Moon orbit and balance dynamic parameter resolving and forecasting method and system

Abstract

The invention discloses a lunar orbit and balance dynamic parameter resolving and forecasting method and system, and the method comprises the steps: considering a mass point gravity model based on a rear Newton frame, the interaction between a lunar graph and other planetary mass points of a solar system, and the influence of an earth graph; establishing a high-precision lunar orbit dynamic model under a generalized relativistic framework; considering the moon rotational inertia and the moon torque, and establishing a double-layer moon balance dynamic attitude dynamic model; when the initial condition of integration meets the preset precision, respectively forecasting the orbit parameters and the balance dynamic parameters by adopting an adaptive step integrator and an adaptive step integrator with a time-delay effect to obtain orbit and balance dynamic parameter initial products with time sequence labels; and when the initial condition of the integration does not meet the preset precision, processing the historical observation data by using a nonlinear solver based on automatic differentiation to obtain the optimal solution of the to-be-estimated parameter in the initial condition, and carrying out forecasting again.

Description

Technical Field

[0001] The present invention belongs to the research field of lunar orbit and libration parameter solution and prediction in lunar exploration missions, and particularly relates to the establishment of a more precise lunar orbit dynamics model and attitude mechanics, a new method for using an adaptive integrator with a time lag effect for prediction, and a nonlinear solver for parameter solution, and specifically relates to a lunar orbit and libration parameter solution and prediction method and system. Background Art

[0002] The precise determination and prediction of the lunar orbit and libration parameters are of great significance in lunar exploration missions. In addition to the existing optical navigation and astronomical navigation technologies, some scholars have proposed methods to enhance lunar navigation using the Global Navigation Satellite System (GNSS). The scientific goals and technical processes have posed unprecedented challenges to the accuracy of the calculation and prediction of the lunar orbit and libration parameters.

[0003] The lunar orbit and libration parameters constitute important elements for describing the position, velocity and attitude of the moon. The time series file composed of these elements is called ephemeris. Accurate ephemeris files are the cornerstone of lunar exploration missions. High-precision predictions of the lunar orbit and libration parameters provide a key solution for mission decision-making. The lunar orbit information mainly refers to 6 state components: three-dimensional position and velocity (x, y, z, vx, vy, vz); and the lunar attitude is used to describe the rotation of the moon, which is mainly described here by 12 libration parameters, referring to the Euler angles and Euler angular velocity components of the lunar mantle and the lunar core: ( θ m ,ψ m ,ω m,x ,ω m,y ,ω m,z , θ m ,ψ m ,ω m,x ,ω m,y ,ω m,z). The prediction of orbital and libration parameters is based on the high-precision orbital dynamics model and the lunar double-layer attitude mechanics model respectively. The prediction process starts with high-precision initial conditions, connects the mechanics model through the integration method, and finally obtains the predicted ephemeris. Generally, the high-precision initial conditions are obtained after the parameter solver processes a large amount of historical observation data. The specific process is as follows: first, starting from the initial orbit and libration parameters of the moon at a certain moment, the orbital dynamics model and libration attitude mechanics model of the moon are rigorously analyzed. The precise orbital mechanics model and attitude model provide the basic form of the second-order ordinary differential equation for the integrator. The integration result is the lunar orbit information and lunar libration information with time tags, which are output as .bsp files through mkspk in SPICE to obtain ephemeris that supports reading by any user. If the accuracy of the initial condition acquisition is limited, it is also necessary to rely on the method of using the solver to process a large amount of observation data to achieve the purpose of parameter optimization in the initial condition.

[0004] In the current field of lunar orbit and libration parameter prediction, although the construction of orbital dynamics models and lunar double-layer attitude dynamics models has undergone a long period of optimization and updating, the time-delay effect of force action is still worth considering under the framework of general relativity; the conventional 8th-order Runge-Kutta integral, as a commonly used method in orbital integration in the past, can more effectively handle complex and high-precision differential equation problems than the classical 4th-order Runge-Kutta integral, but for the part of lunar libration integral, the conventional 8th-order Runge-Kutta integral cannot meet the need to consider time delay in some calculation formulas in the double-layer lunar libration model; for more complex nonlinear problems, manual calculation of the state derivatives with respect to parameters and traditional least squares both show many shortcomings. Summary of the invention

[0005] In order to overcome the deficiencies of the above-mentioned prior art, the present invention provides a method and system for solving and predicting the lunar orbit and libration parameters, which reduces the difference between the lunar orbit and the internationally published ephemeris and achieves the purpose of high-precision prediction of the orbit and libration parameters by optimizing multiple important links such as the orbital dynamics, the establishment of a double-layer libration attitude mechanics model, the setting of an integrator, and the setting of a parameter solver.

[0006] According to one aspect of the present invention, a method for calculating and predicting lunar orbit and libration parameters is provided, comprising:

[0007] Step 1: Considering the particle gravity model in the post-Newtonian framework, the interaction between the lunar figure and the particles of other planets in the solar system, and the influence of the earth figure, a high-precision lunar orbit dynamics model is established in the framework of general relativity;

[0008] Step 2, considering the lunar moment of inertia and lunar torque, establish a double-layer lunar libration attitude dynamics model;

[0009] Step 3: When the initial conditions of the integration meet the preset accuracy, the orbital parameters are predicted based on the lunar orbital dynamics model of step 1 by using an integrator with an adaptive step size, and the libration parameters are predicted based on the double-layer lunar libration attitude dynamics model of step 2 by using an adaptive step size integrator with a time lag effect, so as to obtain the initial products of orbital and libration parameters with time series labels;

[0010] Step 4: When the initial conditions of the integration do not meet the preset accuracy, use a nonlinear solver based on automatic differentiation to process the historical observation data to obtain the optimal solution for the parameters to be estimated in the initial conditions, and return to step 3.

[0011] As a further technical solution, after obtaining the initial products of orbital and libration parameters with time series labels, it also includes:

[0012] The orbit and libration parameters with time series labels are generated as ephemeris files through mkspk in SPICE software.

[0013] As a further technical solution, a high-precision lunar orbit dynamics model based on the general theory of relativity is established, including:

[0014] Step 1.1, calculate the gravity of the particle under parameterized Newton:

[0015]

[0016] Among them, β and γ are post-Newtonian parameters. The particles that interact with the moon include the sun, the eight planets, and the asteroids with larger mass in the main belt.

[0017] Step 1.2, calculate the interaction between the particle and the graphics:

[0018]

[0019] Among them, GM is the gravitational constant of the central body, and It represents the three-dimensional acceleration in the body-fixed coordinate system of the central celestial body, r, λ is the spherical coordinate of the particle to the central celestial body; n1 and n2 are the maximum order of the spherical harmonic coefficient expansion; is the Legendre polynomial of order n; is the Legendre polynomial of order n and degree m; J n It is a harmonic direction; C nm and S nm are the spherical harmonic coefficients.

[0020] As a further technical solution, a double-layer lunar libration attitude dynamics model is established, including:

[0021] Step 2.1, the moment of inertia of the lunar mantle includes rigid body, tidal distortion, spin distortion and the moment of inertia of the lunar core, as shown in the following formula:

[0022] I m =I rigid +I tide +I spin +I c

[0023] In the main axis system, the main moment of inertia of the rigid body is A <B<C,

[0024]

[0025] in:

[0026]

[0027]

[0028] m m is the mass of the moon, R m is the radius of the moon, β L =(CA) / B,γ L =(BA) / C is the moon distance parameter, is the 2-degree band harmonic coefficient of the moon without distortion;

[0029] The formulas for tidal distortion and spin distortion are shown below:

[0030]

[0031] Where ω=(ω x ,ω y ,ω z ), describes the angular velocity of the lunar mantle, and its calculation formula is calculated based on the instantaneous lunar mantle Euler angle provided in the background technology:

[0032]

[0033] also, k 2,m It is the love number of 2 degrees of the moon. is the position of the Moon relative to the Earth, n is the mean motion of the Moon; there is a time delay (tt m ), the calculation formula for the position of the moon relative to the earth is: The angular velocity of the lunar mantle is

[0034] The lunar core is assumed to rotate like a solid and is restricted by the shape of the lunar core-mantle boundary. The calculation formula for the lunar core inertia matrix is:

[0035]

[0036] where α c is the dimensionless coefficient of the ratio of the nuclear to total polar moment of inertia, f c is the flattening of the lunar core;

[0037] Step 2.2, Torque acting on the Moon's rotational motion Including: the gravitational interaction between the moon and the external point mass, and the torque generated by the flatness of the earth on the moon's shape. The total torque calculation formula is:

[0038]

[0039] The calculation formula for the torque generated by the single point mass acting on the moon and affecting the moon's shape is:

[0040]

[0041] in, is the force between the figure and the particle. The calculation formula for the acceleration generated is shown in step 1.2. Corresponding to the three-dimensional acceleration in the body-fixed coordinate system of the central celestial body and is the position of the particle in the lunar body solid coordinate system, M p is the mass of the particle; Refers to the interaction between the Earth and Moon graphics, where the most influential part is retained, and its calculation formula is:

[0042]

[0043] Among them, R e is the radius of the Earth, J 2e is the J2 term of the Earth's gravitational field, m e is the mass of the Earth, It is the Earth-Moon connection. The direction of the Earth's polar axis, η, is defined as:

[0044] Step 2.3, the time derivative expression of the lunar mantle Euler angular velocity is:

[0045]

[0046] The time derivative expression of the Euler angular velocity of the lunar core is:

[0047]

[0048] Among them, ω c is the angular velocity of the lunar core, which is calculated in a similar way to the angular velocity of the lunar mantle; is the torque generated by the interaction between the lunar mantle and the lunar core, given in the lunar mantle frame:

[0049]

[0050] is the friction parameter,

[0051] As a further technical solution, a nonlinear solver based on automatic differentiation is used to process the historical observation data to obtain the optimal solution of the parameters to be estimated in the initial conditions, including:

[0052] Obtain historical observation data and use automatic differentiation to perform derivation;

[0053] Based on the derivative results, the nonlinear solver is used to optimize the parameters and obtain the optimal solution for the parameters to be estimated in the initial conditions.

[0054] According to one aspect of the present invention, a lunar orbit and libration parameter solution and prediction system is provided, which is used to implement the lunar orbit and libration parameter solution and prediction method.

[0055] As a further technical solution, the system includes:

[0056] The first main module is used to consider the particle gravity model in the post-Newtonian framework, the interaction between the lunar figure and the particles of other planets in the solar system, and the influence of the earth figure, and to establish a high-precision lunar orbit dynamics model in the framework of general relativity;

[0057] The second main module is used to establish a double-layer lunar libration attitude dynamics model by considering the lunar moment of inertia and lunar torque;

[0058] The third main module is used to predict the orbital parameters based on the lunar orbit dynamics model by using an integrator with an adaptive step length when the initial conditions of the integration meet the preset accuracy, and to predict the libration parameters based on the double-layer lunar libration attitude dynamics model by using an adaptive step length integrator with a time lag effect, so as to obtain the initial products of the orbital and libration parameters with time series labels;

[0059] The fourth main module is used to process the historical observation data using a nonlinear solver based on automatic differentiation to obtain the optimal solution of the parameters to be estimated in the initial conditions when the initial conditions of the integration do not meet the preset accuracy.

[0060] According to one aspect of the present invention, there is provided a system for calculating and predicting the lunar orbit and libration parameters, comprising a processor and a memory, wherein the memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute the method for calculating and predicting the lunar orbit and libration parameters.

[0061] According to one aspect of the present invention, a non-transitory computer-readable storage medium is provided, wherein the non-transitory computer-readable storage medium stores computer instructions, wherein the computer instructions enable the computer to execute the method for calculating and predicting the lunar orbit and libration parameters.

[0062] Compared with the prior art, the present invention has the following beneficial effects:

[0063] 1. The present invention combines a variety of technical means to make high-precision predictions of the lunar orbit and libration parameters to ensure the smooth implementation of the lunar exploration mission. Specifically, the present invention improves the accuracy and efficiency of the solution by optimizing the orbital dynamics model and the lunar double-layer attitude dynamics model, especially by using an adaptive integrator and an automatic differential solver. In the adaptive integration process, the algorithm with a time-lag effect can better handle the complex changes in the lunar attitude, making the orbit and attitude predictions more accurate. Taking the solution of the lunar mantle Euler angle in the lunar libration as an example, the attached Figure 3 The difference between the prediction results of the traditional least squares solution considering the moon as a rigid body model and the DE430 released by JPL is given in arc seconds, with a maximum difference of 0.5 arc seconds; Figure 4 The prediction results of the double-layer lunar libration refinement model combined with the nonlinear solver of the present invention are expressed in arc seconds, with a maximum difference of 0.25 arc seconds. In comparison, the present invention has greatly improved in performance, especially in the first two angles, with the accuracy improved by an order of magnitude.

[0064] 2. The present invention has important application value in the field of lunar exploration and orbit prediction, and can be used for the precise calculation of lunar orbit and libration parameters in deep space exploration missions. The present invention significantly improves the prediction accuracy by optimizing the initial orbit conditions and using adaptive integration technology, especially considering the time delay effect of force under the framework of general relativity, and is particularly outstanding in complex orbit calculations and attitude parameter predictions. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, a brief introduction is given below to the drawings used in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0066] Figure 1A schematic flow chart of a method for calculating and predicting lunar orbit and libration parameters provided in an embodiment of the present invention.

[0067] Figure 2 A schematic diagram of the relationship between the lunar-fixed coordinate system and the inertial system provided in an embodiment of the present invention, and the definition of the Euler angles is shown.

[0068] Figure 3 This is a comparison chart of the differences between the prediction results of the traditional least squares solution using the existing technology considering the moon as a rigid body model and the DE430 released by JPL.

[0069] Figure 4 A schematic diagram of the prediction results of the double-layer lunar libration refinement model combined with a nonlinear solver provided in an embodiment of the present invention.

[0070] Figure 5 A schematic diagram of the structure of a lunar orbit and libration parameter calculation and prediction system provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0071] In view of the shortcomings of the prior art, the present invention proposes a method for establishing a lunar orbital mechanics model and a lunar double-layer libration attitude model, uses an adaptive integrator with a time lag effect to replace the traditional integrator to predict the lunar libration parameters, and uses a nonlinear solver based on automatic differentiation to optimize the estimated parameters.

[0072] The present invention optimizes several important links in the prediction of lunar orbit and libration parameters, such as the establishment of orbital dynamics, dual-layer libration attitude dynamics model, the setting of integrators, and the setting of parameter solvers. Specifically, the optimized orbital dynamics model and dual-layer libration attitude dynamics model are more in line with the force conditions of the moon; the adaptive integrator with time lag effect is not only more suitable for complex rigidity problems, but also well fits the problem of time delay that needs to be considered in the dual-layer lunar libration model; the nonlinear solver based on automatic differentiation efficiently and accurately calculates partial derivatives, solving the difficulty of deriving derivatives in complex nonlinear problems. At the same time, the nonlinear solver has better expressiveness in the face of complex nonlinear problems due to the traditional least squares method, and can effectively process local optimal solutions.

[0073] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. In addition, the technical features in the various embodiments or single embodiments provided by the present invention are arbitrarily combined with each other to form a new technical solution. This combination is not restricted by the sequence of steps and / or the structural composition mode, but must be based on the ability of ordinary technicians in this field to achieve. When the combination of technical solutions is contradictory or cannot be achieved, it should be considered that this combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0074] In the face of the fact that my country will carry out multiple types of lunar scientific exploration missions in the future and the difficulty of lunar exploration missions has been escalated, it is urgent to use high-precision lunar orbit and libration parameter prediction as the cornerstone of the mission to ensure the correct execution of decisions and support the effective processing of exploration data. The method of the present invention optimizes multiple important links such as orbital dynamics, the establishment of a double-layer libration attitude mechanics model, the setting of an integrator, and the setting of a parameter solver to reduce the difference between the ephemeris published internationally and achieve the purpose of high-precision prediction of orbit and libration parameters.

[0075] Figure 1 This is a flow chart of the calculation and prediction of the lunar orbit and libration parameters in the present invention, which is mainly composed of four modules:

[0076] The first is the parameter management module. The parameter input includes all the prior information, such as the gravity field files of the earth and the moon, the initial orbit parameter information, the initial libration information, and the astronomical information of other celestial bodies related to the calculation.

[0077] The second is the establishment of the celestial dynamics model, which is divided into two parts: orbit and libration. The orbital dynamics mainly relies on the general relativity law to optimize the particle gravity; the libration attitude mechanics model is mainly based on the lunar double-layer model.

[0078] The integrators used for orbital integration and libration integration are both adaptive step-size integrators, which can adapt well to rigidity problems. However, the difference is that the libration attitude mechanics model uses an adaptive integration model with time lag effect, which can better meet the difficulty of considering time delay in the calculation formula of the second-order ordinary differential of the libration Euler angle.

[0079] Finally, there is the solver module, which uses a nonlinear optimal solution method based on automatic differentiation. It is efficient and fast, and more suitable for complex nonlinear problems.

[0080] Figure 2 The relationship between the lunar fixed system and the inertial system ICRF (in blue in the figure), and the definition of Euler angles are also shown. It is important to note that:

[0081] Euler angles ( θ m and ψ m The Euler angles for the rotation from the lunar principal axis (PA) to the inertial ICRF coordinate system are defined as: is the intersection point from the x-axis of the inertial system along the XY plane to the mantle equator; θ m is the inclination of the mantle equator relative to the inertial XY plane; ψ m is the longitude from the intersection of the inertial XY plane with the mantle equator to the prime meridian along the mantle equator. PA is the position vector in the coordinates of the lunar principal axis, then it is converted to r in the inertial coordinate system I The coordinate vector of can be realized by the following formula:

[0082]

[0083] The rotation matrix R x ,R y and R z is a right-hand rotation about the coordinate system, defined as:

[0084]

[0085] As a preferred embodiment, refer to Figure 1 As shown, the method of the embodiment of the present invention includes the following steps:

[0086] (1) A high-precision lunar orbital dynamics model based on the general relativity framework, including the particle gravity model based on the post-Newtonian framework, the interaction between the lunar figure and other planetary particles in the solar system, and the influence of the Earth figure;

[0087] (2) Establish a dual-layer lunar libration attitude dynamics model, including the calculation of the lunar moment of inertia and the lunar torque;

[0088] (3) An adaptive step-size integrator and an adaptive step-size integrator with time lag effect are used to predict the orbital and libration parameters, respectively, to obtain the initial products of the orbital and libration parameters with time series labels.

[0089] (4) Output the file to .bsp through mkspk in SPICE, and obtain the ephemeris that can be read by any user.

[0090] (5) When the initial conditions of the integral are not accurate enough, a large amount of historical observation data is processed using a nonlinear solver based on automatic differentiation to obtain the optimal solution for the parameters to be estimated in the initial conditions, and then steps (3) to (5) are repeated.

[0091] Furthermore, the sub-steps for calculating the high-precision lunar orbit dynamics model under the framework of general relativity in step (1) are as follows:

[0092] Step 1.1, calculate the gravity of the particle under parameterized Newton:

[0093]

[0094] Among them, β and γ are post-Newtonian parameters. The particles that need to be considered to interact with the moon include the sun, the eight planets, and the asteroids with larger mass in the main belt.

[0095] Step 1.2: Interaction between particles and graphics

[0096]

[0097] Among them, GM is the gravitational constant of the central body, and It represents the three-dimensional acceleration in the body-fixed coordinate system of the central celestial body, r, λ is the spherical coordinate of the particle to the central celestial body; n1 and n2 are the maximum order of the spherical harmonic coefficient expansion; is the Legendre polynomial of order n; is the Legendre polynomial of order n and degree m; J n It is a harmonic direction; C nm and S nm are the spherical harmonic coefficients.

[0098] Furthermore, the sub-steps of establishing the double-layer moon model in step (2) are as follows:

[0099] Step 2.1, the moment of inertia of the lunar mantle consists of four parts: rigid body, tidal distortion, spin distortion and lunar core moment of inertia, as shown in the following formula:

[0100] I m =I rigid +I tide +I spin +I c

[0101] In the main axis system, the main moment of inertia of the rigid body is A <B<C

[0102]

[0103] in:

[0104]

[0105] m m is the mass of the moon, R m is the radius of the moon, β L =(CA) / B,γ L =(BA) / C is the moon distance parameter, is the 2 degree harmonic coefficient of the moon without distortion.

[0106] The formulas for tidal distortion and spin distortion are shown below:

[0107]

[0108] Where ω=(ω x ,ω y ,ω z ), describes the angular velocity of the lunar mantle, and its calculation formula is calculated based on the instantaneous lunar mantle Euler angle provided in the background technology:

[0109]

[0110] also, k 2,M It is the moon's love number of 2 degrees. is the position of the Moon relative to the Earth, and n is the mean motion of the Moon. Tidal and spin distortions are represented by time delays (tt m ), so the above position and mantle angular velocity need to take into account the time delay, and the position of the moon relative to the earth is calculated as: The angular velocity of the lunar mantle is

[0111] The lunar core is assumed to rotate like a solid and is restricted by the shape of the lunar core-mantle boundary (CMB). The calculation formula for the lunar core inertia matrix is:

[0112]

[0113] where α c is the dimensionless coefficient of the ratio of the nuclear to total polar moment of inertia, f c The flattening of the lunar core.

[0114] Step 2.2, Torque acting on the Moon's rotational motion Generally, it can be divided into two categories: the gravitational interaction between the moon and external point masses (objects), and the torque generated by the flatness of the earth on the moon's figure, namely the lunar surface point mass torque and the lunar surface-lunar surface torque. The total torque calculation formula is:

[0115]

[0116] The calculation formula for the torque generated by the single point mass acting on the moon and affecting the moon's shape is:

[0117]

[0118] in, is the force between the figure and the particle. The calculation formula for the acceleration generated is shown in step 1.2. Corresponding to the three-dimensional acceleration in the body-fixed coordinate system of the central celestial body and is the position of the particle in the lunar body solid coordinate system, M p is the mass of the particle.

[0119] Refers to the interaction between the Earth and Moon graphics, where the most influential part is retained, and its calculation formula is:

[0120]

[0121] Among them, R e is the radius of the Earth, J 2e is the J2 term of the Earth's gravitational field, m e is the mass of the Earth, It is the Earth-Moon connection. The direction of the Earth's polar axis, η, is defined as:

[0122] Step 2.3, the time derivative expression of the lunar mantle Euler angular velocity is:

[0123]

[0124] The time derivative expression of the Euler angular velocity of the lunar core is:

[0125]

[0126] Among them, ω c is the angular velocity of the lunar core, and its calculation method is similar to that of the lunar mantle. is the torque generated by the interaction between the lunar mantle and the lunar core. In the lunar mantle frame, it is given by:

[0127]

[0128] is the friction parameter,

[0129] Furthermore, the sub-steps of step (3) are as follows:

[0130] Step 3.1: For orbital integral, adaptive step-size integration is used instead of traditional fixed step-size integration, which is more suitable for stiff problems.

[0131] Step 3.2: For the libration integral, the adaptive step-size integral with time lag effect is used instead of the traditional fixed step-size integral to solve the difficulty of considering the time lag effect in the second-order ordinary differential equation of Euler angles;

[0132] Step 3.3, the orbital nuclear libration parameters with time tags are generated into an ephemeris file through the mkspk job in SPICE for subsequent use and reading.

[0133] Furthermore, the sub-steps of step (4) are as follows:

[0134] Step 4.1, using automatic differentiation to obtain derivatives, such as obtaining the derivative of the state quantity with respect to the parameter;

[0135] In step 4.2, a nonlinear solver is used to optimize the parameters instead of the least squares method.

[0136] In the method provided by the embodiment of the present invention, the more precise orbital dynamics is based on the scale of general relativity, and a post-Newtonian framework is used to calculate the gravitational force between particles. At the same time, the interaction between the shape of the moon and the planets in the solar system, as well as the influence of the shape of the earth and tides are strictly considered. In addition, since some calculations of the moon's double-layer libration parameters need to consider the time lag effect, this method introduces an adaptive integrator with a time lag effect, which is more suitable for solving rigid problems; the trust region method nonlinear solver based on automatic differentiation is suitable for complex nonlinear problems and can effectively process local optimal solutions.

[0137] The implementation basis of each embodiment of the present invention is to implement programmed processing through a device with a processor function. Therefore, in engineering practice, the technical solutions and functions of each embodiment of the present invention are encapsulated into various modules. Based on this reality, on the basis of the above embodiments, an embodiment of the present invention provides a lunar orbit and libration parameter solution and prediction system, which is used to execute a lunar orbit and libration parameter solution and prediction method in the above method embodiment.

[0138] See also Figure 5The system includes: a first main module, which is used to consider the particle gravity model under the post-Newtonian framework, the interaction between the lunar figure and the particles of other planets in the solar system, and the influence of the earth figure, and establish a high-precision lunar orbit dynamics model under the framework of general relativity; a second main module, which is used to consider the lunar moment of inertia and lunar torque, and establish a double-layer lunar libration attitude dynamics model; a third main module, which is used to predict the orbit parameters based on the lunar orbit dynamics model using an integrator with an adaptive step size when the initial conditions of the integration meet the preset accuracy, and to predict the libration parameters based on the double-layer lunar libration attitude dynamics model using an adaptive step size integrator with a time lag effect, so as to obtain the initial products of the orbit and libration parameters with time series labels; a fourth main module, which is used to process the historical observation data using a nonlinear solver based on automatic differentiation when the initial conditions of the integration do not meet the preset accuracy, so as to obtain the optimal solution of the parameters to be estimated in the initial conditions.

[0139] The present invention provides a lunar orbit and libration parameter calculation and prediction system, using Figure 5 By optimizing several modules in the system, such as the orbital dynamics, the establishment of the double-layer libration attitude mechanics model, the setting of the integrator and the setting of the parameter solver, the difference between the satellite and the internationally published ephemeris is reduced, and the purpose of high-precision prediction of orbit and libration parameters is achieved.

[0140] It should be noted that the system embodiment provided by the present invention is used to implement the methods in the above method embodiment as well as the methods in other method embodiments provided by the present invention. The only difference is that the corresponding functional modules are set. The principle is basically the same as the principle of the above system embodiment provided by the present invention. As long as the technical personnel in this field refer to the specific technical solutions in other method embodiments on the basis of the above system embodiment, obtain the corresponding technical means and the technical solutions composed of these technical means by combining the technical features, and on the premise of ensuring the practicality of the technical solutions, improve the modules in the above system embodiment to obtain the corresponding system class embodiments, which are used to implement the methods in other method class embodiments. For example:

[0141] Based on the content of the above system embodiment, as a preferred embodiment, a lunar orbit and libration parameter solution and prediction system provided in the embodiment of the present invention also includes: after obtaining the initial products of orbit and libration parameters with time series labels, the orbit and libration parameters with time series labels are generated as ephemeris files through mkspk in SPICE software.

[0142] Based on the same inventive concept as the above-mentioned embodiment, an embodiment of the present invention also provides a lunar orbit and libration parameter solution and prediction system, including a processor and a memory, the memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute the lunar orbit and libration parameter solution and prediction method.

[0143] Based on the same inventive concept as the above-mentioned embodiment, an embodiment of the present invention further provides a non-transitory computer-readable storage medium, wherein the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions enable the computer to execute the method for calculating and predicting the lunar orbit and libration parameters.

[0144] In summary, facing the challenge of high-precision lunar orbit and libration parameter predictions urgently needed for my country's current lunar exploration mission, existing methods have limitations in initial condition acquisition accuracy and parameter optimization, especially in the prediction accuracy of lunar libration parameters. The present invention proposes an innovative method, which optimizes the model of lunar orbit dynamics and lunar double-layer libration attitude dynamics, and introduces an adaptive integrator with time lag effect and a nonlinear solver based on automatic differentiation, aiming to optimize the various environments of the lunar orbit dynamics model and double-layer libration parameter prediction, thereby achieving higher-precision orbit and libration parameter predictions.

[0145] In the method of the present invention, the post-Newtonian effect is taken into account in the orbital dynamics model, and the lunar libration attitude model is established on the double-layer lunar mantle model; compared with the traditional integration method (such as: 8th order Runge-Kutta integration method), the key innovation of the present invention is that the adaptive integrator can effectively handle complex rigidity problems, especially the time delay effect that needs to be considered in the double-layer lunar libration model; at the same time, the nonlinear solver based on automatic differentiation effectively solves the shortcomings of the traditional least squares method in complex nonlinear problems, can calculate partial derivatives more accurately, and optimize the local optimal solution.

[0146] By applying the method provided by the present invention, the prediction accuracy of the lunar orbit and libration parameters is expected to be significantly improved. This will provide more accurate basic data for my country's future manned lunar landing and lunar scientific exploration missions, ensure the smooth execution of the missions, and further promote scientific progress and technological innovation in the field of lunar exploration in my country.

[0147] The terms "including" and "having" and any variations thereof in the specification and claims of the present invention and the above-mentioned drawings are intended to cover non-exclusive inclusions, for example, a process, method, system, product or apparatus comprising a series of steps or units is not necessarily limited to the steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to these processes, methods, products or apparatuses.

[0148] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating and predicting lunar orbit and libration parameters, characterized in that: include: Step 1: Considering the particle gravity model in the post-Newtonian framework, the interaction between the lunar figure and the particles of other planets in the solar system, and the influence of the earth figure, a high-precision lunar orbit dynamics model is established in the framework of general relativity; Step 2, considering the lunar moment of inertia and lunar torque, establish a double-layer lunar libration attitude dynamics model; Step 3: When the initial conditions of the integration meet the preset accuracy, the orbital parameters are predicted based on the lunar orbital dynamics model of step 1 by using an integrator with an adaptive step size, and the libration parameters are predicted based on the double-layer lunar libration attitude dynamics model of step 2 by using an adaptive step size integrator with a time lag effect, so as to obtain the initial products of orbital and libration parameters with time series labels; Step 4: When the initial conditions of the integration do not meet the preset accuracy, use a nonlinear solver based on automatic differentiation to process the historical observation data to obtain the optimal solution for the parameters to be estimated in the initial conditions, and return to step 3.

2. A method for calculating and predicting lunar orbit and libration parameters according to claim 1, characterized in that: After obtaining the initial products of orbital and libration parameters with time series labels, it also includes: The orbit and libration parameters with time series labels are generated as ephemeris files through mkspk in SPICE software.

3. The method for calculating and predicting lunar orbit and libration parameters according to claim 1, characterized in that: A high-precision lunar orbit dynamics model based on the general theory of relativity, including: Step 1.1, calculate the gravity of the particle under parameterized Newton: Among them, β and γ are post-Newtonian parameters. The particles that interact with the moon include the sun, the eight planets, and the asteroids with larger mass in the main belt. Step 1.2, calculate the interaction between the particle and the graphics: Among them, GM is the gravitational constant of the central body, and It represents the three-dimensional acceleration in the body-fixed coordinate system of the central celestial body, r, λ is the spherical coordinate of the particle to the central celestial body; n1 and n2 are the maximum order of the spherical harmonic coefficient expansion; is the Legendre polynomial of order n; is the Legendre polynomial of order n and degree m; J n It is a harmonic direction; C nm and S nm are the spherical harmonic coefficients.

4. The method for calculating and predicting lunar orbit and libration parameters according to claim 1, characterized in that: A double-layer lunar libration attitude dynamics model is established, including: Step 2.1, the moment of inertia of the lunar mantle includes rigid body, tidal distortion, spin distortion and the moment of inertia of the lunar core, as shown in the following formula: I m =I rigid +I tide +I spin +I c In the main axis system, the main moment of inertia of the rigid body is A <B<C, in: m m is the mass of the moon, R m is the radius of the moon, β L =(CA) / B,γ L =(BA) / C is the moon distance parameter, is the 2-degree band harmonic coefficient of the moon without distortion; The formulas for tidal distortion and spin distortion are shown below: Where ω=(ω x ,ω y ,ω z ), describes the angular velocity of the lunar mantle, and its calculation formula is calculated based on the instantaneous lunar mantle Euler angle provided in the background technology: also, k 2,M It is the love number of 2 degrees of the moon. is the position of the Moon relative to the Earth, n is the mean motion of the Moon; there is a time delay (tt m ), the calculation formula for the position of the moon relative to the earth is: The angular velocity of the lunar mantle is The lunar core is assumed to rotate like a solid and is restricted by the shape of the lunar core-mantle boundary. The formula for the calculation of the lunar core inertia matrix is: where α c is the dimensionless coefficient of the ratio of the nuclear to total polar moment of inertia, f c is the flattening of the lunar core; Step 2.2, Torque acting on the Moon's rotational motion Including: the gravitational interaction between the moon and the external point mass, and the torque generated by the flatness of the earth on the moon's shape. The total torque calculation formula is: The calculation formula for the torque generated by the single point mass acting on the moon and affecting the moon's shape is: in, is the force between the figure and the particle. The calculation formula for the acceleration generated is shown in step 1.

2. Corresponding to the three-dimensional acceleration in the body-fixed coordinate system of the central celestial body and is the position of the particle in the lunar body solid coordinate system, M p is the mass of the particle; Refers to the interaction between the Earth and Moon graphics, where the most influential part is retained, and its calculation formula is: Among them, R e is the radius of the Earth, J 2e is the J2 term of the Earth's gravitational field, m e is the mass of the Earth, It is the Earth-Moon connection. The direction of the Earth's polar axis, η, is defined as: Step 2.3, the time derivative expression of the lunar mantle Euler angular velocity is: The time derivative expression of the Euler angular velocity of the lunar core is: Among them, ω c is the angular velocity of the lunar core, which is calculated in a similar way to the angular velocity of the lunar mantle; is the torque generated by the interaction between the lunar mantle and the lunar core, given in the lunar mantle frame: is the friction parameter, 5. The method for calculating and predicting lunar orbit and libration parameters according to claim 1, characterized in that: The historical observation data is processed using a nonlinear solver based on automatic differentiation to obtain the optimal solution for the parameters to be estimated in the initial conditions, including: Obtain historical observation data and use automatic differentiation to perform derivation; Based on the derivative results, the nonlinear solver is used to optimize the parameters and obtain the optimal solution for the parameters to be estimated in the initial conditions.

6. A lunar orbit and libration parameter calculation and prediction system, characterized in that: Used to implement the lunar orbit and libration parameter solution and prediction method as described in any one of claims 1 to 5.

7. A lunar orbit and libration parameter calculation and prediction system according to claim 6, characterized in that: include: The first main module is used to consider the particle gravity model in the post-Newtonian framework, the interaction between the lunar figure and the particles of other planets in the solar system, and the influence of the earth figure, and to establish a high-precision lunar orbit dynamics model in the framework of general relativity; The second main module is used to establish a double-layer lunar libration attitude dynamics model by considering the lunar moment of inertia and lunar torque; The third main module is used to predict the orbital parameters based on the lunar orbit dynamics model by using an integrator with an adaptive step length when the initial conditions of the integration meet the preset accuracy, and to predict the libration parameters based on the double-layer lunar libration attitude dynamics model by using an adaptive step length integrator with a time lag effect, so as to obtain the initial products of the orbital and libration parameters with time series labels; The fourth main module is used to process the historical observation data using a nonlinear solver based on automatic differentiation to obtain the optimal solution of the parameters to be estimated in the initial conditions when the initial conditions of the integration do not meet the preset accuracy.

8. A lunar orbit and libration parameter calculation and prediction system, characterized in that: The method comprises a processor and a memory, wherein the memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute the method for calculating and predicting the lunar orbit and libration parameters as described in any one of claims 1 to 5.

9. A non-transitory computer readable storage medium, characterized in that: The non-transitory computer-readable storage medium stores computer instructions, and the computer instructions enable the computer to execute the method for calculating and predicting lunar orbit and libration parameters as described in any one of claims 1 to 5.

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