing the naval-aircraft missile interception model according to claim 1, wherein the method for calculating the states of a fire channel and a launcher of a naval-aircraft missile weapon system mainly comprises the following steps:
(1) no. k firepower channel state of naval air-borne missile weapon system
Figure FDA0002757611110000034
In the formula:
M_statekfor the k fire channel state, "1" ready, "0" not ready;
t is the current time estimated by the system;
Figure FDA0002757611110000035
the time when the target instruction is received for the k-th fire channel;
Figure FDA0002757611110000036
the time required for the k-th fire channel to be ready (corresponding to the reaction time of the system);
(2) number L launcher preparation state of naval vessel guided missile weapon system
Figure FDA0002757611110000037
In the formula:
L_stateLfor the launcher status No. L, "1" ready, "0" not ready;
Figure FDA0002757611110000038
the moment when the No. L launcher launches the naval vessel-air missile finally;
Figure FDA0002757611110000039
the interval is transmitted again for the L-th launcher.
6. The method for establishing the naval missile interception model according to claim 1, wherein the calculation of the anti-naval missile queuing-waiting naval missile service model comprises the following main steps:
(1) interception condition for launching ship-air missile
When the anti-ship missile is positioned above a launching area, whether the anti-ship missile launches an air-borne missile to intercept needs to meet two conditions:
1) preparing a fire channel of the naval-aircraft missile weapon system;
2) preparing a launching cradle of the naval missile weapon system;
namely, it is
Figure FDA0002757611110000041
Formula (17):
Flag_serveri,kthe sign of whether the ith anti-ship missile is served by the kth ship and aircraft missile is that '1' can be served and '0' cannot be served;
Flag_HLk,ithe method is characterized in that a mark indicating whether an air defense fire channel aiming at the i-th anti-ship missile on the k-th ship is ready or not is provided, wherein 1 is ready and 0 is not ready;
Flag_FSka mark indicating whether a k-th ship launching system is ready, 1 is ready, and 0 is not ready;
(2) aircraft-based missile service determination
When the anti-ship missile is in the launching area and is judged to be Flag _ serveri,kWhen the value is still 0, the anti-ship missile is in a waiting state, and Flag _ wait is seti,kAdding 1 to the total number of waiting number k naval vessel air-borne missile services, and recording the total number as (with the variable being sum _ wait)i,kAnd) sum _ waiti,kIs given to Number _ waiti,kVariable Number _ waiti,kThe meaning of (1) is the serial number of the No. i anti-ship missile waiting for the No. k naval vessel air-borne missile service;
when the anti-ship missile is in the launching area, the Flag _ server is judgedi,kIs 1 and Flag _ waiti,kWhen 1, the Number _ wait is determined according to the first come first serve principlei,kWhether the value of (d) is 1: if the number of the missile is 1, launching an aircraft missile to intercept the anti-aircraft missile, and enabling a variable sum _ waiti,kAnd Number _ waiti,kAnd the sequence numbers of other anti-ship missiles waiting for the service of the k-th naval vessel air-borne missile are respectively reduced by 1; if not, launching the ship-to-ship missile to not intercept the anti-ship missile;
when the anti-ship missile is in the launching area, the Flag _ server is judgedi,kIs 1 and Flag _ waiti,kAnd when the value is 0, launching the ship-to-ship missile to intercept the anti-ship missile.
7. The method for establishing the naval-aircraft missile interception model according to claim 1, wherein the calculation of the flying trajectory of the naval-aircraft missile mainly comprises the following steps:
the guidance and guidance section of the ship-based air missile adopts a proportional guidance mode, namely the following formula is satisfied:
Figure FDA0002757611110000042
in equation (18):
k is a proportionality constant and is generally 3-5;
Figure FDA0002757611110000043
the change rate of the deviation angle of the ship-air missile trajectory is obtained;
Figure FDA0002757611110000044
is the rotational angular velocity of the target line of sight;
the distance from the ship-based air missile to the target is as follows:
Figure FDA0002757611110000045
the equation of motion of the vessel-based missile in the plane is expressed as:
Figure FDA0002757611110000051
the meeting course and time of the ship-air missile and the anti-ship missile can be represented as follows:
Figure FDA0002757611110000052
in equation (21):
Ffjthe direction of the anti-ship missile;
Vfjthe speed of the anti-ship missile;
Vjkthe velocity of the vessel-based air-borne missile;
Qfjattack the bulwark angle of the target naval vessel for the anti-ship missile;
TT is the time required for the ship-to-ship missile to meet the anti-ship missile;
c is the course of the ship-air missile when meeting the anti-ship missile;
Sign(Qfj) To take a variable QfjjSign value function (return ± 1).
8. The method for establishing the naval-aircraft missile interception model according to claim 1, wherein the method for evaluating the target hit of the naval-aircraft missile mainly comprises the following steps:
(1) judging whether the ship-air missile meets the target or not;
(2) the judgment and the processing of the hit of the ship-air missile can be expressed by a formula (22):
Figure FDA0002757611110000053
in equation (22):
r is a random number uniformly distributed according to 0-1;
Pkmthe interception probability of a single ship-borne missile to the ship-borne missile under the condition of no impact interference is obtained.
9. The method for establishing the naval missile interception model according to claim 1, wherein the defense penetration probability of the anti-naval missile to the naval missile can be calculated by adopting a Monte Carlo simulation method:
Figure FDA0002757611110000061
in equation (23):
PJD_iis as followsi-times penetration probability, PJDIs the penetration probability.
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