CN111174643A - Aircraft interception method and system under condition of bait interference - Google Patents

Aircraft interception method and system under condition of bait interference Download PDF

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CN111174643A
CN111174643A CN202010057912.8A CN202010057912A CN111174643A CN 111174643 A CN111174643 A CN 111174643A CN 202010057912 A CN202010057912 A CN 202010057912A CN 111174643 A CN111174643 A CN 111174643A
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chaser
time
evacuee
state
bait
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CN111174643B (en
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郭杨
王少博
王仕成
刘志国
席建祥
廖守亿
张金生
沈涛
张帅
陶雁华
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Rocket Force University of Engineering of PLA
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F41—WEAPONS
    • F41H—ARMOUR; ARMOURED TURRETS; ARMOURED OR ARMED VEHICLES; MEANS OF ATTACK OR DEFENCE, e.g. CAMOUFLAGE, IN GENERAL
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    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

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Abstract

The invention relates to an aircraft interception method and system under the condition of bait interference. The interception method comprises the following steps: an unrecognized bait stage and a recognized bait stage; in the stage that the bait is not identified, judging the bait and a real target by utilizing a prediction guidance law based on a highest probability interval method; in the stage of identifying the bait, in the process of finishing intercepting the target by mutually cooperating a plurality of aircrafts, when a mode of further estimating distance information by cooperating angle measurement of the plurality of aircrafts is adopted, the geometrical configuration of the relative position has great influence on the estimation error, if the plurality of aircrafts and the target are collinear, the relative distance cannot be estimated, and the estimation error is great when the plurality of aircrafts and the target are approximately collinear, so that the problem of formation configuration is considered in the process of aircraft guidance, the optimal guidance law is determined to control the sight separation angle of two chasers relative to the target, and the sight separation angle is increased to reduce the detection error and enhance the guidance precision.

Description

Aircraft interception method and system under condition of bait interference
Technical Field
The invention relates to the field of aircraft interception, in particular to an aircraft interception method and system under the condition of bait interference.
Background
In the field of aircraft interception, in a scene that a plurality of aircrafts intercept an enemy maneuvering target, the enemy maneuvering target transmits a piece of bait with the characteristics similar to those of the target to interfere with the aircrafts of the same party aiming at the interception of the aircrafts of the same party. After the baits need to be identified by the aircrafts of the other party, the maneuvering targets of the enemy are effectively guided.
In the terminal guidance stage, the guidance time is particularly short, and a certain time is needed for identifying the bait, so that a time interval in which the bait cannot be identified exists in the guidance process; in the time interval of the stage in which the bait is not identified, the aircraft of one party cannot quickly distinguish the bait and the real target, so that the real target cannot be identified and intercepted, the maneuvering target of an enemy cannot be effectively intercepted quickly, the intercepting efficiency is reduced, and the guidance precision is low.
Disclosure of Invention
The invention aims to provide an aircraft interception method and system under the condition of bait interference so as to solve the problems of low interception efficiency and low guidance precision of the existing guidance interception method.
In order to achieve the purpose, the invention provides the following scheme:
a method of aircraft interception in a bait jamming situation, comprising: an unrecognized bait stage and a recognized bait stage;
decoy stage not identified: acquiring ideal flight parameters of the aircraft in an ideal state; the aircraft comprises a plurality of chasers and evacuees; the flight parameters comprise speed, acceleration, an overload response time constant and the lateral relative distance between the evacuee and the chaser;
determining a relative motion state equation between the chaser and the evacuee according to the flight parameters;
in the pursuit process, acquiring the measurement noise error of the pursuit person in the measurement process and the relative distance and the line-of-sight angle information between the two pursuit persons;
determining a relative distance between the chaser and the evacuee according to the relative distance between the chasers and the line-of-sight angle information;
determining a relative motion measurement equation between the chaser and the evacuee according to the relative distance between the chaser and the evacuee and the measurement noise error;
acquiring pursuit parameters of the chaser; the pursuit parameters comprise a state reachable set of a state that the chaser transitions from any one time to an interception time, a position component reachable set of a state that a position component of the chaser transitions from any one time to an interception time, and a maximum command acceleration of the chaser;
determining rolling control constraint conditions according to the chasing parameters;
under the rolling control constraint condition, determining an optimal compromise guidance point by using a highest probability interval method, and constructing a prediction guidance law according to the relative motion state equation and the relative motion measurement equation;
giving consideration to bait and real target guidance according to the prediction guidance law;
bait stage is identified: acquiring a state transition matrix; the state transition matrix is a state transition matrix for the moment state of the unrecognized bait stage to the moment state of the recognized bait stage;
determining an optimal guidance law according to the state transition matrix and the optimal compromise guidance point by using an optimal control theory; the optimal guidance law is an optimal guidance law for controlling the sight separation angle;
and intercepting the real target according to the optimal guidance law.
Optionally, the determining a relative motion state equation between the chaser and the evacuee according to the flight parameter specifically includes:
using formulas
Figure BDA0002369493480000021
Determining a relative motion state equation between the chaser and the evacuee; wherein the content of the first and second substances,
Figure BDA0002369493480000022
is a relative motion state equation;
Figure BDA0002369493480000023
Figure BDA0002369493480000031
τPiis the overload response time constant, τ, of the chaserE(ii) an overload response time constant for said evacuee; u. ofPiA control input for the chaser;
Figure BDA0002369493480000032
the command acceleration of the evacuee is shown, and w is noise in the guidance process of the aircraft; t is time.
Optionally, the determining a measurement equation of the relative motion between the chaser and the evacuee according to the relative distance between the chaser and the evacuee and the measurement noise error specifically includes:
using formulas
Figure BDA0002369493480000033
Determining a relative motion measurement equation between the chaser and the evacuee; wherein, H ═ 1000]；xiIs a state vector of the aircraft;
Figure BDA0002369493480000034
measuring a noise obedience distribution for the chaser's gaze; y isiIs the lateral relative distance of the line of sight angle between the chaser and the evacuee.
Optionally, the determining an optimal compromise guidance point by using a highest probability interval method under the rolling control constraint condition, and constructing a prediction guidance law according to the relative motion state equation and the relative motion measurement equation specifically includes:
by using
Figure BDA0002369493480000035
Constructing a prediction guidance law; wherein the content of the first and second substances,
Figure BDA0002369493480000036
is a predictive guidance law;
Figure BDA0002369493480000037
f(tk+1)＝DβΦPi(tf,tk+1)，
Figure BDA0002369493480000038
for optimal consideration of the projection of the guidance points, DβAs a vector separating the position components, phiPi(tk+1,tk) From t for the chaserkTime tk+1State transition matrix of time phiPi(tf,tk+1) From t for the chaserk+1Time tfState transition matrix at time, tfFor the final intercept time, tk+1At any time during the guidance process;
Figure BDA0002369493480000039
τ∈[tk,tk+1]，Φpi(tk+1τ) from time τ to tk+1A state transition matrix of a time;
Figure BDA00023694934800000310
is the largest fingerLet the acceleration.
Optionally, the determining, by using an optimal control theory, an optimal guidance law according to the state transition matrix and the optimal consideration guidance point specifically includes:
using formulas
Figure BDA00023694934800000311
Determining an optimal guidance law; wherein Z isi(t) is a new state variable for the chaser; a, b and c are weight coefficients;
Figure BDA00023694934800000312
tgois the remaining time of the guidance process; Δ t is a positive infinitesimal quantity; d ═ 1000]Is a separation vector; phii(tfT) is from time t to tfA state transition matrix of relative motion at a time.
An aircraft intercept system in the event of a bait disturbance, comprising: an unrecognized bait stage and a recognized bait stage;
an ideal flight parameter acquisition module for the unrecognized bait phase: acquiring ideal flight parameters of the aircraft in an ideal state; the aircraft comprises a plurality of chasers and evacuees; the flight parameters comprise speed, acceleration, an overload response time constant and the lateral relative distance between the evacuee and the chaser;
the relative motion state equation determining module is used for determining a relative motion state equation between the chaser and the evacuee according to the flight parameters;
the parameter acquisition module in the measuring process is used for acquiring the measurement noise error of the chasers in the measuring process and the relative distance and the line-of-sight angle information between the two chasers in the chasing process;
a relative distance determination module for determining a relative distance between the chaser and the evacuee according to the relative distance between the chasers and the line-of-sight angle information;
a relative motion measurement equation determination module, configured to determine a relative motion measurement equation between the chaser and the evacuee according to the relative distance between the chaser and the evacuee and the measurement noise error;
the pursuit parameter acquisition module is used for acquiring pursuit parameters of the pursuit person; the pursuit parameters comprise a state reachable set of a state that the chaser transitions from any one time to an interception time, a position component reachable set of a state that a position component of the chaser transitions from any one time to an interception time, and a maximum command acceleration of the chaser;
the rolling control constraint condition determining module is used for determining a rolling control constraint condition according to the pursuit parameter;
the prediction guidance law building module is used for determining an optimal compromise guidance point by using a highest probability interval method under the rolling control constraint condition and building a prediction guidance law according to the relative motion state equation and the relative motion measurement equation;
the judging module is used for judging baits and real targets according to the prediction guidance law;
a state transition matrix acquisition module to identify a bait phase: acquiring a state transition matrix; the state transition matrix is a state transition matrix for the moment state of the unrecognized bait stage to the moment state of the recognized bait stage;
the optimal guidance law determining module is used for determining an optimal guidance law according to the state transition matrix and the optimal compromise guidance point by using an optimal control theory; the optimal guidance law is an optimal guidance law for controlling the sight separation angle;
and the intercepting module is used for intercepting the real target according to the optimal guidance law.
Optionally, the relative motion state equation determining module specifically includes:
a relative motion state equation determination unit for using the formula
Figure BDA0002369493480000051
Determining relative movement between chaser and evacuee (i ═ {1, 2) }A state equation; wherein the content of the first and second substances,
Figure BDA0002369493480000052
is a relative motion state equation;
Figure BDA0002369493480000053
τPiis the overload response time constant, τ, of the chaserE(ii) an overload response time constant for said evacuee; u. ofPiA control input for the chaser;
Figure BDA0002369493480000054
the command acceleration of the evacuee is shown, and w is noise in the guidance process of the aircraft; t is time.
Optionally, the relative motion measurement equation determining module specifically includes:
a relative motion measurement equation determination unit for using the formula
Figure BDA0002369493480000055
Determining a relative motion measurement equation between the chaser and the evacuee; wherein, H ═ 1000]；xiIs a state vector of the aircraft;
Figure BDA0002369493480000056
measuring a noise obedience distribution for the chaser's gaze; y isiIs the lateral relative distance of the line of sight angle between the chaser and the evacuee.
Optionally, the guidance law prediction building module specifically includes:
a prediction guidance law construction unit for utilizing
Figure BDA0002369493480000057
Constructing a prediction guidance law; wherein the content of the first and second substances,
Figure BDA0002369493480000058
is a predictive guidance law;
Figure BDA0002369493480000059
f(tk+1)＝DβΦPi(tf,tk+1)，
Figure BDA00023694934800000510
for optimal consideration of the projection of the guidance points, DβAs a vector separating the position components, phiPi(tk+1,tk) From t for the chaserkTime tk+1State transition matrix of time phiPi(tf,tk+1) From t for the chaserk+1Time tfState transition matrix at time, tfFor the final intercept time, tk+1At any time during the guidance process;
Figure BDA0002369493480000061
τ∈[tk,tk+1]，Φpi(tk+1τ) from time τ to tk+1A state transition matrix of a time;
Figure BDA0002369493480000062
is the maximum commanded acceleration.
Optionally, the optimal guidance law determining module specifically includes:
an optimal guidance law determining unit for using a formula
Figure BDA0002369493480000063
Determining an optimal guidance law; wherein Z isi(t) is a new state variable for the chaser; a, b and c are weight coefficients;
Figure BDA0002369493480000064
Figure BDA0002369493480000065
tgois the remaining time of the guidance process; Δ t is a positive infinitesimal quantity; d ═ 1000]Is a separation vector; phii(tfT) is from time t to tfA state transition matrix of relative motion at a time.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: the invention provides an aircraft interception method and system under the condition of bait interference, wherein in the stage of not identifying bait, a prediction guidance law is determined based on a method of a highest probability interval (highestprobabilityinterval), and the prediction guidance law can maximize the probability of intercepting a real target under the condition that the bait exists and provide an interception maneuver advantage for the cooperative guidance of the real target; in the bait identification stage, the optimal guidance law is determined based on the optimal control theory, the estimation error can be reduced in the detection process, the interception performance is improved, the sight separation angle of two chasers relative to the target is controlled to be increased, the detection error is reduced, and the guidance precision is enhanced.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a method for intercepting an aircraft in the presence of a bait disturbance in accordance with the present invention;
FIG. 2 is a plan engagement geometry for an evacuee and two chasers;
FIG. 3 is a flow chart of a method for constructing a predictive guidance law according to the present invention;
FIG. 4 is a flowchart of the rolling horizon optimization provided by the present invention;
FIG. 5 is a schematic diagram of the engagement of evacuees, chasers 1, chasers 2 and baits provided by the present invention;
fig. 6 is a diagram of the lateral relative distance variation between the chaser 1 and the chaser 2 and the evacuee provided by the present invention;
FIG. 7 is a schematic acceleration diagram of evacuee, chaser 1 and chaser 2 provided by the present invention;
FIG. 8 is a graph showing the variation of the lateral distance detection error between the chaser 1 and the evacuee under the pure prediction guidance law and the proposed guidance law, taking the chaser 1 as an example, provided by the present invention;
FIG. 9 is a graph of the variation of the view separation angle between two chasers under the pure predictive guidance law and the proposed guidance law provided by the present invention;
FIG. 10 is a graph of variance variation of state estimation error over 500 MC simulations provided by the present invention;
FIG. 11 is a schematic diagram of cumulative distribution functions of miss distance of the chaser 1 under the pure prediction guidance law and the proposed guidance law provided by the present invention;
FIG. 12 is a schematic diagram of cumulative distribution functions of miss distance of the chaser 2 under the pure prediction guidance law and the proposed guidance law provided by the present invention;
FIG. 13 is a diagram illustrating the distribution function of the miss distance of the bait with the bait recognition delay time of 1s, 2s, 3s and 4s under the proposed guidance.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide an aircraft interception method and system under the condition of bait interference, which can reduce detection errors and enhance guidance precision.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a flowchart of an aircraft interception method under a bait jamming condition, and as shown in fig. 1, an aircraft interception method under a bait jamming condition includes: an unrecognized bait stage and a recognized bait stage;
the bait-unidentified stage includes:
step 101: acquiring ideal flight parameters of the aircraft in an ideal state; the aircraft comprises a plurality of chasers and evacuees; the flight parameters include speed, acceleration, overload response time constant, and the lateral relative distance of the evacuee from the chaser.
Step 102: and determining a relative motion state equation between the chaser and the evacuee according to the flight parameters.
Considering the scene that a plurality of aircrafts of our party intercept the maneuvering target of the enemy, the maneuvering target of the enemy aims at the interception of the aircrafts of our party and launches a bait with the characteristics similar to those of the target to interfere the aircrafts of our party. After the baits need to be identified by the aircrafts of the other party, the maneuvering targets of the enemy are effectively guided. Since the guidance time is particularly short in the final guidance phase, it takes some time to identify the bait. In addition, during the cooperative guidance process of the multiple aircrafts, the relative guidance configuration of the aircrafts can influence the detection precision of the target. The present invention therefore divides terminal guidance into two phases: and designing a guidance law respectively in a stage before the bait is identified and a stage after the bait is identified.
At XI-OI-YIEstablishing a dynamics and kinematics model under an inertial coordinate system, and taking a plane engagement geometry diagram of an evacuee and two chasers as shown in figure 2 by E and PiRepresenting evacuee and chaser, and a, v, λ, r and γ represent acceleration, velocity, line-of-sight angle, relative distance and heading angle, respectively. The model of the invention is built under the following assumptions:
1) assuming that the speeds of the evacuee and the chaser are constant and satisfying the establishment condition of a nominal collision triangle;
2) it is assumed that both chasers and evacuees approximate a first order kinetic model.
Establishing a relative motion state equation between the chaser and the evacuee:
neglecting the influence of gravity, the course of engagement of chasers and evacuees can be expressed in the form of polar coordinates (r, λ) associated with the evacuee, i.e. the
Figure BDA0002369493480000081
Figure BDA0002369493480000082
In the formula (I), the compound is shown in the specification,
Figure BDA0002369493480000083
is the relative velocity between the two aircraft;
Figure BDA0002369493480000084
is the line of sight (LOS) rate between the two aircraft.
The acceleration a of the aircraft is normal acceleration with the direction vertical to the speed, the speeds of evacuees and chasers are constant in the whole guidance process, and the normal acceleration a of each aircraft can be obtainediWith course angular velocity gammaiThe relationship between is
Figure BDA0002369493480000085
According to the assumption 1), when the flight course of the two-sided aircraft approximates to a nominal collision triangle, the above-mentioned course can be linearized. In the battle situation shown in fig. 2, there are two collision triangles: one between chaser P1 and evacuee E and the other between chaser P2 and evacuee E.
After the linearization process, under the condition of assumption 2), the state vector can be selected as
Figure BDA0002369493480000091
In the formula (I), the compound is shown in the specification,
Figure BDA0002369493480000092
for the lateral relative distance between evacuee E and chaser Pi,
Figure BDA0002369493480000093
is the lateral relative velocity.
From the state vector, a state equation of the relative motion of the aircraft can be written as
Figure BDA0002369493480000094
In the formula, τPiAnd τEOverload response time constants for chaser Pi and evacuee E, respectively.
From equation (5), a state space can be established described as
Figure BDA0002369493480000095
In the formula (I), the compound is shown in the specification,
Figure BDA0002369493480000096
uPiis the control input of the chaser Pi and satisfies
Figure BDA0002369493480000097
Figure BDA0002369493480000098
And w is the noise in the guidance process of the aircraft, and is the command acceleration of the evacuee E.
Discretizing the linear system in the formula (6) to obtain,
Figure BDA0002369493480000099
w(k)～N(0,Qw(k))
assuming that the simulation time interval of the discrete system is Δ, the matrix F in equation (7)i、Gi、EiAnd QwAre respectively as
Figure BDA0002369493480000101
Figure BDA0002369493480000102
Figure BDA0002369493480000103
Figure BDA0002369493480000104
In the formula (I), the compound is shown in the specification,
Figure BDA0002369493480000105
q acts as a tuning matrix.
Initial relative distances between chasers P1 and P2 and evacuee E were
Figure BDA0002369493480000106
And
Figure BDA0002369493480000107
under the assumption of a nominal collision triangle, the heading angle γiAnd the viewing angle lambdaPiEThe deviation therebetween is small, so that the interception time of the chaser Pi to the evacuee E is fixed as
Figure BDA0002369493480000108
The invention considers the situation that two chasers intercept the evacuee at the same time, so that the interception time of the evacuee by the two chasers is equal, namely tfP1E＝tfP2E. Thus, the relative distances between the two chasers and the evacuee are also equal, i.e. the
Figure BDA0002369493480000109
Step 103: in the pursuit process, the measurement noise error of the pursuit person in the measurement process and the relative distance and the line-of-sight angle information between the two pursuit persons are obtained.
Step 104: and determining the relative distance between the chaser and the evacuee according to the relative distance between the chasers and the line-of-sight angle information.
Step 105: and determining a relative motion measurement equation between the chaser and the evacuee according to the relative distance between the chaser and the evacuee and the measurement noise error.
Each chaser uses an IR sensor to measure the line of sight angle lambda of the evacueePiEAnd each sensor is subjected to a mutually independent measurement noise error v during the measurement processPiAssuming that the line-of-sight measurement noise of each chaser obeys the distribution
Figure BDA0002369493480000111
As can be seen from fig. 2, a baseline of measurement is established between two chasers during engagement relative to an evacuee. Assuming that the chasers can accurately measure the relative states of the chasers and the two chasers can share the measurement information, the relative position information (r, lambda) between the two chasers can be obtainedPiPj)，i,j＝1,2,i≠j。
Thus, the relative distance r and the line-of-sight angle λ between two chasers can be passedP1P2Information on the relative distance between the chaser Pi and the evacuee E, i.e. the distance between the chaser Pi and the evacuee E
Figure BDA0002369493480000112
In the formula (I), the compound is shown in the specification,
Figure BDA0002369493480000113
λP1P2＝arctan2(yP2-yP1,xP2-xP1) (16)
in the formula (x)Pi,yPi) And (x)Pj,yPj) Can be derived from the respective state equations of the chasers, i.e.
Figure BDA0002369493480000114
Wherein the selected state vector is
Figure BDA0002369493480000115
Similarly, the state vector is chosen to be
Figure BDA0002369493480000116
The equation of state of the evacuee can be obtained as
Figure BDA0002369493480000117
In the formula (I), the compound is shown in the specification,
Figure BDA0002369493480000121
by using the assumption that the linearization under the nominal collision triangle is satisfied, the lateral relative distance y perpendicular to the initial LOS can be determinediIs shown as
Figure BDA0002369493480000122
rPiE≈vPiEtgo(20)
In the formula, tgoThe remaining time for the guidance process, defined as,
Figure BDA0002369493480000123
in combination with equation (14), the equation for measuring the relative motion between the chaser and the evacuee can be obtained as
Figure BDA0002369493480000124
Wherein H is [ 1000 ]]，
Figure BDA0002369493480000125
Figure BDA0002369493480000126
From the equation (24), the view angle | λ of the two chasers with respect to the evacuee is shownPiE-λPjEWhen | decreases, the lateral relative distance yiWill increase, resulting in a decrease in state estimation accuracy. It is therefore necessary to control the line-of-sight separation angle of the two chasers with respect to the evacuee at an appropriate stage when designing the guidance law.
Step 106: acquiring pursuit parameters of the chaser; the pursuit parameters comprise a state reachable set of the state where the state of the pursuit is transferred to the state at the interception time at any moment, a reachable set of the position component of the state where the position component of the pursuit is transferred to the state at the interception time at any moment, and a maximum commanded acceleration of the pursuit.
Step 107: and determining rolling control constraint conditions according to the chasing parameters.
The description of the proposed engagement problem above, namely: multiple aircraft cooperatively intercept an enemy target capable of launching bait.
In designing the guidance law, two main issues need to be considered: one is that after the target launches the bait, there are real targets and false targets with characteristics of real targets in the field of view of my aircraft. Under the condition, the aircraft in our party needs to adopt an effective guidance method, can give consideration to two targets for guidance at the same time, and maximizes the probability of intercepting a real target. Secondly, after identifying the bait, considering the influence of the guidance configuration of the aircraft on the detection precision of the target, namely: the line-of-sight separation angle of the two aircraft affects the measurement error on the lateral relative distance. In this case, the sight line separation angle of the aircraft needs to be controlled at the guidance end, so that the aircraft can meet the requirements of the target detection and interception accuracy.
1. Unrecognized bait stage
In the stage, a prediction guidance method is adopted to guide the chaser to the predicted position of the target at the interception moment. The method requires real-time mapping of the shape of the objectThe state is estimated and its state at the moment of interception is predicted. The steering law based on GST design takes into account the PDF of the estimator output, denoted as p (z)E|yk). For a single target, although the maneuver is difficult to predict, the PDF output by the estimator may be approximately considered to follow a normal distribution, whereas the PDF output by the estimator may be multi-peaked in view of the special circumstances in which the target releases bait. At this time, it is not assumed that the PDF output by the estimator is a superposition of one or more normally distributed PDFs, so that these normally distributed PDFs can be considered to correspond to the state estimation of each target and decoy, and fig. 3 is a flow chart of a construction method of the prediction guidance law provided by the present invention, as shown in fig. 3.
The guidance control problem at this stage mainly involves two aspects: first, t solved by rolling control constraintkMoment state is transferred to interception moment tfA predicted state of (a); second, in the rolling time interval [ t ]k,tk+1]And internally solving the segmented optimal controller which meets the rolling control constraint. As shown in fig. 4, the main idea of the phase of guidance law design is presented, namely to maximize its probability density within the reachable set of targets for the aircraft.
1) Computing rolling time domain control constraints
The scroll control constraint is obtained by maximizing the probability that the target is in a certain state within the interceptor's reachable set. Definition of RPi(tf,tk+1) Is the chaser at tkState x of the momentPi(tk+1) Transfer to intercept time tfin addition, define betaPi(tf,tk+1) Is the chaser at tk+1State x of the momentPi(tk+1) The position component in (1) is shifted to the interception time tfcan be located in a reachable set of positions, betaPi(tf,tk+1) Can be expressed as
Figure BDA0002369493480000131
Figure BDA0002369493480000132
to reach betaPi(tf,tk+1) Can be represented as
Figure BDA0002369493480000133
In the formula, Dβ＝[1 0 0]，
Figure BDA0002369493480000134
And
Figure BDA0002369493480000135
for the chaser at maximum commanded acceleration
Figure BDA0002369493480000136
From t under restrictionkTime shift to tfThe state at that time may reach the upper and lower limits of the set interval, θ (t)f,tk+1) From t for the peak of the probability density function of a certain state of the targetk+1Change of moment to tfMaximum displacement value at time.
As can be seen from FIG. 4, the rolling control constraint to be obtained is
Figure BDA0002369493480000141
In the formula (I), the compound is shown in the specification,
Figure BDA0002369493480000142
satisfying optimization problems
Figure BDA0002369493480000143
Figure BDA0002369493480000144
In the formula, U is the target at tk+1Probability that a moment is in the reachable set.
In FIG. 4, the control input u (τ), τ ∈ [ t ]k,tk+1]Can make the state xPi(tk) At the next time tk+1Reaching different values x within the reach setPi(tk+1) Of the optimal solution
Figure BDA0002369493480000145
Can make the target at tk+1The probability U that a moment is in the reachable set is maximized.
The invention can obtain an approximate solution
Figure BDA0002369493480000146
From a plurality of different state values xPi(tk+1) Reachable set of central starting points
Figure BDA0002369493480000147
In the method, an interval which can maximize the probability U is found, the interval is also called a highest probability interval, and the corresponding central starting point is the optimal solution
Figure BDA0002369493480000148
Step 108: and under the rolling control constraint condition, determining an optimal compromise guidance point by using a highest probability interval method, and constructing a prediction guidance law according to the relative motion state equation and the relative motion measurement equation.
2) Calculating control instructions
In solving the control command u (tau), tau epsilon [ tk,tk+1]Because of the need to pass through each time interval tk,tk+1]Calculating the control command u (tau) in the interval, so that the control command u (tau) is a control command comprising a plurality of subintervals [ t (tau) ] in the whole guidance processk,tk+1]The control instructions in the control unit form a piecewise function.
Setting a performance index J related to the segment control command u (tau)OL(tk) By solving the performance index, a segment control instruction u (tau) and a performance index J can be obtainedOL(tk) Can be expressed as
Figure BDA0002369493480000149
Figure BDA00023694934800001410
Figure BDA0002369493480000151
In the formula (I), the compound is shown in the specification,
Figure BDA0002369493480000152
and z (t)k+1|tk) Is in a state
Figure BDA0002369493480000153
And xPi(tk+1|tk) At tk+1The position component of the time at tfA projection over a moment of time.
As can be seen from the analytical expressions (30), (31) and (32), only z (t)k+1|tk) Is a function related to the control command u (τ). Furthermore, no calculations are required
Figure BDA0002369493480000154
To obtain
Figure BDA0002369493480000155
Because of the fact that
Figure BDA0002369493480000156
Is that
Figure BDA0002369493480000157
At tfThe projected point of the HPI at the time is the center point of the HPI, so that the time t is calculatedfThe HPI of the moment can be obtained
Figure BDA0002369493480000158
To solve the performance index JOL(tk) Introduction of theorem III.1, anSetting up
Figure BDA0002369493480000159
And f (t)k+1)＝DβΦPi(tf,tk+1)。
Theorem III.1 considering a state variable as xPi(τ) is equal to R and the state transition matrix is ΦPiThe control input and corresponding matrix are uOL(tau) epsilon R and BPiThe control problem to be solved is
Figure BDA00023694934800001510
Figure BDA00023694934800001511
In the formula, only xPi(tk+1) Is and control input uOL(τ)∈[tk,tk+1]A function of the correlation.
Defining functions
Figure BDA00023694934800001512
Suppose phiPiAnd BPifor a temporally continuous matrix, ξ (τ) does not equal 0 and does not change sign throughoutk,tk+1]There is one satisfy uOL∈AuOf the optimal control instruction
Figure BDA00023694934800001513
The equation (33) is optimized.
Thus, an optimum control command can be found as
Figure BDA00023694934800001514
In the formula (I), the compound is shown in the specification,
Figure BDA00023694934800001515
Figure BDA00023694934800001516
it is demonstrated that assuming the value of equation (33) is equal to the constant c, one can obtain
Figure BDA00023694934800001517
Case 1. assume c ≠ 0, since uOL(r) an uncertainty in the (t),
c＝min{|K(tk)+ρmin|,|K(tk)+ρmax|} (40)
in the formula (I), the compound is shown in the specification,
Figure BDA0002369493480000161
by virtue of the assumption that ξ (τ) is not equal to 0 and does not change sign throughout the process, one obtains
Figure BDA0002369493480000162
Figure BDA0002369493480000163
Therefore, when K (t)k) C ≠ 0, and c ≠ 0, the minimum value of c is obtained as c ═ K (t)k)+ρminL. General formula (39)
The optimum control input available is
Figure BDA0002369493480000164
When K (t)k) C ≠ 0, and the minimum value of c is found to be c ═ K (t)k)+ρmaxI, the optimum control input available is
Figure BDA0002369493480000165
Therefore, the optimal control input can be expressed as
Figure BDA0002369493480000166
Case 2. assuming that c is 0, then there is
Figure BDA0002369493480000167
Because of the fact that
Figure BDA0002369493480000168
and ξ (τ) is not equal to 0, an optimum control input can be obtained as
Figure BDA0002369493480000169
In summary, the optimal control command is shown as equation (36).
Step 109: and judging the bait and the real target according to the prediction guidance law.
3) Applied to relative motion model
Combining equation (24) to find the reachable set of position components in the linear system state vector in equation (17)
Figure BDA00023694934800001610
Figure BDA00023694934800001611
Figure BDA0002369493480000171
Guidance of the target for the chaser, in the time interval τ ∈ [0, t ∈ [ ]f]A lure having characteristics similar to the target is randomly launched and a maximum commanded acceleration in the direction opposite to the target acceleration is applied to interfere with the chaser. At the target hairAfter the bait is shot, the chaser will have two similar objects in the field of view. The PDFs of two similar target states can be calculated by a Kalman filter, the PDFs of the target states are Gaussian-distributed before the bait is launched, the PDFs of the target states can be approximated to the sum of M equal probability Gaussian distributions after the bait is launched, and the value of M can be expressed at any one moment in time
M(tk)＝1+Nd(tk) (51)
In the formula, NdThe number of baits not identified.
The peak value of the probability density function of the target position is from tkTime tfThe maximum variation value at the moment is theta, and according to the state equation (6) and the measurement equation (22), the state estimation value of the equation (6) can be obtained through Kalman filtering
Figure BDA0002369493480000172
Sum variance estimate Pk|k∈R5×5. Suppose the lateral displacement y of the chaserPiLateral velocity
Figure BDA0002369493480000173
And the command acceleration uPiIs known, then the current state estimate of the target is obtained
Figure BDA0002369493480000174
Can represent
Figure BDA0002369493480000175
The current variance estimate may be expressed as
Figure BDA0002369493480000176
In the formula I3×3Is an identity matrix.
According to the mean value and the variance of the current target state and the kinematic equation of the target, the position component of the target state at the terminal time t can be obtainedfMean and variance, i.e.
Figure BDA0002369493480000177
Figure BDA0002369493480000178
Theta is made up of two parts, one from t at maximum commanded accelerationkTime tfthe time of day variation, the alpha standard deviation of the estimate of the position component in the target state, i.e.
θ(tk)＝θ1(tk)+αθ2(tk) (55)
Figure BDA0002369493480000179
Figure BDA00023694934800001710
In combination with equation (36), the linear system in equation (17) satisfies the optimal solution under the condition of equation (30)
Figure BDA0002369493480000181
Can be given by the following two formulas:
Figure BDA0002369493480000182
Figure BDA0002369493480000183
bait stage is identified:
step 110: acquiring a state transition matrix; the state transition matrix is a state transition matrix of the moment state of the unrecognized decoy stage to the moment state of the recognized decoy stage.
Step 111: determining an optimal guidance law according to the state transition matrix and the optimal compromise guidance point by using an optimal control theory; the optimal guidance law is an optimal guidance law for controlling the view separation angle.
If the predictive guidance law is continued after the decoy is recognized, without controlling the line-of-sight angles of the two chasers, it may happen that the line-of-sight separation angle of the two chasers becomes smaller and smaller, because in "when the line-of-sight separation angle of the two chasers with respect to the evacuee | λPiE-λPjEWhen | decreases, the lateral relative distance yiWill increase, resulting in a decrease in the accuracy of the state estimation ", the accuracy of the state estimation will deteriorate.
If after the lure is identified, the chaser with the large initial line-of-sight angle maximizes his line-of-sight angle and the other minimizes his line-of-sight angle, then the line-of-sight separation angle between the two chasers will be large and the estimation accuracy will be enhanced.
Therefore, the optimal control is adopted in the stage to comprehensively consider the miss distance and the energy consumption to achieve the aim.
1) Performance index
By using the assumption of small deviation under nominal collision triangle conditions, the lateral relative distance of the chaser
Figure BDA0002369493480000186
Can be approximated as
Figure BDA0002369493480000184
rPiE≈vPiEtgo(61)
Then, the angle of sight λPiECan be approximated as
Figure BDA0002369493480000185
Thus, introduce
Figure BDA0002369493480000191
This term, and setting the performance index of the optimum control to
Figure BDA0002369493480000192
Where Δ t > 0, is a small amount close to 0.
Note 5. use
Figure BDA0002369493480000193
Instead of the former
Figure BDA0002369493480000194
In order to avoid singularity in the subsequent derivation process, when Δ t → 0,
Figure BDA0002369493480000195
when the weight coefficient a → ∞ is given, a perfect interception guidance law can be generated. If the weighting factor c > 0, the line of sight of the chaser can be minimized, and if c < 0, the line of sight of the chaser can be maximized.
2) Order reduction
In order to reduce the order of solving the optimization problem and obtain the analytic solution of the control input, a terminal projection method is introduced to reduce the order of the model, and a new state variable Z is introducedi(t)，
Zi(t)＝DΦi(tf,t)xi(t) (64)
In the formula phii(tfT) is the state transition matrix associated with equation (6); d is a constant vector used for separating state variable xi(t) elements in (a). When D is [ 1000 ]]Time, separable state variable xiThe lateral relative distance y ini。
Because of the fact that
Figure BDA0002369493480000196
Combination (65) and new state variable Zi(t) derivative with respect to time, can be obtained
Figure BDA0002369493480000197
Formula (66) shows
Figure BDA0002369493480000198
Is state independent, is only relevant to the designed controller, and is connected with D phii(tf,t)BiIs marked as
Figure BDA0002369493480000199
Using the new variables obtained by the reduction of the terminal projection method, the objective function of equation (63) can be expressed as
Figure BDA00023694934800001910
3) Optimal controller Optimal controller
The Hamilton Hamiltonian function of the performance index is
Figure BDA0002369493480000201
From the cross-sectional conditions and the adjoint equation
Figure BDA0002369493480000202
λZ(tf)＝aZi(tf) (70)
From t to formula (69)fIntegration until t and substitution of equation (70) gives
Figure BDA0002369493480000203
From the control equation
Figure BDA0002369493480000204
By substituting formula (72) for formula (66)
Figure BDA0002369493480000205
From t to t for equation (73)fThe integral can be obtained
Figure BDA0002369493480000206
In the formula (I), the compound is shown in the specification,
Figure BDA0002369493480000207
the finishing formula (74) can be obtained
Figure BDA0002369493480000208
Will Zi(tf) Optimal controller obtained in formula (72)
Figure BDA0002369493480000211
When a → ∞ a, a perfect interception guidance law can be generated, that is
Figure BDA0002369493480000212
Step 112: and intercepting the real target according to the optimal guidance law.
Simulation analysis:
the proposed prediction guidance law based on the highest probability interval and the proposed cooperative guidance law based on the optimal control consideration detection configuration, which are designed respectively for two phases, are analyzed by using numerical simulation.
Firstly, simulation parameters are set, the fighting situations of four aircrafts are analyzed, and the estimation precision and guidance performance of a chaser are evaluated by Monte Carlo (MC) simulation.
1. Interception situation and parameter setting:
aiming at the prediction guidance law, the following simulation parameters are set: the chaser 1 and the chaser 2 are both launched simultaneously, and the initial distance between the chaser and the evacuee is equal to
Figure BDA0002369493480000213
Their initial lateral relative distances are respectively
Figure BDA0002369493480000214
And
Figure BDA0002369493480000215
the velocities of the chaser and the dodder are v respectivelyPi700m/s and vE300m/s, the maximum command acceleration of the chaser and the evacuee neglecting the influence of gravity is
Figure BDA0002369493480000216
And
Figure BDA0002369493480000217
the overload of the chaser and the evacuee corresponds to a time constant of tauPi0.2s and τE0.2 s. The simulation time interval of measurement is delta 0.01s, and the standard deviation of the line-of-sight angle measurement noise is sigmaPi,λ＝0.1mrad。
The direction of the acceleration of the bait is opposite to the direction of the acceleration of the evacuee, and the magnitude of the acceleration is equal to the maximum command acceleration of the evacuee, namely
Figure BDA0002369493480000218
To implement MC simulations, the initial conditions for filtering are set to follow a gaussian distribution:
Figure BDA0002369493480000219
in the formula (I), the compound is shown in the specification,
Figure BDA00023694934800002110
is a true initial state, P, defined by equation (4)0Is an initial error variance matrix of
P0＝diag{502,102,12,102} (79)
Fig. 5 is a schematic diagram of the engagement of evacuees, chasers 1, chasers 2 and baits according to the present invention. As shown in fig. 5, the multiple aircraft cooperatively intercept the battle trajectory, the bait deployment and identification time is 2s and 5s, the evacuee launches one bait at 2s to interfere with the chasers 1 and 2, and assuming that the bait identification time of the chaser is 3s, the chaser can identify the real target after 5s and guide the real target. As can be seen from the prediction guidance law, the chaser adopts the prediction guidance law capable of guiding while considering both the targets at the same time before 5s, and the chaser adopts the optimum guidance law capable of controlling the view separation angle after 5 s.
Fig. 6 is a diagram showing the lateral relative distance change between the chaser 1 and the chaser 2 and the evacuee provided by the present invention, as can be seen from fig. 6, the lateral relative distance change between the chaser 1 and the chaser 2 is-400 m and-300 m, and initially, the absolute value of the direction-finding relative distance between the chaser 1 and the chaser 2 decreases from 400m and 300m to zero, but the evacuee launches one bait in 2s until the bait is not recognized in 5s, the chaser 1 and the chaser 2 are affected by the bait, and the relative distance between the chaser and the target starts to increase. Until the bait is identified, the chasers 1 and 2 adopt an optimal guidance law, and the relative distance between the chasers and the evacuees starts to be continuously reduced until the interception moment, and the relative distance reaches near zero.
FIG. 7 is a schematic view of the acceleration of evacuee, chaser 1 and chaser 2 provided by the present invention, the maximum values of the acceleration change of evacuee, chaser 1 and chaser 2 are 3g, 15g and 15g respectively, and the command is given at the maximum acceleration
Figure BDA0002369493480000221
Under the limitation of (2), the change of the acceleration of the chaser 1 and the chaser 2 is basically the same in the first 5s, and after the 2s evacuee launches the bait, the change of the acceleration of the chaser 1 and the chaser 2 is more severe, and the overload limit value is reached quickly. It should be noted that the different acceleration trends of the 5s front and rear chasers 1 and 2 are due to different guidance laws.
2. Evaluation of estimated Performance
Fig. 8 is a graph showing changes in lateral distance detection errors between the chaser 1 and the evacuee in the pure prediction guidance law and the proposed guidance law, taking the chaser 1 as an example, provided by the present invention, and fig. 9 is a graph showing changes in the line-of-sight separation angle between the two chasers in the pure prediction guidance law and the proposed guidance law, provided by the present invention. Comparing fig. 8 to fig. 9, it can be seen that, before 5s, since the line-of-sight angles of the two chasers with respect to the evacuee cannot be controlled by the prediction guidance based on the HPI method, the line-of-sight separation angles of the two chasers are small, and the detection error of the lateral distance of the chasers to the evacuee is large. After 5s, the line-of-sight separation angle under the pure predictive guidance law is still small, but the proposed guidance law is able to control and maximize the line-of-sight separation angle, so the measurement noise decreases until around zero.
Fig. 10 is a variance variation graph of the state estimation error after 500 MC simulations provided by the present invention, and it can be known from fig. 10 that variance variations under the pure prediction guidance law and the proposed guidance law show a trend of increasing first and then gradually decreasing, but the variance under the pure prediction guidance law is obviously greater than the variance under the proposed guidance law at each time. In addition, the proposed guidance law can enable the variance of the state estimation error to finally approach zero, so that the requirement on the estimation accuracy is met, but the pure prediction guidance law cannot ensure that the variance finally approaches zero, so that the final detection error is very large.
3. Assessment of the amount of miss
The closed-loop interception performance of the pure prediction guidance law and the proposed guidance law is analyzed through 500 times of MC simulation.
Fig. 11 is a schematic diagram of the cumulative distribution function of the miss distance of the chaser 1 under the pure prediction guidance law and the proposed guidance law provided by the present invention, and fig. 12 is a schematic diagram of the cumulative distribution function of the miss distance of the chaser 2 under the pure prediction guidance law and the proposed guidance law provided by the present invention, which defines the minimum value of the miss distance of the chaser. Fig. 11-12 compare the Cumulative Distribution Function of miss distance (CDF) between pure and proposed guidance laws, and the Warhead kill range (WLR) required to ensure 95% kill probability.
Table 1 is a comparison table of warhead killing ranges required for ensuring 95% killing probability provided by the present invention, and as shown in table 1, taking the chaser 1 as an example, under the condition of achieving 95% killing probability, the WLR required by the proposed guidance law is 2.91m minimum, and the WLR required by the pure prediction guidance law is 19.63 m. It can be seen that the WLR required for the proposed guidance law is much lower than the pure predictive guidance law. The result shows that the interception performance of the guidance law is superior to that of a pure prediction guidance law.
TABLE 1
Figure BDA0002369493480000231
TABLE 2
Figure BDA0002369493480000232
Figure BDA0002369493480000241
Taking the chaser 1 as an example, fig. 13 is a schematic diagram of the miss distance distribution function with the bait recognition delay times of 1s, 2s, 3s and 4s under the proposed guidance provided by the present invention, and a WLR comparison table required to ensure 95% killing probability under different recognition delay times is given in table 2. As can be seen from Table 2, the WLRs required for the proposed law at 1s, 2s, 3s and 4s delay times are 2.23m, 2.69m, 2.91m and 3.08m, respectively. As can be seen from fig. 13, as the recognition delay time increases, the WLR required by the chaser increases, which indicates that the delay time for recognizing the bait affects the interception performance of the chaser, and a shorter recognition time increases the guidance accuracy of the chaser.
Considering the situation that two chasers of our party intercept an enemy evacuee, the enemy evacuee launches a bait with similar characteristics to the evacuee to interfere the chasers of our party. Aiming at the situation, the invention provides a two-stage cooperative guidance law, namely, a prediction guidance law based on an HPI (high performance indicator) method is adopted in the decoy stage, and an optimal guidance law based on an optimal control theory considering the detection configuration is adopted in the decoy stage.
For the first stage, the PDF of the target is composed of the states of real target and false target, due to the interference of unidentified decoys, assuming the multi-peak state shown in FIG. 4. The multi-peak state is shown. Therefore, the prediction guidance law introducing the GST concept is adopted, the prediction guidance law can simultaneously give consideration to the real target and the false target in the guidance process, and the maneuvering advantage is provided for the guidance of the real target later. And aiming at the second stage, after the bait is identified, considering the influence of the detection configuration on the guidance precision, and adopting an optimal guidance law capable of controlling the sight separation angle of the two chasers relative to the target to reduce estimation errors in the guidance process and enhance the guidance precision.
The performance of the proposed guidance law and the pure prediction guidance law is compared through MC simulation. The result shows that compared with a pure prediction guidance law, the provided guidance law has lower estimation error and higher guidance precision; in addition, a short recognition delay time can improve the interception performance, so that it is necessary to select a fast and effective recognizer.
Compared with the existing multi-aircraft cooperative guidance technology, on one hand, most of designed guidance laws do not consider the condition that an enemy target can emit baits for interference, the method provided by the scheme can effectively process the influence of the baits interference and simultaneously accords with the development trend of the aircraft interception and anti-interception countermeasure technology; on the other hand, the scheme considers the detection error of the relative position information of the two aircrafts cooperatively measuring the target, and contrasts and analyzes the influence of the sight separation angle on the detection precision and the guidance precision. According to simulation, compared with the traditional method, the method provided by the method is lower in estimation error and higher in guidance precision.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (10)

1. A method of intercepting an aircraft in the event of a bait disturbance, comprising: an unrecognized bait stage and a recognized bait stage;
decoy stage not identified: acquiring ideal flight parameters of the aircraft in an ideal state; the aircraft comprises a plurality of chasers and evacuees; the flight parameters comprise speed, acceleration, an overload response time constant and the lateral relative distance between the evacuee and the chaser;
determining a relative motion state equation between the chaser and the evacuee according to the flight parameters;
in the pursuit process, acquiring the measurement noise error of the pursuit person in the measurement process and the relative distance and the line-of-sight angle information between the two pursuit persons;
determining a relative distance between the chaser and the evacuee according to the relative distance between the chasers and the line-of-sight angle information;
determining a relative motion measurement equation between the chaser and the evacuee according to the relative distance between the chaser and the evacuee and the measurement noise error;
acquiring pursuit parameters of the chaser; the pursuit parameters comprise a state reachable set of a state that the chaser transitions from any one time to an interception time, a position component reachable set of a state that a position component of the chaser transitions from any one time to an interception time, and a maximum command acceleration of the chaser;
determining rolling control constraint conditions according to the chasing parameters;
under the rolling control constraint condition, determining an optimal compromise guidance point by using a highest probability interval method, and constructing a prediction guidance law according to the relative motion state equation and the relative motion measurement equation;
judging bait and a real target according to the prediction guidance law;
bait stage is identified: acquiring a state transition matrix; the state transition matrix is a state transition matrix for the moment state of the unrecognized bait stage to the moment state of the recognized bait stage;
determining an optimal guidance law according to the state transition matrix and the optimal compromise guidance point by using an optimal control theory; the optimal guidance law is an optimal guidance law for controlling the sight separation angle;
and intercepting the real target according to the optimal guidance law.
2. The aircraft interception method under decoy jamming condition according to claim 1, wherein said determining a relative motion state equation between a chaser and an evacuee according to said flight parameters specifically comprises:
using formulas
Figure FDA0002369493470000021
Determining a relative motion state equation between the chaser and the evacuee; wherein the content of the first and second substances,
Figure FDA0002369493470000022
is a relative motion state equation;
Figure FDA0002369493470000023
Figure FDA0002369493470000024
τPiis the overload response time constant, τ, of the chaserE(ii) an overload response time constant for said evacuee; u. ofPiA control input for the chaser;
Figure FDA0002369493470000025
the command acceleration of the evacuee is shown, and w is noise in the guidance process of the aircraft; t is time.
3. The method according to claim 1, wherein said determining a relative motion measurement equation between said chaser and said evacuee based on said relative distance between said chaser and said evacuee and said measurement noise error comprises:
using formulas
Figure FDA0002369493470000026
Determining a relative motion measurement equation between the chaser and the evacuee; wherein, H ═ 1000]；xiIs a state vector of the aircraft;
Figure FDA0002369493470000027
measuring a noise obedience distribution for the chaser's gaze; y isiIs the lateral relative distance of the line of sight angle between the chaser and the evacuee.
4. The aircraft interception method under the bait jamming condition according to claim 1, wherein the determining an optimal compromise guidance point by using a highest probability interval method under the rolling control constraint condition and constructing a prediction guidance law according to the relative motion state equation and the relative motion measurement equation specifically comprises:
by using
Figure FDA0002369493470000028
Constructing a prediction guidance law; wherein the content of the first and second substances,
Figure FDA0002369493470000029
is a predictive guidance law;
Figure FDA00023694934700000210
f(tk+1)＝DβΦPi(tf,tk+1)，
Figure FDA00023694934700000211
for the best possible projection of the guide points, DβAs a vector separating the position components, phiPi(tk+1,tk) From t for the chaserkTime tk+1State transition matrix of time phiPi(tf,tk+1) From t for the chaserk+1Time tfState transition matrix at time, tfFor the final intercept time, tk+1At any time during the guidance process;
Figure FDA0002369493470000031
Φpi(tk+1τ) from time τ to tk+1A state transition matrix of a time;
Figure FDA0002369493470000032
is the maximum commanded acceleration.
5. The aircraft interception method under the bait jamming condition according to claim 1, wherein said determining an optimal guidance law according to the state transition matrix and the optimal compromise guidance point by using an optimal control theory specifically comprises:
using formulas
Figure FDA0002369493470000033
Determining an optimal guidance law; wherein Z isi(t) is a new state variable for the chaser; a, b and c are weight coefficients;
Figure FDA0002369493470000034
tgois the remaining time of the guidance process; Δ t is a positive infinitesimal quantity; d ═ 1000]Is a separation vector; phii(tfT) is from time t to tfState transition of relative motion at timeAnd (4) matrix.
6. An aircraft intercept system in the event of a bait disturbance, comprising: an unrecognized bait stage and a recognized bait stage;
an ideal flight parameter acquisition module for the unrecognized bait phase: acquiring ideal flight parameters of the aircraft in an ideal state; the aircraft comprises a plurality of chasers and evacuees; the flight parameters comprise speed, acceleration, an overload response time constant and the lateral relative distance between the evacuee and the chaser;
the relative motion state equation determining module is used for determining a relative motion state equation between the chaser and the evacuee according to the flight parameters;
the parameter acquisition module in the measuring process is used for acquiring the measurement noise error of the chasers in the measuring process and the relative distance and the line-of-sight angle information between the two chasers in the chasing process;
a relative distance determination module for determining a relative distance between the chaser and the evacuee according to the relative distance between the chasers and the line-of-sight angle information;
a relative motion measurement equation determination module, configured to determine a relative motion measurement equation between the chaser and the evacuee according to the relative distance between the chaser and the evacuee and the measurement noise error;
the pursuit parameter acquisition module is used for acquiring pursuit parameters of the pursuit person; the pursuit parameters comprise a state reachable set of a state that the chaser transitions from any one time to an interception time, a position component reachable set of a state that a position component of the chaser transitions from any one time to an interception time, and a maximum command acceleration of the chaser;
the rolling control constraint condition determining module is used for determining a rolling control constraint condition according to the pursuit parameter;
the prediction guidance law building module is used for determining an optimal compromise guidance point by using a highest probability interval method under the rolling control constraint condition and building a prediction guidance law according to the relative motion state equation and the relative motion measurement equation;
the judging module is used for judging baits and real targets according to the prediction guidance law;
a state transition matrix acquisition module to identify a bait phase: acquiring a state transition matrix; the state transition matrix is a state transition matrix for the moment state of the unrecognized bait stage to the moment state of the recognized bait stage;
the optimal guidance law determining module is used for determining an optimal guidance law according to the state transition matrix and the optimal compromise guidance point by using an optimal control theory; the optimal guidance law is an optimal guidance law for controlling the sight separation angle;
and the intercepting module is used for intercepting the real target according to the optimal guidance law.
7. The aircraft intercept system of claim 6 wherein said relative motion state equation determination module comprises in particular:
a relative motion state equation determination unit for using the formula
Figure FDA0002369493470000041
Determining a relative motion state equation between the chaser and the evacuee; wherein the content of the first and second substances,
Figure FDA0002369493470000042
is a relative motion state equation;
Figure FDA0002369493470000043
τPiis the overload response time constant, τ, of the chaserE(ii) an overload response time constant for said evacuee; u. ofPiA control input for the chaser;
Figure FDA0002369493470000044
the command acceleration of the evacuee is shown, and w is noise in the guidance process of the aircraft; t is time.
8. The aircraft intercept system of claim 6 wherein said relative motion measurement equation determination module comprises in particular:
a relative motion measurement equation determination unit for using the formula
Figure FDA0002369493470000051
Determining a relative motion measurement equation between the chaser and the evacuee; wherein, H ═ 1000]；xiIs a state vector of the aircraft;
Figure FDA0002369493470000052
measuring a noise obedience distribution for the chaser's gaze; y isiIs the lateral relative distance of the line of sight angle between the chaser and the evacuee.
9. The aircraft interception system under decoy jamming condition of claim 6, wherein said predictive guidance law construction module specifically comprises:
a prediction guidance law construction unit for utilizing
Figure FDA0002369493470000053
Constructing a prediction guidance law; wherein the content of the first and second substances,
Figure FDA0002369493470000054
is a predictive guidance law;
Figure FDA0002369493470000055
f(tk+1)＝DβΦPi(tf,tk+1)，
Figure FDA0002369493470000056
for the best consideration of guidanceProjection of points, DβAs a vector separating the position components, phiPi(tk+1,tk) From t for the chaserkTime tk+1State transition matrix of time phiPi(tf,tk+1) From t for the chaserk+1Time tfState transition matrix at time, tfFor the final intercept time, tk+1At any time during the guidance process;
Figure FDA0002369493470000057
τ∈[tk,tk+1]，Φpi(tk+1τ) from time τ to tk+1A state transition matrix of a time;
Figure FDA0002369493470000058
is the maximum commanded acceleration.
10. The aircraft interception system under decoy jamming condition of claim 6, wherein said optimal guidance law determination module specifically comprises:
an optimal guidance law determining unit for using a formula
Figure FDA0002369493470000059
Determining an optimal guidance law; wherein Z isi(t) is a new state variable for the chaser; a, b and c are weight coefficients;
Figure FDA00023694934700000510
Figure FDA00023694934700000511
tgois the remaining time of the guidance process; Δ t is a positive infinitesimal quantity; d ═ 1000]Is a separation vector; phii(tfT) is from time t to tfA state transition matrix of relative motion at a time.
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