Lunar balance dynamic parameter high-precision resolving method and system combining LRR and LLR technologies

Abstract

The invention discloses a lunar balance dynamic parameter high-precision resolving method and system combining LRR and LLR technologies, and belongs to the field of deep space exploration and celestial body dynamics, and the method comprises the steps: constructing an LRR and LLR combined observation data set, and carrying out the preprocessing; constructing an LRR and LLR combined moon measurement model, and deducing a partial derivative of the model for a moon rotation parameter and a tidal LOVE number to obtain a combined partial derivative matrix; iterative solution is carried out through nonlinear least square to obtain dynamic parameters of the moon balance; and evaluating a resolving result and optimizing a resolving strategy, and optimizing a resolving scheme by dynamically adjusting the weight, improving a tide model and eliminating abnormal values. According to the method, the parameter calculation error is reduced, the technical advantages of two types of data are effectively integrated, the problem of insufficient observation continuity or precision of a single data source is solved, and reliable parameter support is provided for moon rotation and internal structure research.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of deep space exploration and celestial mechanics, and particularly relates to a lunar libration parameter high-precision calculation method and system combining LRR and LLR technologies. BACKGROUND

[0002] The accurate determination of lunar libration parameters plays an extremely important role in lunar science and exploration. These parameters can provide key information about the internal structure of the moon. For the moon, accurate libration parameters can provide information about the lunar tidal response, tidal dissipation, and the interaction of the core / mantle interface, providing key evidence for the composition of the lunar core. In addition, accurately calculating the lunar rotation, libration, and tidal parameters is also of great significance for improving the landing accuracy of the lander. Therefore, improving the calculation accuracy of lunar libration parameters not only helps to deepen the understanding of the internal structure of the moon, but also provides key technical support for lunar exploration activities.

[0003] Currently, the calculation of lunar libration parameters mainly relies on ground-based lunar laser ranging (LLR) technology. However, this traditional method has many defects.

[0004] 1. Greatly affected by lunar surface environmental factors: The laser reflection prism group is arranged on the lunar surface, lacks equipment maintenance and updates, and is subjected to erosion of various environmental factors on the lunar surface and covering by lunar dust for decades, which inevitably causes a large degree of degradation of its reflection ability. In addition, the influence of moonquakes and other factors, as well as the harsh weather on the lunar surface, will introduce certain errors or blockages to the laser beam in the laser ranging data.

[0005] 2. Weak signal and few returned photons: Due to the very long distance between the moon and the earth, combined with the fact that the laser beam is easily dispersed by atmospheric turbulence in the propagation process, the diffraction effect of the reflecting mirror and the attenuation of the laser emission instrument components also weaken the laser intensity, resulting in very weak laser signals reaching the earth, and very few returned photons received by the ground station, making it difficult to calculate the number of true photons contained therein.

[0006] 3. Unable to observe during full moon and new moon: Laser ranging has the problem of uneven distribution of moon phase angle measurement data, i.e., it cannot accurately observe during full moon and new moon. During full moon, the sun's light directly strikes the lunar surface, and the background noise is too strong, severely reducing the data signal-to-noise ratio; during new moon, it is difficult to accurately locate using a telescope, and the working time is short, making it difficult to successfully observe.

[0007] 4. The influence of lunar libration: Lunar libration is a real spatial swing of the moon. The observation data of LLR is the main source of estimating lunar libration. Affected by libration, the lunar surface reflecting prism cannot keep facing the earth all the time. The distance between different angle reflectors in the prism group and the ground station will be different. When the ground station receives the returned photons, it cannot know which angle reflector they come from. Therefore, the deviation of reflector distance will cause a ranging uncertainty of 24-75 mm in the data.

[0008] 5. Low observation efficiency and poor continuity: There are less than 10 ground stations worldwide that can carry out lunar laser ranging. The influence of visible light in the daytime also limits the distribution of observation time, making the observation time interval smaller. In addition, the observation efficiency of low-latitude laser ranging stations is significantly higher than that of high-latitude stations, but most of the qualified laser ranging ground stations are distributed in middle and high latitudes, resulting in low observation efficiency. At the same time, the requirements for measurement direction and observation environment of this technology are relatively high, so it is difficult to achieve relative continuity of observation data in a single observation arc segment, which is not conducive to the continuous monitoring of the Earth-moon space motion and the study of short-time variation effects of dynamic physical parameters.

[0009] Compared with traditional laser ranging technology, the Earth-moon radio ranging technology (LRR) has unique advantages, and the combination of the two technologies can further improve the accuracy. LRR technology can theoretically achieve all-weather observation, has high observation efficiency, and has less demanding requirements for stations. There are enough ground stations, and relying on China's global deep space network and perfect VLBI network, the signal strength and observation accuracy can reach the same level as laser ranging. In addition, LRR technology has better continuity when observing the moon, which is more conducive to the study of short-time variation effects of dynamic physical parameters in the Earth-moon distance. In contrast, LLR technology has obvious defects in observation continuity. LRR technology also has the advantages of high observation efficiency, easy signal reception and processing, large number of ground stations, easy operation, rich data types, and good measurement continuity. SUMMARY

[0010] The application aims to solve the problems of traditional single lunar ranging technology (such as single LLR observation continuity affected by weather shielding, single LRR ranging accuracy limitation) in lunar rotation parameter solving, and provide a lunar libration parameter high-precision solving method combining LRR and LLR technology, utilize the earth-moon radio ranging (LRR) data (such as microwave ranging data of Chang'e-3 lunar lander measured by Kashi and Jiamusi deep space stations) and ground-based lunar laser ranging (LLR) data (such as high-precision laser ranging data of moon surface reflector measured by French GRSM station and Changchun CHAL station), through a series of data processing and calculation methods such as joint lunar ranging model construction, target parameter partial derivative derivation and nonlinear least square joint solving, improve the solving accuracy of lunar rotation parameters (rotation axis right ascension, declination, rotation angular velocity, etc.) and tidal LOVE numbers, and significantly improve the accuracy and reliability of lunar dynamics key parameter solving.

[0011] According to an aspect of the present application, a lunar libration parameter high-precision solving method combining LRR and LLR technology is provided, comprising:

[0012] Constructing an LRR and LLR joint observation data set and performing preprocessing;

[0013] Based on the preprocessed results, constructing an LRR and LLR joint lunar ranging model;

[0014] Deriving the partial derivative of the LRR and LLR joint lunar ranging model with respect to the lunar rotation parameters and tidal LOVE numbers, and constructing a joint partial derivative matrix;

[0015] Based on the joint partial derivative matrix and the lunar-ear distance calculated value obtained according to the LRR and LLR joint lunar ranging model, performing iterative solving by nonlinear least square to obtain the lunar libration parameters.

[0016] Further, constructing an LRR and LLR joint observation data set and performing preprocessing comprises:

[0017] The LRR and LLR joint observation data set comprises multi-source observation data, ground stations, moon surface target positions and lunar physical parameters;

[0018] The multi-source observation data is subjected to time reference unification and noise filtering, the coordinates of the ground stations are subjected to coordinate system conversion, the moon surface target positions are subjected to tidal displacement correction and inertial system coordinate conversion, and the lunar physical parameters comprise lunar rotation parameters and tidal LOVE numbers.

[0019] Further, based on the preprocessed results, constructing an LRR and LLR joint lunar ranging model comprises:

[0020] Construct a joint lunar observation model using LRR and LLR, with the following expression:

[0021] ,

[0022] in, These are the calculated values ​​for the LLR component in the joint lunar observation model. For the ground station and the lunar reflector respectively and The position vector difference in the J2000 inertial frame at any given moment; These are the calculated values ​​for the LRR component in the joint lunar observation model. For the ground station and the lunar lander respectively and The position vector difference in the J2000 inertial frame at time t; where, , , , Obtained through optical travel time calculation.

[0023] Furthermore, the partial derivatives of the LRR and LLR joint lunar model with respect to the lunar rotation parameters are derived, including:

[0024] ,

[0025] ,

[0026] in, This represents the combined lunar observation model of LRR and LLR; This represents the rotation parameter of the i-th moon; for The position vector of the lunar probe in the lunar-solid system at any given moment; For lunar probes and ground stations and The position vector difference in the J2000 inertial frame at any given moment; correspond The rotation matrix from the J2000 inertial frame to the lunar-fixed frame at time t. This is the lunar rotation parameter matrix.

[0027] Furthermore, the partial derivatives of the LRR and LLR joint lunar measurement model with respect to the tidal LOVE number are derived, including:

[0028] ,

[0029] ,

[0030] in,

[0031] ,

[0032] ,

[0033] wherein, represents a radial tidal LOVE number, represents a tangential tidal LOVE number, is a second-order elastic tidal displacement correction term at a time instant, corresponds to is a rotation matrix of the moon body to the J2000 inertial system at a time instant; is a mass of the tide-raising body, is a radius of the moon, is a mass of the moon, is a mass of the moon, is a distance from the moon to the tide-raising body at a time instant, and are direction vectors of the moon pointing to the lunar surface reflector and the lunar lander and the tide-raising body at a time instant, respectively. Further, based on the joint partial derivative matrix and the calculated value of the moon-earth distance according to the LRR and LLR joint moon-measuring model, a nonlinear least square is used for iterative calculation to obtain the lunar libration parameters, including:

[0034] A joint residual vector is constructed:

[0035]

[0036]

[0037] wherein , are one half of the actual observation values of the LLR and LRR, respectively, , are the corresponding theoretical calculated values of the LLR and LRR, respectively, is a joint residual vector;

[0038] Based on the right ascension and declination of the moon's rotation axis in the J2000 inertial system, the moon's meridian longitude, the rotation speed of the moon's rotation axis, the radial tidal LOVE number, and the tangential tidal LOVE number, the lunar libration parameters are obtained;

[0039] The lunar libration parameters are iteratively solved by least square in combination with the prior weight matrix and the joint residual vector until convergence.

[0040] Further, the lunar libration initial parameters are iteratively solved by least square, including:

[0041] The lunar libration parameters are initialized as the starting point of iteration;

[0042] ​​Using the lunar libration parameters of the current iteration, the theoretical calculation values corresponding to the LLR and LRR are recalculated, the residual and joint residual vectors of the current iteration are obtained, and the lunar libration parameter update value is obtained by solving through least square iteration;

[0043] When the residual change of the current and previous iterations is less than a set value, the iteration is stopped to obtain the final lunar libration parameters.

[0044] According to an aspect of the present application, a lunar libration parameter high-precision solving system combining LRR and LLR technologies is provided, comprising:

[0045] A preprocessing module is configured to construct an LRR and LLR joint observation data set and perform preprocessing;

[0046] A lunar distance calculation value module is configured to construct an LRR and LLR joint moon measurement model based on the preprocessed results;

[0047] A partial derivative module is configured to derive the partial derivative of the LRR and LLR joint moon measurement model with respect to the lunar rotation parameters and tidal LOVE numbers, and construct a joint partial derivative matrix;

[0048] An iterative solving module is configured to perform iterative solving by using nonlinear least squares based on the joint partial derivative matrix and the lunar distance calculation value obtained according to the LRR and LLR joint moon measurement model, so as to obtain the lunar libration parameters.

[0049] According to an aspect of the present application, an electronic device is provided, comprising a memory and a processor, the memory stores a computer program, and the processor implements the steps of the lunar libration parameter high-precision solving method combining LRR and LLR technologies when executing the computer program.

[0050] According to an aspect of the present application, a computer readable storage medium is provided, which stores a computer program, and the computer program implements the steps of the lunar libration parameter high-precision solving method combining LRR and LLR technologies when executed by a processor.

[0051] Compared with the prior art, the present application has the following beneficial effects:

[0052] 1、The present application integrates LRR and LLR observation data, synchronously collects the body-fixed coordinate of the ground station and the lunar target, the lunar shape model and the physical parameters (radius, gravity parameters, etc.), and provides a high-quality data basis for joint solving through time reference unification, light travel time correction and other preprocessing, thereby solving the problem of insufficient observation continuity or precision of a single data source.

[0053] 2, The application is based on the position vector difference of the ground station and the lunar target in the J2000 inertial system, constructs a unified LRR and LLR joint lunar measurement model, takes the lunar rotation parameters and tidal LOVE number as core to-be-solved parameters. The model is linearized through Taylor expansion, the partial derivatives of the model to each parameter (including the derivative of the rotation matrix of the rotation parameter, the displacement correction derivative of the tidal parameter) are derived, the global partial derivative matrix is formed, the key gradient information is provided for the nonlinear least square solution, and the sensitivity and stability of the parameter solution are improved.

[0054] 3, The application adopts an iterative weighted nonlinear least square algorithm, fuses LRR ranging / velocity residual error and LLR ranging residual error, dynamically allocates the weights of the two types of data (based on the noise level of each type) through a priori weight matrix, and iteratively solves the parameter correction number until convergence. After the solution, the parameter accuracy is evaluated through the covariance matrix, the initial value and the iteration threshold are optimized combined with the lunar dynamics theory, and the parameter solution error is further reduced, effectively integrating the technical advantages of the two types of data, solving the precision bottleneck of a single technology under complex observation conditions, and providing reliable parameter support for the study of lunar rotation and internal structure. BRIEF DESCRIPTION OF DRAWINGS

[0055] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed in the embodiment or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and those skilled in the art can also obtain other drawings according to these drawings without creative labor.

[0056] Figure 1 The flow chart of the high-precision lunar libration parameter solution method provided by the combined LRR and LLR technology of the present application.

[0057] Figure 2 The schematic diagram of the prior residual error, posterior residual error and reference residual error solved by each station provided by the present application.

[0058] Figure 3 The schematic diagram of the direct correlation coefficient matrix of the solved parameters provided by the present application. DETAILED DESCRIPTION

[0059] The existing lunar libration parameter solving technology is difficult to meet the demand for high-precision lunar dynamics parameters, and the joint microwave ranging and velocity measurement and laser ranging data has great potential in improving the solving precision but has not been effectively applied. Through simulation analysis, the results show that the true error / formal error of joint solving of ground-based radio ranging and laser ranging data is reduced by about 1 order of magnitude, that is, the ground-based lunar radio ranging technology can effectively improve the further accurate solving of lunar rotation, libration and tidal physical parameters. Therefore, an urgent need exists for a method of joint microwave ranging and velocity measurement and laser ranging to improve the lunar libration parameter solving precision, to improve the precision and reliability of lunar dynamics parameter determination, to ensure the smooth progress of the subsequent lunar exploration project, and to provide technical support for the study of lunar internal structure.

[0060] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of the present application.

[0061] Specifically, as shown in Figure 1 The embodiments of the present application propose a lunar libration parameter high-precision solving method combining LRR and LLR technology, including: using the joint observation data of LRR and LLR, combining the lunar shape model, ground station and lunar target coordinate data (body-fixed coordinate system data) and lunar physical parameters (such as lunar radius, gravity parameters), performing tidal displacement correction of lunar target position and inertial coordinate conversion. By constructing a unified LRR and LLR joint lunar observation model in J2000 inertial system, the partial derivatives of the model to the lunar rotation parameters (rotation axis right ascension, declination, rotation angular velocity, etc.) and tidal LOVE numbers are derived, the fusion of LRR and LLR data is realized, and the nonlinear least squares algorithm is used to accurately solve the lunar rotation parameters. The accuracy of lunar rotation parameter solving (such as the formal error of rotation axis right ascension and declination) is significantly improved, and the true error / formal error is reduced by about 1 order of magnitude on average, providing more accurate lunar dynamics parameter support for lunar exploration missions.

[0062] Specifically, the embodiment of the present application provides a method for constructing a combined observation data set of LRR and LLR, including multi-source observation data collection and preprocessing. First, high-precision lunar shape model data, ground station (such as French GRSM station, Changchun CHAL station, Kashi station and Jiamusi station) and lunar target (lunar reflector LRRR and Chang'e-3 lander) coordinate data in the body-fixed coordinate system are collected. Second, microwave ranging and velocity data of the lunar lander are obtained by using LRR technology, and high-precision laser ranging data of the lunar reflector are obtained by using LLR technology. The multi-source observation data are preprocessed by time reference unification and noise filtering, so as to improve the data quality and facilitate subsequent joint model construction.

[0063] Specifically, the combined observation data set of LRR and LLR is constructed, including: collecting LRR data (such as microwave ranging and velocity data of the Chang'e-3 lunar lander obtained by Kashi and Jiamusi deep space stations) and LLR data (such as high-precision laser ranging data of the lunar reflector LRRR obtained by French GRSM station and Changchun CHAL station), synchronously obtaining the ground station coordinates in the earth-fixed system, the lunar target coordinates in the lunar-fixed system and the lunar physical parameters (gravitational parameters , radius R = 1738 km).

[0064] Specifically, the basic data and observation parameters are collected, and the coordinates of the ground stations participating in the observation and the equipment parameters are collected. The LLR selects French GRSM station and Chinese Changchun CHAL station, and the LRR simulates the radio data from the Chang'e-3 lander to the Kashi deep space station and the Jiamusi deep space station. The lunar-fixed system coordinates and attributes of the lunar observation target are determined. The reference resolution configuration of the ground station coordinates in the earth-fixed system is shown in Table 1.

[0065] Table 1 Resolution configuration information

[0066] Specifically, the combined observation data of LRR and LLR is preprocessed, specifically, the observation equation is constructed and the light travel time correction is performed. All observation times are converted from UTC to TDB time scale by using IERS Conventions model, and finally the preprocessed observation values are obtained. The observation models of the two kinds of observation data are the same, which are both two-way ranging models, and the observation equation is:

[0067]

[0068] wherein, represents the distance between the ground station and the lunar probe, and c represents the speed of light. represents the time when the ground station receives the downlink signal under the Coordinated Universal Time (UTC), (UTC) indicates the time when a ground station transmits an uplink signal under UTC. (TDB) represents the time when the ground station receives the downlink signal under Barycentric Dynamic Time (TDB). (TDB) indicates the time when the ground station transmits the uplink signal under TDB. It should be noted that... It is actually twice the distance between the ground station and the lunar probe. Half of that is the distance measurement observation value.

[0069] Due to the vast distance between the ground station and the lunar probe, the calculations should be performed within the Barycentric Celestial Reference System (BCRS). The first term of the above formula... This represents the propagation distance of uplink and downlink signals under BCRS, taking into account the effect of gravitational delay. The second term... express Distance correction caused by timescale correction when converting time from TDB to UTC. (Third item) express Distance correction caused by timescale conversion from TDB to UTC. The time recorded for each two-way ranging observation is generally the receiving time, i.e. (UTC), which then requires optical travel time calculation to obtain... (TDB), and then the distance observation value is calculated, that is to say, (UTC) is directly obtainable during two-way distance measurement, while (TDB) needs to be calculated using subsequent optical travel time. The formula for calculating optical travel time is as follows:

[0070]

[0071]

[0072] (1.4)

[0073] in, For relativistic light-time correction, a backtracking method is used, following... The steps are used to calculate each time point step by step. (TDB) indicates the moment when the detector receives and forwards the downlink signal under TDB; express Time detector position and The geometric distance between the ground station position and the time; γ is the post-Newton parameter; M is the mass of the Sun; denotes the geometric distance from the Sun to the detector at time t; denotes the geometric distance from the Sun to the ground station at time t; denotes the geometric distance from the ground station to the Moon detector at time t; denotes the geometric distance from the Moon detector to the Moon at time t; denotes the mass of the i-th celestial body in the solar system in order (i denotes the serial number of celestial bodies in the solar system in order, i = 1 to 10 usually refers to Mercury, Venus, Earth, Moon, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto); denotes the geometric distance from the i-th celestial body to the ground station at time t; denotes the geometric distance from the i-th celestial body to the detector at time t; denotes the geometric distance from the ground station to the i-th celestial body at time t; denotes the geometric distance from the Moon detector to the Moon at time t; G represents the gravitational constant. Since is unknown in advance, the initial value of can be set as , and then iteratively solved. After formula (1.4) converges, the subscripts 3 and 2 are replaced by 2 and 1, and formula (1.3) is calculated , that is, formula (1.3) can be solved.

[0074] It should be noted that the above processes are all calculated in the barycentric celestial reference system BCRS, so when calculating the position of the ground station at each time, the conversion from the geocentric celestial reference system GCRS to the barycentric celestial reference system BCRS is required, and the corresponding Lorentz transformation is required, and the formula is:

[0075] (1.5)

[0076] wherein, denotes the velocity of the Earth in BCRS (which can be obtained through ephemeris), c is the speed of light, and higher order terms are ignored. is the position of the ground station in BCRS. is the position of the ground station in GCRS.

[0077] Specifically, the present application simultaneously considers the solid tide, sea tide, polar tide and other correction terms of the ground station to obtain the accurate position of the ground station in GCRS, and the formula is:

[0078] (1.6)

[0079] wherein, For the ground station coordinates (directly observed) under the International Terrestrial Reference Frame (ITRF), For the displacement caused by the Earth tide and ocean tide, which can be calculated by the IERS Conventions model, For the polar motion correction.

[0080] Specifically, the embodiment of the present application constructs a LRR and LLR joint lunar observation model and deduces the partial derivative matrix. The LRR and LLR observation models are the same if the medium correction is not considered, that is, the ground station transmits an uplink signal at , the lunar surface reflector / lunar lander returns a downlink signal at , and finally the ground station receives at . Here, the distance from the ground station to the lunar surface reflector / lunar lander is used as the observation model, and the calculated value can be described as:

[0081] (2.1)

[0082] wherein, is the theoretical calculation value of the LLR part in the joint lunar observation model, is the position vector difference of the ground station and the lunar surface reflector at and in the J2000 inertial system; is the theoretical calculation value of the LRR part in the joint lunar observation model, is the position vector difference of the ground station and the lunar lander at and in the J2000 inertial system. Among them, , , , need to be obtained by solving the light travel time.

[0083] For the ground station, the calculation formula is:

[0084] (2.2)

[0085] wherein, is the rotation matrix from the J2000 inertial system to the ground-fixed system at , which can be obtained by a high-precision ephemeris model. is the position vector of the ground station in the ground-fixed system at .

[0086] Similarly, for the lunar surface reflector / lunar lander, there is:

[0087] (2.3)

[0088] where, corresponding the rotation matrix from J2000 inertial frame to the lunar body-fixed frame at time t, which is given by the lunar rotation model, are the lunar rotation model parameters. are the position vector of the lunar lander / lunar retroreflector in the lunar body-fixed frame at time t, which is calculated by considering the second-order elastic tidal model,

[0089] (2.4)

[0090] where, is the intrinsic position of the lunar lander / lunar retroreflector in the lunar body-fixed frame, is the second-order elastic tidal displacement correction term at time t, which is calculated by,

[0091] (2.5)

[0092] where, is the mass of the tide-generating body (Earth and Sun), is the lunar radius, is the lunar mass, is the distance between the Moon and the tide-generating body at time t, and are the direction vectors of the Moon pointing to the lunar lander / lunar retroreflector and the tide-generating body at time t. and are the second-order tidal LOVE numbers of the Moon.

[0093] Specifically, the steps to derive the partial derivative matrix include: deriving the partial derivatives of the LRR / LLR observation model with respect to the lunar rotation model parameters and the second-order tidal LOVE numbers of the Moon (since the observation models are the same, their partial derivatives are also the same). First, for a single lunar rotation parameter , we have:

[0094] (2.6)

[0095] where, is the position vector difference between the lunar lander / lunar retroreflector and the ground station at and time t in the J2000 inertial frame; the rotation matrix The partial derivative of the rotation parameter is dependent on the specific lunar rotation model. Considering a 4-parameter rotation model with a constant rotation axis and uniform rotation speed, the rotation matrix is:

[0096] (2.7)

[0097] in, , These represent the counterclockwise rotation angles along the z-axis and x-axis, respectively. The corresponding rotation matrix. The rotation parameter is... , These represent the right ascension and declination of the Moon's rotation axis in the J2000 inertial frame, respectively. for Lunar meridian longitude at any time Let be the corresponding rotational speed of the axis. The partial derivatives of the rotation matrix are as follows:

[0098] (2.8)

[0099] in, correspond (This is a simplified version.) It is the unit vector of the x-axis, which is (1, 0, 0). The unit vectors of the y-axis and z-axis are similar. Represents the vector The antisymmetric matrix formed is defined as follows:

[0100] (2.9)

[0101] in, A vector represents any vector, as mentioned in formula (2.8). This is a specific vector, which is equivalent to explaining a commonly used formula definition. If we consider a more complex lunar rotation model, the rotation matrix is ​​described in the same way. and its partial derivatives This allows us to obtain the partial derivatives of the laser lunar observations with respect to each rotation parameter.

[0102] Specifically, regarding the number of tidal LOVEs and Its corresponding partial derivative is in the form of:

[0103] (2.10)

[0104] (2.11)

[0105] in,

[0106] (2.12)

[0107] (2.13)

[0108] The partial derivatives of the laser ranging observations with respect to the respective rotation parameters and the tidal LOVE numbers can finally be obtained. Then a joint partial derivative matrix is constructed:

[0109] (2.14)

[0110] wherein, and are the i-th observation of LRR and LLR, respectively, and the size of the matrix is: (LRR observation number + LLR observation number) rows * 6 columns.

[0111] Specifically, the embodiment of the present application solves the nonlinear least squares iteration by fusing LRR and LLR data. The specific steps are as follows:

[0112] 1. Construct a joint residual vector:

[0113] The residuals of LRR and LLR can be expressed as:

[0114] (3.1)

[0115] wherein, , is the pre-processed observation value, , is the corresponding observation calculation value, and the joint residual vector can be expressed as:

[0116] (3.2)

[0117] 2. Construct the prior weight matrix P: the weight value is calculated by using the inverse of the observation noise variance:

[0118] (3.3)

[0119] wherein, is the uncertainty (standard deviation) of the i-th observation value, which is usually obtained together with the observation value, and then the prior weight matrix can be constructed as:

[0120] (3.4)

[0121] wherein, , are the number of LRR and LLR observation values, respectively.

[0122] 3. Solve the normal equation, and the expression of the normal equation is as follows:

[0123] (3.5)

[0124] wherein, J is the Jacobian matrix, i.e. the above-mentioned joint partial derivative matrix, The correction of lunar libration parameters is obtained by solving the equation .

[0125] 4. Iterative update of parameters, the parameter update formula is:

[0126] (3.6)

[0127] wherein is the parameter correction of the kth iteration. The parameter iteration process is as follows:

[0128] (1) Initialization: set the initial parameters (such as the prior value corresponding to the parameters).

[0129] (2) kth iteration: use the updated parameters to recalculate , , and recalculate the residual error. Calculate the Jacobian matrix , solve the normal equation to obtain , and update the parameters to obtain .

[0130] (3) Convergence criterion: stop iteration when the residual error change is less than a specified value, such as .

[0131] Specifically, based on the converged parameter covariance matrix , the formal error of lunar libration parameters is calculated , and the true error and the true error / formal error ratio are calculated by comparing the parameter solution value with the true value (reference solution configuration). The results are shown in Table 2, Figure 2 and Figure 3 .

[0132] Table 2 Parameter simulation solution results

[0133] Under the same conditions, the data obtained by using only LRR for calculation is shown in Table 3.

[0134] Table 3 Parameter simulation solution results

[0135] Under the same conditions, the data obtained by using only LLR for calculation is shown in Table 4.

[0136] Table 4 Parameter simulation solution results

[0137] From Tables 2-4, compared with parameter solving by using LLR data or LRR data alone, the true error / formal error of joint solving by using both kinds of data is much smaller, and is reduced by about 1 order of magnitude on average, which shows that the lunar radio ranging technology can improve the observation accuracy of the lunar libration parameters, and the tidal change of the lunar surface target position is detected by using the laser ranging data, the lunar rotation model is combined, and the solving of the LOVE number based on the second-order elastic tidal model is realized. and .

[0138] Specifically, the present application provides an efficient method for improving the precise solving of the lunar rotation parameters by using the joint observation data of LRR and LLR, which can effectively improve the solving accuracy of the key parameters of the lunar dynamics, has good stability and adaptability, is suitable for multiple important fields such as lunar exploration, deep space orbit optimization, lunar internal structure research, realizes the joint solving of the ground-based lunar radio ranging (LRR) and laser ranging (LLR) data, deeply fuses the all-weather high-frequency observation data of LRR and the high-precision ranging data of LLR, and significantly improves the solving accuracy of the lunar rotation parameters (the right ascension, declination and rotation speed of the lunar rotation axis, and the lunar meridian longitude) and the tidal LOVE number ( 、 ).

[0139] The implementation basis of each embodiment of the present application is realized by the programmed processing of the device with the processor function. Therefore, in the engineering practice, the technical solutions and functions of each embodiment of the present application are packaged into various modules. Based on this actual situation, on the basis of the above-mentioned embodiments, the embodiments of the present application provide a lunar libration parameter high-precision solving system combining LRR and LLR technologies, which is used to execute one of the above-mentioned joint LRR and LLR technology lunar libration parameter high-precision solving methods.

[0140] The system comprises: a preprocessing module for constructing and preprocessing the LRR and LLR joint observation data set; a lunar-terrestrial distance calculation value module for constructing the LRR and LLR joint lunar ranging model based on the preprocessed results; a partial derivative module for deriving the partial derivative of the LRR and LLR joint lunar ranging model with respect to the lunar rotation parameters and the tidal LOVE number, and constructing the joint partial derivative matrix; and an iterative solving module for performing iterative solving by using the nonlinear least squares based on the joint partial derivative matrix and the lunar-terrestrial distance calculation value obtained from the LRR and LLR joint lunar ranging model, so as to obtain the lunar libration parameters.

[0141] The moon libration parameter high-precision solving system provided by the embodiment of the present application combines LRR and LLR technologies, and is used to solve the problems of the traditional single moon measurement technology (such as the observation continuity of the single LLR affected by weather blocking and the limited ranging accuracy of the single LRR) in solving the moon rotation parameters, and the problems of the observation condition restriction, the high parameter solving error and the like. The embodiment adopts a plurality of modules, utilizes the ground-based moon radio ranging data (such as the microwave velocity and ranging data of the Kashi and Jiamusi deep space stations to the Chang'e No. 3 lunar lander) and the laser moon measurement (LLR) data (such as the high-precision laser ranging data of the French GRSM station and the Changchun CHAL station to the moon reflector), and solves the moon rotation parameters (the right ascension and declination of the rotation axis, the rotation angular velocity and the like) and the tidal LOVE number through a series of data processing and calculation methods such as the joint moon measurement model construction, the target parameter partial derivative derivation and the nonlinear least square joint solution, so as to improve the solving accuracy of the moon dynamics key parameters and the reliability of the moon dynamics key parameters.

[0142] Based on the same inventive concept as the foregoing embodiments, the embodiment of the present application further provides an electronic device, including a memory and a processor, the memory is used to store computer executable instructions, and the processor is used to execute the computer executable instructions to realize the moon libration parameter high-precision solving method combining LRR and LLR technologies as proposed in the foregoing embodiments.

[0143] The embodiment of the present application further provides a computer readable storage medium, and the computer program is stored on the computer readable storage medium. When the program is executed by the processor, the solving accuracy of the moon rotation parameters (the right ascension and declination of the rotation axis, the rotation angular velocity and the like) and the tidal LOVE number is improved, the accuracy and reliability of the moon dynamics key parameters are significantly improved, and the problem of the observation continuity or the insufficient accuracy of the single data source is solved.

[0144] In summary, based on the deep integration of LRR and LLR joint observation technology and lunar dynamics model, an innovative lunar rotation parameter precise solution method is developed. By introducing high-precision coordinate unified conversion, joint observation data model construction and nonlinear least squares joint solution algorithm, the all-weather high-frequency observation data of LRR and high-precision ranging data of LLR are integrated, and the problems of observation condition restriction and high parameter solution error in lunar rotation parameter solution of traditional single lunar measurement technology (single LLR affected by weather blocking, single LRR limited ranging accuracy) are successfully overcome, which significantly improves the accuracy, stability and reliability of lunar rotation parameter and tidal Love number solution, and the true error / formal error is reduced by about 1 order of magnitude on average. This innovative method not only provides solid technical support for lunar dynamics parameter acquisition in Chang'e series lunar exploration missions (such as lunar lander precise positioning, lunar libration research), but also has important scientific value and wide application prospect in promoting the development of China's lunar exploration technology and expanding the application range of deep space orbit determination theory.

[0145] In summary, the joint solution algorithm details will be continuously optimized (such as dynamically adjusting the prior weight matrix, improving the high-order terms of the tidal correction model), the adaptability and processing efficiency under complex observation scenarios (such as lunar back observation, extreme weather conditions) will be improved, and innovative modes of LRR / LLR data fusion with lunar base observation data (such as lunar seismometer data) will be explored, and the lunar rotation parameter solution capability will be continuously strengthened, providing more reliable technical support for the continuous advancement of lunar exploration missions (such as manned lunar landing, lunar base construction) and the dynamics parameter solution of subsequent deep space exploration projects (such as asteroid exploration).

[0146] Finally, it should be noted that the above specific embodiments are only representative examples of the present application. Obviously, the present application is not limited to the above specific embodiments, and can have many variations. Any simple modification, equivalent change and modification made in accordance with the technical essence of the present application to the above specific embodiments shall be considered as falling within the protection scope of the present application.

Claims

1. A method for high-precision solution of lunar libration parameters by combining LRR and LLR techniques, characterized in that, The method comprises the following steps: constructing a LRR and LLR combined observation data set and preprocessing the same; constructing a LRR and LLR combined lunar orbit determination model based on the preprocessed result; deriving partial derivatives of the LRR and LLR combined lunar orbit determination model with respect to lunar rotation parameters and tidal LOVE numbers, and constructing a combined partial derivative matrix; performing iterative solution by using a nonlinear least square based on the combined partial derivative matrix and lunar- Earth distance calculated values obtained according to the LRR and LLR combined lunar orbit determination model, so as to obtain lunar libration parameters.

2. The method according to claim 1, wherein, The method of constructing a LRR and LLR combined observation data set and preprocessing the same comprises the following steps: The LRR and LLR combined observation data set comprises multi-source observation data, ground station, lunar surface target position and lunar physical parameters. The multi-source observation data is subjected to time reference unification and noise filtering, the coordinates of the ground station are subjected to coordinate system conversion, the lunar surface target position is subjected to tidal displacement correction and inertial system coordinate conversion, and the lunar physical parameters comprise lunar rotation parameters and tidal LOVE numbers.

3. The method according to claim 1, wherein, The method of constructing a LRR and LLR combined lunar orbit determination model based on the preprocessed result comprises the following steps: The LRR and LLR combined lunar orbit determination model is constructed, and the expression is as follows: ， wherein is the calculated value of the LLR part of the joint lunar model, is the position vector difference between the ground station and the lunar reflector at and respectively, in the J2000 inertial system; is the calculated value of the LRR part of the joint lunar model, is the position vector difference between the ground station and the lunar lander at and respectively, in the J2000 inertial system; wherein , , , is obtained by solving for the light time.

4. The method according to claim 1, wherein, The method of deriving partial derivatives of the LRR and LLR combined lunar orbit determination model with respect to lunar rotation parameters comprises the following steps: ， ， wherein, denotes the LRR and LLR combined lunar ephemeris model; denotes the i-th lunar rotation parameter; is the position vector of the lunar probe in the lunar body-fixed system at time is the position vector of the lunar probe in the lunar body-fixed system at time is the position vector difference between the lunar probe and the ground station at time and is the position vector difference between the lunar probe and the ground station at time corresponds to is the rotation matrix from the J2000 inertial system to the lunar body-fixed system at time is the lunar rotation parameter matrix.

5. The method according to claim 1, wherein, The method of deriving partial derivatives of the LRR and LLR combined lunar orbit determination model with respect to tidal LOVE numbers comprises the following steps: ， ， wherein, ， ， where, represents the radial tidal LOVE number, represents the tangential tidal LOVE number, is the second order elastic tidal displacement correction term at time t, corresponds to the rotation matrix from the lunar body-fixed system to the J2000 inertial system at time t; is the mass of the tidal body, is the radius of the moon, is the mass of the moon, is the distance from the moon to the tidal body at time t, and are the direction vectors of the moon pointing to the lunar surface reflector and the lunar lander and the tidal body at time t, respectively.

6. The method according to claim 1, wherein, The method of performing iterative solution by using a nonlinear least square based on the combined partial derivative matrix and lunar- Earth distance calculated values obtained according to the LRR and LLR combined lunar orbit determination model, so as to obtain lunar libration parameters comprises the following steps: constructing a combined residual vector: , wherein , are one half of the actual observed values of the LLR and LRR, respectively, , are the theoretical calculated values corresponding to the LLR and LRR, respectively, is the joint residual vector; obtaining the lunar libration parameters based on the right ascension and declination of the lunar rotation axis in the J2000 inertial system, the lunar meridian longitude, the rotation speed of the lunar rotation axis, the radial tidal LOVE number and the tangential tidal LOVE number; combining the prior weight matrix and the combined residual vector, and performing iterative solution on the lunar libration parameters by using a nonlinear least square until convergence.

7. The method according to claim 6, wherein the method is characterized by, The method of performing iterative solution on the lunar libration initial parameters by using a nonlinear least square comprises the following steps: initializing the lunar libration parameters as an iterative starting point; re-calculating the theoretical calculation values corresponding to the LLR and LRR by using the lunar libration parameters of the current iteration, obtaining the residual and the combined residual vector of the current iteration, and obtaining the updated value of the lunar libration parameters by using a least square iterative solution; stopping the iteration when the residual variation of the current and previous iterations is less than a set value, so as to obtain the final lunar libration parameters.

8. A lunar libration parameter high-precision solution system combining LRR and LLR techniques, characterized in that, The method comprises the following steps: a preprocessing module, which is configured to construct a LRR and LLR combined observation data set and preprocess the same; a lunar- Earth distance calculation value module, which is configured to construct a LRR and LLR combined lunar orbit determination model based on the preprocessed result; a partial derivative module, which is configured to derive partial derivatives of the LRR and LLR combined lunar orbit determination model with respect to lunar rotation parameters and tidal LOVE numbers, and construct a combined partial derivative matrix; an iterative solution module, which is configured to perform iterative solution by using a nonlinear least square based on the combined partial derivative matrix and lunar- Earth distance calculated values obtained according to the LRR and LLR combined lunar orbit determination model, so as to obtain lunar libration parameters. 9.An electronic device comprising a memory and a processor, the memory storing a computer program, wherein, The computer program is executed by the processor to realize the steps of the high-precision lunar libration parameter resolving method combining LRR and LLR technology according to any one of claims 1-7.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to realize the steps of the high-precision lunar libration parameter resolving method combining LRR and LLR technology according to any one of claims 1-7.

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