Parameter-adaptive spatial mass block motion state acquisition method and system

Abstract

The invention discloses a parameter-adaptive spatial mass block motion state acquisition method and system. The method comprises the following steps: constructing a linear random time-varying system for a motion state equation of mass block motion; obtaining a time-varying coefficient matrix and a time-varying disturbance input matrix; constructing a parameter-adaptive time-varying Runge-Kutta solver, and obtaining a to-be-determined parameter list of the Runge-Kutta solver; according to a self-adaptive parameter constraint formula, the dependency relationship of all parameters in the parameter list is solved, free parameters and other parameters are determined, and the free parameters are optimized and iteratively updated by adopting an optimization algorithm in a mode of comparing with an analytic solution until optimal free parameter selection is obtained. The method can be widely applied to high-precision satellite state acquisition of space science and technology. The method is not only suitable for acquiring the motion state of the mass block in a single scientific satellite, but also suitable for acquiring the motion state of a plurality of mass blocks running in a formation.

Description

Technical Field

[0001] The invention belongs to the field of high-precision computer simulation, and in particular relates to a parameter-adaptive spatial mass block motion state acquisition method and system. Background Art

[0002] For space gravitational wave detection satellites, how to calculate the motion of the mass block in space with high precision is a prerequisite for determining the orbit of the space gravitational wave detection satellite. At the same time, the position of the mass block changing with time is one of the inputs of the drag-free control system of the space gravitational wave detection satellite. Obtaining the high-precision position of the mass block can make the drag-free control system play a better role.

[0003] During the motion of the mass block, it can be regarded as a dynamic system, the essence of which is to calculate the linear random time-varying differential equations with high precision. At present, the solver used for the calculation of linear random time-varying differential equations uses the Runge-Kutta algorithm with a solution step number of 4. Experiments have shown that this algorithm cannot meet the solution accuracy requirements of space gravitational wave detection satellites. It is necessary to further develop the modeling of the motion equations of the space mass block and use parameter adaptive methods to optimize the solution process and improve the accuracy. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the prior art and propose a parameter-adaptive spatial mass block motion state acquisition method and system.

[0005] In view of this, the present invention proposes a parameter-adaptive spatial mass block motion state acquisition method, comprising:

[0006] Step 1) construct a linear random time-varying system based on the motion state equation of the mass block;

[0007] Step 2) obtaining a time-varying coefficient matrix and a time-varying disturbance input matrix;

[0008] Step 3) constructing a parameter-adaptive time-varying Runge-Kutta solver and obtaining a list of parameters to be determined for the Runge-Kutta solver;

[0009] Step 4) According to the adaptive parameter constraint formula, the dependency relationship of each parameter in the parameter list is obtained, the free parameters and other parameters are determined, and the free parameters are optimized by using an optimization algorithm by comparing with the analytical solution, and iteratively updated until the optimal free parameter selection is obtained.

[0010] Preferably, the motion state equation of the mass block motion in step 1) is:

[0011]

[0012] Among them, x, y, and z represent the coordinates of the mass block in the x, y, and z directions respectively. The specific coordinates are (x 0 ,y 0 ,z 0 ), and Respectively represent the speed of the mass block in the x, y and z directions, and the specific speed values ​​are

[0013] Preferably, the linear random time-varying 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(t) is the time-varying coefficient matrix, which is an n-order square matrix, G(t) is the time-varying disturbance input matrix, which is an n×m matrix, and Z(t) is the external interference term. represents the acceleration of the mass block in the x direction, represents the acceleration of the mass block in the y direction, represents the acceleration of the mass block in the z direction, f x represents the sum of the external disturbance and internal control torque of the mass block in the x direction, f y represents the sum of the external disturbance and internal control torque on the mass block in the y direction, f z It represents the sum of the external disturbance and internal control torque on the mass block in the z direction.

[0016] Preferably, the step 3) comprises:

[0017] 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 to 4;

[0018] 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 parameter adaptive Runge-Kutta iteration formula is as follows:

[0019]

[0020] Among them, Aji represents the coefficient of the parameter adaptive Runge-Kutta algorithm, Z j is a random number, k i is the iteration coefficient, c j is the step length coefficient, which satisfies the statistical properties and satisfies the following formula:

[0021]

[0022] Among them, q j is the coefficient to be determined, and the covariance matrix Q(t) is set to a constant matrix, denoted by Q; T represents transpose;

[0023] Y using parameter adaptive Runge-Kutta iteration k+1 The solution formula is as follows:

[0024]

[0025] Get the list of parameters to be determined for the Gekutta solver, including the following parameters: 21 , A 31 , A 32 , A 41 , A 42 , A 43 ,q 1 ,q 2 ,q 3 ,q 4 , C 1 , C 2 , C 3 , C 4 , B 1 , B 2 , B 3 , B 4 and Order.

[0026] Preferably, the adaptive parameter constraint formula of step 4) satisfies the following formula:

[0027]

[0028] Where Pk is the variance of the numerical solution Ytk of Y(tk) at time tk obtained by numerical solution, P(t k ) represents the true variance, O(h 5 ) indicates that 5 For infinitesimals of the same order, T represents transpose.

[0029] Preferably, the dependency relationship of each parameter in the parameter list of step 4) is:

[0030] When Order = 4,

[0031]

[0032]

[0033]

[0034] Take C 2 and C 3 As a free parameter, we get:

[0035]

[0036] Preferably, the step 4) uses an optimization algorithm to optimize the free parameters, and iteratively updates until the optimal free parameter selection is obtained; including:

[0037] According to the set total number of time points TIMEN, the free parameter C is randomly initialized 2 , C 3 , and obtain the values ​​of the remaining 15 parameters; the parameter adaptive Runge-Kutta method is used to calculate the solution Y of Order = 4 at the i-th time point RK (t) and the analytical solution Y Real (t), based on the fitness function of the optimization algorithm, iteratively optimizes two free parameters C 2 , C 3 The value of , and according to the fitness function Value, the most appropriate free parameter value is adaptively selected to derive the other 15 parameters.

[0038] Preferably, the fitness function Value of the optimization algorithm is:

[0039]

[0040] Among them, Y RK (t i ) and Y Real (t i ) are the solution result and analytical solution at the ith time point respectively.

[0041] Preferably, the step 4) further comprises: if no analytical solution exists, randomly selecting a free parameter that meets the constraint conditions.

[0042] On the other hand, the present invention proposes a parameter-adaptive spatial mass block motion state acquisition system, comprising:

[0043] The mass block motion modeling module is used to construct a linear random time-varying system for the motion state equation of the mass block motion; and obtain the time-varying coefficient matrix and the time-varying disturbance input matrix;

[0044] The parameter-adaptive Runge-Kutta solver module is used to construct a parameter-adaptive time-varying Runge-Kutta solver and obtain a list of parameters to be determined for the Runge-Kutta solver.

[0045] The adaptive parameter selection module is used to obtain the dependency relationship of each parameter in the parameter list according to the adaptive parameter constraint formula, determine the free parameters and other parameters, optimize the free parameters by using the optimization algorithm by comparing with the analytical solution, and iterate and update until the optimal free parameter selection is obtained.

[0046] Compared with the prior art, the advantages of the present invention are:

[0047] 1. The present invention constructs a parameter-adaptive Runge-Kutta solution method, which can be used to solve the time-varying motion equation of a mass block with high precision, and can be widely used in the high-precision acquisition of satellite states in space science and technology.

[0048] 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 acquisition of motion state.

[0049] 3. The present invention constructs three modules including mass block motion modeling, parameter adaptive Runge-Kutta solution and adaptive parameter selection, which is not only suitable for obtaining the motion state of mass blocks in a single scientific satellite, but also suitable for obtaining the motion state of multiple mass blocks running in formation. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a flow chart of a parameter adaptive spatial mass block motion state acquisition method and system;

[0051] Figure 2 It is the result of obtaining the motion state of the mass block by using the system proposed by the present invention;

[0052] Figure 3 It is a comparison between the x-direction result of the orbit equation using the system proposed by the present invention and the theoretical result;

[0053] Figure 4 It is a comparison between the results obtained in the x direction of the orbit equation using the existing solver and the theoretical results;

[0054] Figure 5 Comparison chart of time-varying differential equation results obtained using ode45 algorithm and analytical results. DETAILED DESCRIPTION

[0055] In view of the accuracy limitation of the prior art, the present invention proposes a parameter-adaptive spatial mass block motion state acquisition method and system. The flow chart is as follows: Figure 1 As shown, it includes three subsystems: mass block motion state modeling, parameter adaptive Runge-Kutta solution and adaptive parameter selection.

[0056] Space gravitational wave detection satellites usually consist of three spacecraft, which use laser interferometry to measure the distance between satellites and then invert the gravitational wave signal. In the specific operation, in order to accurately characterize the distance between the two spacecraft, a mass block in free fall motion is placed in each spacecraft, and the precise distance between the mass blocks in different spacecraft is measured to observe whether there are gravitational waves. Accurately solving the motion equation of the mass block includes the following steps:

[0057] Step 1) construct a linear random time-varying system for the orbit equation of the mass motion;

[0058] The motion state equation of the mass block satisfies the following formula:

[0059]

[0060] Among them, x, y, and z represent the coordinates of the mass block in the x, y, and z directions respectively. The specific coordinates are (x 0 ,y 0 ,z 0 ), and Respectively represent the speed of the mass block in the x, y and z directions, and the specific speed values ​​are

[0061] In step 1), the linear random time-varying system satisfies the following formula:

[0062]

[0063]

[0064] 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(t) is the time-varying coefficient matrix, which is an n-order square matrix, G(t) is the time-varying disturbance input matrix, which is an n×m matrix, and Z(t) is the external interference term. represents the acceleration of the mass block in the x direction, represents the acceleration of the mass block in the y direction, represents the acceleration of the mass block in the z direction, f x represents the sum of the external disturbance and internal control torque of the mass block in the x direction, f y represents the sum of the external disturbance and internal control torque on the mass block in the y direction, f z It represents the sum of the external disturbance and internal control torque on the mass block in the z direction.

[0065] Step 2) obtaining a time-varying coefficient matrix and a time-varying disturbance input matrix;

[0066] The time-varying coefficient matrix F(t) and the time-varying disturbance input matrix G(t) in step 2) can be constructed according to the actual mass block motion model.

[0067] Step 3) constructing a parameter-adaptive time-varying Runge-Kutta solver and obtaining a list of parameters to be determined for the Runge-Kutta solver;

[0068] include:

[0069] 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 to 4;

[0070] 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 parameter adaptive Runge-Kutta iteration formula is as follows:

[0071]

[0072] 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, c j is the step length coefficient. The statistical properties satisfy the following formula:

[0073]

[0074] Among them, q j is the coefficient to be determined, and the covariance matrix Q(t) is set to a constant matrix, denoted by Q.

[0075] Y using parameter adaptive Runge-Kutta iteration k+1 The solution formula is as follows:

[0076]

[0077] Step 4) According to the adaptive parameter constraint formula, the dependency relationship of each parameter in the parameter list is obtained, the free parameters and other parameters are determined, and the free parameters are optimized by using an optimization algorithm by comparing with the analytical solution, and iteratively updated until the optimal free parameter selection is obtained. If there is no analytical solution, the free parameters that meet the constraint conditions are randomly selected.

[0078] Specifically include:

[0079] The following adaptive parameter constraint formula is used to derive the subsequent formulas to obtain the dependency between the parameters set by the Runge-Kutta solver, namely:

[0080]

[0081] Among them, P k is the time t obtained by numerical solution k Y(t k ) k The variance of Pt k represents the true variance, O(h 5 ) indicates that 5 Infinitesimals of the same order.

[0082] According to the constraint formula, when Order = 4, the dependency relationship between the parameters is as follows:

[0083]

[0084]

[0085]

[0086] Further derivation, take C 2 and C 3 is a free parameter, and the parameter can be expressed as:

[0087]

[0088] According to the set total number of time points TIMEN, the free parameter C is randomly initialized 2 , C 3 , and obtain the values ​​of the remaining 15 parameters. The parameter adaptive Runge-Kutta method is used to calculate the solution Y of Order = 4 at the i-th time point RK (t) and the analytical solution Y Real (t), based on the fitness function of the optimization algorithm, iteratively optimizes two free parameters C 2 , C 3 The value of , and according to the fitness function Value, the most appropriate free parameter value is adaptively selected, and finally the other 15 parameters are derived.

[0089] The fitness function Value of the optimization algorithm is:

[0090]

[0091] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0092] Example 1

[0093] Embodiment 1 of the present invention proposes a parameter-adaptive method for acquiring the motion state of a spatial mass block, which comprises the following steps:

[0094] Step 1) construct a linear random time-varying system based on the motion state equation of the mass block;

[0095] Step 2) obtaining a time-varying coefficient matrix and a time-varying disturbance input matrix;

[0096] Step 3) constructing a parameter-adaptive time-varying Runge-Kutta solver and obtaining a list of parameters to be determined for the Runge-Kutta solver;

[0097] Step 4) According to the adaptive parameter constraint formula, the dependency relationship of each parameter in the parameter list is obtained, the free parameters and other parameters are determined, and the free parameters are optimized by using an optimization algorithm by comparing with the analytical solution, and iteratively updated until the optimal free parameter selection is obtained.

[0098] The equation of motion of the mass block satisfies the linear random time-varying differential equation, specifically:

[0099]

[0100] Among them, x represents the x-direction coordinate of the mass block, y represents the x-direction coordinate of the mass block, and z represents the z-direction coordinate of the mass block. represents the velocity of the mass block in the x direction, represents the velocity of the mass block in the y direction, Represents the velocity of the mass block in the z direction.

[0101] set up Then the time-varying differential equation of mass motion can be modeled as follows:

[0102]

[0103] in,

[0104]

[0105] in,

[0106]

[0107] When e=0,

[0108]

[0109] Expand it, and you get

[0110]

[0111] in, In this embodiment, T=1, that is, n=2π, represents the acceleration of the mass block in the x direction, represents the acceleration of the mass block in the y direction, represents the acceleration of the mass block in the z direction.

[0112] The linear random time-varying system in step 1) satisfies the following equation:

[0113]

[0114]

[0115] 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(t) is the time-varying coefficient matrix, which is an n-order square matrix, G(t) is the time-varying disturbance input matrix, which is an n×m matrix, and Z(t) is the external interference term. represents the acceleration of the mass block in the x direction, represents the acceleration of the mass block in the y direction, represents the acceleration of the mass block in the z direction, f x represents the sum of the external disturbance and internal control torque of the mass block in the x direction, f y represents the sum of the external disturbance and internal control torque on the mass block in the y direction, f z It represents the sum of the external disturbance and internal control torque on the mass block in the z direction.

[0116] Step 2) The time-varying coefficient matrix F(t) and the time-varying disturbance input matrix G(t) can be constructed according to the actual mass block motion model.

[0117] Step 3) includes:

[0118] 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 to 4;

[0119] 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 parameter adaptive Runge-Kutta iteration formula is as follows:

[0120]

[0121] 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, c j is the step length coefficient, which satisfies the statistical properties and satisfies the following formula:

[0122]

[0123] Among them, q j is the coefficient to be determined, and the covariance matrix Q(t) is set to a constant matrix, denoted by Q.

[0124] Y using parameter adaptive Runge-Kutta iteration k+1 The solution formula is as follows:

[0125]

[0126] In step 4), the following adaptive parameter constraint formula is used to derive the subsequent formula to obtain the dependency relationship between the parameters set by the Runge-Kutta solver, that is,

[0127]

[0128] Among them, P k is the time t obtained by numerical solution k Y(t k ) k The variance of Pt k represents the true variance, O(h 5 ) indicates that 5 Infinitesimals of the same order.

[0129] According to the constraint formula, when Order = 4, the dependency relationship between the parameters is as follows:

[0130]

[0131]

[0132] Further derivation, take C 2 and C 3 is a free parameter, and the parameter can be expressed as:

[0133]

[0134] Preferably, the free parameter C is randomly initialized according to the set total number of time points TIMEN 2 , C 3, and obtain the values ​​of the remaining 15 parameters. The parameter adaptive Runge-Kutta method is used to calculate the solution Y of Order = 4 at the i-th time point RK (t) and the analytical solution Y Real (t), based on the fitness function of the optimization algorithm, iteratively optimizes two free parameters C 2 , C 3 The value of , and according to the fitness function Value, the most appropriate free parameter value is adaptively selected, and finally the other 15 parameters are derived.

[0135] Preferably, the fitness function Value of the genetic algorithm is:

[0136]

[0137] 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.

[0138] The optimized free parameters are used to solve the other 15 parameters for subsequent calculations.

[0139] In a specific embodiment, the adaptive parameter selection subsystem is used to determine 17 parameters to be determined, specifically:

[0140] Step 1: Determine the solution accuracy criterion. Use the following formula as the constraint standard between parameters:

[0141]

[0142] Step 2: Establish a nonlinear algebraic equation system and solve it to obtain 17 parameter solutions, including two free parameters C 2 , C 3 .

[0143]

[0144] Step 3: Since it is difficult to obtain an analytical solution for this time-varying differential equation, random numbers are used to randomly determine the free parameter C 2 , C 3 The value of .

[0145] Step 4: Based on the free parameter values ​​obtained in step 3, the values ​​of the other 15 parameters are obtained to achieve adaptive parameter selection.

[0146] Random setting C 2 =0.22, C 3 =3 / 4, and the values ​​of the other 15 parameters are derived based on these two parameters. Then, the Runge-Kutta solver with the determined parameters is used to solve the problem. The solution is as follows: Figure 3 shown.

[0147] The following time-varying differential equation is used to verify the solution accuracy of the algorithm proposed in the present invention.

[0148] Step 1) Construct a time-varying differential equation as follows:

[0149]

[0150] Step 2) Construct the F matrix and the G matrix, that is, F = [-sin(t)], G = [0].

[0151] Step 3) Obtain the dependency relationship between the 17 parameters according to the adaptive parameter constraint formula.

[0152] Step 4) respectively uses an optimization algorithm to optimize the free parameter selection method and a method of randomly specifying the free parameters that meet the constraints.

[0153] Step 5) The free parameter after optimization by the optimization algorithm is selected as C 2 =0.4380, C 3 =0.5683, the initial state is set to Y 0 =1, the solution step h is set to 0.01, the state of Y(t) in [0,10] is solved and compared with the analytical solution. The results are as follows Figure 3 As shown in Figure 2, the maximum residual is 9.9036e-12.

[0154] Step 6) Randomly specify the free parameters that satisfy the constraints as C 2 =0.22, C 3 =3 / 4, the initial state is set to Y 0 =1, the solution step h is set to 0.01, the state of Y(t) in [0,10] is solved and compared with the analytical solution. The results are as follows Figure 4 As shown in Figure 2, the maximum residual is 4.4579e-11.

[0155] Step 7) Use ode45 algorithm to obtain Y(t), and the initial state is set to Y 0 =1, solve the state of Y(t) in [0,10] and compare it with the analytical solution. The results are as follows Figure 5 As shown in Figure 2, the maximum residual is 6.7442e-04.

[0156] By comparing step 5), step 6), and step 7), we can see that the free parameter selection after optimization by the optimization algorithm can obtain the result closest to the analytical solution. However, in reality, the time-varying differential equation system usually cannot obtain an analytical solution. In this case, the method of randomly specifying free parameters can be selected for solution. By comparison, it can be seen that even if the method of randomly specifying free parameters is selected, it is still about 7 orders of magnitude higher than the classic ode45 algorithm, which can meet the needs of actual space science missions.

[0157] Example 2

[0158] Embodiment 2 of the present invention proposes a parameter-adaptive spatial mass block motion state acquisition system, which is implemented based on the method of embodiment 1 and includes:

[0159] The mass block motion modeling module is used to construct a linear random time-varying system for the motion state equation of the mass block motion; and obtain the time-varying coefficient matrix and the time-varying disturbance input matrix;

[0160] The parameter-adaptive Runge-Kutta solver module is used to construct a parameter-adaptive time-varying Runge-Kutta solver and obtain a list of parameters to be determined for the Runge-Kutta solver.

[0161] The adaptive parameter selection module is used to obtain the dependency relationship of each parameter in the parameter list according to the adaptive parameter constraint formula, determine the free parameters and other parameters, optimize the free parameters by using the optimization algorithm by comparing with the analytical solution, and iterate and update until the optimal free parameter selection is obtained.

[0162] 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 parameter-adaptive spatial mass block motion state acquisition method, comprising: Step 1) construct a linear random time-varying system based on the motion state equation of the mass block; Step 2) obtaining a time-varying coefficient matrix and a time-varying disturbance input matrix; Step 3) constructing a parameter-adaptive time-varying Runge-Kutta solver and obtaining a list of parameters to be determined for the Runge-Kutta solver; Step 4) According to the adaptive parameter constraint formula, the dependency relationship of each parameter in the parameter list is obtained, the free parameters and other parameters are determined, and the free parameters are optimized by using an optimization algorithm by comparing with the analytical solution, and iteratively updated until the optimal free parameter selection is obtained.

2. The parameter-adaptive spatial mass block motion state acquisition method according to claim 1, characterized in that: The motion state equation of the mass block motion in step 1) is: Among them, x, y, and z represent the coordinates of the mass block in the x, y, and z directions respectively, and the specific coordinates are (x0, y0, z0). and Respectively represent the speed of the mass block in the x, y and z directions, and the specific speed values ​​are 3. The parameter-adaptive spatial mass block motion state acquisition method according to claim 2, characterized in that: The linear random time-varying system of step 1) 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(t) is the time-varying coefficient matrix, which is an n-order square matrix, G(t) is the time-varying disturbance input matrix, which is an n×m matrix, and Z(t) is the external interference term. represents the acceleration of the mass block in the x direction, represents the acceleration of the mass block in the y direction, z represents the acceleration of the mass block in the z direction, and f x represents the sum of the external disturbance and internal control torque of the mass block in the x direction, f y represents the sum of the external disturbance and internal control torque on the mass block in the y direction, f z It represents the sum of the external disturbance and internal control torque on the mass block in the z direction.

4. The parameter-adaptive spatial mass block motion state acquisition method according to claim 3, 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 to 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 parameter adaptive 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, c j is the step length coefficient, which satisfies the statistical properties and satisfies the following formula: Among them, q j is the coefficient to be determined, and the covariance matrix Q(t) is set to a constant matrix, denoted by Q; T represents transpose; Y using parameter adaptive Runge-Kutta iteration k+1 The solution formula is as follows: Get the list of parameters to be determined for the Gekutta solver, including the following parameters: A 21 , A 31 , A 32 , A 41 , A 42 , A 43 , q1, q2, q3, q4, C1, C2, C3, C4, B1, B2, B3, B4 and Order.

5. The parameter-adaptive spatial mass block motion state acquisition method according to claim 4, characterized in that: The adaptive parameter constraint formula of step 4) satisfies the following formula: Where Pk is the variance of the numerical solution Ytk of Y(tk) at time tk obtained by numerical solution, P(t k ) represents the true variance, O(h 5 ) indicates that 5 For infinitesimals of the same order, T represents transpose.

6. The parameter-adaptive spatial mass block motion state acquisition method according to claim 5, characterized in that: The dependency relationship of each parameter in the parameter list of step 4) is: When Order = 4, Taking C2 and C3 as free parameters, we get:

7. The parameter-adaptive spatial mass block motion state acquisition method according to claim 6, characterized in that: The step 4) uses an optimization algorithm to optimize the free parameters, and iteratively updates until the optimal free parameter selection is obtained; including: According to the set total number of time points TIMEN, the free parameters C2 and C3 are randomly initialized to obtain the values ​​of the remaining 15 parameters; the parameter adaptive Runge-Kutta method is used to calculate the solution Y at the i-th time point Order = 4 RK (t) and the analytical solution Y Real (t), based on the fitness function of the optimization algorithm, iteratively optimize the values ​​of the two free parameters C2 and C3, and according to the fitness function Value, adaptively select the most appropriate free parameter values ​​to derive the other 15 parameters.

8. The parameter-adaptive spatial mass block motion state acquisition method according to claim 7, characterized in that: The fitness function Value of the optimization algorithm 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.

9. The parameter-adaptive spatial mass block motion state acquisition method according to claim 8, characterized in that: The step 4) further comprises: if no analytical solution exists, randomly selecting free parameters that meet the constraint conditions.

10. A parameter-adaptive spatial mass block motion state acquisition system, characterized in that: include: The mass motion modeling module is used to construct a linear random time-varying system based on the motion state equation of the mass motion; Obtain the time-varying coefficient matrix and the time-varying disturbance input matrix; The parameter-adaptive Runge-Kutta solver module is used to construct a parameter-adaptive time-varying Runge-Kutta solver and obtain a list of parameters to be determined for the Runge-Kutta solver. and The adaptive parameter selection module is used to obtain the dependency relationship of each parameter in the parameter list according to the adaptive parameter constraint formula, determine the free parameters and other parameters, optimize the free parameters by using the optimization algorithm by comparing with the analytical solution, and iterate and update until the optimal free parameter selection is obtained.

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