Time-invariant orbit information acquisition method based on parameter self-adaption

Abstract

The invention discloses a parameter self-adaption-based time-invariant orbit information acquisition method, which comprises the following steps of: constructing a linear random time-invariant system aiming at an orbit equation of spacecraft motion, and determining an initial state quantity and an external disturbance term; obtaining a constant coefficient matrix and a constant disturbance input matrix based on the initial state quantity and the external disturbance term; inputting the established parameter adaptive Runge-Kutta solver to obtain a to-be-solved orbit parameter list; according to a self-adaptive parameter constraint formula, the dependency relationship of all parameters in the parameter list is solved, free parameters in the parameter list are optimized according to a genetic algorithm, iterative updating is carried out until parameters with the optimal judgment standard are obtained, the parameters serve as parameters of a Runge-Kutta solver, orbit information is solved through iteration of the Runge-Kutta solver, and the optimal judgment standard is obtained. And obtaining of track information is realized. The method can be widely applied to the satellite orbit solving aspect of space science and technology, and is not only suitable for determining a single scientific satellite orbit, but also suitable for formulating a scientific satellite constellation orbit.

Description

Technical Field

[0001] The invention belongs to the field of high-precision computer simulation, and in particular relates to a method for acquiring time-invariant orbit information based on parameter adaptation. Background Art

[0002] For space science and technology satellites used for deep space exploration, how to solve and simulate the orbit of spacecraft constellations with high precision is one of the primary tasks in mission establishment. In the process of solving the orbit with high precision, the entire dynamic system can be regarded as a linear random time-invariant system, so how to solve the linear random time-invariant differential equation with high precision is the key to the problem.

[0003] In the field of deep space exploration, space science and technology satellites usually require extremely high orbital accuracy, such as the position and velocity of the satellite at any time. The existing linear random time-invariant differential equation solution algorithm cannot achieve high-precision solutions. There are usually some deviations in the solution of satellite position and velocity, which cannot well meet the needs of space science and technology satellite orbit determination. In addition, since space science and technology satellites have extremely high orbital accuracy requirements, but in actual situations, satellites are affected by a large number of interference sources, such as micrometeoroids, solar light pressure and other space environments. Therefore, how to introduce these noise sources in a suitable way in solving the Clohessy-Wiltshire (CW) equation and achieve high-precision orbit solution and simulation is a problem that needs to be solved urgently. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the prior art and propose a method and system for obtaining time-invariant orbit information based on parameter adaptation.

[0005] In view of this, the present invention proposes a method for obtaining time-invariant orbit information based on parameter adaptation, comprising:

[0006] Step 1) construct a linear random time-invariant system for the orbital equation of the spacecraft motion, and determine the initial state quantity and external disturbance term;

[0007] Step 2) based on the initial state quantity and the external disturbance term, a constant coefficient matrix and a constant disturbance input matrix are obtained;

[0008] Step 3) inputting the established parameter adaptive Runge-Kutta solver to obtain a list of parameters to be solved;

[0009] Step 4) According to the adaptive parameter constraint formula, the dependency relationship of each parameter in the parameter list is obtained, and the free parameters are optimized according to the genetic algorithm, and iteratively updated until the parameters with the best judgment criterion are obtained. These optimized parameters are used as the parameters of the Runge-Kutta solver, and the orbital information is iteratively solved by the Runge-Kutta solver to obtain the orbital information.

[0010] Preferably, the orbital equation of the spacecraft motion in step 1) satisfies the following formula:

[0011]

[0012] Among them, x, y, and z represent the coordinates of the spacecraft in the x, y, and z directions respectively, and the specific coordinates are (x0, y0, z0). and Respectively represent the speed of the spacecraft in the x, y and z directions, and the specific speed values ​​are

[0013] Preferably, the linear random time-invariant system in step 1) satisfies the following formula:

[0014]

[0015] Among them, t is time, represents the independent variable, Y(t) is the state quantity of the equation, which is an n×1 dimensional vector, n is the number of state quantities of the equation, F is the constant coefficient matrix, which is an n-order square matrix, G is the constant disturbance input matrix, which is an n×m matrix, and Z(t) is the external interference term. represents the acceleration of the spacecraft in the x direction, represents the acceleration of the spacecraft in the y direction, represents the spacecraft acceleration in the z direction, f x represents the sum of the external disturbance and internal control torque of the spacecraft in the x direction, f y represents the sum of the external disturbance and internal control torque of the spacecraft in the y direction, f z It represents the sum of the external disturbance and internal control torque of the spacecraft in the z direction.

[0016] Preferably, in step 2), the constant coefficient matrix F and the constant disturbance input matrix G respectively satisfy the following formulas:

[0017]

[0018] Where ω represents the angular velocity of the spacecraft.

[0019] Preferably, the step 3) comprises:

[0020] Set time t k The equation state quantity Y(t) obtained at is denoted as Yt k , set the solver integration step size to h, and set the solver iteration order Order value range to [3,4];

[0021] Set time t k+1 =t k +h, set Y k Indicates time t kThe equation state quantity Y(t k ) value, set Y k+1 Indicates time t k+1 The equation state quantity Y(t k+1 ), solve for Y k+1 The value at, the fourth-order Runge-Kutta iteration formula is as follows:

[0022]

[0023] Among them, A ji represents the coefficient of the parameter adaptive Runge-Kutta algorithm, Z j is a random number, k j is the iteration coefficient, and the statistical properties satisfy the following formula:

[0024]

[0025] Where T represents transpose;

[0026] Y using parameter adaptive Runge-Kutta iteration k+1 The solution formula is as follows:

[0027]

[0028] Get the parameter list to be requested, including the following parameters: A 21 , A 31 , A 32 , A 41 , A 42 , A 43 , q1, q2, q3, q4, B1, B2, B3, B4 and Order, where s represents the total number of orders, k j Represents the iteration coefficient.

[0029] Preferably, the adaptive parameter constraint formula of step 4) satisfies the following formula:

[0030] P k =E[Y k Y k T ]=P(t k )+O(h Order+1 )

[0031] Among them, T represents transpose, Y k represents the numerical solution, P k is the t obtained by numerical solution k The numerical solution Y k The variance of P(t k ) represents the true variance, O(h Order+1 ) indicates that Order+1 Infinitesimals of the same order.

[0032] Preferably, according to the adaptive parameter constraint formula, the dependency relationship of each parameter in the parameter list of step 4) is:

[0033] When Order = 3, A 41 =0, A 42 =0, A 43 =0, q4=0, B4=0, and other parameters satisfy the following formula:

[0034]

[0035] Taking B1 as a free parameter, we get:

[0036]

[0037] When Order=4, the following equation is satisfied between the parameters:

[0038]

[0039] Taking B1 and B4 as free parameters, we get:

[0040]

[0041] Preferably, the step 4) optimizes the free parameters therein according to a genetic algorithm, iteratively updates until the optimal parameters of the judgment criterion are obtained, thereby obtaining the orbit information; comprising:

[0042] According to the set total number of time points TIMEN, the free parameters B1 and B4 are randomly initialized to obtain the values ​​of the remaining 12 parameters; the parameter adaptive Runge-Kutta method is used to calculate the solution Y at the i-th time point Order = 3 or Order = 4 RK (t) and the analytical solution Y Real (t), based on the fitness function of the genetic algorithm, the values ​​of the two free parameters B1 and B4 are iteratively optimized, and the solution order is adaptively selected according to the fitness function Value to obtain the other 12 parameters.

[0043] Preferably, the fitness function Value is:

[0044]

[0045] Among them, Y RK (t i ) and Y Real (t i ) are the solution result and analytical solution at the ith time point respectively.

[0046] Preferably, the step 4) uses the optimized parameters as the parameters of the Runge Kutta solver, and iteratively solves the orbital information through the Runge Kutta solver to obtain the orbital information, including: after obtaining the optimized free parameters, obtaining the other 12 parameters, using these parameters as the parameters of the Runge Kutta solver, and calculating the orbital information according to Y(t k ) value, iteratively solve Y(t k+1 ) until the solution is obtained. end ), where t end Indicates the end time of the solution.

[0047] Compared with the prior art, the advantages of the present invention are:

[0048] 1. The present invention constructs a parameter-adaptive Runge-Kutta solution method, which can be used to solve linear random time-invariant differential equations in orbit equation modeling with high precision, and can be widely used in solving satellite orbits in space science and technology.

[0049] 2. The present invention adopts an adaptive free parameter design based on legacy algorithm optimization. By comparing with the analytical solution and optimizing the parameter selection, a more accurate solution result can be obtained under the same conditions to meet the needs of high-precision solution.

[0050] 3. The present invention constructs four subsystems including orbital equation modeling, parameter adaptive Runge-Kutta solution, accuracy evaluation and adaptive parameter selection, which is not only suitable for determining the orbit of a single scientific satellite but also for formulating the orbit of a scientific satellite constellation. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a flow chart of a method for obtaining time-invariant orbit information based on parameter adaptation;

[0052] Figure 2 It is the flow chart of the accuracy assessment subsystem;

[0053] Figure 3 It is the result of solving the orbit equation using the system proposed by the present invention;

[0054] Figure 4 It is a comparison between the solution of the orbit equation in the x direction using the system proposed by the present invention and the analytical solution;

[0055] Figure 5 It is a comparison between the solution of the orbit equation in the x direction using the existing solver and the analytical solution. DETAILED DESCRIPTION

[0056] In view of the accuracy limitation of the prior art, the present invention proposes a method for obtaining time-invariant orbit information based on parameter adaptation. The flow chart is as follows: Figure 1As shown in Figure 1, it includes four subsystems: orbit equation modeling, parameter adaptive Runge-Kutta solution, accuracy evaluation and adaptive parameter selection. The flow chart of the adaptive parameter selection subsystem is shown in Figure 1. Figure 2 shown.

[0057] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0058] Example

[0059] An embodiment of the present invention proposes a method for acquiring time-invariant orbit information based on parameter adaptation.

[0060] Step 1) construct a linear random time-invariant system for the orbital equation of the spacecraft motion, and determine the initial state quantity and external disturbance term;

[0061] Step 2) based on the initial state quantity and the external disturbance term, a constant coefficient matrix and a constant disturbance input matrix are obtained;

[0062] Step 3) inputting the established parameter adaptive Runge-Kutta solver to obtain a list of parameters to be solved;

[0063] Step 4) According to the adaptive parameter constraint formula, the dependency relationship of each parameter in the parameter list is obtained, and the free parameters are optimized according to the genetic algorithm, and iteratively updated until the parameters with the best judgment criterion are obtained. These optimized parameters are used as the parameters of the Runge-Kutta solver, and the orbital information is iteratively solved by the Runge-Kutta solver to obtain the orbital information.

[0064] The orbital equation modeling subsystem satisfies the linear stochastic time-invariant differential equation, specifically:

[0065]

[0066] Among them, x represents the x-direction coordinate of the spacecraft, y represents the x-direction coordinate of the spacecraft, and z represents the z-direction coordinate of the spacecraft. represents the spacecraft speed in the x direction, represents the spacecraft speed in the y direction, Represents the speed of the spacecraft in the z direction.

[0067] According to the CW equation of motion, the differential equation of the spacecraft motion orbit can be modeled as follows:

[0068]

[0069] Where ω represents the angular velocity of the spacecraft, represents the acceleration of the spacecraft in the x direction, represents the acceleration of the spacecraft in the y direction, represents the acceleration of the spacecraft in the z direction.x represents the sum of the external disturbance and internal control torque of the spacecraft in the x direction, f y represents the sum of the external disturbance and internal control torque of the spacecraft in the y direction, f z It represents the sum of the external disturbance and internal control torque of the spacecraft in the z direction.

[0070] The differential equation of the spacecraft motion trajectory is further modeled as follows:

[0071]

[0072] in,

[0073]

[0074] The parameter-adaptive Runge-Kutta method is a numerical method for solving ordinary differential equations. By properly setting the coefficients of each order of the Runge-Kutta method, the solution error can be minimized, thereby achieving higher accuracy.

[0075] The parameter adaptive Runge-Kutta solution subsystem is specifically:

[0076] Step 1: Construct the general expression of the linear stochastic time-invariant differential equation as follows:

[0077]

[0078] Among them, t is time, represents the independent variable, Y(t) is the state quantity of the equation, which is an n×1 dimensional vector, n is the number of state quantities in the equation, F is the constant coefficient matrix, which is an n-order square matrix, G is the constant disturbance input matrix, which is an n×m matrix, and Z(t) is the external interference term, which can be modeled according to actual conditions. As the noise of each state quantity, it is usually modeled as a Gaussian white noise random quantity in the m-dimensional real space, with a mean of zero and a variance of E(Z(t)Z(t-σ))=Q(t)δ(σ), Q(t) is the covariance matrix, and δ(σ) is the Dirac function.

[0079] Step 2: Construct the initial state quantities and external disturbance terms of the equations in the orbit solution of a specific space science and technology satellite, and construct the constant coefficient matrix F and the constant disturbance input matrix G.

[0080] Step 3: Construct a parameter-adaptive Runge-Kutta solver.

[0081] Step 3.1: Set time t k The equation state quantity Y(t) obtained at is denoted as Yt k , set the solver integration step to h, and set the solver iteration order to 4.

[0082] Step 3.2: Set time t k+1 =tk +h, set Y k Indicates time t k The equation state quantity Y(t k ) value, set Y k+1 Indicates time t k+1 The equation state quantity Y(t k+1 ), solve for Y k+1 The value at, the fourth-order Runge-Kutta iteration formula is as follows:

[0083]

[0084] Among them, A ji represents the Runge-Kutta solver parameters, Z j is a random number that satisfies the statistical properties of the following formula:

[0085]

[0086] Y using the fourth-order Runge-Kutta iteration k+1 The solution formula is as follows:

[0087]

[0088] According to formula (6)-formula (8), the parameters to be determined are A 21 , A 31 , A 32 , A 41 , A 42 , A 43 , q1, q2, q3, q4, B1, B2, B3, B4.

[0089] The accuracy assessment subsystem includes:

[0090] Step 1: Determine the linear random time-invariant differential equation without interference source, as shown in the following formula:

[0091]

[0092] Wherein, G is an n×m all-zero matrix.

[0093] Step 2: The analytical solution of the orbit of a space science and technology satellite in the absence of interference sources can usually be expressed using the CW equation, that is,

[0094]

[0095] Among them, Y(t) and Y(t0) represent the state quantities of the equation at time t and time t0 respectively, and φ(τ) is the state matrix corresponding to the analytical solution.

[0096] Step 3: Adopt the adaptive parameter selection subsystem to determine 14 parameters to be determined, including 2 free parameters. The other 12 parameters can be determined by linear combinations of free parameters.

[0097] Step 4: Take 100 time points and calculate the solution result Y of the parameter adaptive Runge-Kutta solver at each time point RK (t) and the analytical solution Y Real (t) Solve the result and set the fitness function of the genetic algorithm to

[0098]

[0099] Step 5: Based on the fitness function in step 4, a genetic algorithm is used to optimize the values ​​of the two free parameters to obtain the optimized values ​​of the free parameters.

[0100] Step 6: Use the optimized free parameters to solve the other 12 parameters for subsequent calculations.

[0101] The adaptive parameter selection subsystem is used to determine 14 parameters to be determined, specifically:

[0102] Step 1: Use the adaptive parameter constraint formula to constrain the parameters. The formula is as follows:

[0103] P k =E[Y k Y k T ]=P(t k )+O(h Order+1 ) (12)

[0104] Among them, T represents transpose, Y k represents the numerical solution. k is the t obtained by numerical solution k The numerical solution Y k The variance of P(t k ) represents the true variance, O(h Order+1 ) indicates that Order+1 Infinitesimals of the same order.

[0105] Step 2: According to the adaptive parameter constraint formula, the following nonlinear algebraic equations are established and solved to obtain solutions for 14 parameters.

[0106]

[0107] By solving the above algebraic equation, we get a solution of 14 parameters, which includes two free parameters B1 and B4.

[0108]

[0109] Step 3: Use random numbers to randomly determine the values ​​of free parameters B1 and B4.

[0110] Step 4: Based on the free parameter values ​​obtained in step 3, the values ​​of the other 12 parameters are obtained, and this set of parameter values ​​is input into the adaptive parameter selection subsystem.

[0111] After solving, the accuracy assessment subsystem obtained B1 = 0.2753, B4 = 0.1837, and the values ​​of the other 12 parameters were derived based on these two parameters. After that, the Runge-Kutta solver with determined parameters was used to solve the problem. The solution results are as follows: Figure 3 As shown in the figure, the spacecraft x-direction solution is compared with the theoretical solution. Figure 4 As shown. Setting the same initial parameters, using ode45 to solve, the spacecraft x-direction solution is compared with the theoretical solution. Figure 5 As shown. Figure 4 and Figure 5 It can be seen that the solution method proposed in this paper, in the case of this embodiment, is about 4 orders of magnitude higher in solution accuracy than the ode45 solver.

[0112] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention and should be included in the scope of the claims of the present invention.

Claims

1. A method for obtaining time-invariant orbit information based on parameter adaptation, comprising: Step 1) construct a linear random time-invariant system for the orbital equation of the spacecraft motion, and determine the initial state quantity and external disturbance term; Step 2) based on the initial state quantity and the external disturbance term, a constant coefficient matrix and a constant disturbance input matrix are obtained; Step 3) inputting the established parameter adaptive Runge-Kutta solver to obtain a list of parameters to be solved; Step 4) According to the adaptive parameter constraint formula, the dependency relationship of each parameter in the parameter list is obtained, and the free parameters are optimized according to the genetic algorithm, and iteratively updated until the parameters with the best judgment criterion are obtained. These optimized parameters are used as the parameters of the Runge-Kutta solver, and the orbital information is iteratively solved by the Runge-Kutta solver to obtain the orbital information.

2. The method for obtaining time-invariant orbit information based on parameter adaptation according to claim 1, characterized in that: The orbit equation of the spacecraft motion in step 1) satisfies the following formula: Among them, x, y, and z represent the coordinates of the spacecraft in the x, y, and z directions respectively, and the specific coordinates are (x0, y0, z0). and Respectively represent the speed of the spacecraft in the x, y and z directions, and the specific speed values ​​are 3. The method for obtaining time-invariant orbit information based on parameter adaptation according to claim 2, characterized in that: In step 1), the linear random time-invariant system satisfies the following formula: Among them, t is time, represents the independent variable, Y(t) is the state quantity of the equation, which is an n×1 dimensional vector, n is the number of state quantities of the equation, F is the constant coefficient matrix, which is an n-order square matrix, G is the constant disturbance input matrix, which is an n×m matrix, and Z(t) is the external interference term. represents the acceleration of the spacecraft in the x direction, represents the acceleration of the spacecraft in the y direction, represents the spacecraft acceleration in the z direction, f x represents the sum of the external disturbance and internal control torque of the spacecraft in the x direction, f y represents the sum of the external disturbance and internal control torque of the spacecraft in the y direction, f z It represents the sum of the external disturbance and internal control torque of the spacecraft in the z direction.

4. The method for obtaining time-invariant orbit information based on parameter adaptation according to claim 3 is characterized in that: In step 2), the constant coefficient matrix F and the constant disturbance input matrix G respectively satisfy the following formulas: Where ω represents the angular velocity of the spacecraft.

5. The method for obtaining time-invariant orbit information based on parameter adaptation according to claim 4, characterized in that: The step 3) comprises: Set time t k The equation state quantity Y(t) obtained at is denoted as Yt k , set the solver integration step size to h, and set the solver iteration order Order value range to [3,4]; Set time t k+1 =t k +h, set Y k Indicates time t k The equation state quantity Y(t k ) value, set Y k+1 Indicates time t k+1 The equation state quantity Y(t k+1 ), solve for Y k+1 The value at, the fourth-order Runge-Kutta iteration formula is as follows: Among them, A ji represents the coefficient of the parameter adaptive Runge-Kutta algorithm, Z j is a random number, k i is the iteration coefficient, and the statistical properties satisfy the following formula: Where T represents transpose; Y using parameter adaptive Runge-Kutta iteration k+1 The solution formula is as follows: Get the parameter list to be requested, including the following parameters: A 21 , A 31 , A 32 , A 41 , A 42 , A 43 , q1, q2, q3, q4, B1, B2, B3, B4 and Order, where s represents the total number of orders, k j Represents the iteration coefficient.

6. The method for obtaining time-invariant orbit information based on parameter adaptation according to claim 5, characterized in that: The adaptive parameter constraint formula of step 4) satisfies the following formula: Among them, T represents transpose, Y k represents the numerical solution, P k is the t obtained by numerical solution k The numerical solution Y k The variance of P(t k ) represents the true variance, O(h Order+1 ) indicates that Order+1 Infinitesimals of the same order.

7. The method for obtaining time-invariant orbit information based on parameter adaptation according to claim 6, characterized in that: The dependency relationship of each parameter in the parameter list of step 4) is: When Order = 3, A 41 =0, A 42 =0, A 43 =0, q4=0, B4=0, and other parameters satisfy the following formula: Taking B1 as a free parameter, we get: When Order=4, the following equation is satisfied between the parameters: Taking B1 and B4 as free parameters, we get:

8. The method for obtaining time-invariant orbit information based on parameter adaptation according to claim 7, characterized in that: The step 4) optimizes the free parameters according to the genetic algorithm, iteratively updates until the optimal parameters of the judgment criteria are obtained to achieve the acquisition of orbit information; including: According to the set total number of time points TIMEN, the free parameters B1 and B4 are randomly initialized to obtain the values ​​of the remaining 12 parameters; the parameter adaptive Runge-Kutta method is used to calculate the solution Y at the i-th time point Order = 3 or Order = 4 RK (t) and the analytical solution Y Real (t), based on the fitness function of the genetic algorithm, the values ​​of the two free parameters B1 and B4 are iteratively optimized, and according to the fitness function Value, the solution order is adaptively selected to obtain the other 12 parameters to achieve the acquisition of orbital information.

9. The method for obtaining time-invariant orbit information based on parameter adaptation according to claim 8, characterized in that: The fitness function Value is: Among them, Y RK (t i ) and Y Real (t i ) are the solution result and analytical solution at the ith time point respectively.

10. The method for obtaining time-invariant orbit information based on parameter adaptation according to claim 8, characterized in that: The step 4) uses the optimized parameters as the parameters of the Runge-Kutta solver, and iteratively solves the orbital information through the Runge-Kutta solver to obtain the orbital information, including: After obtaining the optimized free parameters, the other 12 parameters are obtained and used as the parameters of the Runge-Kutta solver. k ) value, iteratively solve Y(t k+1 ) until the solution is obtained. end ), where t end Indicates the end time of the solution.

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