Carrier rocket active section flight trajectory simulation method based on non-cooperative measured data

Abstract

The invention provides a carrier rocket active section flight trajectory simulation method based on non-cooperative measured data, which comprises the following steps: performing dynamic modeling on a carrier rocket active section, solving a motion acceleration vector of the rocket active section by using the non-cooperative measured data, and designing a rocket active section flight trajectory integral solving method; and carrying out carrier rocket active section flight process analogue simulation, and designing a corresponding active section trajectory simulation process aiming at two conditions that the last stage is a solid rocket engine and the last stage is a liquid rocket engine. The method can achieve the high-precision simulation of the flight path of the rocket active section under the condition that a non-cooperative measurement carrier rocket only has the measurement data of the outer trajectory of the rocket active section. The problem that the design of the flight trajectory of the carrier rocket active section can only be realized by depending on a rocket design department to know detailed parameters and characteristics such as the working state and aerodynamic parameters of each stage of engine of the rocket, each stage of structural quality and navigation control model is avoided.

Description

Technical Field

[0001] The invention belongs to the technical field of launch vehicle trajectory, and in particular relates to a launch vehicle active phase flight trajectory simulation method based on non-cooperative measured data. Background Art

[0002] The active phase of a launch vehicle refers to the flight arc in which the rocket engine actively works before the rocket is separated from its payload. Through the maneuvering flight of the active phase, the launch vehicle will give the payload the desired initial velocity and initial position, or send the payload into a predetermined orbit. The existing launch vehicle active phase flight trajectory design method mainly uses the integral solution of control equations and dynamic equations. It requires the working state of each stage of the rocket engine, aerodynamic parameters, structural mass of each stage, engine specific impulse, fuel mass flow rate, navigation control model and other detailed parameters and characteristics. These parameters and characteristics are only mastered by the rocket design department that designs the rocket. Therefore, the existing launch vehicle active phase flight trajectory design method is also only applicable to the rocket design department.

[0003] For non-cooperatively measured launch vehicles, in the case of only exterior ballistic measurement data, non-rocket design departments cannot know the above-mentioned parameters and characteristics of the rocket's engines at each stage, and cannot use existing methods to effectively restore the rocket's active phase flight trajectory. The high-precision simulation of the rocket's active phase flight trajectory is of great value to research areas such as launch vehicle sub-stage landing area calculation, launch vehicle orbital capability analysis, rocket launch window analysis, and missile attack and defense confrontation. Summary of the invention

[0004] The purpose of the present invention is to solve the problem in the prior art that the non-cooperative measurement of the launch vehicle cannot restore the flight trajectory of the active stage of the rocket due to the inability to know the parameters and characteristics of its engines at each stage, and to provide a launch vehicle active stage flight trajectory simulation method based on non-cooperative measured data, carry out dynamic modeling of the launch vehicle active stage, realize high-precision simulation of the launch vehicle active stage flight trajectory, and accurately simulate the active stage flight characteristics.

[0005] To achieve the above purpose, the technical solution provided by the present invention is:

[0006] A method for simulating the active phase flight trajectory of a launch vehicle based on non-cooperative measured data is special in that it includes the following steps:

[0007] Step 1: Conduct dynamic modeling of the active stage of the launch vehicle and use non-cooperative measured data to solve the motion acceleration vector a of the active stage of the launch vehicle. R,t :

[0008] a R,t =a G,t +a T,t

[0009] In the formula, a G,t is the inertial position vector r of the rocket assembly at time t t The function of T,t is a function of the thrust acceleration at time t and is calculated using the following sub-steps:

[0010] Step 1.1, calculate the thrust acceleration:

[0011]

[0012] In the formula, I sp,t is the engine specific impulse at time t, V fm,t is the propellant mass flow rate at time t, g0 is the standard gravitational acceleration at sea level, M t The remaining mass ratio of the rocket at time t is:

[0013]

[0014] Where T0=0 is the time when the rocket ignition command is issued, T start,1 To T start,n is the relative time when the first to nth stage rockets start working, T end,1 To T end,n is the relative time when the first to nth stage rockets finish working, Isp1 to Isp n is the equivalent specific impulse of the rocket's first to nth stage engines, Vfm1 to Vfm n is the specific mass flow rate of the propellant of the rocket engine from the 1st to the nth stage;

[0015] Step 1.2, solving the thrust acceleration direction, including:

[0016] Step 1.2.1, solve the expected flight speed at the current moment:

[0017] [v Ke,t ,v Target ]=Kepler(r t ,r Target ,T La -t)

[0018] In the formula, Kepler is the Kepler equation for solving the elliptical orbit of two bodies, r Target is the inertial position of a certain point in the process of unpowered flight of the rocket after the rocket and its payload are separated, v Ke,t is r obtained by solving Kepler's equation t The velocity vector of the inertial frame corresponding to the point, v Target is r obtained by solving Kepler's equation Target The velocity of the inertial system corresponding to the point, T Lais the time from time T0 until the rocket flies to r Target The total time taken, t is the relative flight time relative to time T0, and the position of the rocket inertial system at time T0 is recorded as r0;

[0019] Step 1.2.2, design the turn end time sequence to solve the program turn time period based on the measured data, including the program turn start time T start,turn and the end time of the program turn T end,turn :

[0020]

[0021] In the formula, the subscript k is the variable ordinal number, St is the time series step, and T end,1 Finishing work on the rocket's first stage

[0022] time;

[0023] Step 1.2.3, design the thrust vector calculation equation:

[0024]

[0025] In the formula, v Ke,t is the expected speed at time t, v t is the actual velocity vector of the rocket at time t, a G,t Fire at time t

[0026] The gravity acceleration of the arrow, p 1,t and p 2,t is the control coefficient, D t is the direction coefficient:

[0027]

[0028] Where Δt is the integration step length;

[0029] Step 2: Design the integral solution of the rocket active phase flight trajectory:

[0030]

[0031] Where T is the target time, s T is the state vector at the target time, s0 is the state vector at T0, For t The derivative of s t is the rocket's geocentric inertial system state vector, s t =[r t ,v t ] T , where r t is the position vector, v t is the velocity vector;

[0032] Step 3, simulation of the active phase flight process of the launch vehicle, includes the following sub-steps:

[0033] Step 3.1, let r Target is the expected value of the inertial system position vector of a point on the unpowered gliding section of the payload after the rocket is separated from its payload, v Target is the expected value of the velocity vector at the point, r0 is the position vector of the inertial system at the rocket launch point, T La is the time from time T0 until the rocket flies to r Target The total time consumed, solving the flight time T La The corresponding r Target Point velocity vector v Ke,Target :

[0034] [v Ke,0 ,v Ke,Target ]=Kepler(r0,r Target ,T La );

[0035] Step 3.2: According to the scene, v Target The total time required to solve the direction is T La ;

[0036] Step 3.3, determine the type of the rocket's final stage. If the final stage is a solid rocket engine, proceed to step 3.4. If the final stage is a liquid rocket engine, proceed to step 3.5.

[0037] Step 3.4, simulation of the rocket flight process with the last stage being a solid rocket engine, includes:

[0038] Step 3.4.1, determine the working time of the final stage, and set the time when the final stage of the rocket starts working to T start,n Equal to the time when the previous level finishes work T end,n-1 , the moment when the rocket's last stage stops working is T end,n It is equal to the time when the previous stage finishes working plus the working time of the rocket's final stage T. continue ;

[0039] Step 3.4.2, use the total time T La and the determined final stage working time, solve the trajectory according to step 2, and calculate the expected flight speed v corresponding to time t according to step 1.2.1 in each integral during the solution process Ke,t ;

[0040] Step 3.4.3, judge whether the rocket model has the ability to achieve the goal of moving from point r0 to r according to the following judgment conditions Target Orbital maneuverability:

[0041]

[0042] In the formula, ε V is the speed deviation threshold, ε D is the speed direction deviation threshold; if there is a time t in the integration process that satisfies the first two conditions in the formula, but t<T start,n , by shortening the total flight time T La , re-integrate, and we can find the time t that satisfies all the conditions of the formula. At this time, it is determined that the rocket model has the ability to achieve the goal of moving from point r0 to r Target Orbital maneuverability, go to step 3.3.4; if there is no time t that satisfies the first two conditions in the formula during the integration process, it is determined that the rocket model does not have the ability to move from point r0 to r Target orbital maneuverability;

[0043] Step 3.4.4, solving the ignition time of the final stage rocket, includes:

[0044] Step 3.4.4.1, design time judgment conditions:

[0045]

[0046] In the formula, ε T is the time deviation threshold;

[0047] Step 3.4.4.2, design the final working time:

[0048] T start,n =T end,n-1 +T inte , T end,n =T end,n-1 +T inte +T continue

[0049] Where, T inte Waiting for ignition time for the final stage;

[0050] Step 3.4.4.3, solve the final stage waiting ignition time T inte : Make the last stage wait for ignition time T inte Start from 0 and increase. After each increase, integrate the whole trajectory according to step 2. In each integration, calculate the time t that satisfies the formula in step 3.4.3 according to step 1.2.1 until the time t that satisfies both the formula in step 3.4.3 and the formula in step 3.4.4.1 appears. Then the final stage waiting ignition time T is obtained. inte ;

[0051] Step 3.4.4.4, the obtained final stage waiting ignition time T inte Re-assign T according to step 3.4.4.2 start,n 、Tend,n After updating the corresponding parameters in step 1, follow step 2 to complete the process from the launch point r0 to the aiming point r Target Full flight track integration;

[0052] Step 3.5, simulation of the rocket flight process with the last stage being a liquid rocket engine, includes:

[0053] Step 3.5.1, use the total time T La Solve the trajectory according to step 2, and calculate the expected flight speed v corresponding to time t according to step 1.2.1 for each integral in the solution process Ke,t ;

[0054] Step 3.5.2: Determine whether the rocket model has the ability to move from point r0 to point r according to the following judgment conditions. Target Orbital maneuverability:

[0055]

[0056] In the formula, ε V is the speed deviation threshold, ε D is the velocity direction deviation threshold; if there is no time t that satisfies the three conditions in the formula during the integration process, it is determined that the rocket model does not have the ability to travel from point r0 to r Target If the three conditions in the formula are met at a certain time t = Tn during the integration process, the rocket model is judged to have the ability to achieve orbital maneuverability from point r0 to r Target The orbital maneuverability is determined, and the time Tn is recorded as the final stage shutdown time, and the process goes to step 3.5.3;

[0057] Step 3.5.3, after updating the corresponding parameters in step 1 with the obtained final stage shutdown time Tn, complete the process from the launch point r0 to the aiming point r according to step 2. Target The complete flight track integration.

[0058] Further, in step 1.1, the propellant specific mass flow rate V fm,t Solve by following the steps below:

[0059] The first step is to establish a transcendental equation based on the Tsiolkovsky equation and the energy conservation formula:

[0060]

[0061] Where V start,i is the measured inertial system velocity when the i-th stage rocket starts working, V end,i is the measured inertial velocity of the i-th stage rocket at the end of operation, ΔH i is the measured height of the rocket rising in the working interval of the i-th stage rocket, m start,iis the total mass of the i-th stage rocket when it starts working, m end,i is the total mass of the i-th stage rocket at the end of its operation;

[0062] The second step is to calculate the initial value of the propellant mass flow rate of the i-th stage rocket:

[0063]

[0064] The third step is to calculate the initial value of the propellant mass flow rate Vfm i Perform iterative correction:

[0065]

[0066] Vfm i,mid,0 =Vfm i

[0067]

[0068] In the formula, the first digit of Vfm is the current rocket stage number, the second digit max, mid, and max represent the minimum, median, and maximum values ​​respectively, and the third digit represents the number of iterations. The number of iterations is set to k, and k = 0 for the first iteration;

[0069] The fourth step is to convert the corrected Vfm i,mid,k Substitute into step 2 to solve:

[0070]

[0071] In the formula, s Tendi,k The first digit of the superscript indicates the end time of integration. At the current time, Tendi=T end,i It is the shutdown time of rocket stage i, and the second digit of the superscript represents the number of iterations;

[0072] Step 5: Let v Tendi,R T end,i The measured rocket velocity vector at the moment, the deviation dv between the measured velocity at the current moment and the velocity solved by integration is defined as follows:

[0073] dv Tendi,k =||v Tendi,k ||-||v Tendi,k ||

[0074] Step 6: Iterate continuously according to the following iteration rules:

[0075] If dv Tendi,k <0, which means Vfm i,mid,k If it is too large, then in the next iteration:

[0076]

[0077] If dv Tendi,k >0, which means Vfm i,mid,k If it is too small, then in the next iteration:

[0078]

[0079] Until DV Tendi,k is less than the accuracy threshold, then the propellant mass flow rate Vfm for the i-th stage rocket i Make the final assignment:

[0080] Vfm i =Vfm i,mid,k

[0081] Step 7. Repeat this step, and input the actual speed after each stage of the rocket is completed, and complete the assignment of the propellant specific mass flow rate from the first stage to the last stage of the rocket.

[0082] Further, step 1.2.2 includes:

[0083] Step 1.2.2.1, design the turn end time sequence:

[0084]

[0085] In the formula, the subscript k is the variable ordinal number, St is the time series step, and T end,1 The moment when the first stage of the rocket ends its work;

[0086] Step 1.2.2.2, T end,turn,k Substitute the sequence into step 2 for solution:

[0087] s Tend1,k =[r Tend1,k ,v Tend1,k ] T

[0088] Get the first-level shutdown speed set v Tend1,k , v Tend1,k The first subscript of Tend1=T end,1 It is the moment when the first stage of the rocket is shut down. The second digit of the superscript is the ordinal number of the variable;

[0089] Step 1.2.2.3, the measured level 1 shutdown speed is v Tend1,R , define the velocity difference sequence as dv k :

[0090]

[0091] Step 1.2.2.4, calculate the optimal T end,turn :

[0092]

[0093] Where m is the number of iterations.

[0094] Furthermore, in step 1.1, the rocket's remaining specific mass M t The calculation is as follows:

[0095]

[0096] In the formula, min(T end,i , t) is the minimum value between the end time of the i-th stage rocket and the current time, Mc i It is the ratio of the structural mass of the i-th stage rocket to the total mass of the rocket at time T0.

[0097] Furthermore, in step 1.1, calculate the rocket's residual mass M t Mc i Designed as fixed value:

[0098] The advantages of the present invention are:

[0099] The present invention's method for simulating the active stage flight trajectory of a launch vehicle based on non-cooperative measured data takes into account that the non-cooperative measurement launch vehicle cannot obtain the parameters and characteristics of its engines at various stages, performs dynamic modeling on the active stage of the non-cooperative measurement launch vehicle, obtains the motion acceleration vector of the active stage of the rocket, designs an integral solution method for the flight trajectory of the active stage, and simulates the flight process of the active stage for rockets with solid rocket engines and liquid rocket engines at the final stage. Therefore, the present invention can achieve high-precision simulation of the flight trajectory of the active stage of the rocket for non-cooperative measurement launch vehicles with only the external ballistic measurement data of the active stage of the rocket, and avoids the problem that the design of the flight trajectory of the active stage of the launch vehicle can only be realized by relying on the rocket design department to obtain detailed parameters and characteristics such as the working state of the engines at various stages of the rocket, aerodynamic parameters, structural mass at various stages, and navigation control models. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] The above and / or other features and advantages of the present invention will become more easily understood through the following description with reference to the accompanying drawings, which are not drawn to scale and some features are exaggerated or reduced to show details of specific components. In the accompanying drawings:

[0101] Figure 1 It is a flow chart of the launch vehicle active phase flight trajectory simulation method based on non-cooperative measured data of the present invention;

[0102] Figure 2 It is a time-height curve comparison between the simulation data obtained in the example of the present invention and the measured data;

[0103] Figure 3 is the elevation difference between the simulated data and the measured data at the same time obtained in the example of the present invention;

[0104] Figure 4 is the elevation error ratio between the simulated data and the measured data at the same time obtained in the example of the present invention;

[0105] Figure 5 It is a comparison of the time-speed curve of the simulation data obtained in the example of the present invention and the measured data;

[0106] Figure 6 is the speed difference between the simulated data and the measured data at the same time obtained in the example of the present invention;

[0107] Figure 7 is the speed error ratio between the simulation data and the measured data at the same time obtained in the example of the present invention;

[0108] Figure 8 It is a comparison of the range-elevation curve of the orbital entry data at time T1 and time T2 obtained in the example of the present invention;

[0109] Fig. 9 It is a comparison of the time-elevation curves of the orbital entry data at time T1 and time T2 obtained in the example of the present invention;

[0110] Fig.10 It is a comparison of the time-velocity curves of the orbital entry data at time T1 and time T2 obtained in the example of the present invention;

[0111] Fig.11 is the angle between the velocity and the gravity direction under different orbital entry states obtained in the examples of the present invention;

[0112] Fig.12 It is a comparison of the range-elevation curve of the orbital entry data at time T3 and time T4 obtained in the example of the present invention;

[0113] Fig.13 It is a comparison of the time-elevation curves of the orbital entry data at time T3 and time T4 obtained in the example of the present invention;

[0114] Fig.14 It is a comparison of the time-velocity curves of the orbital entry data at time T3 and time T4 obtained in the example of the present invention. DETAILED DESCRIPTION

[0115] The present invention will be described in detail below with reference to the accompanying drawings by means of exemplary embodiments of the present invention. It should be noted that the following detailed description of the present invention is only for the purpose of illustration, and is not intended to limit the present invention.

[0116] The present invention provides a method for simulating the active phase flight trajectory of a launch vehicle based on non-cooperative measured data. The method can solve the key parameters of a non-cooperative measurement launch vehicle with only the external ballistic measurement data of the rocket's active phase, thereby realizing high-precision simulation of the launch vehicle's active phase flight trajectory. The method has great value in research fields such as calculation of launch vehicle sub-stage landing area, analysis of launch vehicle's orbit insertion capability, analysis of rocket launch window, and missile attack and defense confrontation.

[0117] Reference Figure 1 As an exemplary embodiment of the present invention, a method for simulating the active phase flight trajectory of a launch vehicle based on non-cooperative measured data includes:

[0118] Step S1, dynamic modeling of the active stage of the launch vehicle, solving the motion acceleration vector of the active stage of the rocket using non-cooperative measured data, and designing a method for solving the integral of the flight track of the active stage of the rocket;

[0119] Step S2, simulating the flight process of the active phase of the launch vehicle, and designing the corresponding active phase trajectory simulation process for the two cases where the last stage is a solid rocket engine and the last stage is a liquid rocket engine.

[0120] During the flight of a rocket, it is affected by the combined effects of engine thrust, air resistance, and gravity. If its flight process needs to be accurately simulated, a large number of parameters such as the engine specific impulse, propellant mass flow rate, structural mass, assembly mass-drag ratio, and assembly drag coefficient of each stage of the rocket must be known. It is impossible to fit all of the above parameters only through limited length measurement data, so it is necessary to partially simplify the dynamic equations. According to analysis, the thrust of the rocket engine is almost opposite to the direction of air resistance, and often only the working arc of the first-stage rocket is located in the dense atmosphere, while the atmospheric resistance magnitude of the working arc of the second and third-stage engines is much lower than the thrust magnitude. Based on the above analysis, the combined force of air resistance and engine thrust can be equivalent to an equivalent thrust that is smaller than the actual thrust of the engine. In this way, only the dynamic modeling and solution of the thrust can be completed to realize the simulation of the active stage flight process of the rocket, which greatly reduces the requirements for the accuracy and length of external measurement data.

[0121] Step S1 may include step S1.1: performing dynamic modeling on the active section of the launch vehicle.

[0122] Under the above assumptions, the acceleration of the rocket's active phase motion is R,t It can be decomposed into the gravitational acceleration a T,t , equivalent thrust acceleration a T,t sum:

[0123] a R,t =a G,t +a T,t (1)

[0124] In the formula, a G,t is the inertial position of the rocket assembly r t The function can be solved by calculating the gravity function. It is a general algorithm and will not be described here. T,t It is a function of the thrust acceleration at time t, and its modeling and solution will be explained in detail in the following steps.

[0125] The expression for obtaining the thrust acceleration at any time t is designed as follows:

[0126]

[0127] In the formula, I sp,t is the engine specific impulse at time t, V fm,t is the propellant mass flow rate at time t, g0 is the standard gravitational acceleration at sea level, M t is the remaining specific mass of the rocket at time t.

[0128] Specific impulse I sp,t The calculation formula can be designed as follows:

[0129]

[0130] Where T0=0 is the time when the rocket ignition command is issued, T start,1 To T start,n is the relative time when the first to nth stage rockets start working, T end,1 To T end,n is the relative time when the rocket from the first stage to the nth stage ends its work, and the value of this time is extracted through the analysis of measured data; Isp1 to Isp n It is the equivalent specific impulse of the 1st to nth stage engines of the rocket. Different types of rocket engines have different values. Usually, the average specific impulse of the engine type used in the rocket can be taken. If there are higher requirements for simulation accuracy, the equivalent specific impulse can be fine-tuned according to the actual situation.

[0131] Designable propellant specific mass flow rate V fm,t The expression is as follows:

[0132]

[0133] Where, Vfm1 to Vfm n is the specific mass flow rate of the propellant of the 1st to nth stage rocket engines, which can be calculated in particular by the value-taking method of step S1.3, but this is not intended to limit the present invention, and other methods may also be used.

[0134] Optionally, design the rocket residual specific mass M t The calculation formula is as follows:

[0135]

[0136] Where M t is the relative mass at time t, which is defined as the ratio of the total mass of the rocket at time t to the total mass of the rocket at time T0. The specific mass at time t is the specific mass at time T0 minus the mass of fuel consumed from T0 to time t and the mass of the discarded structure; min(T end,i , t) is the minimum value between the end time of the i-th stage rocket and the current time, Mc i is the ratio of the structural mass of the i-th stage rocket to the total mass of the rocket at time T0. This value and the mass flow rate work together to affect the relative mass. In order to control the scale of the variable, Mc i Designed as fixed value:

[0137]

[0138] So far, the modeling of the thrust acceleration magnitude has been completed. Now let’s solve the desired thrust acceleration direction.

[0139] The purpose of the rocket engine is to make the rocket achieve the expected flight speed, so the expected flight speed needs to be solved. The expected flight speed at the current moment is solved as follows:

[0140] [v Ke,t ,v Target ]=Kepler(r t ,r Target ,T La -t) (7)

[0141] In the above formula, Kepler is the Kepler equation for solving the elliptical orbit of two-body motion. This algorithm is a general algorithm and will not be described here. t is the inertial position vector of the rocket assembly at time t; r Target v is the position of a certain point in the inertial system during the unpowered flight of the rocket after the rocket and its payload are separated. Usually, the point should be selected as close as possible to the separation point; Ke,t is r obtained by solving Kepler's equation t The point corresponds to the velocity vector of the inertial system; v Target is r obtained by solving Kepler's equation Target Point corresponds to the inertial system velocity; T La is the time from time T0 until the rocket flies to r Target The total time taken, t is the relative flight time relative to time T0; the position of the rocket inertial system at time T0 is recorded as r0.

[0142] In the actual rocket flight process, in order to prevent the rocket from tipping over during the ascent, and the adjustable range of the engine thrust direction is limited, the expected velocity direction at time t cannot be consistent with v Ke,tTo maintain complete consistency, it is necessary to introduce control of the program turning period at the beginning of rocket takeoff. Based on the above analysis, the thrust vector calculation equation is designed as follows:

[0143]

[0144] In the formula, v t is the actual velocity vector of the rocket at time t; T start,turn is the start time of the rocket program turn, T end,turn is the end time of rocket program turn; p 1,t 、p 2,t is the control coefficient, and its expression is shown in formula (9); D t is the directional coefficient, and its expression is shown in formula (10), where Δt is the integration step length, v Ke,t is the expected velocity at time t, that is, r obtained by solving the Kepler equation t The velocity vector of the inertial frame corresponding to the point, v t is the actual speed at time t, a G,t is the gravitational acceleration of the rocket at time t, which is the same as the above mentioned a G,t Seek consistency in the law.

[0145]

[0146] Step S1 also includes step S1.2, designing a method for solving the active segment flight trajectory integral.

[0147] The rocket's geocentric inertial state vector s t It is expressed as follows, where r t is the position vector, v t is the velocity vector.

[0148]

[0149] s t The derivative of is as follows:

[0150]

[0151] right The state vector s can be realized by integration t Continuous calculation of and generation of rocket flight trajectory:

[0152]

[0153] T is the target time, s T is the state vector at the target time, and s0 is the state vector at T0.

[0154] Step S1 also includes step S1.3: solving the propellant specific mass flow rate based on the measured data.

[0155] For the convenience of calculation, the altitude change rate of a single-stage rocket during flight is equivalent to a constant, and a transcendental equation can be established based on the Tsiolkovsky equation and the energy conservation formula:

[0156]

[0157] V start,i is the measured inertial system velocity when the i-th stage rocket starts working, V end,i is the measured inertial velocity of the i-th stage rocket at the end of operation, ΔH i is the measured height of the rocket rising in the working interval of the i-th stage rocket, m start,i is the total mass of the i-th stage rocket when it starts working, m end,i is the total mass of the i-th stage rocket at the end of operation (before stage separation). Substituting the corresponding measured data into the transcendental equation, we can achieve Solve for the initial value of .

[0158] The initial value of the propellant specific mass flow rate of the i-th stage rocket is calculated as follows:

[0159]

[0160] Since formula (14) simplifies the motion process, the initial value of mass flow rate Vfm i There is a certain error with the actual equivalent mass flow rate, which needs to be corrected iteratively. Initialize the initial value of the iteration:

[0161]

[0162] Vfm i,mid,0 =Vfm i (16)

[0163]

[0164] In the formula, the first digit of Vfm's subscript is the current rocket stage number; the second digit max, mid, and max represent the minimum, median, and maximum values ​​respectively; the third digit represents the number of iterations, and the number of iterations is set to k. k=0 for the first iteration.

[0165] Vfm i,mid,k Substitute into equation (13) and solve:

[0166]

[0167] s Tendi,k =[r Tendi,k ,v Tendi,k ] T

[0168] In the formula, s Tendi,kThe first subscript of is the end time of integration. At the current time, Tendi=T end,i is the shutdown time of rocket stage i; the second digit of the superscript represents the number of iterations. Let v Tendi,R T end,i The measured rocket velocity vector at the time, the deviation dv between the measured velocity at the current time and the velocity solved by integration is defined as follows, and its subscript definition is the same as s Tendi,k The definition of superscript is consistent:

[0169] dv Tendi,k =||v Tendi,k ||-||v Tendi,k || (18)

[0170] If dv Tendi,k <0, which means Vfm i,mid,k If it is too large, then in the next iteration:

[0171] Vfm i,min,k+1 =Vfm i,min,k

[0172]

[0173] Vfm i,max,k+1 =Vfm i,mid,k

[0174] If dv Tendi,k >0, which means Vfm i,mid,k If it is too small, then in the next iteration:

[0175] Vfm i,min,k+1 =Vfm i,mid,k

[0176]

[0177] Vfm i,max,k+1 =Vfm i,max,k

[0178] Continue to iterate until dv Tendi,k If the propellant mass flow rate Vfm of the i-th stage rocket is smaller than the accuracy threshold, i Make the final assignment:

[0179] Vfm i =Vfm i,mid,k (twenty one)

[0180] Repeat this step and input the measured speed of each stage of the rocket after the work is completed in turn, so as to complete the assignment of the propellant specific mass flow rate from the first stage to the last stage of the rocket in turn.

[0181] Step S1 also includes step S1.4: solving the program turning time period based on the measured data.

[0182] After solving the propellant mass flow rate based on the measured data, it is necessary to complete the program turn start time T used in formula (8) based on the measured data. start,turn and the end time of the program turn T end,turn The solution of T start,turn It can be directly obtained by analyzing the measured data, and the moment when the angle between the velocity direction and the opposite direction of gravity exceeds a certain threshold is assigned as T start,turn Through the analysis of measured data, it can be known that the program turn of a general launch vehicle is completed by the first-stage rocket, so the design turn end time sequence is:

[0183]

[0184] T end,turn,k The subscript k is the variable ordinal number; St is the time series step, usually set to 2 to 4 seconds; T end,1 This is the moment when the first stage of the rocket ends its work. start,turn is the start time of the program turn. end,turn,k Substitute the sequence into equation (13) and solve:

[0185]

[0186] Get the first-level shutdown speed set v Tend1,k , v Tend1,k The first subscript of Tend1=T end,1 is the moment when the rocket first stage is shut down, and the second digit of the superscript is the variable ordinal number. The measured first stage shutdown speed is v Tend1,R , define the velocity difference sequence as dv k :

[0187]

[0188] In DV k There is a minimum value dv in the sequence m , dv m-1 、dv m 、dv m+1 The three points are quadratically distributed, so the optimal T end,turn The calculation method is as follows:

[0189]

[0190] Where m is the number of iterations.

[0191] When the active stage dynamics model of the launch vehicle designed in step S1 is used for application scenarios such as orbital capability analysis and launch window calculation, since the parameters such as the target orbital altitude and speed used for simulation analysis are different from the measured data used for reverse modeling, it is necessary to adjust some parameters on the basis of the existing rocket dynamics model to achieve orbital altitude and speed control. Usually, the working state of the first few stages of the launch vehicle is fixed, that is, under normal conditions, there is no thrust controlled termination capability, the separation time is determined, and the ignition timing is fixed, while the final stage usually has the ability to delay ignition or shut down in advance to achieve effective control of the head-body separation state. Step S2 designs a simulation method for the active stage flight process of the rocket in view of the situation where the launch vehicle uses different final stage engines, which mainly includes how to use the existing dynamics model to simulate different types of rockets to achieve the desired maneuvering purpose.

[0192] Assume r Target is the expected value of the inertial system position vector of a point on the unpowered gliding section of the payload after the rocket and its payload are separated, v Target is the expected value of the velocity vector at the point, r0 is the position vector of the inertial system at the rocket launch point, T La is the time from time T0 until the rocket flies to r Target The total time consumed by the flight can be obtained by substituting it into the Kepler equation of formula (26) and solving it. La The corresponding r Target Point velocity vector v Ke,Target ,The solution of Kepler's equation is a general algorithm and will not be described here.

[0193] [v Ke,0 ,v Ke,Target ]=Kepler(r0,r Target ,T La ) (26)

[0194] In the simulation of rockets carrying satellites into orbit, v Target There are requirements for the direction, and the design criteria are as follows:

[0195]

[0196] By adjusting T La The duration of v Ke,Target With v Target The angle is less than a certain deviation threshold ε D When T La Under the parameter conditions, r Target point can be reached; if you adjust T anyway La The duration of the above threshold condition cannot be obtained. Ke,Target , then it is proved that the orbital point r TargetIncorrect selection or failure to launch rocket from R0 directly into R Target 、v Target The corresponding track.

[0197] When simulating ballistic missile targets, r Target is the coordinate of the inertial system of the landing point. At this time, v Target There is no requirement for the direction, and the design reachability criteria are as follows:

[0198] ||v Ke,Target ||≤v max (28)

[0199] Where v max is the maximum speed to which this type of launch vehicle can be accelerated. Ke,Target || is too large, you can increase T La Make||v Ke,Target ||Decrease.

[0200] Solve for T that satisfies the above conditions La Finally, the two cases of the final stage being a liquid rocket and a solid rocket are distinguished, and the flight process of the active phase of the rocket is simulated, which are respectively step S2.1 for simulating the rocket flight process for a solid rocket engine and step S2.2 for simulating the rocket flight process for a liquid rocket engine.

[0201] First, step S2.1 is described: simulation of the rocket flight process with a solid rocket engine as the last stage.

[0202] A launch vehicle with a solid rocket engine as the last stage usually can only wait for the propellant to burn out and shut down after the last stage is ignited. Therefore, separation state control is achieved by controlling the ignition time of the last stage.

[0203] First, the final stage working time in formulas (3) and (4) is redesigned, and the start time of the final stage (nth stage) of the rocket is T start,n Equal to the time when the previous level finishes work T end,n-1 , the moment when the rocket's last stage stops working is T end,n It is equal to the time when the previous stage finishes working plus the working time of the rocket's final stage T. continue :

[0204]

[0205] Use the method of step S1.1 and step S1.2 to assign the new value of T start,n 、T end,n Substitute into formula (3) and (4), and replace T La Substitute formula (13) to solve the trajectory, and use formula (7) to calculate the expected velocity v at time t at each step of the integration. Ke,t, the design judgment conditions are as follows:

[0206]

[0207] where ε V is the speed deviation threshold, ε D is the velocity direction deviation threshold, v t is the actual speed at time t, T start,n is the time when the last stage rocket starts working, T end,n is the time when the last stage rocket ends working. If there is a time t in the integration process that satisfies the first two conditions described in formula (30), but t<T start,n , by shortening the total flight time T La , and re-integrate to obtain the time t that satisfies all the conditions of formula (30). At this time, the rocket model has the ability to achieve the goal of moving from point r0 to r Target If there is no moment t that satisfies the first two conditions of formula (30) during the integration process, then the rocket model does not have the ability to move from point r0 to r Target orbital maneuverability.

[0208] After confirming that the rocket model has the corresponding orbital maneuverability, it is necessary to solve the ignition time of the final stage rocket. First, the time judgment condition formula (31) is designed, ε T is the time deviation threshold.

[0209]

[0210] The final stage working time in the redesigned formulas (3) and (4) is as follows:

[0211]

[0212] Where T start,n is the moment when the last stage rocket starts working, T end,n The moment when the last stage rocket finishes working, T end,n-1 The moment when the upper stage rocket finished working, T inte It is the time difference between the end of the work of the first stage rocket and the start of the work of the last stage rocket, which can also be called the last stage waiting for ignition time. inte It starts from 0 and increases continuously. After each increase, the whole trajectory is integrated using steps S1.1 and S1.2. In each integration, the time t that satisfies the criteria of formula (30) is calculated using formula (7) until a t that satisfies both the criteria of formula (30) and formula (31) appears. At this time, the corresponding T inte That is the time when the final stage of the solid rocket model is waiting for ignition.

[0213] T inte Substitute the final value into formula (32) to get Tstart,n 、T end,n After re-assignment, update the corresponding parameters of formulas (3) and (4), and use step S1.2 to complete the process from the launch point r0 to the aiming point r Target The complete flight track integration realizes the full process simulation of the active stage with the solid rocket as the last stage.

[0214] Now, step S2.2 is described: simulation of the rocket flight process with the last stage being a liquid rocket engine.

[0215] The launch vehicle with a liquid rocket engine as the last stage realizes separation state control by controlling the shutdown time of the last stage.

[0216] After completing the Target 、v Target The corresponding T La After solving, use the method of step S1.1 and step S1.2 to convert T La Substitute formula (13) to solve the trajectory, and use formula (7) to calculate the expected velocity v at time t at each step of the integration. Ke,t , the design judgment conditions are as follows:

[0217]

[0218] where ε V is the speed deviation threshold, ε D is the velocity direction deviation threshold, v t is the actual speed at time t, T start,n is the moment when the last stage rocket starts working, T end,n is the moment when the last stage rocket ends its operation. If there is no moment t that satisfies the condition described in formula (33) during the integration process, it means that the rocket model cannot complete the operation from point r0 to r Target If a certain time t=Tn during the integration process satisfies the condition described in formula (33), the time Tn is recorded as the final stage shutdown time.

[0219] T end,n =Tn is substituted into formula (3) and (4) and re-assigned. Then, step S1.2 is used to complete the process from the launch point r0 to the aiming point r Target The complete flight track integration realizes the full process simulation of the active stage of the liquid rocket as the last stage.

[0220] As described above, the method for simulating the active stage flight trajectory of a launch vehicle based on non-cooperative measured data of the present invention takes into account that the parameters and characteristics of the engines at various stages of the non-cooperative measurement launch vehicle cannot be known, and the non-cooperative measurement launch vehicle active stage is dynamically modeled, and the motion acceleration vector of the active stage of the rocket is obtained by solving, and the active stage flight track integral solution method is designed, and the active stage flight process simulation is performed for rockets with solid rocket engines and liquid rocket engines as the last stage. Therefore, the present invention can realize high-precision simulation of the flight track of the active stage of the rocket for non-cooperative measurement launch vehicles with only the external ballistic measurement data of the active stage of the rocket, and avoids the problem that the flight trajectory design of the active stage of the launch vehicle can only be realized by relying on the rocket design department to know the detailed parameters and characteristics such as the working state, aerodynamic parameters, structural quality at various stages and navigation control model of the engines at various stages of the rocket.

[0221] Next, the launch vehicle active phase flight trajectory simulation method based on non-cooperative measured data provided by the present invention is further explained with three embodiments in combination with examples.

[0222] In Example 1, a certain type of sounding rocket is used as the simulation object. The rocket is a sounding rocket used for meteorological sounding payload tests. It is a single-stage solid rocket. The rocket can send a payload to an altitude of 35km within 50 seconds and give the payload an initial velocity of about 1.7km / s. In order to control the landing area of ​​the payload, the rocket will perform a programmed turn 5s after takeoff, and the end time of the programmed turn is unknown.

[0223] In the simulation process, the dynamic modeling of the rocket was carried out through step S1.1. In order to verify the effectiveness of the method and the simulation accuracy, the main direct parameters used in the dynamic model were extracted from the measured data of the external ballistics: In formula (3), the first-stage specific impulse is taken as the common specific impulse of solid rocket Isp1=200s, and the first-stage rocket startup time T start,1 = 0s, first stage rocket shutdown time T end,1 =50s; the range aiming point r used in formula (7) Target The rocket shutdown point in the measured data is used, the initial position r0 is the rocket launch point in the measured data, and the total flight time is T La =50s; the program turning start time in formula (8) is extracted from the measured data T start,turn =2.4s.

[0224] Use step S1.3 to complete the solution for the propellant equivalent mass flow rate, Vfm1 = 0.0140922.

[0225] Use step S1.4 to complete the calculation of the end time of the program turn, T end,turn =41.7s.

[0226] After all parameters are solved, the active phase flight trajectory of the rocket is simulated through the calculation process of step S1.2 with a step size of 0.1s, and compared with the measured trajectory. Figure 2 Shown is a comparison of the time-elevation curves of the simulation data and the measured data, where the solid line is the measured data and the dotted line is the simulation data; Figure 3 The figure shows the elevation difference between the simulated data and the measured data at the same time. The elevation difference is defined as follows:

[0227] Elevation difference = measured data elevation - simulated data elevation

[0228] Figure 4 It is the elevation error ratio between the simulated data and the measured data at the same time. The elevation error ratio is defined as follows:

[0229]

[0230] Figure 5 Comparison of time-velocity curves between simulation data and measured data; Figure 6 It is the speed difference between the simulated data and the measured data at the same time. The speed difference is defined as follows:

[0231] Speed ​​difference = measured data combined speed - simulated data combined speed

[0232] Figure 7 is the speed error ratio between the simulated data and the measured data at the same time. The speed error ratio is defined as follows:

[0233]

[0234] pass Figures 2 to 4 It can be seen that the maximum elevation deviation between the simulated trajectory and the real trajectory is about 330m, and the maximum elevation error ratio is less than 1%, and the trajectory shape has achieved high-precision simulation. Figures 5 to 7 It can be seen that the maximum speed deviation between the simulated trajectory and the real trajectory is about 30m / s, and the maximum speed error ratio is less than 2%, and the trajectory speed has achieved high-precision simulation.

[0235] Therefore, in Example 1, based on the measured data of the active section of a certain type of sounding rocket, dynamic modeling of the active section of the rocket was carried out, key parameters such as the propellant mass flow rate and the start time of the program turn were solved, and the feasibility of the method related to step S1 was verified by comparing the simulated trajectory with the measured trajectory.

[0236] In the second embodiment, the active phase flight process of a two-stage solid rocket from launch to payload orbital entry is simulated, emulating two situations: normal orbital entry and abnormal orbital entry.

[0237] In this embodiment, the actual launch point of a certain type of existing carrier rocket is used as the design rocket launch point r0, the target orbit is a 120km high near-circular orbit, and the orbit entry point is point rTarget The rocket parameters are constructed and generated to simulate the full trajectory of a two-stage rocket from ignition to the payload entering orbit. The first and second stages of the simulated rocket are both solid rocket engines, which can be ignited under control but have no controlled shutdown capability. The second-stage engine controls the state of the orbital point by controlling the ignition time. All key construction parameters of the rocket are as follows:

[0238]

[0239] Use step S2.1 to solve the distance from the launch point r0 to the orbit entry point r Target Total flight time T La And the final stage waiting ignition time T inte The theoretical orbital velocity in formula (30) is ||v Ke,t ||=7.505km / s、ε V =0.1km / s, ε D =1°, ε in formula (31) T = 0.1s, solve for T La =T1, T inte =6.3, actual speed when entering orbit||v T1 ||=7.504km / s,v T1 The angle between the theoretical orbital velocity and the target velocity is 0.23°, which satisfies the condition described in formula (30). inte Growth, let T La = T2, the launch point and aiming point remain unchanged, and the integral is used to solve another active segment flight track to be used with T La =T1's orbital trajectory, in which ||v T2 ||=7.587km / s,v T2 The included angle with the theoretical orbital velocity is about 1.52°, which does not meet the orbital conditions described in formula (30).

[0240] Figure 8 Comparison of the range-elevation curves of the orbital entry data at time T1 and time T2. Fig. 9 Comparison of the time-elevation curves of the orbital entry data at time T1 and time T2. Fig.10 The time-velocity curves of the orbital data at time T1 and time T2 are compared. It can be observed that the orbital data at time T2 has a higher firing angle than that at time T1, and has a longer waiting time for ignition. The final stage rocket of the orbital data at time T1 also completes the ballistic lift while accelerating, while the final stage rocket of the orbital data at time T2 has a certain ballistic downward pressure while accelerating. Fig.11The figure shows the angle between the orbital velocity and the direction of gravity. Since the target orbit is a near-circular orbit, the angle between the target velocity and the direction of gravity is about 90°. It is only necessary to observe the relationship between the orbital velocity, the angle between the direction of gravity and the horizontal direction to know whether it meets the orbital conditions. By bringing in different total flight times T La , we can observe the changing trend of the angle between the orbital velocity and the gravity direction.

[0241] In summary, Example 2 refers to the launch point and orbit entry point parameters of a certain existing model of rocket, constructs the necessary parameters to establish a two-stage rocket model, whose last stage is a solid rocket, and solves the maneuvering trajectory from launch to orbit entry, verifying the feasibility of step S2.1.

[0242] Example 3 simulates the flight process of the active phase of a rocket with a liquid rocket engine as the last stage. The parameters of the two-stage rocket used in this example are exactly the same as those in the previous example, and the launch point, aiming point, and expected orbit are also the same, but the second-stage rocket is changed from a solid rocket to a liquid rocket, and the second-stage ignition time T start,2 Changed to a fixed value, the maximum working time of the second level is still 51s:

[0243]

[0244] Use the algorithm in step S2.2 to solve the problem of the distance from the launch point r0 to the orbit entry point r Target Total flight time T La And the final shutdown time T end,2 The theoretical orbital velocity in formula (33) is ||v Ke,t ||=7.504km / s、ε V =0.1km / s, ε D = 1°, solve for T La =T3, T end,2 =108.3, actual speed when entering orbit||v T1 ||=7.543km / s,v T1 The angle between the theoretical orbital velocity and the total flight time T is 0.87°, which satisfies the condition described in formula (33). La Growth, let T La = T4, the launch point and aiming point remain unchanged, and the integral is used to solve another active segment flight track to be used with T La =T3's orbital trajectory, in which ||v T2 ||=5.078km / s,v T2 The angle with the theoretical orbital velocity is about 21.74°, which does not meet the orbital conditions of formula (33).

[0245] Fig.12 Comparison of the range-elevation curves of the orbital entry data at time T3 and time T4. Fig.13Comparison of the time-elevation curves of the orbital entry data at time T3 and time T4. Fig.14 The time-velocity curves of the orbital data at T3 and T4 are compared. It can be observed that the orbital data at T4 has a higher launch angle than that at T3, but the secondary working time is shorter, and the final velocity of the orbital data at T4 is much lower than that at T3.

[0246] It can be seen that, based on Example 2, Example 3 changes the final stage rocket to a liquid rocket, solves the maneuvering trajectory from launch to orbit entry, and verifies the feasibility of step S2.2. So far, the effectiveness of the launch vehicle active phase flight trajectory simulation method based on non-cooperative measured data provided by the present invention has been verified.

[0247] Finally, it should be noted that the features mentioned and / or shown in the above description of the exemplary embodiments of the present invention may be combined in the same or similar manner into one or more other embodiments, combined with the features in other embodiments or substituted for the corresponding features in other implementations. The technical solutions obtained by these combinations or substitutions shall also be deemed to be included in the protection scope of the present invention.

Claims

1. A method for simulating the active phase flight trajectory of a launch vehicle based on non-cooperative measured data, characterized in that: The following steps are involved: Step 1: Conduct dynamic modeling of the active stage of the launch vehicle and use non-cooperative measured data to solve the motion acceleration vector a of the active stage of the launch vehicle. R,t : a R,t =a G,t +a T,t In the formula, a G,t is the inertial position vector r of the rocket assembly at time t t The function of T,t is a function of the thrust acceleration at time t and is calculated using the following sub-steps: Step 1.1, calculate the thrust acceleration: In the formula, I sp,t is the engine specific impulse at time t, V fm,t is the propellant mass flow rate at time t, g0 is the standard gravitational acceleration at sea level, M t The remaining mass ratio of the rocket at time t is: Where T0=0 is the time when the rocket ignition command is issued, T start,1 To T start,n is the relative time when the first to nth stage rockets start working, T end,1 To T end,n is the relative time when the 1st to nth stage rockets finish working, Isp1 to Isp n is the equivalent specific impulse of the rocket's first to nth stage engines, Vfm1 to Vfm n is the specific mass flow rate of the propellant of the rocket engine from the 1st to the nth stage; Step 1.2, solving the thrust acceleration direction, including: Step 1.2.1, solve the expected flight speed at the current moment: [v Ke,t ,v Target ]=Kepler(r t ,r Target ,T La -t) In the formula, Kepler is the Kepler equation for solving the elliptical orbit of two bodies, r Target is the inertial position of a certain point in the process of unpowered flight of the rocket after the rocket and its payload are separated, v Ke,t is r obtained by solving Kepler's equation t The velocity vector of the inertial frame corresponding to the point, v Target is r obtained by solving Kepler's equation Target The velocity of the inertial system corresponding to the point, T La is the time from time T0 until the rocket flies to r Target The total time taken, t is the relative flight time relative to time T0, and the position of the rocket inertial system at time T0 is recorded as r0; Step 1.2.2, design the turn end time sequence to solve the program turn time period based on the measured data, including the program turn start time T start,turn and the end time of the program turn T end,turn : In the formula, the subscript k is the variable ordinal number, St is the time series step, and T end,1 The moment when the first stage of the rocket ends its work; Step 1.2.3, design the thrust vector calculation equation: In the formula, v Ke,t is the expected speed at time t, v t is the actual velocity vector of the rocket at time t, a G,t is the gravitational acceleration of the rocket at time t, p 1,t and p 2,t is the control coefficient, D t is the direction coefficient: Where Δt is the integration step length; Step 2: Design the integral solution of the rocket active phase flight trajectory: Where T is the target time, s T is the state vector at the target time, s0 is the state vector at T0, s t For t The derivative of s t is the rocket's geocentric inertial system state vector, s t =[r t ,v t ] T , where r t is the position vector, v t is the velocity vector; Step 3, simulation of the active phase flight process of the launch vehicle, includes the following sub-steps: Step 3.1, let r Target is the expected value of the inertial system position vector of a point on the unpowered gliding section of the payload after the rocket is separated from its payload, v Target is the expected value of the velocity vector at the point, r0 is the position vector of the inertial system at the rocket launch point, T La is the time from time T0 until the rocket flies to r Target The total time consumed, solving the flight time T La The corresponding r Target Point velocity vector v Ke,Target : [v Ke,0 ,v Ke,Target ]=Kepler(r0,r Target ,T La ); Step 3.2: According to the scene, v Target The total time required to solve the direction is T La ; Step 3.3, determine the type of the rocket's final stage. If the final stage is a solid rocket engine, proceed to step 3.

4. If the final stage is a liquid rocket engine, proceed to step 3.

5. Step 3.4, simulation of the rocket flight process with the last stage being a solid rocket engine, includes: Step 3.4.1, determine the working time of the last stage, and set the time when the last stage of the rocket starts working to T start,n Equal to the time when the previous level finishes work T end,n-1 , the moment when the rocket's last stage stops working is T end,n It is equal to the time when the previous stage finishes working plus the working time of the rocket's final stage T. continue ; Step 3.4.2, use the total time T La and the determined final stage working time, solve the trajectory according to step 2, and calculate the expected flight speed v corresponding to time t according to step 1.2.1 in each integral during the solution process Ke,t ; Step 3.4.3, judge whether the rocket model has the ability to achieve the goal of moving from point r0 to r according to the following judgment conditions Target Orbital maneuverability: In the formula, ε V is the speed deviation threshold, ε D is the speed direction deviation threshold; if there is a time t in the integration process that satisfies the first two conditions in the formula, but t<T start,n , by shortening the total flight time T La , re-integrate, and we can find the time t that satisfies all the conditions of the formula. At this time, it is determined that the rocket model has the ability to achieve the goal of moving from point r0 to r Target Orbital maneuverability, go to step 3.3.4; if there is no time t that satisfies the first two conditions in the formula during the integration process, it is determined that the rocket model does not have the ability to move from point r0 to r Target orbital maneuverability; Step 3.4.4, solving the ignition time of the final stage rocket, includes: Step 3.4.4.1, design time judgment conditions: In the formula, ε T is the time deviation threshold; Step 3.4.4.2, design the final working time: T start,n =T end,n-1 +T inte ,T end,n =T end,n-1 +T inte +T continue Where, T inte Waiting for ignition time for the final stage; Step 3.4.4.3, solve the final stage waiting ignition time T inte : Make the last stage wait for ignition time T inte Start from 0 and increase. After each increase, integrate the whole trajectory according to step 2. In each integration, calculate the time t that satisfies the formula in step 3.4.3 according to step 1.2.1 until the time t that satisfies both the formula in step 3.4.3 and the formula in step 3.4.4.1 appears. Then the final stage waiting ignition time T is obtained. inte ; Step 3.4.4.4, the obtained final stage waiting ignition time T inte Re-assign T according to step 3.4.4.2 start,n , T end,n After updating the corresponding parameters in step 1, follow step 2 to complete the process from the launch point r0 to the aiming point r Target Full flight track integration; Step 3.5, simulation of the rocket flight process with the last stage being a liquid rocket engine, includes: Step 3.5.1, use the total time T La Solve the trajectory according to step 2, and calculate the expected flight speed v corresponding to time t according to step 1.2.1 for each integral in the solution process Ke,t ; Step 3.5.2: Determine whether the rocket model has the ability to move from point r0 to point r according to the following judgment conditions. Target Orbital maneuverability: In the formula, ε V is the speed deviation threshold, ε D is the velocity direction deviation threshold; if there is no time t that satisfies the three conditions in the formula during the integration process, it is determined that the rocket model does not have the ability to travel from point r0 to r Target If the three conditions in the formula are met at a certain time t = Tn during the integration process, the rocket model is judged to have the ability to achieve orbital maneuverability from point r0 to r Target The orbital maneuverability is determined, and the time Tn is recorded as the final stage shutdown time, and the process goes to step 3.5.3; Step 3.5.3, after updating the corresponding parameters in step 1 with the obtained final stage shutdown time Tn, complete the process from the launch point r0 to the aiming point r according to step 2. Target The complete flight track integration.

2. The method for simulating the active phase flight trajectory of a launch vehicle based on non-cooperative measured data according to claim 1, characterized in that: In step 1.1, the propellant specific mass flow rate V fm,t Solve by following the steps below: The first step is to establish a transcendental equation based on the Tsiolkovsky equation and the energy conservation formula: Where V start,i is the measured inertial system velocity when the i-th stage rocket starts working, V end,i is the measured inertial velocity of the i-th stage rocket at the end of operation, ΔH i is the measured height of the rocket rising in the working interval of the i-th stage rocket, m start,i is the total mass of the i-th stage rocket when it starts working, m end,i is the total mass of the i-th stage rocket at the end of its operation; The second step is to calculate the initial value of the propellant mass flow rate of the i-th stage rocket: The third step is to calculate the initial value of the propellant mass flow rate Vfm i Perform iterative correction: Vfm i,mid,0 =Vfm i In the formula, the first digit of Vfm is the current rocket stage number, the second digit max, mid, and max represent the minimum, median, and maximum values ​​respectively, and the third digit represents the number of iterations. The number of iterations is set to k, and k = 0 for the first iteration; The fourth step is to convert the corrected Vfm i,mid,k Substitute into step 2 to solve: In the formula, s Tendi,k The first digit of the superscript indicates the end time of integration. At the current time, Tendi=T end,i It is the shutdown time of rocket stage i, and the second digit of the superscript represents the number of iterations; Step 5: Let v Tendi,R T end,i The measured rocket velocity vector at the moment, the deviation dv between the measured velocity at the current moment and the velocity solved by integration is defined as follows: dv Tendi,k =||v Tendi,k ||-||v Tendi,k || Step 6: Continue iterating according to the following iteration rules: If dv Tendi,k <0, which means Vfm i,mid,k If it is too large, then in the next iteration: If dv Tendi,k >0, which means Vfm i,mid,k If it is too small, then in the next iteration: Until DV Tendi,k is less than the accuracy threshold, then the propellant mass flow rate Vfm for the i-th stage rocket i Make the final assignment: Vfm i =Vfm i,mid,k Step 7. Repeat this step, and input the actual speed after each stage of the rocket is completed, and complete the assignment of the propellant specific mass flow rate from the first stage to the last stage of the rocket.

3. The method for simulating the active phase flight trajectory of a launch vehicle based on non-cooperative measured data according to claim 1 or 2, characterized in that: Step 1.2.2 includes: Step 1.2.2.1, design the turn end time sequence: In the formula, the subscript k is the variable ordinal number, St is the time series step, and T end,1 The moment when the first stage of the rocket ends its work; Step 1.2.2.2, T end,turn,k Substitute the sequence into step 2 for solution: s Tend1,k =[r Tend1,k ,v Tend1,k ] T Get the first-level shutdown speed set v Tend1,k , v Tend1,k The first subscript of Tend1=T end,1 It is the moment when the first stage of the rocket is shut down. The second digit of the superscript is the ordinal number of the variable; Step 1.2.2.3, the measured level 1 shutdown speed is v Tend1,R , define the velocity difference sequence as dv k : Step 1.2.2.4, calculate the optimal T end,turn : Where m is the number of iterations.

4. The method for simulating the active phase flight trajectory of a launch vehicle based on non-cooperative measured data according to claim 1 or 2, characterized in that: In step 1.1, the remaining specific mass of the rocket is M t The calculation is as follows: In the formula, min(T end,i , t) is the minimum value between the end time of the i-th stage rocket and the current time, Mc i It is the ratio of the structural mass of the i-th stage rocket to the total mass of the rocket at time T0.

5. The method for simulating the active phase flight trajectory of a launch vehicle based on non-cooperative measured data according to claim 4 is characterized in that: In step 1.1, calculate the rocket's residual mass M t Mc i Designed as fixed value:

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