A near space vehicle interception window searching method considering intersection angle constraint

Abstract

The application relates to a near-space vehicle interception window searching method considering intersection angle constraints. The application aims to solve the problem that the Pock-Chop diagram method has a long calculation time and is easy to cause the calculation to lose the timeliness of a launch opportunity. The process is as follows: I. determining an interception missile dynamics model and a target device kinematics model; II. estimating an interception missile launch time searching range [0, t 1max ] and an interception time searching range [t fmax ]; III. considering the launch speed constraint of the interception missile, solving a nonlinear equation to obtain a feasible range of the interception time under the condition of a given interception missile launch time; IV. considering the intersection angle constraint at the time of the handover between the middle and the end within the feasible range of the interception time, using coarse search and combining an ITP method to obtain an interception time range under the condition of satisfying the two constraints; and V. obtaining an interception window. The application is used in the field of vehicle interception window searching.

Description

TECHNICAL FIELD

[0001] The present application relates to a method for searching an interception window of a near space vehicle considering a constraint of a intersection angle. BACKGROUND

[0002] The near space refers to an airspace 20-100 km away from the ground, and has attracted extensive attention of various countries in the late 20th century due to its special strategic value. A vehicle capable of hypersonic flight in the near space is referred to as a near space hypersonic vehicle, which has the characteristics of high flight speed, high flight altitude and wide coverage compared with a traditional aircraft, and has the characteristics of simple structure, low cost and strong maneuverability compared with a space vehicle. Therefore, the near space hypersonic vehicle has extremely broad military application prospects.

[0003] When the near space hypersonic vehicle is intercepted, the interception window of the interceptor is small due to the high flight speed of the near space hypersonic vehicle, and the interception opportunity is fleeting. In addition, if the interceptor missile does not form a good interception posture relative to the target at the middle-end handover moment, the interception task may not be completed in the terminal guidance phase. The Pock-Chop graph method is a commonly used task opportunity search algorithm, which is widely used in launch opportunity search problems of deep space exploration tasks. When applied to the interception problem, this method traverses the launch time and the interception time according to the set search step, and solves the corresponding Lambert problem, so as to obtain the interception window satisfying all constraints. However, this method is essentially a traversal algorithm, so the calculation time of this method is long, the calculation efficiency is low, and the constraint conditions cannot be considered in the search process.

[0004] Considering that the entire interception process is short, the faster the calculation speed of the algorithm used in the interception window search is, the better. The calculation time of the Pock-Chop graph method is long, which easily leads to the loss of timeliness of the calculated launch opportunity, so it is very important to find a fast search algorithm for the near space vehicle interception window considering the launch speed constraint and the middle-end handover intersection angle constraint. SUMMARY

[0005] The purpose of the present application is to solve the problem that the entire interception process is short, the faster the calculation speed of the algorithm used in the interception window search is, the better, and the calculation time of the Pock-Chop graph method is long, which easily leads to the loss of timeliness of the calculated launch opportunity, and a method for searching an interception window of a near space vehicle considering a constraint of a intersection angle is provided.

[0006] The specific process of a method for searching an interception window of a near space vehicle considering a constraint of a intersection angle is as follows:

[0007] Step 1: Determine the dynamic model of the interceptor missile and the kinematic model of the target.

[0008] Step 2: Given an initial time t0 and the initial position vector r of the target at that time. 20 and initial velocity vector v 20 Given the launch position of the interceptor missile in a fixed Earth coordinate system.

[0009] The estimated launch time t1 of the interceptor missile can be searched within the range [0, t]. 1max and interception time t f The search range is [t1,t] fmax ];

[0010] Step 3: Consider the launch velocity constraint of the interceptor missile as v 1max Given the interceptor missile launch time t1, the interception time t is obtained by solving a nonlinear equation. f Feasible range

[0011] Step 4: During the interception time t f Feasible range Within, consider the intersection angle constraint α at the end of the shift handover. max By using a coarse search combined with the ITP method, the interception time range under the two constraints can be further obtained.

[0012] Step 5: Obtain the interception window.

[0013] The beneficial effects of this invention are as follows:

[0014] This invention presents a near-space vehicle interception window search algorithm that considers rendezvous angle constraints. Compared with previous studies, this algorithm has high computational efficiency and incorporates the interceptor launch velocity constraint and the rendezvous angle constraint at the mid-to-terminal handover time into the launch opportunity search process, providing favorable initial conditions for the subsequent terminal guidance process of the interceptor. Selecting the appropriate interceptor launch time and interception time according to the search results of this algorithm is beneficial to the successful completion of the interception mission.

[0015] In the present application, firstly, the search method of the interceptable time interval is given when the launch time is fixed, considering the launch speed constraint of the interceptor and the constraint of the intersection angle at the middle-end handover. Further, by searching the feasible interval of the launch time, and in the feasible interval, the search method of the interceptable time interval under the fixed launch time is used, the whole interception window of the near space vehicle is searched. When the present application is used to solve the problem of searching the interception window of the near space vehicle considering the intersection angle constraint, the search efficiency is high, the interception window under various constraint conditions can be solved in a short time, which is conducive to the smooth realization of the interception task. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 Flow chart of the fast search algorithm of the near space vehicle interception window considering the intersection angle constraint according to the present application;

[0017] Figure 2 Geometric diagram of the interception process and the intersection angle at the middle-end handover time;

[0018] Figure 3 Contour diagram of the required speed size at the launch time of the interceptor;

[0019] Figure 4 Contour diagram of the intersection angle at the middle-end handover time;

[0020] Figure 5 Schematic diagram of the near space vehicle interception window searched by the Pock-Chop diagram method;

[0021] Figure 6 Schematic diagram of the near space vehicle interception window searched by the method proposed in the present application;

[0022] Figure 7 Comparison diagram of the calculation results of the Pock-Chop diagram method and the method proposed in the present application. DETAILED DESCRIPTION

[0023] Embodiment one: the specific process of the method for searching the near space vehicle interception window considering the intersection angle constraint is as follows:

[0024] The present application designs a search algorithm for the near space vehicle interception window considering the intersection angle constraint. Compared with the previous research, the calculation efficiency of the present algorithm is high, and the launch speed constraint of the interceptor and the intersection angle constraint at the middle-end handover time are included in the search process of the launch opportunity, which provides good initial conditions for the subsequent terminal guidance process of the interceptor, and the selection of the corresponding launch time and interception time according to the search results of the present algorithm is conducive to the smooth realization of the interception task.

[0025] Step one, determine the dynamic model of the interceptor and the kinematic model of the target vehicle;

[0026] Step 2: Given an initial time t0 and the initial position vector r of the target at that time. 20 and initial velocity vector v 20 Given the launch position of the interceptor missile in a fixed Earth coordinate system.

[0027] The estimated launch time t1 of the interceptor missile can be searched within the range [0, t]. 1max and interception time t f The search range is [t1,t] fmax ];

[0028] Step 3: Consider the launch velocity constraint of the interceptor missile as v 1max Given the interceptor launch time t1, the interception time t is obtained by solving a nonlinear equation (13). f Feasible range

[0029] Step 4: During the interception time t f Feasible range Within, consider the intersection angle constraint α at the end of the shift handover. max By using a coarse search combined with the ITP method, the interception time range under the two constraints can be further obtained.

[0030] Step 5: Obtain the interception window.

[0031] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that: in step one, the dynamic model of the interceptor missile and the kinematic model of the target are determined; the specific process is as follows:

[0032] In this algorithm, the dynamic model used for the interceptor missile is a two-body model, expressed as:

[0033]

[0034] Where μ represents the Earth's gravitational constant, and r and v represent the position vector and velocity vector of the J2000 inertial frame, respectively. This indicates the magnitude of the corresponding position vector; Denotes the first derivative of r; This represents the first derivative of v;

[0035] This algorithm only considers the kinematic model of the target, given that the target's flight altitude is fixed at h and its flight speed is fixed at v. m The trajectory of the target is a circle in space; given the initial position and velocity vector of the target, r... 20 and v 20The following vector can be defined:

[0036]

[0037] n, a, and b represent intermediate variables; This represents the magnitude of the target's position vector at the initial moment. This represents the magnitude of the target's velocity vector at the initial moment;

[0038] The kinematic model of the target is then expressed as:

[0039]

[0040] Where θ0 = 0 represents the angle of the target at the initial moment. R represents the angular velocity of the target. e This represents the radius of the Earth.

[0041] It should be noted that this invention only presents one possible kinematic model of the target. In specific tasks, the kinematic model of the target can be obtained based on prior data or observation information and then replaced accordingly, without affecting other aspects of this invention.

[0042] The other steps and parameters are the same as in Specific Implementation Method 1.

[0043] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that: in step two, the search range for estimating the launch time t1 of the interceptor missile is [0, t]. 1max and interception time t f The search range is [t1,t] fmax The specific process is as follows:

[0044] First, based on the transformation relationship between the J2000 geocentric inertial frame and the Earth-fixed coordinate system, the position r of the interceptor launch point in the J2000 geocentric inertial frame at the initial time t0 can be determined. 10 ;

[0045] Considering that the interceptor missile must be launched and complete the interception before the target reaches its airspace, the target distance r is selected. 10 The most recent moment is used as the maximum search range t for the interceptor missile launch time t1. 1max ;

[0046] Due to the Earth's rotation, the maximum search range for interception changes with the launch time. Given the interceptor launch time t1, the position r1 of the interceptor launch point in the J2000 geocentric inertial frame at that time can be obtained. Therefore, the interception time t... f Maximum search range t fmax It can be determined by the moment when the target is closest to r1;

[0047] The target distance r 10 The closest time is obtained by one-dimensional search through the golden section method;

[0048] The closest time is obtained by one-dimensional search through the golden section method.

[0049] The other steps and parameters are the same as those in embodiment one or two.

[0050] Embodiment four: The difference between this embodiment and one of embodiments one to three is that the launch speed constraint of the interceptor in step three is v 1max In the case of a given launch time t1 of the interceptor, the feasible range of the interception time t f is obtained by solving a nonlinear equation (13).

[0051] The specific process is as follows:

[0052] Given the launch time t1 of the interceptor, the initial position r1 of the interceptor in the J2000 geocentric inertial system is determined according to the conversion relationship between the J2000 geocentric inertial system and the earth-fixed coordinate system.

[0053] Given the interception time t f of the interceptor, the terminal interception position r2 of the interceptor in the J2000 geocentric inertial system is determined according to the kinematic model of the target. f Assuming that the interception time t f of the interceptor is known), the terminal interception position r2 of the interceptor in the J2000 geocentric inertial system is determined according to the kinematic model of the target.

[0054] The chord vector c = r2-r1 is defined, and the size of the chord vector c is ||| is the modulus.

[0055] The chord sum and the radial are defined as and where is the size of the orbital radius corresponding to the initial position r1.

[0056] is defined as the size of the orbital radius corresponding to the interception position r2.

[0057] Then the initial launch speed vector v1 of the interceptor is further obtained as

[0058] v1 = z c i c +z r i r1 (4)

[0059] where z c and z rrespectively, and

[0060]

[0061] where μ is the gravitational constant, p is the semi-latus rectum of the transfer orbit, is the transfer angle;

[0062] and the product of z c and z r can be expressed as

[0063]

[0064] where Q is the product of z c and z r , constant is a constant;

[0065] Therefore, z r can be expressed as z r = Q / z c ;

[0066] Taking the modulus of equation (4), the magnitude of the initial launch speed of the interceptor missile is

[0067]

[0068] Thus, the constraint of the initial launch speed of the interceptor missile can be expressed as

[0069]

[0070] where v 1max is the upper bound of the constraint of the initial launch speed of the interceptor missile;

[0071] Squaring equation (8), the constraint of the initial launch speed of the interceptor missile is further converted into a quartic inequality about z c

[0072]

[0073] For a fixed launch time t1of the interceptor missile, the position vector r1of the interceptor missile can be determined; at this time, only the interception time t f is given, the initial launch speed can be obtained by solving the Lambert problem; therefore, the interception time t f is the only independent variable;

[0074] When the orbit of the interceptor missile is an ellipse, the transfer flight time of the interceptor missile can be expressed as

[0075]

[0076] ​where a denotes the semi-major axis of the interceptor transfer orbit, e denotes the eccentricity of the interceptor transfer orbit, and E1 and E2 denote the eccentric anomaly of the initial position and the terminal position of the interceptor transfer orbit, respectively;

[0077] In the case where the initial position r1 and the terminal position r2 of the interceptor are given, the above variables can be expressed as z c , and thus the transfer time can be expressed as a function of z c (see Zhang G. Terminal-Velocity-Based Lambert Algorithm [J]. Journal of Guidance Control and Dynamics, 2020, 43(8): 1529-1539.); it should be noted that the interception of a near-space target is often a short-time interception, and thus the multi-orbit transfer case does not need to be considered.

[0078] When the interceptor orbit is a hyperbolic orbit, the transfer flight time of the interceptor can be expressed as

[0079]

[0080] where H1 and H2 denote the hyperbolic anomaly of the initial position and the terminal position of the transfer orbit, respectively, and which can also be expressed as a function of z c ;

[0081] The transfer flight time of the target vehicle can be expressed as

[0082] ΔT=t f -t1 (12)

[0083] At this point, the interception condition can be expressed as

[0084] η(t f ) = Δt - ΔT = 0 (13)

[0085] where η(t f ) denotes the difference between the transfer flight time of the interceptor and the transfer flight time of the target vehicle;

[0086] When the initial launch speed of the interceptor is taken as the constraint boundary value v 1max , the root of the nonlinear equation (13) is solved, and the initial launch speed constraint v 1max of the interceptor can be obtained. f The feasible range of the interception time t

[0087] The other steps and parameters are the same as one of the first to third embodiments.

[0088] Specific implementation five: different from one of the specific implementations one to four is that: when the initial launch speed of the interceptor missile takes the constraint boundary value v 1max , the root of the nonlinear equation (13) is solved, and the initial launch speed constraint v 1max of the interceptor missile is obtained f The feasible range of the interception time t corresponding to the given launch time t1 is given below

[0089] When solving the roots of the quartic polynomial corresponding to equation (9), the roots obtained by solving may be virtual roots. To ensure that the roots obtained are all real roots, the condition to be met is

[0090]

[0091] In the formula, Δ, P represent discriminants; Δ(t f ), P(t f ) are functions with the interception time t f as the independent variable;

[0092] It can be seen that only the zero roots of Δ=0 and P=0 need to be solved, and the intersection of the zero roots of Δ=0 and P=0 is obtained, that is, the range in which the quartic equation has real roots exists;

[0093] It is known that the coefficients of the quartic polynomial in equation (9) are only related to the terminal interception time t f , so the above discriminants are also functions of the interception time t f , but their forms are more complex. In order to obtain all the zero roots of the quartic polynomial corresponding to equation (9), the golden section method is used to search for extreme values to determine the root interval; in the root interval, the secant method is used to solve the zero roots.

[0094] The specific process of solving the roots of Δ=0 and P=0 is as follows:

[0095] Taking the solution of the zero roots of Δ(t f ) as an example, the specific process of solving the zero roots of Δ(t f ) by the piecewise golden section method is as follows:

[0096] 1) Use the piecewise golden section method to obtain all the extreme points of Δ(t f ) in the search range [t1, t fmax ] of the interception time t f Where N is the number of extreme points;

[0097] At the same time, let

[0098] Therefore, the entire independent variable interval is divided into N+1 subintervals​

[0099] 2) For each subinterval if If no solution exists in the subinterval, then it is considered that there is no solution; otherwise, if a solution exists in the interval, the secant method is used to find the corresponding solution.

[0100] By finding the intersection of the zero roots of Δ=0 and P=0, the range in which the quartic equation has real roots can be obtained. After determining the range in which the quartic equation corresponding to equation (9) has real roots, the root of the nonlinear equation corresponding to equation (13) is solved using the secant method within the range in which real roots exist, thus obtaining the interception time interval that satisfies the initial launch velocity constraint of the interceptor missile.

[0101] The other steps and parameters are the same as those in specific implementation methods one through four.

[0102] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One through Five in that: in step four, during the interception time t... f Feasible range Within, consider the intersection angle constraint α at the end of the shift handover. max By using a coarse search combined with the ITP method, the interception time range under the two constraints can be further obtained. The specific process is as follows:

[0103] In steps three and four, the ITP (Interpolation, Truncation, and Projection) method is an algorithm for solving the roots of a nonlinear equation within a given interval (see Oliveira IF, Takahashi RH. An enhancement of the bisection method average performance preserving minmax optimality[J]. ACM Transactions on Mathematical Software, 2021, 47(1):1-24.).

[0104] Step 4.1 Solving for the intersection angle constraint α max The corresponding shift handover time t s ;

[0105] Step 42: Based on the mid-to-late shift handover time t obtained in Step 41 s Solve for the final shift handover time t. s The angle of intersection;

[0106] Step 43: Based on the mid-to-late shift handover time t obtained in Step 41 sand the intersection angle obtained in step four two, the intersection time range under two constraint conditions (intersection angle constraint a max and the intercept missile launch speed constraint v 1max ) is obtained

[0107] Other steps and parameters are the same as in specific embodiment one to five to one.

[0108] Specific embodiment seven: this embodiment is different from one of specific embodiments one to six: in step four one, the intersection angle constraint a max corresponding to the middle-end shift time t s ; the specific process is:

[0109] In step three, considering that the maximum detection distance of the interceptor seeker is p max , the middle-end shift time t s can be considered as the time when the distance between the interceptor and the target reaches p max , that is, at this time, the interceptor completes the middle-end shift and directly enters the terminal guidance phase; the specific calculation method of the middle-end shift time is as follows:

[0110] After the launch time t1 of the interceptor and the interception time t f of the interceptor (the interception time t f of the interceptor is assumed to be known), the launch speed of the interceptor is first obtained by solving the Lambert problem; the position of the interceptor at any time can be obtained by solving the Kepler equation, and the position of the interceptor at the middle-end shift time t s can be expressed as

[0111] r 1s = f1(t s ) (15)

[0112] In the formula, f1(·) represents a function of the trajectory recursion of the interceptor obtained by solving the Kepler equation;

[0113] The position of the target at the middle-end shift time t s is expressed as

[0114] r 2s = f2(t s ) (16)

[0115] In the formula, f2(·) represents the kinematic model of the target;

[0116] According to the condition that the distance between the interceptor and the target at the middle-end shift time t s is p max , the following equation can be obtained

[0117] ||r 1s-r 2s ||=p max (17)

[0118] The above formula can be recorded as

[0119] f(t s ) = ||r 1s -r 2s || - p max = 0 (18)

[0120] In the formula, f(·) represents the distance between the interceptor and the target object;

[0121] Solving the middle-end handover time t s is to find the root of the nonlinear equation (18);

[0122] It should be noted that before and after the interceptor interception time t f , there is one solution for the nonlinear equation (18), and the middle-end handover time t s needs to meet the following conditions

[0123] t s < t f (19)

[0124] Based on this, the Newton iteration method is used to solve the root of the above nonlinear equation (18), wherein the first derivative of f(t s ) is obtained by the finite difference method, and the initial guess of the Newton iteration method can be selected as (t f - τ s ), τ s is a small positive number; thus, the root obtained finally is the middle-end guidance handover time t s .

[0125] The other steps and parameters are the same as one of the first to sixth embodiments.

[0126] Embodiment eight: The embodiment is different from one of the first to seventh embodiments in that: in the step four two, the middle-end handover time t s obtained based on the step four one is used to solve the intersection angle of the middle-end handover time t s ; the specific process is as follows:

[0127] After obtaining the middle-end handover time t s , the position and velocity of the interceptor at this time [r 1s , v 1s ] can be obtained by solving the Kepler equation, and the position r 2s of the target object can be obtained by the kinematic model of the target object; then the vector of the line connecting the interceptor and the target object is

[0128] q = r2s -r 1s (20)

[0129] Thus, the intersection angle at this time can be obtained as

[0130]

[0131] wherein represents the size of the line connecting the interceptor missile and the target, represents the size of the interceptor missile speed;

[0132] The intersection angle constraint about the time of the handover from the middle to the end is

[0133] α≤α max (22)

[0134] wherein α max represents the upper limit value of the intersection angle constraint at the time of the handover from the middle to the end.

[0135] The other steps and parameters are the same as one of the first to seventh embodiments.

[0136] The ninth embodiment is different from one of the first to eighth embodiments in that: in step four three, based on the time of the handover from the middle to the end t s obtained in step four one and the intersection angle obtained in step four two, the interception time range satisfying two constraint conditions (the intersection angle constraint α max and the interceptor missile launch speed constraint v 1max ) is obtained. The specific process is as follows:

[0137] In the interception time interval , the intersection angle constraint α max about the time of the handover from the middle to the end is considered, and a coarse search is performed to obtain the interception time range satisfying two constraint conditions by combining the ITP method.

[0138] Step four three one, for the interception time interval , a fixed small step τ is set as the search step of the coarse search according to the task requirement;

[0139] Step four three two, let It should be noted that N may not be an integer, so let

[0140] When N is an integer, L is equal to N; otherwise, L is equal to the integer part of N;

[0141] Thus, L+1 interception times can be generated, i.e.

[0142] wherein t f,kdenotes the kth intercept time;

[0143] Step 433, for each intercept time t f,k , the launch speed of the interceptor missile is obtained by solving the Lambert problem;

[0144] for each intercept time t f,k , the mid-end handover time t s,k and the intersection angle a k at this time of the interceptor missile are obtained based on step 4331 and step 4332;

[0145] If a k ≤ a max , it means that t f,k satisfies the intersection angle constraint of the mid-end handover time, and a flag sign k = 1 is set; otherwise, the flag sign k = -1 is set to indicate that the time does not satisfy the intersection angle constraint of the mid-end handover time;

[0146] Step 434, after all sign k (k = 0, 1, …, L) are determined, it is checked whether there are two adjacent flags that are different; if sign j ≠ sign j+1 (j = 0, 1, …, L-1), there must be a boundary point of the intercept time in the interval [t f,j , t f,j+1 ]; then, the boundary point of the intercept time in the interval [t f,j , t f,j+1 ] can be obtained by the ITP method;

[0147] The ITP (Interpolation, Truncation, and Projection) method is an algorithm for solving the root of a nonlinear equation in a given interval (see Oliveira IF, Takahashi RH. An enhancement of the bisection method average performance preserving minmax optimality [J]. ACM Transactions on Mathematical Software, 2021, 47(1): 1-24.); in addition, a higher solution precision of the ITP method can be set to obtain accurate results.

[0148] In this way, all the boundary points of the intercept time that satisfy the constraint can be obtained in The interception time range under two constraints can be determined based on the boundary points obtained from the search.

[0149] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0150] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One through Nine in that: the interception window is obtained in step five; the specific process is as follows:

[0151] Step 51: Initially search within the launch time range [0, t] 1max Within [the specified range], determine the feasible range for the launch time t1. β represents the number of feasible ranges;

[0152] Step 52, within the launch time range Within this range, the launch time is traversed at a specified step size τ2 to obtain the interception time range at each moment. Finally, all the intercepted windows are obtained;

[0153] In step five-one, the initial search range at launch time is [0, t]. 1max Within [the specified range], determine the feasible range for the launch time t1. β represents the number of feasible ranges; the specific process is as follows:

[0154] Step 5.11: For the initial search range of launch time [0, t] 1max According to the mission requirements, the search step size for the coarse search in the launch time dimension is set to a fixed small step size τ1;

[0155] Step 512, let N1 = (t 1max -0) / τ1, note that N1 may not be an integer, therefore denote

[0156] When N1 is an integer, L1 equals N1; otherwise, L1 equals N1 rounded down.

[0157] Thus, L1+1 emission times can be generated, i.e., t 1,m =m·τ1;

[0158] In the formula t 1,m This represents the m-th launch time; m = 0, 1, ..., L1;

[0159] Step 513: For each launch time t 1,m By employing a solution method that calculates the interceptable time interval under a fixed launch time (where the launch time t is...), 1,m Replace t1 in step 3 and execute the solution process of steps 3 and 4 to obtain the interceptable time interval at the launch time;

[0160] If the range is non-empty, it means that t 1,m is feasible, and a flag sign m = 1 is set; otherwise, a flag sign m = -1 is set, which means that the obtained interceptable time interval at the launch time is empty.

[0161] Step five: After all the sign m (m = 0, 1, …, L1) are determined, it is checked whether there are two adjacent flags that are different; if sign n ≠ sign n+1 (n = 0, 1, …, L1-1), then there must be a boundary point of the launch time in the interval [t 1,n , t 1,n+1 ]; under the condition that the interval [t 1,n , t 1,n+1 ] is known, the boundary point of the launch time is obtained by the ITP method (the boundary point is the left and right boundary value of the feasible range of the launch time t1);

[0162] Through the above steps, the feasible range of the launch time t1 is obtained

[0163] In the step five two, the launch time is traversed in the launch time range with a specified step size τ2, and the interceptable time range at each time is obtained; finally, all the intercept windows are obtained; the specific process is as follows:

[0164] Let Note that N β may not be an integer, so let

[0165] When N β is an integer, L β is equal to N β ; otherwise, L β is equal to N β downwardly rounded.

[0166] For each launch time , the interceptable time interval at the launch time is obtained by using the method for solving the interceptable time interval at a fixed launch time (replace t1 in step three with the launch time , and execute the solving process of step three and step four);

[0167] After the traversal is completed, all the near space vehicle intercept windows are finally obtained.

[0168] Other steps and parameters are the same as one of embodiments one to nine.

[0169] The beneficial effects of the present application are verified by the following embodiments:

[0170] Embodiment one:

[0171] The task initial time is set to January 1, 2022, 0:00:00, and the orbital height of the near space vehicle target is kept at h = 40 km during the entire flight process, and the flight speed is set to v m = 6Ma, i.e. 2.04km / s, and the angular velocity can be solved as The position and velocity vector of the target vehicle in the J2000 Earth-centered inertial coordinate system at the initial time are

[0172]

[0173] The launch position of the interceptor missile is fixed in the ground-based system and is represented as

[0174]

[0175] The closest time of the target vehicle to the launch point of the interceptor missile is obtained by one-dimensional search using the golden section method, t 1max = 769.0s, so the initial search range of the launch time of the interceptor missile is t1∈[0,t 1max ]. The interception time range of the interceptor missile is t f ∈[t1,t fmax ], wherein due to the rotation of the earth, the launch position of the interceptor missile in the inertial system changes with the launch time, so the maximum interception time t fmax is not the same.

[0176] The task constraint conditions are set as follows:

[0177] (1) The launch speed constraint of the interceptor missile is v 1max = 2.5km / s;

[0178] (2) The intersection angle of the interceptor missile at the handover time is not more than 30°, i.e. a max = 30°.

[0179] The Pock-Chop chart method is widely used in searching for launch opportunities, i.e. the Lambert problem is solved by traversing according to the set step length, so as to obtain all the interceptable opportunities that meet the constraints. Among them, the launch time and interception time search step length of the Pock-Chop chart method are both set to 1s. The obtained results are referred to Figures 3 to 5 . Figure 5The region enclosed in the middle represents the interception window which meets both the condition that the intersection angle at the end of the shift is less than 30° and the condition that the speed of the interceptor missile at the time of launching is less than 2.5km / s. The time consumed by the Pock-Chop graph method for calculating all the interception windows of the near space vehicle is 22.517s.

[0180] When the fast search algorithm for the interception window of the near space vehicle considering the intersection angle constraint is used, the coarse search step of the launching time dimension is set to 60s, the coarse search step of the interception time dimension is set to 30s, and the precision of the ITP method is set to 0.1s. The final launching opportunity is shown in the figure. Figure 6 The calculation time for searching the launching opportunity by using the method of the present application is 0.793s.

[0181] In order to prove the accuracy of the calculation result of the method of the present application, Figure 7 The comparison figure of the launching opportunity calculated by the method of the present application and the Pock-Chop graph method is shown. The enclosed region represents the result calculated by the Pock-Chop graph method, and the envelope line represents the result calculated by the method of the present application. It can be seen that the boundary of the envelope line and the enclosed region is basically completely consistent, which proves the accuracy of the method of the present application. In summary, the calculation result of the launching opportunity search algorithm considering the intersection angle constraint is accurate, and compared with the widely used Pock-Chop graph method, the calculation efficiency is greatly improved. In the embodiment, the calculation time is only 3.52% of that of the Pock-Chop graph method.

[0182] The present application also has other various embodiments. Those skilled in the art can make various corresponding changes and modifications to the present application without departing from the spirit and essence of the present application. However, these corresponding changes and modifications should all belong to the protection scope of the claims attached to the present application.

Claims

1. A near space vehicle interception window search method considering intersection angle constraint, characterized in that: The method specifically comprises the following steps: Step one, determining a kinetic model of the interceptor and a kinematic model of the target vehicle; the specific process is as follows: The kinetic model adopted by the interceptor is a two-body model, which is expressed as: where μ denotes the gravitational constant of the Earth, r and v denote the position and velocity vectors in the J2000 inertial system, respectively, denotes the magnitude of the respective position vector; denotes the first derivative of r; denotes the first derivative of v; Given the target's flight height is fixed as h, flight speed size is fixed as v m , the target's trajectory is a circle in space; in the known initial moment of the target's position and velocity vector is r 20 and v 20 , the following vector can be defined, n, a', b represent intermediate variables; denotes the magnitude of the position vector of the target at the initial moment in time, denotes the magnitude of the velocity vector of the target at the initial moment in time; The kinematic model of the target vehicle is expressed as where θ0= 0 represents the angle of the target at the initial time, represents the angular velocity of the target, R e represents the radius of the earth; Step two, given an initial time, t0, and the initial position vector of the target, r 20 and initial velocity vector, v 20 ; given the launch position of the interceptor missile in the Earth-fixed coordinate system Estimate the launch time t1 of the interceptor missile search range [0, t 1max ] and the interception time t f search range [t1, t fmax ] Step three, considering the launch speed constraint of the interceptor as v 1max Given the launch time of the interceptor t1, the feasible range of the intercept time t f is obtained by solving a nonlinear equation Step four, the interception time t f is considered within the feasible range , considering the intersection angle constraint α max at the end of the shift, the interception time range under two constraints is further obtained by using coarse search combined with ITP method Step five, obtaining an interception window.

2. The method of claim 1, wherein: The step two estimates the search range [0, t 1max ] of the launch time t f and the search range [t fmax , t of the intercept time t ; the specific process is as follows: Firstly, the position of the interception missile launching point in J2000 geocentric inertial system at initial time t0 can be determined according to the conversion relationship between J2000 geocentric inertial system and earth fixed coordinate system 10 ; Targeter selects distance r 10 Latest time as maximum search range t for intercept missile launch time t1 1max ; Due to the rotation of the earth, the maximum search range of the intercept time changes with the launch time. When the launch time t1 of the interceptor is given, the position r1 of the launch point of the interceptor in the J2000 earth-centered inertial system can be obtained, and then the maximum search range t f of the intercept time t fmax can be determined by the time when the target is closest to r1. The target distance r 10 The most recent time is obtained by one-dimensional search using the golden section method. The moment when the target vehicle is closest to r1 is obtained through one-dimensional search by the golden section method.

3. The method of claim 2, wherein: The launch velocity constraint considered in step three is v 1max The feasible range of the interception time t f is obtained by solving a nonlinear equation given the launch time t1 The detailed procedure is as follows: Given the moment t1 after the launch of the interceptor, the position r1 of the launch point of the interceptor at this moment in the J2000 Earth-centered inertial system is obtained. It is known that at a given interception time t f , the interception position r2 of the interceptor missile at the end of the trajectory in the J2000 geocentric inertial system is determined according to the kinematic model of the target f It is known that at a given interception time t f , the interception position r2 of the interceptor missile at the end of the trajectory in the J2000 geocentric inertial system is determined according to the kinematic model of the target Let c = r2 - r1 be the chord vector, with chord vector magnitude ‖ ‖ is the modulus; The tangential and radial directions are defined as and wherein r1 is the initial position corresponding to the size of the orbit radius; Definitions r2 is the radius of the orbit corresponding to the interception position; Then, the initial launch speed vector v1 of the interceptor is further obtained as v1 = z c i c +z r i r1 (4) where z c and z r denote the tangential and radial velocity components, respectively, expressed as wherein μ is the Earth's gravitational constant, p is the semi-major axis of the transfer orbit, is the transfer angle; And the product of z c and z r can be expressed as wherein Q is z c and the product of z r is defined as constant is a constant;​ Thus, z r may be expressed as z r = Q / z c ; The modulus of formula (4) is taken to obtain the size of the initial launch speed of the interceptor as Therefore, the constraint of the initial launch speed of the interceptor can be expressed as where v 1max is an upper bound on the initial launch velocity of the interceptor; Squaring equation (8) further transforms the initial launch velocity constraint of the interceptor missile into a quartic inequality in z c ​ When the orbit of the interceptor is an ellipse, the transfer flight time of the interceptor can be expressed as In the formula, a represents the semi-major axis of the transfer orbit of the interceptor, e represents the eccentricity of the transfer orbit of the interceptor, E1 and E2 represent the eccentric anomaly of the initial position and the terminal position of the transfer orbit of the interceptor respectively; When the orbit of the interceptor is a hyperbola, the transfer flight time of the interceptor can be expressed as In the formula, H1 and H2 represent the hyperbolic pericenter angle of the initial position and the terminal position of the transfer orbit respectively; The transit time of the target can be expressed as ΔT = t f - t1(12) Up to this point, the intercept condition can be expressed as η(t f ) = Δt - ΔT = 0 (13) In the formula η(t) f The ) represents the time difference between the interceptor missile's transfer flight and the target's transfer flight; When the initial launch speed of the interceptor missile takes the constraint boundary value v 1max , the root of the nonlinear equation (13) is solved, and the constraint v 1max of the initial launch speed of the interceptor missile is obtained. f The feasible range of the interception time t 4. The method of claim 3, wherein: The feasible range of the initial launch speed v 1max of the interceptor is obtained by solving the root of the nonlinear equation (13) when the initial launch speed of the interceptor takes the constraint boundary value v 1max The feasible range of the initial launch speed v f of the interceptor is obtained by solving the root of the nonlinear equation (13) when the initial launch speed of the interceptor takes the constraint boundary value v The specific process is as follows: When solving the roots of the fourth-degree polynomial corresponding to formula (9), the roots obtained may be virtual roots. If it is required to ensure that the obtained roots are all real roots, the condition to be met is where Δ, P represent discriminants; Δ(t f ), P(t f ) are functions with the interception time t f as the argument; It can be seen that only the zero roots of Δ=0 and P=0 need to be solved, and the intersection of the zero roots of Δ=0 and P=0 is obtained, that is, the range in which the fourth-degree equation has real roots exists; The specific process of solving the roots of Δ=0 and P=0 is as follows: The specific process for solving the zero root of Δ(t f ) by using the piecewise golden section method is as follows: 1) Obtain Δ(t) by using the segmented golden section method f ) The whole extreme points of the search range [t1, t f ] at the intercept time t fmax ] are Where N is the number of extreme points; Meanwhile, the Thus, the entire argument interval is divided into N+1 sub-intervals 2) For each sub-interval If then the sub-interval is considered to have no solution; otherwise, the interval has one solution, and the corresponding solution is found using the secant method; The intersection of the zero roots of Δ=0 and P=0 is obtained, i.e. the range in which the quartic equation has real roots; after determining the range in which the quartic equation corresponding to equation (9) has real roots, the roots of the non-linear equation corresponding to equation (13) are solved by using the secant method in the range in which the real roots exist, and the interception time interval satisfying the initial launching speed constraint of the interceptor is obtained 5. The method of claim 4, wherein: The step four in intercept time t f The feasible range Within the range of the feasible range, the intersection angle constraint α max of the end of shift time is considered, and the intercept time range under the two constraints is further obtained by using coarse search combined with the ITP method The specific process is: Step four one, solving considering intersection angle constraint a max Corresponding mid-shift time t s ; Step four two, based on the step four one get the end of shift time t s , solve the end of shift time t s of the intersection angle; Step four three, based on the end-of-shift time t obtained in step four one s and the intersection angle obtained in step four two, obtain the range of interception times that satisfy both constraints 6. The method of claim 5, wherein: The step four in solving considering the intersection angle constraint α max The corresponding mid-shift time t s The specific process is: The position of the interceptor missile at the handover time t s is denoted as r 1s = f1(t s ) (15) In the formula, f1(·) represents a function of the orbit recursion of the interceptor by solving the Kepler equation; The target's position at the end of shift time t s is denoted r 2s = f2(t s ) (16) In the formula, f2(·) represents the kinematic model of the target vehicle; According to the time t of the end of the shift s The distance between the interceptor and the target is p max The condition can be obtained ||r 1s -r 2s ||= p max (17) The above equation can be written as f(t s ) = ||r 1s - r 2s || - p max = 0 (18) In the formula, f(·) represents the distance between the interceptor and the target vehicle; Solving the end-of-shift time t s i.e. finding the root of the nonlinear equation (18); Mid-shift handover time t s The following conditions must be met t s <t f (19) Based on this, the Newton iteration method is used to solve the root of the above nonlinear equation (18), where the first derivative of f(t s ) is obtained by the finite difference method, and the initial guess of the Newton iteration method can be chosen as (t f -τ s ), τ s is a small positive number; thus, it can be ensured that the finally obtained root is the sought midcourse guidance handover time t s .

7. The method of claim 6, wherein: The step four two is based on the step four one obtained in the end of shift time t s , the intersection angle of the solution of the end of shift time t s ; The specific process is: At the time t of obtaining the end-of-mid-shift s , the position and velocity of the interceptor at this time can be obtained by solving the Kepler equation as [r 1s , v 1s ], and the position of the target object r 2s is obtained by using the kinematic model of the target object; then the vector of the line connecting the interceptor and the target object is q = r 2s -r 1s (20) Therefore, the intersection angle at this moment is obtained as wherein represents the size of the interceptor and target line of connection, represents the size of the interceptor velocity; The intersection angle constraint about the middle-end shift moment is α≤α max (22) In the formula, α max represents the upper limit value of the constraint of the intersection angle at the end of the shift.

8. The method of claim 7, wherein: The step four three obtains the end-of-shift time t based on the end-of-shift time t obtained in step four one s And the intersection angle obtained in step four two, the interception time range under two constraint conditions is obtained The specific process is: Step four three one, for intercepting time interval The search step length of the coarse search is set as a fixed small step length τ; Step four three two, record Record When N is an integer, L is equal to N; Otherwise, L is equal to N rounded down. Thus, L+1 intercept instants can be generated, i.e. where t f,k denotes the kth intercept time; Step four three, for each intercept time t f,k the launch speed of the interceptor missile is obtained by solving the Lambert problem; For each intercept time t f,k , the time t s,k of the end of the shift of the interceptor missile and the intersection angle a k at this time are obtained based on step four three one and step four three two; If α k ≤ α max , then t f,k is the time satisfying the intersection angle constraint at the end of the shift, and a flag sign k = 1 is set. Otherwise, set flag sign k = -1 indicates that the intersection angle constraint at the end of shift is not satisfied at this moment. Step four three four, in all the sign k After the determination of sign j (k = 0, 1, …, L), check whether there are two adjacent signs different; if sign j+1 (j = 0, 1, …, L-1), then in the interval [t f,j , t f,j+1 ], there must be a boundary point of intercept time; then in the interval [t f,j , t f,j+1 ] known, the boundary point of intercept time can be solved by ITP method. Determining a range of interception times that satisfy two constraint conditions based on a boundary point 9. The method of claim 8, wherein: The step five of obtaining the interception window; the specific process is as follows: Step five, solve the feasible range of the transmission time t1 in the initial search range [0, t 1max ] at the transmission time β represents the number of feasible ranges Step five two, in the emission time range, traverse the emission time with specified step τ2, obtain the interception time range at each time Finally, get all the interception windows ​ The step five in the initial search range [0, t 1max ] in the transmission time t1 feasible range β represents the number of feasible range; the specific process is: Step five-1, for the initial search range [0, t 1max ], set the search step of the coarse search of the transmission time dimension as a fixed small step τ1; Step five two, let N1 = (t 1max -0) / τ1, let When N1 is an integer, L1 is equal to N1; otherwise, L1 is equal to N1 rounded down. Thus, L1+1 transmission instants, i.e. t 1,m = m-τ1; where t 1,m denotes the mth transmission instant; m = 0, 1,..., Li; Step five three, for each transmission time t 1,m , by using the solving method of interceptable time interval under fixed transmission time, the interceptable time interval under the transmission time is obtained; If the range is non-empty, then t 1,m is feasible, while setting a flag sign m = 1; Otherwise, set flag sign m = -1 means that the interceptable time interval found at this transmission moment is an empty set; Step five 414, in all sign m After the determination of sign n (m = 0, 1, …, L1), check whether there are two adjacent signs different; if sign n+1 (n = 0, 1, …, L1-1), then in the interval [t 1,n , t 1,n+1 ], there must be a boundary point of the transmission time; in the case of known interval [t 1,n , t 1,n+1 ], the boundary point of the transmission time is obtained by solving by ITP method; A feasible range of emission time t1 is obtained The step five two in the emission time range , according to the specified step length τ2, the interception time range At each time, the interception window is obtained; the specific process is: Recall Recall When N β is an integer, L β equals N β ; otherwise, L β equals N β rounded down. for each transmission time By using the solving method of the interceptable time interval under the fixed transmission time, the interceptable time interval under the transmission time is obtained After the traversal is completed, all the near-space vehicle interception windows are finally obtained.

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