A method for reconstructing cooperative flight time in mid- to terminal guidance

Abstract

The present invention discloses a method for reconstructing the coordinated flight time of mid-terminal guidance. Using the method, after multiple hypersonic glide missiles encounter an interception penetration during the glide phase, the method can reconstruct and coordinate the flight times of the glide phase and the terminal guidance phase by changing the speed of the mid-terminal handover point, based on the premise that the parameters of the mid-terminal handover point remain unchanged, to achieve a coordinated attack on the target. To address the problem of still being able to fly in coordination during the glide phase when encountering a penetration, the method simultaneously adjusts the flight times of the mid-terminal and terminal guidance phases by changing the speed of the mid-terminal handover point, based on the premise that the parameter information of the mid-terminal handover point is the same as that during the original coordinated flight. Given the total flight time proposed by the present invention, the speed of the mid-terminal handover point corresponding to the time is calculated, and then the corresponding flight time distribution of the glide phase and the terminal guidance phase is obtained, ultimately achieving coordinated flight of multiple missiles and simultaneous target impact.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft collaborative guidance and control, and in particular to a mid-terminal guidance collaborative flight time reconstruction method. Background Art

[0002] The development of hypersonic glide missiles has forced the US Missile Defense Agency to implement a regional glide phase intercept weapon system defense plan. As defense systems strengthen, the survivability and combat capabilities of individual glide missiles face severe challenges, making multi-missile coordinated operations of great significance.

[0003] At present, the research on the coordination strategy of multiple glide bombs is mainly divided into the coordination strategy research of the glide phase and the terminal guidance phase. In order to solve the time coordination problem of the glide phase, the prior art [1] (see Wang Xiao, Guo Jie, Tang Shengjing, Qi Shuai. Time coordination reentry guidance based on analytical profile [J]. Acta Aeronautica Sinica, 2019, 40(03): 239-250.) introduced the flight time and range requirements into the design of the reference profile, and achieved reentry time coordination by adjusting the parameters. The prior art [2] (Liang Z, Yu J, et al. Trajectory planning for cooperative flight of two hypersonic entry vehicles [C] / / 21st AIAA International Space Planes and Hypersonics Technologies Conference. 2017: 2251.) adjusted the line of sight corridor width according to the error between the expected flight time and the estimated flight time to achieve a time-controlled reentry flight. Prior art [3] (see Song Rui, Zhu Yong, et al. Cooperative reentry trajectory planning for hypersonic aircraft based on sequential convex optimization [J]. Tactical Missile Technology, 2020(06):7-16.) uses a convex optimization method to solve the reentry glide guidance problem that meets the flight time constraint. In order to solve the time coordination problem in the terminal guidance phase, prior art [4] adjusts the velocity lead angle in the yaw direction based on the error between the remaining range and the expected range for missiles with uncontrollable speed and certain longitudinal motion, and achieves time coordination by realizing simultaneous multi-missile attack on the target. Prior art [5] uses the error between the estimated remaining flight time and the expected flight time as feedback to construct an optimization model to meet the attack time constraint.

[0004] The above existing technologies all study the design problem of collaborative guidance methods under the premise of given expected flight times of the gliding segment (also called "mid-guidance segment") and the terminal guidance segment, and mainly focus on designing algorithms to meet given time constraints. However, the given and coordinated design problems of the expected flight times of the mid-guidance segment and the terminal guidance segment are not involved.

[0005] In actual combat, if a gliding missile encounters a mid-course interception, the flight time of the mid- and terminal guidance sections will change after the penetration. At this time, the gliding missile may not be able to achieve the expected flight time originally specified in each stage. In order to ensure that multiple gliding missiles can still reach the target at the same time, it is necessary to coordinate and reconstruct the expected flight time of the mid- and terminal guidance sections of the gliding missile. However, no research in this regard has been seen so far. Summary of the Invention

[0006] In view of this, the present invention provides a method for reconstructing the coordinated flight time of mid-terminal guidance. After multiple hypersonic gliding missiles encounter interception and penetration in the gliding phase, based on the premise that the parameters of the mid-terminal handover point remain unchanged, the method can reconstruct and coordinate the flight time of the gliding phase and the terminal guidance phase by changing the speed of the point, so as to achieve a coordinated attack on the target.

[0007] To achieve the above object, the technical solution of the present invention includes the following steps:

[0008] M glide bombs are expected to have a total flight time t z In coordinated flight, the glide segment flight time of each gliding bomb is designated as t hx , the flight time of the terminal guidance phase is t mo .

[0009] Determine when the defensive missile enters the detection range of N gliding missiles When t1 is reached, the N missiles are recorded as Class II missiles, and penetration measures are taken for Class II missiles. The remaining gliding missiles are recorded as Class I missiles, and no penetration measures are taken for Class I missiles. The moment of successful penetration is t1; N≤M.

[0010] After the penetration is successful, the estimated flight time range of M missiles from the moment of successful penetration to the moment of hitting the target, and the intersection of the remaining total flight time range of Class I missiles is T I , the intersection of the remaining total flight time range of Class II projectiles is T II , the expected remaining total flight time is

[0011] like If , then the Class I projectile does not need to be reconstructed, and the Class II projectile can be reconstructed as follows: Let the remaining expected total flight time of the Class II projectile be Use the calculation method of the speed of the middle and end handover points that meets the expected total flight time to calculate the speed that meets the expected total flight time. The speed of the Class II projectile at the mid-term handover point

[0012] like If not established, then judge Whether it is established, there are two situations:

[0013] like If it is established, then the time is selected from the intersection of the remaining total flight time ranges of Class I and Class II projectiles As the remaining expected total flight time of Class I and Class II ammunition, the speed calculation method of the mid-term and final handover points that meet the expected total flight time is used to calculate the speed that meets the expected total flight time. The speed of the middle and end handover points

[0014] like If it is not true, reconstruction is impossible.

[0015] Furthermore, the calculation method of the speed at the mid-to-end handover point that meets the expected total flight time is as follows:

[0016] Step 1: Under the premise of determining the terminal guidance law, for the same initial state - the missile-target distance r MT , height h M 、Ballistic inclination angle θ M and the leading angle η in the yaw direction M , its minimum terminal velocity constraint determines the minimum initial velocity V of the terminal guidance min_m The available overload constraint determines the maximum initial velocity V of the terminal guidance. max_m , based on this construction [r MT ,h M ,θ M ,η M ] as input, [V min_m ,V max_m ] is the output of the first neural network:

[0017] [V min_m ,V max_m ]=f1(r MT ,h M ,θ M ,η M ):

[0018] The glide missile's initial moment in the terminal guidance phase MT ,h M ,V M ,θ M ,η M ] determines the flight time t of the terminal guidance phase mo , V M is the speed of the gliding missile, and its value range is [V min_m ,V max_m ], build with [r MT ,h M ,V M ,θ M ,η M ] is the input, and the flight time t of the terminal guidance segment is mo The second neural network is the output:

[0019] t mo =f2(r MT ,h M ,V M ,θ M ,η M ).

[0020] Step 3: Training the dual network composed of the first neural network and the second neural network;

[0021] For the terminal guidance phase with different initial states, the time range of the terminal guidance phase is obtained by applying the trained first neural network and the second neural network online: First, the input initial state quantity X = [r MT ,h M ,θ M ,η M ] is brought into the first neural network to obtain the speed range [V min_m ,V max_m ], then [r MT ,h M ,θ M ,η M ] and [V min_m ,V max_m ] is brought into the second neural network as input to obtain the flight time range of the terminal guidance segment.

[0022] Step 4: For the terminal guidance phase with different initial states, the two trained neural networks are applied online to obtain the time range of the terminal guidance phase: First, the input initial state quantity X = [r MT ,h M ,θ M ,η M ] is brought into the first neural network to obtain the initial velocity range of the terminal guidance phase [V min_m ,V max_m ], then [r MT ,h M ,θ M ,η M ] and [V min_m ,V max_m ] is taken as input into the second neural network to obtain the flight time range of the terminal guidance segment.

[0023] Step 5: Let the time when the glide missile starts gliding be t0 and the time when the penetration ends be t1; in the time period from t0 to t1, the flight time t of the glide segment is predicted by analytical method. hx , the flight time t in the analytical method hx It is only related to the terminal velocity, that is, the terminal velocity range of the gliding segment determines the flight time range of the gliding segment.

[0024] According to the initial velocity range of the terminal guidance segment [V min_m ,V max_m ], the terminal velocity range of the gliding section is [V min_m ,min(V max_hx ,V max_m )],V max_hx is the maximum speed at the terminal of the gliding segment.

[0025] The flight time range of the gliding segment is obtained according to the terminal speed range of the gliding segment.

[0026] Step 6: Expected total flight time is t z When the expected total flight time is met, the speed at the middle and end handover points is V c * The mid-terminal handover point is the intersection of the gliding section and the terminal guidance section, that is, the speed at the mid-terminal handover point is the terminal speed of the gliding section.

[0027] The expected total flight time t is calculated by Newton iteration method z The speed at the middle and end handover points

[0028]

[0029] Where, the subscript k represents the number of iterations;

[0030] Each iteration corresponds to Indicates the speed of the middle and end handover points The corresponding total flight time and the expected total flight time t z The function of the difference is as follows:

[0031]

[0032] Where, For Substitute the glide velocity into the second neural network to obtain the terminal guidance flight time, For The flight time obtained analytically as the terminal velocity, for The derivative of

[0033] The total number of iterations of the Newton iteration method is set, and the final iteration obtains the speed of the mid-to-end handover point that meets the expected total flight time.

[0034] Furthermore, an analytical method is used to predict the flight time t hx , the flight time t in the analytical method hx Only relevant for terminal velocity, specifically:

[0035] At t = t0 and t = t1, the flight time is predicted analytically as follows:

[0036]

[0037] Where R0 is the radius of the earth, g0 is the acceleration of gravity, S go is the remaining range, V M is the glide velocity, V f is the terminal speed of the glide segment.

[0038] Remaining distance S go It is obtained from the following formula:

[0039] S go =R0 arccos(cosφ M cosφ f cos(λ M -λ f )+sinφ M sinφ f )

[0040] where φ f is the latitude of the gliding segment terminal, λ f is the longitude of the terminal of the gliding segment, φ M is the current latitude of the glide missile, λ M is the current longitude of the glider; if V is known M and current location information, the terminal location remains unchanged, S go It is certain.

[0041] Flight time t hx The remaining distance S go 、Current speed V M and terminal velocity V f Determine, therefore the flight time t hx Only with terminal velocity V f The terminal velocity range of the gliding segment determines the flight time range of the gliding segment.

[0042] Furthermore, V max_hx is the maximum speed at the end of the gliding phase, V max_hx Solve it as follows:

[0043] From the relationship between the remaining range of the gliding segment, the terminal velocity, and the current velocity, we can obtain:

[0044]

[0045] Among them, R0 is the radius of the earth, g0 is the acceleration of gravity, S go is the remaining range, V M is the glide velocity, V fis the terminal speed of the gliding phase; L M and D M is the lift and drag of the gliding missile; σ M is the roll angle of the glide bomb.

[0046] Take cosσ M =1; take the maximum lift-to-drag ratio, and based on this, calculate V f The value is taken as the maximum speed V at the end of the gliding segment max_hx estimated value.

[0047] Furthermore, the dual network composed of the first neural network and the second neural network is trained in the following manner: data samples are obtained by simulation method, 80% of the data samples are used as training sets and 20% as test sets, the LM algorithm is used as the training function, and the mean square error is used as the performance function; after the training set is input into the network, the corresponding prediction network is obtained after the error converges.

[0048] Beneficial effects:

[0049] 1. The present invention provides a method for reconstructing the coordinated flight time of mid- and terminal guidance. To address the problem of coordinated flight during the gliding phase when encountering a penetration, the method adopts the premise that the parameter information of the mid- and terminal handover points is the same as that during the original coordinated flight. By changing the speed of the mid- and terminal handover points, the flight time of the mid- and terminal guidance phases is adjusted simultaneously. The method proposes a given total flight time, solves the speed of the mid- and terminal handover points corresponding to the time, and then obtains the corresponding flight time distribution of the gliding phase and the terminal guidance phase, ultimately achieving the coordinated flight of multiple missiles and simultaneous target hits.

[0050] 2. The present invention provides a method for reconstructing the coordinated flight time of mid-terminal guidance. To solve the problem that the remaining flight time of a hypersonic gliding missile is difficult to predict, the present invention uses a trained first neural network to obtain the initial velocity range of the terminal guidance segment [V min_m ,V max_m ], and the maximum terminal velocity V can be achieved by combining the gliding section max_hx The final initial velocity range of the terminal guidance section is [V min_m ,min(V max_hx ,V max_m )], and then the second neural network obtains the flight time range of the terminal guidance phase. Compared with existing technologies that use offline neural network training, online estimation can quickly predict the flight time of the terminal guidance phase. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Schematic diagram of the flight time reconstruction strategy flow;

[0052] Figure 2The figure is a schematic diagram of the coordinated flight trajectory of two gliding bombs in the terminal guidance phase;

[0053] Figure 3 This is a schematic diagram of control instructions for the gliding phase;

[0054] Figure 4 Schematic diagram of process constraints for the gliding stage;

[0055] Figure 5 This is a schematic diagram of the mean square error of the first neural network;

[0056] Figure 6 This is the result graph of the first neural network test set;

[0057] Figure 7 is the mean square error graph of the second neural network;

[0058] Figure 8 This is the result graph of the second neural network test set;

[0059] Figure 9 This is the ballistic diagram after the breakthrough;

[0060] Figure 10 is the speed change diagram;

[0061] Figure 11 This is a diagram of the change in trajectory inclination. DETAILED DESCRIPTION

[0062] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0063] The present invention provides a method for reconstructing the coordinated flight time of mid- to terminal guidance. This method addresses the coordination problem of multiple hypersonic glide missiles after encountering an interception penetration during the glide phase. First, the following model is constructed for the glide missiles:

[0064] Assuming that the earth is a uniform sphere and its rotation is ignored, the three-degree-of-freedom equations of the gliding missile are:

[0065]

[0066] Among them, V M ,θ M , ψ vM , σ M 、R M ,λ M 、φ M m M , L M and D M are the speed, ballistic inclination, ballistic deviation, roll angle, distance from the center of the earth, longitude, latitude, mass, lift and drag of the gliding missile, t is the flight time, and g is the acceleration due to gravity.

[0067] The present invention uses the gliding missile launching point (λ M0 ,φ M0 , R M0 ) is used as the origin to establish the emission coordinate system (λ M0 ,φ M0 , R M0 are the longitude, latitude, and distance from the center of the Earth (the x-axis points to the target, the y-axis is positive upward in the vertical plane through the x-axis, and the z-axis is defined by the right-hand rule. The coordinates of the aircraft (glide missile) in the launch coordinate system can be described as:

[0068]

[0069] Where A0 is the azimuth; φ is the latitude, and the subscript M refers to the glide bomb; λ is the longitude; R M is the distance from the center of the Earth.

[0070] Where, the magnitude of the azimuth angle A0 is:

[0071]

[0072] where λ T is the longitude of the target, subscript T is the target; φ T is the latitude of the target;

[0073] Assuming that multiple gliding missiles fly in coordination, the gliding phase adopts convex optimization algorithm to fly in coordination, and within the set expected flight time t hx Arrive at the designated gliding segment terminal point at the right time.

[0074] When the gliding missile encounters an interception during the gliding process, the longitudinal command is obtained by convex optimization, and the initial angle of attack command required for the optimization is α M =10°. The lateral penetration guidance law based on optimal control theory is adopted in the prior art (see Wang Xiaofang, Zhang Xin, Lin Ping, Li Wen. Penetration and strike integrated strategy based on optimal control [J / OL]. Flight Mechanics: 1-11 [2022-08-23].) to penetrate the defense, and its normal acceleration is:

[0075]

[0076] Among them, a, b and c are penalty coefficients. a is generally taken as a larger value. b and c are set according to the maneuverability of the defensive missile D and the gliding missile M. x(t) represents the lateral line of sight rotation angular velocity between the gliding missile and the defensive missile. is time, q zMD It is the lateral sight rotation angle between the gliding missile and the defensive missile. MD is the distance between the gliding missile and the defensive missile; ψ vM Yaw angle; the yaw rate is obtained from the normal acceleration:

[0077]

[0078] Will Substitute the third equation of formula (1) Ignore V M 2 / R M The influence of the rolling angle command σ is obtained M_com for:

[0079]

[0080] Replace the corresponding variables in the defense missile model with those of the gliding missile (subscript changed to M), and set the thrust to 0. This is the mathematical model of the gliding missile in the terminal guidance phase. The gliding missile uses an extended proportional guidance law with an angle of impact constraint to attack the target:

[0081]

[0082] where a yM is the normal acceleration of the glide projectile in the vertical plane, a zM is the normal acceleration of the gliding projectile in the horizontal plane, where k1 and k2 are proportional coefficients, θ f is the desired trajectory inclination, the remaining time t go =r MT / V M . r MT is the distance between the glide bomb and the target; q yMT The line-of-sight angle between the glide projectile and the target.

[0083] Assuming that the gliding missile is intercepted by the enemy's defensive missile during the gliding phase, the motion equations of the defensive missile are:

[0084]

[0085] The meanings of the variables are the same as those in formula (1), the subscript “D” represents the defensive projectile, and x D 、y D 、z D Its center of mass coordinate in the launch system, P D For its thrust, a yD and a zD The normal accelerations of the vertical and horizontal planes are:

[0086]

[0087] Among them, k3 and k4 are proportional coefficients, and It is the longitudinal and lateral components of the angular velocity of the line of sight between the gliding missile and the defensive missile.

[0088] The thrust scheme of the defensive projectile is:

[0089]

[0090] in, is the mass flow rate per second, I s is the engine specific impulse, t * The moment when the engine stops working.

[0091] The relative motion relationship between the glide missile M, the defensive missile D and the target T is as follows:

[0092]

[0093] In the formula, i=M, j=D (or i=D, j=M) represents the relative motion relationship between the gliding missile and the defensive missile, and i=T, j=M represents the relative motion relationship between the gliding missile and the target it attacks.

[0094] Based on the above motion model, the present invention provides a method for reconstructing the coordinated flight time of mid-terminal guidance, the process of which is as follows: Figure 1 As shown, the following steps are included:

[0095] M glide bombs are expected to have a total flight time t z In coordinated flight, the glide segment flight time of each gliding bomb is designated as t hx , the flight time of the terminal guidance phase is t mo ;

[0096] Determine when the defensive missile enters the detection range of N gliding missiles When t1 is reached, the N missiles are recorded as Class II missiles, which take penetration measures, and the remaining gliding missiles are recorded as Class I missiles, which do not take penetration measures. The moment of successful penetration is t1; N≤M;

[0097] After the penetration is successful, the estimated flight time range of M missiles from the moment of successful penetration to the moment of hitting the target, and the intersection of the remaining total flight time range of Class I missiles is T I , the intersection of the remaining total flight time range of Class II projectiles is T II , the expected remaining total flight time is

[0098] like If , then the Class I projectile does not need to be reconstructed, and the Class II projectile can be reconstructed as follows: Let the remaining expected total flight time of the Class II projectile be Use the calculation method of the speed of the middle and end handover points that meets the expected total flight time to calculate the speed that meets the expected total flight time. The speed of the Class II projectile at the mid-term handover point

[0099] like If not established, then judge Whether it is established, there are two situations:

[0100] like If it is established, then the time is selected from the intersection of the remaining total flight time ranges of Class I and Class II projectiles As the remaining expected total flight time of Class I and Class II ammunition, the speed calculation method of the mid-term and final handover points that meet the expected total flight time is used to calculate the speed that meets the expected total flight time. The speed of the middle and end handover points

[0101] like If it is not true, it cannot be reconstructed.

[0102] Step 1: Terminal guidance phase flight time range prediction method based on dual networks under multiple constraints

[0103] In the present invention, the method for calculating the speed at the mid-to-end handover point that meets the expected total flight time is specifically as follows:

[0104] Step 1: Construct a neural network to predict the initial speed range of terminal guidance under terminal speed and overload constraints, i.e. the first neural network:

[0105] Under the premise of determining the terminal guidance law, for the same initial state - the missile-target distance r MT , height h M 、Ballistic inclination angle θ M and the leading angle η in the yaw direction M , its minimum terminal velocity constraint determines the minimum initial velocity V of the terminal guidance min_m The available overload constraint determines the maximum initial velocity V of the terminal guidance. max_m Therefore, we can construct [r MT ,h M ,θ M ,η M ] is the input, [V min_m ,V max_m ] is the output of the first neural network:

[0106] [V min_m ,V max_m ]=f1(r MT ,h M ,θ M ,η M ).

[0107] Step 2: Construct the terminal guidance flight time prediction neural network and the second neural network

[0108] Under the premise of determining the terminal guidance law, the glide missile's [r MT ,h M ,V M ,θM ,η M ] determines its flight time t mo Considering the dynamic characteristics of the gliding missile and the complexity of the flight environment, it is difficult to obtain the analytical relationship between them. Therefore, in order to predict the flight time of the terminal guidance phase, a [r MT ,h M ,V M ,θ M ,η M ] is input, flight time t mo The second neural network is the output:

[0109] t mo =f2(r MT ,h M ,V M ,θ M ,η M ).

[0110] Step 3: Train the dual network composed of the first neural network and the second neural network.

[0111] For the terminal guidance phase with different initial states, the time range of the terminal guidance phase is obtained by applying the trained first neural network and second neural network online: First, the input initial state quantity X = [r MT ,h M ,θ M ,η M ] is brought into the first neural network to obtain the speed range [V min_m ,V max_m ], then [r MT ,h M ,θ M ,η M ] and [V min_m ,V max_m ] is brought into the second neural network as input to obtain the flight time range of the terminal guidance segment.

[0112] In the embodiment of the present invention, a simulation method is used to obtain data samples. 80% of the data samples are used as a training set and 20% as a test set. The training function uses the LM (Levenberg-Marquardt) algorithm, and the performance function uses the mean square error. After the training set is input into the network, the corresponding prediction network is obtained after the error converges. mo For example, the mean square error is expressed as

[0113]

[0114]

[0115] Among them, t mois the time prediction value, is the actual time value in the training set, MSE is the mean square error, is the relative error, p is the number of samples, V Mmin and V Mmax The same is true for the mean square error.

[0116] For the terminal guidance phase with different initial states, the two trained neural networks are applied online to obtain the time range of the terminal guidance phase: First, the input initial state quantity X = [r MT ,h M ,θ M ,η M ] is brought into the first neural network to obtain the speed range [V min_m ,V max_m ], then [r MT ,h M ,θ M ,η M ] and [V min_m ,V max_m ] is brought into the second neural network as input to obtain the flight time range of the terminal guidance segment.

[0117] Step 4: For the terminal guidance phase with different initial states, the two trained neural networks are applied online to obtain the time range of the terminal guidance phase: First, the input initial state quantity X = [r MT ,h M ,θ M ,η M ] is brought into the first neural network to obtain the initial velocity range of the terminal guidance phase [V min_m ,V max_m ], then [r MT ,h M ,θ M ,η M ] and [V min_m ,V max_m ] is taken as input into the second neural network to obtain the flight time range of the terminal guidance segment;

[0118] Step 5: Let the time when the glide missile starts gliding be t0 and the time when the penetration ends be t1; in the time period from t0 to t1, the flight time t of the glide segment is predicted by analytical method. hx , the flight time t in the analytical method hx It is only related to the terminal velocity, that is, the terminal velocity range of the gliding segment determines the flight time range of the gliding segment.

[0119] According to the initial velocity range of the terminal guidance segment [V min_m ,V max_m ], the terminal velocity range of the gliding section is [V min_m ,min(V max_hx,V max_m )],V max_hx is the maximum speed at the terminal of the gliding segment.

[0120] The flight time range of the gliding segment is obtained according to the terminal speed range of the gliding segment.

[0121] Gliding flight time prediction method

[0122] If a gliding missile encounters an interception during its mid-guidance phase, it will use the command shown in equation (6) to perform a lateral penetration. Let t0 be the time when the gliding missile starts gliding and t1 be the time when the penetration ends. At t = t0 and t = t1, the flight time is predicted using an analytical method as follows:

[0123]

[0124] Where R0 is the radius of the earth, g0 is the acceleration of gravity, S go is the remaining range, V M is the glide velocity, V f is the terminal speed of the glide segment.

[0125] Where, the remaining range S go It is obtained from the following formula:

[0126] S go =R0arccos(cosφ M cosφ f cos(λ M -λ f )+sinφ M sinφ f ) (15)

[0127] where φ f is the latitude of the gliding segment terminal, λ f is the longitude of the terminal of the gliding segment, φ M is the current latitude of the glide missile, λ M is the current longitude of the glider; if V is known M and current location information, the terminal location remains unchanged, S go It is certain;

[0128] From formula (14), we know that the flight time t hx The remaining distance S go 、Current speed V M and terminal velocity V f Determine. Known V M and current location information, assuming the terminal location remains unchanged, we know from formula (15) that S at this moment is go is determined, so the flight time t hx Only with terminal velocity V fThe terminal velocity range of the gliding segment determines the flight time range of the gliding segment. f Latitude of the end of the glide segment; λ f Longitude of the glide segment terminal;

[0129] First, find the speed range at the end of the gliding segment. Based on the relationship between the remaining range of the gliding segment, the terminal speed, and the current speed, we can get:

[0130]

[0131] Among them, R0 is the radius of the earth, g0 is the acceleration of gravity, S go is the remaining range, V M is the glide velocity, V f is the terminal speed of the gliding phase; L M and D M is the lift and drag of the gliding missile; σ M is the roll angle of the glide projectile.

[0132] V at a certain moment M and S go is certain, take cosσ M =1, and take the maximum lift-to-drag ratio, based on which the V f The value can be used as the maximum speed V at the end of the gliding segment max_hx estimated value.

[0133] According to the initial speed range of the terminal guidance phase [V min_m ,V max_m ]. For V min_m , the missile can always reach the target by circling the glide phase, so compared with V max_hx and V max_m , the terminal velocity range of the gliding section is [V min_m ,min(V max_hx ,V max_m )].

[0134] After obtaining the speed range at the end of the gliding segment, the flight time range of the gliding segment can be obtained according to formula (14).

[0135] Step 6: Expected total flight time is t z When the expected total flight time is met, the speed at the middle and end handover points is The mid-terminal handover point is the intersection of the gliding segment and the terminal guidance segment, that is, the speed at the mid-terminal handover point is the terminal speed of the gliding segment.

[0136] Considering that the velocity at the junction of the glide and terminal guidance phases (abbreviated as the "mid-terminal handover point") significantly influences the flight times of both the glide and terminal guidance phases, we first analyze the impact of this velocity on the flight times of both phases. For the same initial glide phase velocity, a higher velocity at the mid-terminal handover point results in a shorter glide phase flight time, while a lower velocity results in a longer flight time. During the terminal guidance phase, while meeting the minimum terminal velocity requirement, a higher velocity at the handover point results in a shorter flight time. Based on this analysis, without changing other parameters of the mid-terminal handover point, the flight times of each glide missile's mid-terminal and terminal guidance phases can be adjusted to achieve coordinated reconstruction.

[0137] The expected total flight time t is calculated by Newton iteration method z The speed at the middle and end handover points

[0138]

[0139] Where, the subscript k represents the number of iterations;

[0140] Each iteration corresponds to Indicates the speed of the middle and end handover points The corresponding total flight time and the expected total flight time t z The function of the difference is as follows:

[0141]

[0142] Where, For Substitute the glide velocity into the second neural network to obtain the terminal guidance flight time, For The flight time obtained analytically as the terminal velocity, for The derivative of The derivative of It can be obtained by difference approximation:

[0143]

[0144] The total number of iterations of the Newton iteration method is set, and the final iteration obtains the speed of the mid-to-end handover point that meets the expected total flight time.

[0145] Example

[0146] The simulation analysis is conducted using the coordinated flight of two gliding missiles, missile A and missile B. The initial positions and velocities of the gliding missiles are shown in Table 1.

[0147] Table 1 Initial position and velocity of the gliding bomb

[0148] Initial Information Glide bomb A Glide B <![CDATA[Longitude λ M (°)]]> 47.2844 48.4337 <![CDATA[Latitude φ M (°)]]> 24.2956 20.8171 <![CDATA[Height h M (km)]]> 40.200 40.217 <![CDATA[Velocity V M (m / s)]]> 4805.74 4851.22 <![CDATA[Ballistic inclination angle θ M (°)]]> -0.44 -0.36 <![CDATA[Ballistic deflection angle ψ vM (°)]]> 73.07 58.97

[0149] The terminal position of the glide bomb, its speed magnitude and direction are given in the range shown in Table 2.

[0150] Table 2 Terminal constraints of glide bombs

[0151] Terminal Constraints Glide bomb A Glide B <![CDATA[Longitude λ M (°)]]> 74.0008 74.1335 <![CDATA[Latitude φ M (°)]]> 30.0065 29.5765 <![CDATA[Height h M (km)(]]> 24.576 25.385 <![CDATA[Velocity V M (m / s)]]> 1400～1800 1400～1800 <![CDATA[Ballistic inclination angle θ M (°)]]> -1～1 -1～1 <![CDATA[Ballistic deflection angle ψ vM (°)]]> 89～93 73～77

[0152] The target is a stationary target, and its longitude λ T =75°, latitude φ T =30°, height h T = 0. Position of the defensive missile: longitude λ D =73.73°, latitude φ D =29.84°, height h D = 0, and the proportional coefficient of its guidance law is k1 = k2 = 3. The proportional coefficient of the guidance law of the terminal guidance phase of the gliding missile is k3 = k4 = 6. The heat flux, overload and dynamic pressure constraints of the gliding missile are 5500kw / m 2 , 5g and 150kPa. The control constraints are: the angle of attack is no more than 25°, the roll angle is no more than 80°, the terminal speed is no less than 750m / s, and the landing angle is no less than 80°.

[0153] Based on Tables 1 and 2, the flight time ranges of the mid- and terminal guidance segments can be estimated using Equation (14) and two neural networks, and the expected flight time can be selected, as shown in Table 3.

[0154] Table 3 Expected flight time of each stage of the glide bomb

[0155] Missile type Glide bomb A Glide B Middle time range(s) [796,841] [806,851] Expected time of middle segment (s) 820 820 Final time range(s) [74,97] [77,99] Expected time of the last segment (s) 81.1 81.1

[0156] Based on the above simulation conditions, assuming that there is no interception during the flight, the collaborative flight simulation results are as follows: Figures 2-4 shown.

[0157] Figure 2 It is the ballistic diagram of the gliding phase and terminal guidance phase of the two gliding bombs in the launch coordinate system; Figure 3 and Figure 4 It can be seen that both control variables and process constraints are met. The simulation results show that the two missiles hit the target simultaneously at 901.1 seconds. Their glide phases are both 820 seconds, and their terminal guidance phases are both 81.1 seconds. Both phases have achieved the expected flight time.

[0158] Considering the subsequent breakthrough, time prediction requires information on the middle and final shift handover points. The data obtained by simulation are shown in Table 4.

[0159] The data of the last shift handover point in Table 4

[0160] parameter Glide bomb A Glide B <![CDATA[Longitude λ M (°)]]> 74.0008 74.1335 <![CDATA[Latitude φ M (°)]]> 30.0065 29.5765 <![CDATA[Height h M (km)]]> 24.576 25.385 <![CDATA[Velocity V M (m / s)]]> 1654.01 1719.05 <![CDATA[Ballistic inclination angle θ M (°)]]> -0.75 0.31 <![CDATA[Ballistic deflection angle ψ vM (°)]]> 91.17 75.81

[0161] 1) Performance verification of terminal guidance time and velocity range prediction network

[0162] When entering terminal guidance, the typical flight altitude range of the gliding missile in this article is [20km, 30km], the speed range is [1200m / s, 2000m / s], and the MT =[99km,100km], enter terminal guidance, trajectory inclination angle θ M The range is [-1°, 1°], and the lead angle η in the yaw direction M The range of is [0°, 20°]. Taking values ​​in the above range, we get the sample input parameters of the second neural network, as shown in Table 5.

[0163] Table 5 Input parameters of database samples

[0164] Input parameters Range of variation <![CDATA[h M (km)]]> (20，22，24，26，28，30) <![CDATA[V M (m / s)]]> (1200，1400，1600，1800，2000) <![CDATA[η M (°)]]> (0，4，8，12,16,20) <![CDATA[r MT (km)]]> (99，100) <![CDATA[θ M (°)]]> (-1，-0.5，0，0.5，1)

[0165] The first neural network transforms the h in Table 5 M ,η M ,r MT ,θ M The terminal guidance model of the gliding missile is brought into the simulation. Based on the minimum terminal velocity of 750m / s and the maximum overload of 5g, 360 sets of input and output data are obtained, including 288 sets of training sets and 72 sets of test sets. The number of hidden layer nodes is 8 and the network learning rate is 0.001. The second neural network substitutes the input in the table into the terminal guidance model of the gliding missile for simulation and obtains 1800 sets of input and output data, including 1440 sets of training sets and 360 sets of test sets. The number of hidden layer nodes is 10 and the network learning rate is 0.001. The network training results are as follows: Figures 5 to 8 shown.

[0166] From the simulation results, we know that the mean square errors of the maximum speed and the minimum speed in the first neural network are 6.8036e -4 and 5.2089e -5 , the final value of the mean square error of the flight time in the second neural network is 6.2674e -5 .Depend on Figure 5 and Figure 7 It is known that the mean square error of the prediction model gradually converges with the number of iterations. Figure 6 and Figure 8 It can be seen that the correlation between the predicted value and the true value of the test set is 0.99974 and 0.99879, indicating that the network has good accuracy in predicting the initial velocity range and flight time of the terminal guidance phase of the gliding missile.

[0167] 2) Collaborative flight time coordination method verification

[0168] This section presents a simulation analysis of the coordination of the mid- and terminal guidance phases after a gliding missile successfully penetrates a defense missile during gliding. Assuming the defense missile detection range is 100km, the gliding missile detection range is 20km, and a=1e in the penetration command 6 , b=2,c=1. When the gliding missile stops penetrating,

[0169] From the simulation results, we know that when t=751.16s, the defense missile detects missile A and launches. When t=780.40s, missile A detects the defense missile and starts to penetrate and ends the penetration at t=784.37s. At this time, the miss distance r MD = 495.89 m. Missile B failed to detect the defensive missile throughout its journey and therefore did not penetrate. When Missile A completed its penetration, at t = 784.37 s, the positions and velocities of the two missiles are shown in Table 6.

[0170] Table 6 Position and velocity of the gliding bomb at the end of penetration

[0171] Initial Information Glide bomb A Glide B <![CDATA[Longitude λ M (°)]]> 73.4665 73.4807 <![CDATA[Latitude φ M (°)]]> 29.9761 29.4614 <![CDATA[Velocity V M (m / s)]]> 1850.24 1900.77

[0172] Without changing the terminal constraints, combined with Tables 4 and 6, the remaining flight time t of the glide phase of missile A is predicted by formula (14): hxA = 29.42s, the flight time of the terminal guidance phase is still t moA = 81.1s, that is, the remaining total flight time of missile A is 110.52s, and the remaining total flight time of missile B is t zB =820+81.1-784.37=116.73s. If there is no coordination, there will be a time difference of 6.21s between the two bombs hitting the target.

[0173] Will play A's [ rMT, h M, θ M, η M ] is used as input, and its value is [99.996km, 23.839km, -0.75°, 0.63°], which is brought into the first neural network to obtain [V min_m ,V max_m ]=[1410.40m / s,1752.61m / s], and V is obtained from formula (13): max_hx =1774.63m / s, the final speed range of the middle and last shift handover points is [1410.4m / s,1752.61m / s]. MT ,h M ,θ M ,η M] is brought into the first neural network, and the predicted flight time range of the terminal guidance phase is [76.39s, 96.25s]. According to the speed range and formula (14), the remaining flight time range of the gliding phase is [28.62s, 31.61s]. That is, the remaining total flight time range of missile A is [105.01s, 127.86s], and the remaining total flight time t zB = 116.73s Within the time range of missile A, that is, situation (a) in Section 4, the speed of the mid-terminal handover point can be changed to coordinate the flight time. The expected remaining total flight time is t z =116.73s, and the speed V at the middle and end handover points is obtained from formula (15): c * =1553.7m / s. The simulation results are as follows Figures 9-11 shown.

[0174] In the figure, A1 is the trajectory reconstructed after missile A penetrates the defense, * is the original trajectory of missile A, A2 is the unreconstructed trajectory of missile A after it penetrates the defense, B is the trajectory of missile B, D is the trajectory of the defensive missile, and T is the target.

[0175] After reconstruction, the glide phase flight time of missile A is 814.66s, and the terminal guidance flight time is 86.89s, so the total flight time is 901.55s. The total flight time of missile B is 901.1s, with a difference of 0.45s. Compared with the 6.21s without reconstruction, the time error is reduced by 92.75%. Figure 9 It is known that the trajectories A1 and A2 are different from the original trajectory A due to the penetration. * After the penetration is completed, track A1 is separated from track A2 due to the change of the mid-term handover speed, and finally flies in coordination with missile B. Figure 10 and Figure 11 It is known that the terminal velocity and landing angle of the reconstructed gliding missile meet the constraints.

[0176] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for reconstructing mid-terminal guidance coordinated flight time, characterized in that: The steps include: M Expected total flight time of a glide bomb In coordinated flight, the flight time of each gliding bomb is , the flight time of the terminal guidance phase is ; Determine when the defensive bullet enters N Detection range of a glide bomb When N The bombs are recorded as Class II bombs, and the Class II bombs take penetration measures. The remaining gliding bombs are recorded as Class I bombs, and the Class I bombs do not take penetration measures. The moment of successful penetration is t 1; ; After the penetration is successful, the estimated time from the moment of successful penetration to hitting the target is M The intersection of the flight time range of each projectile and the remaining total flight time range of type I projectile is T I , the intersection of the remaining total flight time range of Class II projectiles is T II , the expected remaining total flight time is ; like If it holds, then the Class I projectile does not need to be reconstructed, and the reconstruction of the Class II projectile is: Let the remaining expected total flight time of the Class II projectile be , using the calculation method of the speed of the middle and end handover points that meet the expected total flight time, calculate the speed that meets The speed of the Class II projectile at the mid-term handover point ; like If not established, then judge Whether it is established, there are two situations: like If it is established, then the time is selected from the intersection of the remaining total flight time ranges of Class I and Class II projectiles As the remaining expected total flight time of Class I and Class II ammunition, the speed calculation method of the mid-term and final handover points that meet the expected total flight time is used to calculate the speed that meets the expected total flight time. The speed of the middle and end handover points ; like If it is not true, reconstruction is impossible.

2. The method for reconstructing the coordinated flight time of mid- to terminal guidance according to claim 1, wherein: The method for calculating the speed at the mid-to-end handover point that meets the expected total flight time is specifically as follows: Step 1: Under the premise of determining the terminal guidance law, for the same initial state - missile-target distance ,high , ballistic inclination and the leading angle in the yaw direction , its minimum terminal velocity constraint determines the minimum initial velocity of terminal guidance , the available overload constraint determines the maximum initial velocity of the terminal guidance , based on which As input, The first neural network output is: ； The glide missile's initial moment in the terminal guidance phase Determines the flight time of the terminal guidance phase , V M is the speed of the gliding projectile, and its value range is , constructed with The input is the flight time of the terminal guidance segment The second neural network is the output: ； Step 3: Training the dual network composed of the first neural network and the second neural network; Step 4: For the terminal guidance phase with different initial states, the two trained neural networks are applied online to obtain the time range of the terminal guidance phase: First, the input initial state quantity Substitute into the first neural network to obtain the initial velocity range of the terminal guidance segment , and then and The flight time range of the terminal guidance phase is obtained by taking it into the second neural network as input; Step 5: Set the gliding time of the gliding missile to , the breakthrough ends at ; In the time period t0~t1, the gliding segment uses analytical methods to predict the flight time , the flight time in the analytical method It is only related to the terminal velocity, that is, the terminal velocity range of the gliding segment determines the flight time range of the gliding segment; According to the initial velocity range of the terminal guidance segment obtained , the terminal velocity range of the gliding section is , is the maximum speed at the terminal of the gliding phase; The flight time range of the gliding segment is obtained according to the terminal speed range of the gliding segment; Step 6: The expected total flight time is When the expected total flight time is met, the speed at the middle and end handover points is The mid-terminal handover point is the intersection of the gliding section and the terminal guidance section, that is, the speed at the mid-terminal handover point is the terminal speed of the gliding section; Calculate the expected total flight time using Newton's iteration method The speed at the middle and end handover points : In the formula, the subscript k represents the number of iterations; Each iteration corresponds to Indicates the speed of the middle and end handover points Corresponding total flight time and expected total flight time The function of the difference is as follows: Where, For Substitute the glide velocity into the second neural network to obtain the terminal guidance flight time, For The flight time obtained by the analytical method is used as the terminal velocity, for The derivative of The total number of iterations of the Newton iteration method is set, and the final iteration obtains the speed of the mid-to-end handover point that meets the expected total flight time.

3. The method for reconstructing mid- to terminal guidance coordinated flight time according to claim 2, wherein: The analytical method for predicting flight time , the flight time in the analytical method Only relevant for terminal velocity, specifically: exist and When , the analytical method is used to predict the flight time as follows: Where R0 is the radius of the earth, g0 is the acceleration due to gravity, For the remaining distance, is the glide velocity, is the terminal speed of the glide segment; Remaining distance It is obtained from the following formula: in is the latitude of the gliding segment terminal, is the longitude of the terminal of the gliding segment, is the current latitude of the glide missile, is the current longitude of the glide bomb; and current location information, the terminal location remains unchanged, It is certain; Flight time Remaining distance , current speed and terminal velocity Decision, therefore flight time Only with terminal velocity The terminal velocity range of the gliding segment determines the flight time range of the gliding segment.

4. The method for reconstructing the coordinated flight time of mid- to terminal guidance according to claim 2, wherein: described is the maximum speed at the terminal of the gliding phase, Solve it as follows: From the relationship between the remaining range of the gliding segment, the terminal velocity, and the current velocity, we can obtain: ； Where R0 is the radius of the earth, g0 is the acceleration due to gravity, For the remaining distance, is the glide velocity, is the terminal speed of the glide segment; and The lift and drag of the gliding missile; is the roll angle of the glide bomb; Pick ; Take the maximum lift-to-drag ratio, and based on this we get The value is taken as the maximum speed at the end of the glide segment estimated value.

5. The method for reconstructing mid-terminal guidance coordinated flight time according to claim 2, wherein: The dual network composed of the first neural network and the second neural network is trained in the following way: The simulation method is used to obtain data samples, 80% of the data samples are used as training sets and 20% as test sets. The training function uses the LM algorithm and the performance function uses the mean square error. After the training set is input into the network, the corresponding prediction network is obtained after the error converges.

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