A parameter-adaptive time-invariant track information acquisition method

Abstract

The application discloses a kind of based on parameter self-adapting time-invariant track information acquisition method, comprising: for the orbit equation of spacecraft motion, construct linear random time-invariant system, determine initial state quantity and external disturbance term;Based on initial state quantity and external disturbance term, obtain constant coefficient matrix and constant disturbance input matrix;Input the parameter self-adaptive Runge-Kutta solver established, obtain the list of to-be-solved orbit parameters;According to the adaptive parameter constraint formula, the dependent relationship of each parameter in parameter list is solved, free parameters therein are optimized according to genetic algorithm, iteratively updated until the optimal parameters of determination standard are obtained, these parameters are used as the parameters of Runge-Kutta solver, and the orbit information is iteratively solved by Runge-Kutta solver to realize the acquisition of orbit information.The application can be widely applied to space science and technology satellite orbit solving aspect, and is not only suitable for single scientific satellite orbit determination, but also suitable for scientific satellite constellation orbit formulation.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of computer high-precision simulation, and particularly relates to a time-invariant orbit information acquisition method based on parameter self-adaption. BACKGROUND

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

[0003] In the field of deep space exploration, the orbit precision required by the space science and technology satellite is extremely high, such as the position and speed of the satellite at any time. The existing linear random time-invariant differential equation solving algorithm cannot achieve high-precision solving, and there is usually some deviation in the solving of the satellite position and speed, which cannot well meet the needs of the orbit determination of the space science and technology satellite. In addition, due to the extremely high orbit precision requirement of the space science and technology satellite, the satellite is affected by a large number of interference sources in the actual situation, such as micro-meteoroids, solar pressure and other space environment, and therefore how to introduce these noise sources in a suitable way in the solving of the Clohessy-Wiltshire (CW) equation and achieve high-precision solving and simulation of the orbit is a problem to be solved at present. SUMMARY

[0004] The application aims to overcome the defects of the prior art and provide a time-invariant orbit information acquisition method and system based on parameter self-adaption.

[0005] Therefore, the application provides a time-invariant orbit information acquisition method based on parameter self-adaption, which comprises the following steps.

[0006] Step 1) For the orbit equation of the spacecraft motion, a linear random time-invariant system is constructed, and the initial state quantity and the external disturbance term are determined.

[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) The established parameter self-adaptive Runge-Kutta solver is inputted, and a parameter list to be solved is obtained.

[0009] Step 4) The dependent relationship of each parameter in the parameter list is solved according to the self-adaptive parameter constraint formula, the free parameters are optimized according to the genetic algorithm, and the iteration is updated until the optimal parameters of the determination standard are obtained. The optimized parameters are taken as the parameters of the Runge-Kutta solver, the orbit information is iteratively solved by the Runge-Kutta solver, and the acquisition of the orbit information is realized.

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

[0011]

[0012] Where x, y, and z represent the spacecraft's coordinates in the x, y, and z directions, respectively, specifically (x0, y0, z0). and These represent the spacecraft's velocities in the x, y, and z directions, respectively, with specific velocity values...

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

[0014]

[0015] Where t is time, represents the independent variable, Y(t) is the state variable of the equation, an n×1 dimensional vector, n is the number of state variables in the equation, F is the constant coefficient matrix, an n-order square matrix, G is the constant disturbance input matrix, an n×m matrix, and Z(t) is the external disturbance term. This represents the acceleration of the spacecraft in the x-direction. This represents the acceleration of the spacecraft in the y-direction. f represents the acceleration of the spacecraft in the z-direction. x f represents the sum of external disturbances and internal control torques experienced by the spacecraft in the x-direction. y f represents the sum of external disturbances and internal control torques experienced by the spacecraft in the y-direction. z This represents the sum of external disturbances and internal control torques experienced by the spacecraft in the z-direction.

[0016] Preferably, in step 2), the constant coefficient matrix F and the constant perturbation input matrix G respectively satisfy the following equations;

[0017]

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

[0019] Preferably, step 3) includes:

[0020] Set time t k The state variable Y(t) obtained from the equation is denoted as Yt. k Set the solver integration step size to h, and set the solver iteration order to a range of [3,4].

[0021] Set time t k+1 =t k +h, set Y k Represents time t kThe value of the equation state quantity Y(t k ) obtained at time t k+1 , Y k+1 is set to the value of the equation state quantity Y(t k+1 ) obtained at time t k+1 , and the value of Y ji is solved. The fourth-order Runge-Kutta iteration formula is as follows:

[0022]

[0023] Wherein, A j represents the parameter adaptive Runge-Kutta algorithm coefficient, Z j is a random number, k k+1 is an iteration coefficient, and the statistical properties satisfy the following formula:

[0024]

[0025] Wherein, T represents transposition.

[0026] The Y 21 solving formula using the parameter adaptive Runge-Kutta iteration is as follows:

[0027]

[0028] The parameter list to be solved is obtained, including the following parameters: A 31 , A 32 , A 41 , A 42 , A 43 , q1, q2, q3, q4, B1, B2, B3, B4 and Order, wherein s represents the total number of orders, and 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] Wherein, T represents transposition, Y k represents the numerical solution, P k is the variance of the numerical solution Y k at t k obtained by numerical solution, P(t k ) represents the true variance, and O(h Order+1 ) represents an infinitesimal of the same order as h Order+1 .

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

[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 the free parameter, we obtain:

[0036]

[0037] When Order = 4, each parameter satisfies the following formula:

[0038]

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

[0040]

[0041] Preferably, step 4) optimizes the free parameters therein according to a genetic algorithm, iteratively updates, until the parameters optimal for the determination criterion are obtained, and the acquisition of the orbital information is realized; including:

[0042] According to the 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 solving result Y RK (t) of Order = 3 or Order = 4 at the i-th time point, the values of the two free parameters B1 and B4 are iteratively optimized based on the fitness function of the genetic algorithm, and the other 12 parameters are obtained according to the fitness function Value and the adaptive selection of the solving order. Real

[0043] Preferably, the fitness function Value is as follows:

[0044]

[0045] Wherein, Y RK (t i ) and Y Real (t i ) are the solving result and the analytical solution at the i-th time point, respectively.

[0046] ​Preferably, the step 4) takes the optimized parameters as parameters of the Runge-Kutta solver, and iteratively solves the orbit information by the Runge-Kutta solver to obtain the orbit information, including: after obtaining the optimized free parameters, obtaining other 12 parameters, taking the parameters as parameters of the Runge-Kutta solver, and iteratively solving the value of Y(t k ) according to the value of Y(t k+1 ) until Y(t end ) is solved, wherein t end represents the termination time of the solution.

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

[0048] 1. The present application constructs a parameter adaptive Runge-Kutta solving method, which can be used to solve linear stochastic time-invariant differential equations in orbit equation modeling with high precision, and can be widely used in space scientific and technological satellite orbit solving.

[0049] 2. The present application adopts adaptive free parameter design based on inheritance algorithm optimization, and through comparison with analytical solution, the optimized parameter selection can obtain better accurate solving results under the same conditions, and is used to meet the needs of high-precision solving.

[0050] 3. The present application constructs four subsystems including orbit equation modeling, parameter adaptive Runge-Kutta solving, precision evaluation and adaptive parameter selection, which is not only suitable for single scientific satellite orbit determination but also suitable for scientific satellite constellation orbit formulation. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 is a flow chart of the parameter adaptive time-invariant orbit information acquisition method;

[0052] Figure 2 is a flow chart of the precision evaluation subsystem;

[0053] Figure 3 is the solving result of the orbit equation by the system proposed in the present application;

[0054] Figure 4 is a comparison of the solving result of the orbit equation in the x direction by the system proposed in the present application with the analytical solution;

[0055] Figure 5 is a comparison of the solving result of the orbit equation in the x direction by the existing solver with the analytical solution. DETAILED DESCRIPTION

[0056] In view of the precision limitation of the prior art, the present application proposes a parameter adaptive time-invariant orbit information acquisition method. Its flow chart is as follows: Figure 1As shown, including orbit equation modeling, parameter adaptive Runge-Kutta solver, precision evaluation and adaptive parameter selection four subsystems, wherein the adaptive parameter selection subsystem flow chart is as shown in Figure 2 As shown.

[0057] The technical solutions of the present application will be described in detail below in combination with the drawings and examples.

[0058] Embodiments

[0059] The embodiments of the present application propose a time-invariant orbit information acquisition method based on parameter adaptation.

[0060] Step 1) For the orbit equation of spacecraft motion, a linear stochastic time-invariant system is constructed, and the initial state quantity and external disturbance term are determined;

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

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

[0063] Step 4) According to the adaptive parameter constraint formula, the dependency relationship of each parameter in the parameter list is solved, the free parameters are optimized according to the genetic algorithm, and the iteration is updated until the optimal parameters of the determination standard are obtained. These optimized parameters are used as the parameters of the Runge-Kutta solver, and the orbit information is solved by the Runge-Kutta solver to realize the acquisition of the orbit information.

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

[0065]

[0066] Wherein, x represents the x direction coordinate of the spacecraft, y represents the x direction coordinate of the spacecraft, z represents the z direction coordinate of the spacecraft, represents the x direction velocity of the spacecraft, represents the y direction velocity of the spacecraft, represents the z direction velocity of the spacecraft.

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

[0068]

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

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

[0071]

[0072] wherein,

[0073]

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

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

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

[0077]

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

[0079] Step 2: Construct the initial state quantity of the equation and the external disturbance term in the orbit solving of the 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 the time t k at which the equation state quantity Y(t) is obtained as Y t k , set the solver integration step size h, and set the solver iteration order Order as 4.

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

[0083]

[0084] wherein A ji denotes the Runge-Kutta solver parameter, Z j is a random number, and satisfies the statistical property as follows:

[0085]

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

[0087]

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

[0089] The precision evaluation subsystem comprises:

[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 orbit of the space science and technology satellite under the condition of no interference source can be usually represented by using the C-W equation, that is,

[0094]

[0095] wherein Y(t) and Y(t0) respectively denote the state variable of the equation at time t and t0, and φ(τ) is the state matrix corresponding to the analytical solution.

[0096] Step 3: Adopting the adaptive parameter selection subsystem, 14 parameters to be solved are determined, including 2 free parameters, and other 12 parameters can be determined by linear combination of the free parameters.

[0097] Step 4: Taking 100 time points, respectively calculating the parameter adaptive Runge-Kutta solver solving results Y RK (t) and the analytical solution Y Real (t) solving result, set the fitness function of genetic algorithm as

[0098]

[0099] Step 5: Based on the fitness function of step 4, the value of 2 free parameters is optimized by genetic algorithm, and the optimized free parameter value is obtained.

[0100] Step 6: Using the optimized free parameters, other 12 parameters are solved for subsequent calculation.

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

[0102] Step 1: The parameters are constrained by using adaptive parameter constraint formula, the formula is as follows:

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

[0104] Wherein, T represents transposition, Y k represents numerical solution, P k is the variance of the numerical solution Y k at t k obtained by numerical solution, P(t k ) represents the true variance, O(h Order+1 ) represents an infinitesimal of the same order as h Order+1 .

[0105] Step 2: According to the adaptive parameter constraint formula, the following nonlinear algebraic equation group is established to solve, and the solution of 14 parameters is obtained.

[0106]

[0107] By solving the above algebraic equation, the solution of 14 parameters is obtained, including two free parameters B1 and B4.

[0108]

[0109] Step 3: Randomly determine the values of free parameters B1, B4 using random numbers.

[0110] Step 4: According to the values of free parameters obtained in step 3, obtain the values of other 12 parameters, and input the values of this set of parameters into the adaptive parameter selection subsystem.

[0111] After solving, the precision evaluation subsystem obtains B1=0.2753 and B4=0.1837, and according to these two parameters, the values of other 12 parameters are derived. Then, the Runge-Kutta solver with determined parameters is used for solving, and the solving result is as shown in Figure 3 The solving result of the spacecraft in the x direction is compared with the theoretical solution as shown in Figure 4 The same initial parameters are set, and ode45 is used for solving, and the solving result of the spacecraft in the x direction is compared with the theoretical solution as shown in Figure 5 From Figure 4 and Figure 5 It can be seen that the solving method proposed in this paper has a solving precision of about 4 orders of magnitude higher than that of the ode45 solver in the case of this embodiment.

[0112] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and are not limiting. Although the present application has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent replacements of the technical solutions of the present application do not deviate from the spirit and scope of the present application, and they should be covered in the scope of the claims of the present application.

Claims

1. A parameter-adaptive based time-invariant orbit information acquisition method, comprising: Step 1) constructing a linear stochastic time-invariant system for an orbit equation of a spacecraft motion, determining an initial state quantity and an external disturbance term; Step 2) obtaining a constant coefficient matrix and a constant disturbance input matrix based on the initial state quantity and the external disturbance term; Step 3) inputting the established parameter-adaptive Runge-Kutta solver to obtain a parameter list to be solved; Step 4) obtaining a dependency relationship of each parameter in the parameter list according to an adaptive parameter constraint formula, optimizing a free parameter therein according to a genetic algorithm, iteratively updating until a parameter optimal in a judgment standard is obtained, taking these optimized parameters as parameters of the Runge-Kutta solver, iteratively solving orbit information through the Runge-Kutta solver to realize acquisition of the orbit information; The step 4) includes: According to the set time point number 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 result Y of the i-th time point with Order=3 or Order=4 RK (t) and the analytical solution Y Real (t), a fitness function of the genetic algorithm is established based on the solution result and the analytical solution of each time point, 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; when Order=3, the value range of the free parameters B1 and B4 is restricted as 0 The fitness function Value is: where Y RK (t i ) and Y Real (t i ) are the solution and analytical solution at the i-th time point, respectively.

2. The parametric adaptive based time-invariant track information acquisition method of claim 1, wherein, The orbit equation of the spacecraft motion in the step 1) satisfies the following formula: Wherein, x, y, z respectively represent the coordinates of the spacecraft in x, y and z directions, and the specific coordinates are (x0, y0, z0), and respectively represent the velocity of the spacecraft in x, y and z directions, and the specific velocity values are 3. The parametric adaptive based time-invariant track information acquisition method of claim 2, wherein, The linear stochastic time-invariant system in the step 1) satisfies the following formula: where t is time, Y(t) is the state of the equation, is an n×1 dimensional vector, n is the number of state of the equation, F is a constant coefficient matrix, is an n order square matrix, G is a constant disturbance input matrix, is an n×m matrix, Z(t) is an external disturbance term, x represents the spacecraft x direction acceleration, represents the spacecraft y direction acceleration, represents the spacecraft z direction acceleration, x represents the spacecraft x direction received external disturbance and internal control torque sum, y represents the spacecraft y direction received external disturbance and internal control torque sum, z represents the spacecraft z direction received external disturbance and internal control torque sum.

4. The parametric adaptive based time-invariant track information acquisition method of claim 3, wherein, The constant coefficient matrix F and the constant disturbance input matrix G in the step 2) satisfy the following formulas respectively; Wherein, ω represents an angular velocity of the spacecraft motion.

5. The parametric adaptive based time-invariant track information acquisition method of claim 4, wherein, The step 3) includes: Set time t k The state quantity Y(t) obtained by solving the equation is denoted as Yt k The integrator step size h of the solver is set, and the value range of the iteration order Order of the solver is set as [3, 4]; Set time t k+1 =t k +h, set Y k Represents time t k The state variable Y(t) obtained from the equation is... k The value of ) is set to Y. k+1 Represents time t k+1 The state variable Y(t) obtained from the equation is... k+1 Find the value of Y. k+1 The value at point , the fourth-order Runge-Kutta iterative formula is as follows: wherein A ji denotes the parameter adaptive Runge-Kutta algorithm coefficients, Z j is a random number, k i is an iteration coefficient, satisfying the statistical property satisfying the following formula: Wherein, T represents transposition; Y k+1 The solution formula is as follows: A list of parameters to be solved is obtained, 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, wherein s represents the total number of orders, k j represents the iteration coefficient.

6. The parametric adaptive based time-invariant track information acquisition method of claim 5, wherein, The adaptive parameter constraint formula of the step 4) satisfies the following formula: P k = E[Y k | X = x] = P(t k | X = x) + O(h T ) k = P(t Order+1 | X = x) + O(h where T denotes transpose, Y k denotes the numerical solution, P k is the numerical solution obtained by numerical solution k denotes the numerical solution at t k , P(t k ) denotes the true variance, O(h Order+1 ) denotes an infinitesimal of the same order as h Order+1 .

7. The parametric adaptive based time-invariant track information acquisition method of claim 6, wherein, The dependency relationship of each parameter in the parameter list of the step 4) is: When Order = 3, A 41 = 0, A 42 = 0, A 43 = 0, q4 = 0, B4 = 0, and the following equations are satisfied among other parameters: Taking B1 as a free parameter, the following is obtained: When Order = 4, the parameters satisfy the following formula: Taking B1 and B4 as free parameters, the following is obtained:

8. The parametric adaptive based time-invariant track information acquisition method of claim 7, wherein, The step 4) includes: The step 4) includes: After the optimized free parameters are obtained, the other 12 parameters are obtained, which are used as the parameters of the Runge-Kutta solver, and the value of Y(t k ) is iteratively solved according to the value of Y(t k+1 ) until the value of Y(t end ) is obtained, wherein t end represents the termination time of the solution.

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