Method and system for solving and predicting lunar orbit and libration parameters

Abstract

The application discloses a lunar orbit and libration parameter solving and forecasting method and system, and the method comprises the following steps: considering the interaction among the mass point gravity model based on the post-Newtonian framework, the moon figure, other planet mass points in the solar system and the influence of the earth figure, a high-precision lunar orbit dynamics model is established under the general relativity framework; considering the lunar moment of inertia and the lunar torque, a double-layer lunar libration attitude dynamics model is established; when the initial conditions of integration meet the preset accuracy, an adaptive step integrator and an adaptive step integrator with time delay effect are used to respectively forecast the orbit parameters and the libration parameters, and initial products of the orbit and the libration parameters with time sequence labels are obtained; when the initial conditions of integration do not meet the preset accuracy, an automatic differentiation-based nonlinear solver is used to process historical observation data, and the optimal solution of the to-be-estimated parameters in the initial conditions is obtained, and re-forecasting is performed.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of lunar orbit and libration parameters determination and prediction in lunar exploration missions, and particularly relates to a more precise lunar orbit dynamics model and attitude dynamics model, a new method of using an adaptive integrator with time delay effect for prediction, and a nonlinear solver for parameter solving, and specifically relates to a lunar orbit and libration parameters determination and prediction method and system. BACKGROUND

[0002] Precise determination and prediction of lunar orbit and libration parameters are of great significance in lunar exploration missions. In addition to existing optical navigation and celestial navigation technologies, some scholars have proposed a method of using global satellite navigation system (GNSS) to enhance lunar navigation. Scientific objectives and technical processes have posed unprecedented challenges to the precision of lunar orbit and libration parameter determination and prediction.

[0003] Lunar orbit and libration parameters constitute important elements for describing the position, velocity and attitude of the moon, and the time series file composed of these elements is called ephemeris. Precise ephemeris files are the cornerstone of lunar exploration missions, and high-precision lunar orbit and libration parameter prediction provides a key solution for mission decision-making. Lunar orbit information mainly refers to six state components: three-dimensional position and velocity (x, y, z, vx, vy, vz); while lunar attitude is used to describe the rotation of the moon, which is mainly described by 12 libration parameters, referring to the Euler angles and Euler angle velocity components of the lunar mantle and 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 the orbit and libration parameters is based on high-precision orbit dynamics model and lunar double-layer attitude dynamics model, respectively. The prediction process starts from high-precision initial conditions, connects the dynamics models through the integration method, and finally obtains the predicted ephemeris. Generally, the high-precision initial conditions are obtained based on the processing of a large amount of historical observation data by the parameter solver. The specific process is as follows: first, starting from the initial orbit and libration parameters of the moon at a certain time, the orbit dynamics model and the libration attitude dynamics model of the moon are analyzed rigorously. The precise orbit dynamics model and the 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 the lunar libration information with a time tag. The output in the form of.bsp file through mkspk in SPICE can be read by any user to obtain ephemeris. If the accuracy of the initial conditions is limited, the parameter solver needs to be used to process a large amount of observation data to achieve the purpose of parameter optimization in the initial conditions.

[0004] In the current field of lunar orbit and libration parameter prediction, although the construction of the orbit dynamics model and the lunar double-layer attitude dynamics model has undergone a long period of optimization and update, the time delay effect of force under the framework of general relativity is still worth considering. As a method commonly used in the past orbit integration, the conventional 8th order Runge-Kutta integration, although it can more effectively handle complex and high-precision differential equation problems than the classical 4th order Runge-Kutta, cannot meet the needs of the double-layer lunar libration model that needs to consider the time delay of some calculation formulas for the part of the lunar libration integration. For more complex nonlinear problems, manual calculation of the derivative of the state with respect to the parameter and traditional least squares all show many shortcomings. SUMMARY

[0005] To overcome the shortcomings of the prior art, the present application provides a lunar orbit and libration parameter solving and prediction method and system, which optimizes multiple important links such as the establishment of orbit dynamics, double-layer libration attitude dynamics model, the setting of integrator and the setting of parameter solver, reduces the difference between the published ephemeris and the international ephemeris, and realizes the purpose of high-precision prediction of orbit and libration parameters.

[0006] According to one aspect of the present application, a lunar orbit and libration parameter solving and prediction method is provided, comprising:

[0007] Step 1: considering the interaction between the particle gravity model based on the post-Newtonian framework, the moon figure and the other planet particles in the solar system, the influence of the earth figure, establishing a high-precision lunar orbit dynamics model under the framework of general relativity;

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

[0009] Step 3, when the initial conditions of integration meet the preset accuracy, based on the lunar orbit dynamics model of step 1, an adaptive step integrator is used to predict the orbit parameters, and based on the double-layer moon libration attitude dynamics model of step 2, an adaptive step integrator with time delay effect is used to predict the libration parameters, to obtain the initial product of orbit and libration parameters with time sequence label;

[0010] Step 4, when the initial conditions of integration do not meet the preset accuracy, the historical observation data is processed using an automatic differentiation based nonlinear solver to obtain the optimal solution of the to-be-estimated parameters in the initial conditions, and returns to step 3.

[0011] As a further technical solution, after obtaining the initial product of orbit and libration parameters with time sequence label, it further includes:

[0012] The orbit and libration parameters with time sequence label are generated as ephemeris file by mkspk in SPICE software.

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

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

[0015]

[0016] Where β and γ are the post-Newtonian parameters, and the particles considered to interact with the moon include the sun, the eight major planets, and the small asteroids with large mass in the main belt;

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

[0018]

[0019] Where GM is the gravitational constant of the central celestial body, And 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 spherical harmonic coefficient expansion; is the n-order Legendre polynomial; is the n-order m-order Legendre polynomial; J n is the harmonic direction; C nm And S nm are spherical harmonic coefficients.

[0020] As a further technical solution, a two-layer lunar libration attitude dynamics model was 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 lunar distance parameter, is the 2-degree band harmonic coefficient of the moon without distortion;

[0029] The formulas for tidal distortion and spin distortion are as follows:

[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 moon's 2-degree love number. is the position of the Moon relative to the Earth, n is the mean motion of the Moon; there is a time delay due to tidal and spin distortion (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 constrained by the shape of the core-mantle boundary. The formula for the inertia matrix of the lunar core is:

[0035]

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

[0037] Step 2.2, the torque acting on the lunar rotation includes the gravitational interaction between the Moon and the external point mass, and the torque due to the lunar figure perturbed by the oblateness of the Earth. The total torque is given by:

[0038]

[0039] The torque due to the lunar figure perturbed by the external point mass is given by:

[0040]

[0041] where, is the force acting between the figure and the point mass, whose acceleration is given in Step 1.2, corresponds to the three-dimensional acceleration in the central body body-fixed coordinate system and is the position of the point mass in the lunar body-fixed coordinate system, M p is the mass of the point mass; denotes the interaction between the Earth figure and the Moon figure, where the most significant part is retained, and its formula is:

[0042]

[0043] where, 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, is the line connecting the Earth and the Moon, the Earth's polar axis pointing, 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 lunar core Euler angular velocity is:

[0047]

[0048] where ω c is the angular velocity of the lunar core, which is calculated in a similar way as the lunar mantle angular velocity; 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, the historical observation data is processed using an automatic differentiation-based nonlinear solver to obtain the optimal solution of the estimated parameters in the initial conditions, including:

[0052] The historical observation data is obtained, and automatic differentiation is used for derivation;

[0053] Based on the results of the derivation, a nonlinear solver is used to optimize the parameters to obtain the optimal solution of the estimated parameters in the initial conditions.

[0054] According to an aspect of the present application, a lunar orbit and libration parameter solving and forecasting system is provided for implementing the lunar orbit and libration parameter solving and forecasting method.

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

[0056] The first main module is used to consider the interaction between the particle gravity model based on the post-Newtonian framework, the moon figure and the other planets in the solar system, 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 consider the lunar moment of inertia and the lunar torque, and to establish a double-layer lunar libration attitude dynamics model.

[0058] The third main module is used to predict the orbit parameters based on the lunar orbit dynamics model using an adaptive step integrator 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 integrator with time delay effect, to obtain the initial product of the orbit and libration parameters with time sequence labels.

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

[0060] According to an aspect of the present application, a lunar orbit and libration parameter solving and forecasting system is provided, comprising a processor and a memory, the memory being configured to store program instructions, and the processor being configured to invoke the stored instructions in the memory to execute the lunar orbit and libration parameter solving and forecasting method.

[0061] According to an aspect of the present application, a non-transitory computer readable storage medium is provided, the non-transitory computer readable storage medium storing computer instructions, the computer instructions causing the computer to execute the lunar orbit and libration parameter solving and forecasting method.

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

[0063] 1. The present application combines multiple technical means to accurately forecast the lunar orbit and libration parameters, ensuring the smooth implementation of lunar exploration missions. Specifically, the present application optimizes the orbit dynamics model and the lunar double-layer attitude dynamics model, especially using an adaptive integrator and an automatic differentiation solver, to improve the accuracy and efficiency of the solution. In the adaptive integration process, the algorithm with time delay effect can better handle the complex changes of the lunar attitude, making the orbit and attitude prediction more accurate. Taking the solution of the lunar mantle Euler angles in the lunar libration as an example, the differences between the prediction results of the traditional least squares solution considering the lunar rigid body model and the DE430 released by JPL are given, with the unit being angular seconds, and the maximum difference being 0.5 angular seconds. Figure 3 The prediction results of the double-layer lunar libration refinement model combined with the nonlinear solver of the present application are given, with the unit being angular seconds, and the maximum difference being 0.25 angular seconds. Compared with the prior art, the present application has greatly improved performance, especially in the first two angles, with an order of magnitude improvement in accuracy. Figure 4

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

[0065] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings used in the embodiments or prior art description will be briefly described as follows. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0066] Figure 1 ​A flowchart of a lunar orbit and libration parameter solving and forecasting method provided by an embodiment of the present application is shown.

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

[0068] Figure 3 A comparison diagram between a prediction result of a rigid body model of the moon under traditional least square solving and DE430 published by JPL is shown for the prior art.

[0069] Figure 4 A prediction result diagram of a double-layer lunar libration refinement model combined with a nonlinear solver provided by an embodiment of the present application is shown.

[0070] Figure 5 A structure diagram of a lunar orbit and libration parameter solving and forecasting system provided by an embodiment of the present application is shown. DETAILED DESCRIPTION

[0071] The present application proposes a method for establishing a lunar orbit mechanical model and a double-layer lunar libration attitude model, uses an adaptive integrator with time delay effect to replace a traditional integrator to forecast lunar libration parameters, and uses an automatic differentiation-based nonlinear solver to optimize to-be-estimated parameters, aiming at the deficiencies of the prior art.

[0072] The present application optimizes multiple important links in the forecasting of lunar orbit and libration parameters, such as the establishment of an orbit dynamics model and a double-layer libration attitude dynamics model, the setting of an integrator, and the setting of a parameter solver. Specifically, the optimized orbit dynamics model and double-layer libration attitude dynamics model are more consistent with the force conditions of the moon; the adaptive integrator with time delay effect is not only more suitable for complex rigid problems, but also well fits the problem of time delay that needs to be considered in the double-layer lunar libration model; the automatic differentiation-based nonlinear solver efficiently and accurately calculates partial derivatives, solves the difficulty of derivative derivation in complex nonlinear problems, and the nonlinear solver effectively processes local optimal solutions in the face of complex nonlinear problems.

[0073] To make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application. In addition, the technical features in each embodiment or in a single embodiment provided by the present application can be combined with each other at will to form new technical solutions, and the combination is not restricted by the order of steps and / or structure composition mode, but should be based on the implementation by a person of ordinary skill in the art. When the combination of technical solutions appears contradictory or cannot be implemented, it should be considered that the combination of technical solutions does not exist and is not within the protection scope of the present application.

[0074] In the face of the situation that the difficulty of the lunar exploration mission is upgraded and a plurality of lunar scientific exploration missions will be carried out in China in the future, high-precision lunar orbit and libration parameter prediction is urgently needed as a cornerstone of the mission to ensure correct implementation of the decision and support effective processing of the exploration data. The method of the present application optimizes a plurality of important links such as establishment of an orbit dynamics model, a double-layer libration attitude dynamics model, setting of an integrator and setting of a parameter solver, reduces the difference between the method and internationally published ephemeris, and achieves the purpose of high-precision prediction of the orbit and the libration parameters.

[0075] Figure 1 The flowchart of the lunar orbit and libration parameter solving and prediction in the present application mainly consists of four modules.

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

[0077] Secondly, establishment of a celestial dynamics model, which is divided into two parts of orbit and libration. In the orbit dynamics, the gravity of a mass point is optimized mainly by relying on a general relativity rule; the libration attitude dynamics model is mainly established on the basis of a double-layer model of the moon.

[0078] The integrators for orbit integration and libration integration are self-adaptive step integrators, which can well adapt to the rigid problem, but the difference is that the libration attitude dynamics model uses a self-adaptive integration model with time delay effect, which can better meet the difficulty of considering time delay in the second-order ordinary differential calculation formula of the libration Euler angle.

[0079] Finally, a solver module, which adopts a nonlinear optimal solution method based on automatic differentiation, is high in efficiency and fast, and is more suitable for complex nonlinear problems.

[0080] Figure 2 The relationship between the lunar body-fixed and inertial ICRF (in blue in the figure) is shown, along with the definition of the Euler angles. Note that in this step:

[0081] Euler angles ( θ m and ψ m are the core parameters to establish the direction model of the lunar exterior (including the lunar mantle and the lunar core), which link the mantle rotating with the moon as the center to the inertial system. The Euler angles that define the rotation from the lunar principal axis (PA) coordinate system to the inertial ICRF coordinate system are: is the intersection of 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 and the mantle equator to the prime meridian along the mantle equator. r PA is the position vector of the lunar principal axis in the coordinate, then it is converted to the coordinate vector of r I in the inertial coordinate system, which can be realized by:

[0082]

[0083] where the rotation matrices R x , R y and R z are right-hand rotations of the coordinate system directions, defined as:

[0084]

[0085] As a preferred embodiment, referring to FIG. 1, the method of the embodiment of the present application comprises the following steps: Figure 1

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

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

[0088] (3) Use an adaptive step integrator and an adaptive step integrator with time delay effect to predict the orbit and libration parameters respectively, to obtain the initial products of the orbit and libration parameters with time sequence labels.

[0089] (4) Output as a.bsp file in SPICE to obtain ephemeris supporting reading by any user. ​

[0090] (5) When the initial condition of integration is not accurate enough, the optimal solution of the parameters to be estimated in the initial condition is obtained by processing a large amount of historical observation data using an automatic-differentiation-based nonlinear solver, and then steps (3)-(5) are repeated.

[0091] Further, the high-precision lunar orbit dynamics model under the general relativity framework in step (1) is calculated in the following sub-steps:

[0092] Step 1.1, calculation of the particle gravity based on the post-Newtonian parameters:

[0093]

[0094] where β and γ are post-Newtonian parameters, and the particles that need to be considered for interaction with the Moon include the Sun, the eight major planets, and the small asteroids with large mass in the main belt.

[0095] Step 1.2, interaction between particles and figures

[0096]

[0097] where GM is the gravitational constant of the central celestial body, and denote 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 n-order Legendre polynomial; is the n-order m-order Legendre polynomial; J n is the harmonic direction; C nm and S nm are the spherical harmonic coefficients.

[0098] Further, the double-layered Moon model establishment in step (2) is as follows:

[0099] Step 2.1, the inertia tensor of the lunar mantle contains four parts, i.e., the rigid body, tidal distortion, spin distortion, and the inertia tensor of the lunar core, as shown in the following formula:

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

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

[0102]

[0103] where:

[0104]

[0105] m m is the mass of the Moon, R m is the radius of the Moon, β L = (C - A) / B, γ L = (B - A) / C is the lunar distance parameter, is the lunar non-tidal 2-degree zonal coefficient.

[0106] The formulae for tidal and spin distortions are as follows:

[0107]

[0108] where ω = (ω x , ω y , ω z ), describing the lunar mantle angular velocity, which is calculated from the instantaneous lunar mantle Euler angles provided in the background art:

[0109]

[0110] In addition, k 2,M is the lunar 2-degree Love number. is the position of the Moon with respect to the Earth, n is the mean motion of the Moon. Tidal and spin distortions are delayed in time (t - t m ), so the position of the Moon with respect to the Earth and the mantle angular velocity need to take into account the time delay, the position of the Moon with respect 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 subject to the shape of the core-mantle boundary (CMB), the formula for the calculation of the inertia matrix of the lunar core is:

[0112]

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

[0114] Step 2.2, the moment of force acting on the rotational motion of the Moon Generally divided into two categories: the gravitational interaction between the Moon and external point mass (object) and the gravitational interaction between the Moon and external point mass (object), and the moment of force generated by the influence of the flattening of the Earth on the figure of the Moon, i.e. the moment of force of the point mass on the lunar surface and the moment of force of the lunar surface-lunar surface. The formula for calculating the total torque is:

[0115]

[0116] The moment of the single point mass acting on the Moon is given by:

[0117]

[0118] where, is the force acting between the figure and the point mass, whose acceleration is given by step 1.2, corresponds to the three-dimensional acceleration in the central body's body-fixed coordinate system and is the position of the point mass in the Moon's body-fixed coordinate system, M p is the mass of the point mass.

[0119] denotes the interaction between the Earth figure and the Moon figure, where the most significant part is retained, and is given by:

[0120]

[0121] where, 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, is the geodesic connecting the Earth and the Moon, the Earth's polar axis pointing, η is defined as:

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

[0123]

[0124] The time derivative expression of the Euler angular velocity of the Moon's core is:

[0125]

[0126] where, ω c is the angular velocity of the Moon's core, which is calculated in a similar manner to the Moon's mantle angular velocity. is the torque generated by the interaction between the Moon's mantle and the Moon's core. It is given in the Moon's mantle frame:

[0127]

[0128] is the friction parameter,

[0129] Further, step (3) is divided into the following sub-steps:

[0130] Step 3.1, for the orbit integral, the adaptive step-size integrator is used instead of the traditional fixed step-size integrator, which is more suitable for rigid problems;

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

[0132] Step 3.3, the obtained orbit kernel libration parameters with time label are generated into ephemeris files through mkspk work in SPICE for subsequent use and reading.

[0133] Further, the step (4) is divided into the following sub-steps:

[0134] Step 4.1, the derivative is obtained by using automatic differentiation, for example, the derivative of the state quantity with respect to the parameter;

[0135] Step 4.2, the parameter is optimized by using a nonlinear solver instead of a least square method.

[0136] In the method provided by the embodiment of the application, more precise orbit dynamics is based on the scale of general relativity, the post-Newtonian framework is used to calculate the gravity between particles, and the interaction between the moon shape and the solar system planets, and the influence of the earth shape and the tide are strictly considered. In addition, in view of the fact that the partial calculation of the moon double-layer libration parameters needs to consider the time lag effect, the adaptive integrator with time lag effect is introduced, 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 application is that the processing is realized by the device with the processor function. Therefore, in engineering practice, the technical solutions and functions of each embodiment of the application are packaged into various modules. Based on this actual situation, on the basis of each embodiment described above, the embodiment of the application provides a moon orbit and libration parameter solving and forecasting system, which is used to execute the moon orbit and libration parameter solving and forecasting method in the method embodiment.

[0138] Reference is made to Figure 5The system comprises: a first main module for establishing a high-precision lunar orbit dynamics model under the framework of general relativity by considering the interaction between the mass point gravity model under the post-Newtonian framework, the moon figure and other planet mass points in the solar system, the influence of the earth figure; a second main module for establishing a double-layer lunar libration point attitude dynamics model by considering the lunar moment of inertia and the lunar torque; a third main module for, when the initial conditions of integration meet the preset accuracy, predicting the orbit parameters by using an adaptive step integrator based on the lunar orbit dynamics model, and predicting the libration parameters by using an adaptive step integrator with time lag effect based on the double-layer lunar libration point attitude dynamics model, to obtain initial products of the orbit and libration parameters with time sequence labels; and a fourth main module for, when the initial conditions of integration do not meet the preset accuracy, processing the historical observation data by using an automatic differentiation-based nonlinear solver to obtain the optimal solution of the to-be-estimated parameters in the initial conditions.

[0139] The system for solving and predicting lunar orbit and libration parameters provided in the embodiment of the application adopts Figure 5 several modules in the system, and optimizes multiple important links such as the establishment of the orbit dynamics and double-layer libration point attitude dynamics models, the setting of the integrator and the setting of the parameter solver, so as to reduce the difference from the internationally published ephemeris and achieve the purpose of predicting the orbit and libration parameters with high accuracy.

[0140] It should be noted that the system embodiments provided in the application are used to implement the methods in the method embodiments and are also used to implement the methods in other method embodiments provided in the application, the difference is only that corresponding function modules are set, the principle is basically the same as that of the above-mentioned system embodiments provided in the application, as long as the technical personnel in the art improve the modules in the above-mentioned system embodiments by combining technical features to obtain corresponding technical means and technical solutions composed of these technical means on the premise of ensuring the practicability of the technical solutions, the corresponding system embodiments are obtained, which are used to implement the methods in other method embodiments. For example:

[0141] Based on the content of the above-mentioned system embodiments, as a preferred embodiment, the system for solving and predicting lunar orbit and libration parameters provided in the embodiment of the application further comprises: after obtaining the initial products of the orbit and libration parameters with time sequence labels, generating the orbit and libration parameters with time sequence labels into ephemeris files by using mkspk in the SPICE software.

[0142] Based on the same inventive concept as the above embodiments, the present embodiment also provides a lunar orbit and libration parameter solving and forecasting system, comprising 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 solving and forecasting method.

[0143] Based on the same inventive concept as the above embodiments, the present embodiment also provides a non-transitory computer readable storage medium, which stores computer instructions, and the computer instructions make the computer execute the lunar orbit and libration parameter solving and forecasting method.

[0144] In summary of the above embodiments, in the face of the challenge of the urgent need for high-precision lunar orbit and libration parameter forecasting in China's current lunar exploration mission, the existing method has limitations in the accuracy of initial condition acquisition and parameter optimization, especially in the prediction accuracy of lunar libration parameters. The present application proposes an innovative method, which optimizes the model of lunar orbit dynamics and lunar double-layer libration attitude dynamics, introduces an adaptive integrator with time delay effect and an automatic differentiation-based nonlinear solver, aiming to optimize each environment of the lunar orbit dynamics model and double-layer libration parameter forecasting, so as to realize higher-precision orbit and libration parameter forecasting.

[0145] In the method of the present application, the post-Newtonian effect is considered in the orbit dynamics model, and the lunar libration attitude model is established on the basis of the double-layer lunar mantle model. Compared with the traditional integral method (such as 8-order Runge-Kutta integral method), the key innovation of the present application is that the adaptive integrator can effectively handle complex rigid problems, especially the time delay effect that needs to be considered in the lunar double-layer libration model. At the same time, the automatic differentiation-based nonlinear solver effectively solves the shortcomings of the traditional least squares method in complex nonlinear problems, can more accurately calculate the partial derivative, and optimizes the local optimal solution.

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

[0147] The terms "comprise" and "have" and any variations thereof in the specification and claims of the present application and the above drawings are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device comprising a series of steps or units does not have to be limited to the steps or units clearly listed, but can include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0148] Finally, it should be noted that the above examples are only used to illustrate the technical solutions of the present application, and are not intended to limit the same; although the present application has been described in detail with reference to the foregoing examples, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing examples, or make equivalent replacements for part or all of the technical features thereof; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present application.

Claims

1. A method for calculating and predicting lunar orbit and libration parameters, characterized in that: include: Step 1: Considering the point-mass gravity model in the post-Newtonian framework, the interaction between the lunar figure and the other planetary masses in the solar system, and the influence of the Earth figure, a high-precision lunar orbital dynamics model is established in the framework of general relativity. Step 2: Considering the lunar moment of inertia and lunar torque, a double-layer lunar libration attitude dynamics model is established; Step 3: When the initial conditions of the integration meet the preset accuracy, the orbital parameters are predicted using an adaptive step-size integrator based on the lunar orbital dynamics model of Step 1. The libration parameters are also predicted using an adaptive step-size integrator with a time lag effect based on the dual-layer lunar libration attitude dynamics model of Step 2. Initial products of the orbital and libration parameters with time series labels are obtained. 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 of 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 using 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: Where β and γ are post-Newtonian parameters. The particles interacting with the Moon include the Sun, the eight planets, and the asteroids with larger masses in the main belt. A, B, and C are the indices of the celestial bodies involved in the calculation of acceleration interactions. pm indicates that the force between particles is being calculated. C is the speed of light. v A ,v B are the velocity scalars of celestial body A and celestial body B respectively; V A ,V B are the velocity vectors of celestial body A and celestial body B respectively; a B is the acceleration of celestial body B; 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 orders of the spherical harmonic coefficient expansion; is a 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 is the spherical harmonic coefficient; R is the radius of the celestial body; is the nth order and mth degree Legendre polynomial with respect to the independent variable The first derivative of ; is the nth order 0th degree Legendre polynomial with respect to the independent variable The first derivative of ; as well as They are The trigonometric functions of sine, cosine, and secant.

4. The method for calculating and predicting lunar orbit and libration parameters according to claim 1, wherein: Establish a two-layer lunar libration attitude dynamics model, 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 lunar distance parameter, is the 2-degree band harmonic coefficient of the moon without distortion; The formulas for tidal distortion and spin distortion are as follows: 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 moon's 2-degree love number. is the position of the Moon relative to the Earth, n is the mean motion of the Moon; there is a time delay due to tidal and spin distortion (tt m ), the calculation formula for the position of the moon relative to the earth is: The angular velocity of the lunar mantle is t is the current time, t m is the lunar tidal spin delay time parameter, r is the moon relative to the earth at tt m Position at the moment, m e is the mass of the Earth, R M is the radius of the moon, (φ m ,θ m ,ψ m ) is the three-dimensional lunar mantle Euler angle, is the three-dimensional lunar mantle Euler angular velocity, is the differential of the three-dimensional Euler angle with respect to time; The lunar core is assumed to rotate like a solid and is constrained by the shape of the lunar core-mantle boundary. The formula for 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 This includes the gravitational interaction between the Moon and external point masses, as well as the torque caused by the Earth's flatness affecting the Moon's shape. The total torque is calculated as: The formula for calculating the torque generated by a single point mass acting on the moon and affecting the moon's shape is: in, is the force between the figure and the particle, Corresponding to the three-dimensional acceleration in the central celestial body fixed coordinate system and is the position of the particle in the lunar body solid coordinate system, M p is the mass of the particle; It 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 average radius of the Earth, is the position vector from the moon to the earth, R e is the radius of the Earth, J 2e is the J2 term of the Earth's gravity field, m e is the mass of the Earth, It's the Earth-Moon line. 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: I m is the moment of inertia of the lunar mantle, is the differential of the lunar mantle moment of inertia with respect to time is the Euler angular velocity of the lunar core; 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 as: 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: 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 claimed 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 two-layer lunar libration attitude dynamics model considering the lunar moment of inertia and lunar torque; The third main module is used to predict the orbital parameters using an adaptive step-size integrator based on the lunar orbital dynamics model when the initial conditions of the integration meet the preset accuracy. It also predicts the libration parameters using an adaptive step-size integrator with a time lag effect based on the dual-layer lunar libration attitude dynamics model, thereby obtaining initial orbital and libration parameter products with time series labels. The fourth main module is used to process 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.

8. 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 lunar orbit and libration parameter calculation and prediction method according to any one of claims 1 to 5.

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