A lunar libration parameter high-precision solving method and system combining LRR and LLR technologies

Abstract

This invention discloses a high-precision method and system for calculating lunar libration parameters using a combination of LRR and LLR technologies, belonging to the field of deep space exploration and celestial dynamics. The method includes: constructing and preprocessing a joint LRR and LLR observation dataset; constructing a joint LRR and LLR lunar model and deriving the partial derivatives of this model with respect to lunar rotation parameters and tidal love numbers to obtain a joint partial derivative matrix; iteratively solving the lunar libration parameters using nonlinear least squares; evaluating the solution results and optimizing the solution strategy by dynamically adjusting weights, improving the tidal model, and removing outliers. This invention reduces parameter calculation errors, effectively integrates the technical advantages of both types of data, and solves the problem of insufficient continuity or accuracy of observations from a single data source, providing reliable parameter support for the study of lunar rotation and internal structure.

Description

Technical Field

[0001] This invention belongs to the field of deep space exploration and celestial dynamics, specifically relating to a high-precision calculation method and system for lunar libration parameters that combines LRR and LLR technologies. Background Technology

[0002] Precise determination of lunar libration parameters is of paramount importance in lunar science and exploration. These parameters provide crucial information about the Moon's internal structure. For the Moon, accurate libration parameters provide information on lunar tidal response, tidal dissipation, and core / mantle interface interactions, offering key evidence for the composition of the lunar core. Furthermore, accurate calculation of lunar rotation, libration, and tidal parameters is essential for improving the landing accuracy of landers. Therefore, improving the accuracy of lunar libration parameter calculations not only deepens our understanding of the Moon's internal structure but also provides crucial 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 shortcomings.

[0004] 1. Significantly affected by lunar surface environmental factors: The laser reflector prism assembly is deployed on the lunar surface, lacking equipment maintenance and updates. After decades of erosion from various lunar surface environmental factors and the covering of lunar dust, its reflectivity will inevitably degrade to a considerable extent. In addition, the influence of other factors such as moonquakes, as well as severe weather on the lunar surface, will introduce certain errors into the laser lunar measurement data or block the laser beam.

[0005] 2. Weak signal and few returned photons: Due to the great distance between the moon and the earth, the laser beam is easily dispersed by atmospheric turbulence during propagation. The diffraction effect of the reflector and the attenuation of the laser emission instrument components also weaken the laser intensity, resulting in a very weak laser signal reaching the earth. The number of returned photons received by the ground station is very small, making it difficult to calculate the number of real photons contained in it.

[0006] 3. Inability to observe during full moon and new moon: Laser lunar profiling suffers from uneven distribution of lunar phase angle measurement data, meaning that accurate observation is not possible during full moon and new moon phase angles. During a full moon, direct sunlight on the lunar surface results in excessive background noise, severely reducing the signal-to-noise ratio. During a new moon, accurate positioning with a telescope is difficult, and the working time is too short to facilitate successful observation.

[0007] 4. The Influence of Lunar Apparent Libration: Lunar apparent libration is the actual spatial wobble of the Moon, and LLR observational data is the primary source for estimating lunar apparent libration. Due to the influence of libration, the lunar reflector prism cannot always remain directly facing Earth. The distances between different corner reflectors in the prism assembly and the ground station will vary. When the ground station receives a returned photon, it cannot determine which corner reflector it originated from. Therefore, the deviation in reflector distance will cause a ranging uncertainty of 24–75 mm in the data.

[0008] 5. Low observation efficiency and poor continuity: Globally, there are fewer than 10 ground stations capable of lunar laser ranging. The influence of visible light during the day also limits the distribution of observation periods, making the observation time intervals even smaller. Furthermore, while low-latitude lunar laser ranging stations have significantly higher observation efficiency than high-latitude stations, most qualified ground stations are located in mid-to-high latitudes, resulting in low observation efficiency. Simultaneously, this technology has relatively high requirements for measurement direction and the observation environment, making it difficult to achieve relative continuity of observation data within a single observation arc. This is detrimental to continuous monitoring of Earth-Moon space motion and the study of short-term variations in dynamic physical parameters.

[0009] Compared to traditional laser lunar ranging, Earth-Moon radio ranging (LRR) has unique advantages, and combining the two technologies can further improve accuracy. Theoretically, LRR can achieve all-weather observation, has high observation efficiency, and is less demanding on station requirements, with a sufficient number of ground stations. In terms of signal strength and observation accuracy, relying on my country's globally deployed deep space network and comprehensive VLBI network, it can achieve levels comparable to laser lunar ranging. Furthermore, LRR offers better continuity in lunar observations, making it more suitable for studying the short-term variations in dynamic physical parameters of the Earth-Moon distance. In contrast, LLR technology has significant shortcomings in observation continuity. LRR also boasts outstanding advantages such as high observation efficiency, easy signal reception and processing, a large number of ground stations, convenient operation, rich data types, and good measurement continuity. Summary of the Invention

[0010] The purpose of this invention is to address the problems of traditional single lunar ranging techniques (such as LLR alone, which suffers from the impact of weather obstruction on observation continuity, and LRR alone, which has limited ranging accuracy) in the calculation of lunar rotation parameters due to the constraints of observation conditions and the high error rate in parameter calculation. This invention provides a high-precision calculation method for lunar libration parameters that combines LRR and LLR technologies. Utilizing Earth-Moon radio ranging (LRR) data (such as microwave velocimetry and ranging data from the Kashgar and Jiamusi deep space stations on lunar landers like Chang'e-3) and ground-based lunar laser ranging (LLR) data (such as high-precision laser ranging data from the French GRSM station and the Changchun CHAL station on lunar reflectors), and through a series of data processing and calculation methods including the construction of a joint lunar ranging model, derivation of partial derivatives of target parameters, and nonlinear least squares joint calculation, the accuracy of lunar rotation parameters (right ascension, declination, rotation angular velocity, etc.) and tidal LOVE numbers is improved, significantly enhancing the accuracy and reliability of the calculation of key lunar dynamic parameters.

[0011] According to one aspect of the present invention, a method for high-precision calculation of lunar libration parameters combining LRR and LLR technologies is provided, comprising:

[0012] Construct a joint observation dataset of LRR and LLR and perform preprocessing;

[0013] Based on the preprocessed results, a joint lunar measurement model of LRR and LLR is constructed;

[0014] The partial derivatives of the LRR and LLR joint lunar model with respect to the lunar rotation parameters and tidal LOVE number are derived, and the joint partial derivative matrix is ​​constructed.

[0015] Based on the joint partial derivative matrix and the calculated Earth-Moon distance obtained from the joint LRR and LLR lunar measurement model, nonlinear least squares is used for iterative solution to obtain the lunar libration parameters.

[0016] Furthermore, a joint observation dataset of LRR and LLR is constructed and preprocessed, including:

[0017] The LRR and LLR joint observation dataset includes multi-source observation data, ground stations, lunar target locations, and lunar physical parameters;

[0018] The multi-source observation data undergoes time reference unification and noise filtering; the coordinates of the ground stations are transformed; the lunar target position is corrected for tidal displacement and transformed for inertial coordinates; the lunar physical parameters include lunar rotation parameters and tidal LOVE numbers.

[0019] Furthermore, based on the preprocessed results, a joint lunar observation model of LRR and LLR is constructed, including:

[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] in, Represents the radial tidal LOVE number. This represents the tangential tidal LOVE number. for The second-order elastic tidal displacement correction term at time t. correspond The rotation matrix from the fixed frame to the J2000 inertial frame at any given moment; For the mass of the tidal body, The radius of the moon, With the mass of the moon, for The distance between the moon and the tidal body at any given time. and They are respectively The direction vector of the moon pointing towards the lunar surface reflector, the lunar lander, and the tidal body at any given moment.

[0034] Furthermore, based on the joint partial derivative matrix and the calculated Earth-Moon distance obtained from the joint LRR and LLR lunar measurement model, nonlinear least squares iterative calculation is used to obtain the lunar libration parameters, including:

[0035] Construct the joint residual vector:

[0036]

[0037] in , These are half of the actual observed values ​​of LLR and LRR, respectively. , These are the theoretical calculated values ​​for LLR and LRR, respectively. For the joint residual vector;

[0038] Based on the right ascension and declination of the lunar rotation axis in the J2000 inertial frame, the longitude of the lunar meridian, the rotational speed of the lunar rotation axis, the radial tidal LOVE number, and the tangential tidal LOVE number, the lunar libration parameters are obtained.

[0039] By combining the prior weight matrix and the joint residual vector, the lunar libration parameters are iteratively solved using least squares until convergence.

[0040] Furthermore, the initial parameters of lunar libration are solved iteratively using least squares, including:

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

[0042] Using the lunar libration parameters of the current iteration, the theoretical values ​​corresponding to LLR and LRR are recalculated to obtain the residual and joint residual vector of the current iteration. The updated values ​​of the lunar libration parameters are obtained by least squares iteration.

[0043] The iteration stops when the change in residual between the previous and subsequent iterations is less than a set value, in order to obtain the final lunar libration parameters.

[0044] According to one aspect of the present invention, a high-precision system for calculating lunar libration parameters combining LRR and LLR technologies is provided, comprising:

[0045] The preprocessing module is used to construct and preprocess the joint observation dataset of LRR and LLR;

[0046] The Earth-Moon distance calculation module is used to construct a joint lunar measurement model of LRR and LLR based on the preprocessed results;

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

[0048] The iterative solution module is used to perform iterative solutions based on the joint partial derivative matrix and the lunar distance calculated according to the joint lunar measurement model of LRR and LLR, using nonlinear least squares to obtain the lunar libration parameters.

[0049] According to one aspect of the present invention, an electronic device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the method for high-precision calculation of lunar libration parameters using the combined LRR and LLR technologies.

[0050] According to one aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for high-precision calculation of lunar libration parameters using the combined LRR and LLR technologies.

[0051] Compared with the prior art, the beneficial effects of the present invention are:

[0052] 1. This invention integrates two types of observation data, LRR and LLR, and simultaneously collects the solid-body coordinates, lunar shape model and physical parameters (radius, gravitational parameters, etc.) of ground stations and lunar targets. Through preprocessing such as time standardization and optical time correction, it provides a high-quality data foundation for joint calculation and solves the problem of insufficient continuity or accuracy of observations from a single data source.

[0053] 2. This invention constructs a unified LRR and LLR joint lunar measurement model based on the position vector difference between the ground station and the lunar target in the J2000 inertial frame, using the lunar rotation parameter and tidal LOVE number as the core parameters to be solved. The model is linearized through Taylor expansion, deriving the partial derivatives of the model with respect to each parameter (including the rotation matrix derivative of the rotation parameter and the displacement correction derivative of the tidal parameter), forming a global partial derivative matrix. This provides crucial gradient information for nonlinear least squares solutions, improving the sensitivity and stability of parameter calculations.

[0054] 3. This invention employs an iterative weighted nonlinear least squares algorithm, fusing LRR ranging / velocity residuals and LLR ranging residuals. Weights for the two data types are dynamically allocated using a priori weight matrix (based on their respective noise levels), and parameter corrections are iteratively solved until convergence. After calculation, parameter accuracy is evaluated using the covariance matrix, and the initial values ​​and iteration thresholds are optimized using lunar dynamics theory to further reduce parameter calculation errors. This effectively integrates the technical advantages of both data types, solving the accuracy bottleneck of single techniques under complex observation conditions and providing reliable parameter support for the study of lunar rotation and internal structure. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 The flowchart illustrates the high-precision calculation method for lunar libration parameters using the combined LRR and LLR technologies provided by this invention.

[0057] Figure 2 This is a schematic diagram of the a priori residuals, posterior residuals, and reference residuals calculated for each station provided by the present invention.

[0058] Figure 3 This is a schematic diagram of the correlation coefficient matrix between the solution parameters provided by this invention. Detailed Implementation

[0059] Existing techniques for calculating lunar translational parameters are insufficient to meet the demands for high-precision lunar dynamic parameters. While combining microwave ranging and velocimetry with laser lunar data holds significant potential for improving accuracy, it has not been effectively utilized. Simulation analysis shows that using ground-based radio ranging and laser lunar data for joint calculation reduces the true error / formal error by approximately one order of magnitude on average. This demonstrates that ground-based lunar radio ranging technology can effectively improve the accuracy of calculations for physical parameters such as lunar rotation, libration, and tides. Therefore, there is an urgent need for a method that combines microwave ranging and velocimetry with laser lunar data to improve the accuracy of lunar translational parameter calculations. This would enhance the precision and reliability of lunar dynamic parameter determination, ensure the smooth progress of subsequent lunar exploration projects, and provide technical support for the study of the lunar internal structure.

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] Specifically, such as Figure 1 As shown in the embodiments of this invention, a high-precision solution method for lunar libration parameters combining LRR and LLR technologies is proposed. This method includes: utilizing joint observation data from LRR and LLR, combined with a lunar shape model, ground station and lunar target coordinate data (body-fixed coordinate system data), and lunar physical parameters (such as lunar radius and gravitational parameters), to perform tidal displacement correction and inertial frame coordinate transformation for the lunar target position. By constructing a unified LRR and LLR joint lunar measurement model in the J2000 inertial frame, the partial derivatives of this model with respect to lunar rotation parameters (right ascension, declination, rotation angular velocity, etc.) and tidal LOVE numbers are derived, achieving the fusion of LRR and LLR data. A nonlinear least squares algorithm is then used to accurately solve for the lunar rotation parameters. This significantly improves the accuracy of lunar rotation parameter calculations (such as the formal errors of right ascension and declination), reducing the true error / formal error by an average of approximately one order of magnitude, providing more accurate lunar dynamic parameter support for lunar exploration missions.

[0062] Specifically, this embodiment of the invention provides a method for constructing a joint LRR and LLR observation dataset, including multi-source observation data collection and preprocessing. First, high-precision lunar shape model data, coordinate data of ground stations (such as the French GRSM station, Changchun CHAL station, Kashgar station, and Jiamusi station) and lunar targets (lunar reflector LRRR, Chang'e-3 lander) in a body-fixed coordinate system are collected. Second, microwave velocity and ranging data of the lunar lander are obtained using LRR technology, and high-precision laser ranging data of the lunar reflector are obtained using LLR technology. Preprocessing of the acquired multi-source observation data, such as time standardization and noise filtering, improves data quality and facilitates subsequent joint model construction.

[0063] Specifically, a joint LRR and LLR observation dataset will be constructed, including: collecting LRR data (such as microwave velocimetry and ranging data of the Chang'e-3 lunar lander from the Kashgar and Jiamusi deep space stations) and LLR data (such as high-precision laser ranging data of the LRRR of the lunar reflector from the French GRSM station and the Changchun CHAL station), and simultaneously acquiring the Earth-solid coordinates of the ground stations, the lunar-solid coordinates of the lunar target, and lunar physical parameters (gravitational parameters). (Radius R = 1738 km).

[0064] Specifically, basic data and observation parameters were collected, including the coordinates and equipment parameters of the ground stations participating in the observations. LLR used the French GRSM station and the Chinese Changchun CHAL station, while LRR simulated radio data from the Chinese Kashgar and Jiamusi deep space stations to the Chang'e-3 lander. The lunar-fixed coordinates and attributes of the lunar observation targets were determined. The reference solution configuration for the Earth-fixed coordinates of each station is shown in Table 1.

[0065] Table 1 Solution Configuration Information

[0066] Specifically, the joint LRR and LLR observation data were preprocessed, including the construction of observation equations and optical travel time correction. The IERS Conventions model was used to convert all observation times from UTC to the TDB time scale, ultimately yielding the preprocessed observation values. The observation models for both types of data are identical, both being two-way ranging models, with the following observation equations:

[0067]

[0068] in, denoted by , where is the distance between the ground station and the lunar probe, and 'c' represents the speed of light. (UTC) indicates the time at which a ground station receives downlink signals under 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 corrections, 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; Mass of the Sun; express The geometric distance between the sun and the probe at any given time; express The geometric distance from the sun to the ground station at any given time; express ground station at time The geometric distance of the lunar probe at any given moment; This indicates the mass of the planets and moon in the solar system in sequential order (i represents the sequence number of the celestial bodies in the solar system, i=1 to 10 usually refers to Mercury, Venus, Earth, Moon, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto). express The geometric distance from the i-th celestial body to the ground station at time i; express The geometric distance from the i-th celestial body to the detector at time i; express ground station at time The geometric distance of the lunar probe at any given moment; G represents the gravitational constant. Because... Unknown beforehand, can be set The initial value is Then, the solution is iteratively obtained. After formula (1.4) converges, the subscripts 3 and 2 are replaced with 2 and 1, and the calculation is performed. Formula (1.3) can then be obtained.

[0074] It is important to note that the above process is all performed in the BCRS (Body Center Celestial Reference System). Therefore, calculating the position of the Earth station at each moment involves a conversion from the GCRS to the BCRS, requiring a corresponding Lorentz transformation. The formula is as follows:

[0075] (1.5)

[0076] in, This represents the Earth's speed in the BCRS (which can be obtained through ephemeris), where c is the speed of light, and higher-order terms are ignored. This indicates the location of the ground station under BCRS. This indicates the location of the ground station under GCRS.

[0077] Specifically, this invention simultaneously considers corrections for solid tides, ocean tides, and polar tides at ground stations to obtain the precise location of the ground stations under GCRS, as shown in the formula:

[0078] (1.6)

[0079] in, These are the coordinates of ground stations under the International Earth Reference Frame (ITRF) (obtained through direct observation). Displacements caused by solid tides and ocean tides can be calculated using the IERS Conventions model. This is for polar shift correction.

[0080] Specifically, this embodiment of the invention constructs a joint lunar observation model of LRR and LLR and derives the partial derivative matrix. The construction of the joint lunar observation model of LRR and LLR is as follows: if medium correction is not considered, the LRR and LLR observation models are identical, both based on ground-based observation stations. The lunar surface reflector / lander is constantly transmitting uplink signals. The downlink signal is returned in a timely manner, and finally transmitted by the ground station. Real-time reception. Here, the distance from the ground station to the lunar reflector / lander is used as the observation model; the calculated value can be described as follows:

[0081] (2.1)

[0082] in, These are the theoretically 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 theoretical calculation 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 any given time. , , , It needs to be obtained through optical travel time calculation.

[0083] For ground-based stations, the calculation formula is:

[0084] (2.2)

[0085] in, for The rotation matrix from the J2000 inertial frame to the Earth-fixed frame at a given time can be obtained using a high-precision ephemeris model. for The position vector of the ground station in the Earth-fixed system at any given time.

[0086] Similarly, for lunar reflectors / lunar landers, we have:

[0087] (2.3)

[0088] in, correspond The rotation matrix from the J2000 inertial frame to the lunar-fixed frame at time t is given by the lunar rotation model. These are the parameters for the lunar rotation model. for The position vector of the lunar surface reflector / lander in the lunar-solid system at any given moment is calculated using the lunar second-order elastic tidal model, and the formula is as follows:

[0089] (2.4)

[0090] in, This represents the inherent position of the lunar surface reflector / lander in the lunar-solar system. for The formula for calculating the second-order elastic tidal displacement correction at time t is:

[0091] (2.5)

[0092] in, The mass of the tidal bodies (Earth and Sun) The radius of the moon, With the mass of the moon, for The distance between the moon and the tidal body at any given time. and They are respectively The direction vector of the moon pointing towards the lunar surface reflector / lunar lander and tidal body at any given moment. and This is the second-order tidal LOVE number for the moon.

[0093] Specifically, the steps for deriving 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 partial derivatives for the lunar second-order tidal LOVE number (since the observation models are the same, their partial derivatives are also the same). First, for a single lunar rotation parameter... ,have:

[0094] (2.6)

[0095] in, For lunar probes and ground stations and Position vector difference in the J2000 inertial frame at any given time; rotation matrix For rotation parameters partial derivatives It depends on the specific lunar rotation model. Considering a 4-parameter rotation model with a constant axis of rotation 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] Finally, the partial derivatives of the laser lunar observations with respect to their respective rotation parameters and tidal love numbers can be obtained. Then, a joint partial derivative matrix can be constructed:

[0109] (2.14)

[0110] in, and Let i be the i-th observation of LRR and LLR respectively. The size of the matrix is: (number of LRR observations + number of LLR observations) rows * 6 columns.

[0111] Specifically, this embodiment of the invention performs nonlinear least squares iterative solution by fusing LRR and LLR data. The specific steps are as follows:

[0112] 1. Construct the joint residual vector:

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

[0114] (3.1)

[0115] in, , These are the preprocessed observations. , Given the corresponding observed calculated values, the joint residual vector can be expressed as:

[0116] (3.2)

[0117] 2. Construct the prior weight matrix P: Calculate the weights using the reciprocal of the observation noise variance.

[0118] (3.3)

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

[0120] (3.4)

[0121] in, , These represent the number of LRR and LLR observations, respectively.

[0122] 3. Solve the normal equation. The expression for the normal equation is as follows:

[0123] (3.5)

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

[0125] 4. Iteratively update the parameters. The parameter update formula is:

[0126] (3.6)

[0127] in, This represents the parameter correction for the k-th iteration. The parameter iteration process is as follows:

[0128] (1) Initialization: Set initial parameters (such as the prior value of the corresponding parameter).

[0129] (2) k-th iteration: Recalculate using the updated parameters , Then recalculate the residuals. Calculate the Jacobian matrix. Solving the normal equation yields Update parameters to obtain .

[0130] (3) Convergence Criterion: When the change in residual is less than a specified value, such as... Then stop iterating.

[0131] Specifically, based on the converged parameter covariance matrix Formal error in calculating lunar libration parameters The true error is calculated by comparing the calculated parameter values ​​with the true values ​​(refer to the solution configuration). The ratio of true error to formal error The results are shown in Table 2. Figure 2 as well as Figure 3 As shown.

[0132] Table 2 Parameter simulation results

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

[0134] Table 3 Parameter simulation 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 results

[0137] As shown in Table 2-4, compared to using LLR or LRR data alone for parameter calculation, the true error / formal error of using both types of data for joint calculation is much smaller, averaging about one order of magnitude lower. This indicates that ground-based radio lunar ranging technology can significantly improve the observation accuracy of lunar libration parameters. Furthermore, by using laser lunar ranging data to detect tidal changes at lunar target positions and combining this with a lunar rotation model, it is possible to achieve LOVE numbers based on a second-order elastic tidal model. and The solution.

[0138] Specifically, this invention provides an efficient method for improving the precise calculation of lunar rotation parameters using joint observation data from Lunar Radio Ranging (LRR) and Lunar Laser Ranging (LLR). This method effectively enhances the calculation accuracy of key lunar dynamic parameters, exhibits good stability and adaptability, and is applicable to multiple important fields such as lunar exploration, deep space orbital optimization, and lunar internal structure research. It achieves joint calculation of ground-based lunar radio ranging (LRR) and laser lunar ranging (LLR) data, deeply integrating all-weather high-frequency observation data from LRR with high-precision ranging data from LLR, significantly improving lunar rotation parameters (right ascension, declination, rotational speed, and lunar meridian longitude) and tidal LOVE numbers (…). , The solution accuracy is improved, with the true error / formal error reduced by an average of about one order of magnitude.

[0139] The implementation of the various embodiments of this invention is based on programmed processing by a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of this invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of this invention provide a high-precision lunar libration parameter calculation system combining LRR and LLR technologies. This system is used to execute a high-precision lunar libration parameter calculation method combining LRR and LLR technologies from the above method embodiments.

[0140] The system includes: a preprocessing module for constructing and preprocessing the LRR and LLR joint observation dataset; a lunar distance calculation module for constructing the LRR and LLR joint lunar observation model based on the preprocessed results; a partial derivative module for deriving the partial derivatives of the LRR and LLR joint lunar observation model with respect to the lunar rotation parameters and tidal LOVE numbers, and constructing a joint partial derivative matrix; and an iterative solution module for performing iterative solutions using nonlinear least squares based on the joint partial derivative matrix and the lunar distance calculation values ​​obtained from the LRR and LLR joint lunar observation model to obtain the lunar libration parameters.

[0141] The high-precision lunar libration parameter calculation system combining LRR and LLR technologies provided in this invention addresses the problems of traditional single lunar ranging technologies (such as LLR alone, which suffers from weather obstruction affecting observation continuity, and LRR alone, which has limited ranging accuracy) in calculating lunar rotation parameters due to observational constraints and high parameter calculation errors. This system employs several modules, utilizing ground-based lunar radio ranging data (such as microwave velocimetry and ranging data from the Kashgar and Jiamusi deep space stations for lunar landers like Chang'e-3) and laser lunar ranging (LLR) data (such as high-precision laser ranging data from the French GRSM station and the Changchun CHAL station for lunar reflectors). Through a series of data processing and calculation methods, including the construction of a joint lunar ranging model, derivation of target parameter partial derivatives, and nonlinear least squares joint calculation, the system improves the accuracy of lunar rotation parameters (right ascension, declination, rotation angular velocity, etc.) and tidal LOVE numbers, significantly enhancing the accuracy and reliability of calculating key lunar dynamic parameters.

[0142] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also 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 a high-precision solution method for lunar libration parameters combining LRR and LLR technologies as proposed in the above embodiments.

[0143] This invention also provides a computer-readable storage medium storing a computer program thereon. When executed by a processor, this program improves the calculation accuracy of lunar rotation parameters (right ascension, declination, rotation angular velocity, etc.) and tidal LOVE numbers, significantly enhancing the accuracy and reliability of calculating key lunar dynamic parameters and solving the problem of insufficient continuity or accuracy of observations from a single data source.

[0144] In summary, this invention, based on the deep integration of LRR and LLR joint observation technology with a lunar dynamics model, develops an innovative method for precise calculation of lunar rotation parameters. By introducing high-precision coordinate transformation, joint observation data model construction, and nonlinear least squares joint calculation algorithm, the invention integrates all-weather high-frequency observation data from LRR with high-precision ranging data from LLR. This successfully overcomes the challenges of traditional single lunar measurement techniques (where LLR alone suffers from weather-induced observational continuity issues and LRR alone has limited ranging accuracy) in calculating lunar rotation parameters, which are constrained by observation conditions and result in high calculation errors. This significantly improves the accuracy, stability, and reliability of lunar rotation parameter and tidal Love number calculations, with the true error / formal error decreasing by an average of approximately one order of magnitude. This innovative method not only provides solid technical support for obtaining lunar dynamic parameters in the Chang'e lunar exploration missions (such as precise positioning of the lunar lander and lunar libration research), but also has significant scientific value and broad application prospects in promoting the development of my country's lunar exploration technology and expanding the application scope of deep space orbit determination theory.

[0145] In summary, this invention will continuously optimize the details of the joint solution algorithm (such as dynamically adjusting the prior weight matrix and improving the higher-order terms of the tidal correction model), enhance its adaptability and processing efficiency in complex observation scenarios (such as lunar far-side observation and extreme weather conditions), and explore innovative modes of fusion between LRR / LLR data and lunar-based observation data (such as lunar seismometer data), continuously strengthening the ability to solve lunar rotation parameters, and providing more reliable technical support for the continuous advancement of lunar exploration missions (such as manned lunar landing and lunar base construction) and subsequent deep space exploration projects (such as asteroid exploration) in terms of dynamic parameter solution.

[0146] Finally, it should be noted that the above specific embodiments are merely representative examples of the present invention. Obviously, the present invention is not limited to the above specific embodiments and many variations are possible. Any simple modifications, equivalent changes, and alterations made to the above specific embodiments based on the technical essence of the present invention should be considered within the protection scope of the present invention.

Claims

1. A high-precision method for calculating lunar libration parameters using a combination of LRR and LLR technologies, characterized in that, include: Construct a joint observation dataset of LRR and LLR and perform preprocessing; Based on the preprocessed results, a joint lunar measurement model of LRR and LLR is constructed; The partial derivatives of the LRR and LLR joint lunar model with respect to the lunar rotation parameters and tidal LOVE number are derived, and the joint partial derivative matrix is ​​constructed. The partial derivatives of the LRR and LLR joint lunar model with respect to the lunar rotation parameters are derived, including: ， ， 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; The partial derivatives of the LRR and LLR joint lunar measurement model with respect to the tidal LOVE number are derived, including: ， ， in, ， ， in, Represents the radial tidal LOVE number. This represents the tangential tidal LOVE number. for The second-order elastic tidal displacement correction term at time t. correspond The rotation matrix from the fixed frame to the J2000 inertial frame at any given moment; For the mass of the tidal body, The radius of the moon, With the mass of the moon, for The distance between the moon and the tidal body at any given time. and They are respectively The direction vector of the moon pointing towards the lunar surface reflector, the lunar lander, and the tidal body at any given moment; Based on the joint partial derivative matrix and the calculated Earth-Moon distance obtained from the joint LRR and LLR lunar measurement model, nonlinear least squares is used for iterative solution to obtain the lunar libration parameters.

2. The method for high-precision calculation of lunar libration parameters using a combination of LRR and LLR technologies as described in claim 1, characterized in that, Construct and preprocess the joint observation dataset of LRR and LLR, including: The LRR and LLR joint observation dataset includes multi-source observation data, ground stations, lunar target locations, and lunar physical parameters; The multi-source observation data undergoes time reference unification and noise filtering; the coordinates of the ground stations are transformed; the lunar target position is corrected for tidal displacement and transformed for inertial coordinates; the lunar physical parameters include lunar rotation parameters and tidal LOVE numbers.

3. The method for high-precision calculation of lunar libration parameters using a combination of LRR and LLR technologies as described in claim 1, characterized in that, Based on the preprocessed results, a joint lunar observation model combining LRR and LLR is constructed, including: Construct a joint lunar observation model using LRR and LLR, with the following expression: ， 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.

4. The high-precision calculation method for lunar libration parameters combining LRR and LLR technologies according to claim 1, characterized in that, Based on the joint partial derivative matrix and the calculated Earth-Moon distance obtained from the joint LRR and LLR lunar measurement model, nonlinear least squares iterative solution is used to obtain the lunar libration parameters, including: Construct the joint residual vector: ， in , Each is half of the actual observed values ​​of LLR and LRR. , These are the theoretical calculated values ​​for LLR and LRR, respectively. For the joint residual vector; Based on the right ascension and declination of the lunar rotation axis in the J2000 inertial frame, the longitude of the lunar meridian, the rotational speed of the lunar rotation axis, the radial tidal LOVE number, and the tangential tidal LOVE number, the lunar libration parameters are obtained. By combining the prior weight matrix and the joint residual vector, the lunar libration parameters are iteratively solved using nonlinear least squares until convergence.

5. The method for high-precision calculation of lunar libration parameters using a combination of LRR and LLR technologies according to claim 4, characterized in that, The initial parameters of lunar libration are solved iteratively using nonlinear least squares, including: The lunar libration parameters are initialized as the starting point for iteration; Using the lunar libration parameters of the current iteration, the theoretical values ​​corresponding to LLR and LRR are recalculated to obtain the residual and joint residual vector of the current iteration. The updated values ​​of the lunar libration parameters are obtained by least squares iteration. The iteration stops when the change in residual between the previous and subsequent iterations is less than a set value, in order to obtain the final lunar libration parameters.

6. A high-precision calculation system for lunar libration parameters combining LRR and LLR technologies, used to implement the high-precision calculation method for lunar libration parameters combining LRR and LLR technologies as described in any one of claims 1-5, characterized in that, include: The preprocessing module is used to construct and preprocess the joint observation dataset of LRR and LLR; The Earth-Moon distance calculation module is used to construct a joint lunar measurement model of LRR and LLR based on the preprocessed results; The partial derivative module is used to derive the partial derivatives of the LRR and LLR joint lunar measurement model with respect to the lunar rotation parameters and tidal LOVE numbers, and to construct the joint partial derivative matrix; The iterative solution module is used to perform iterative solutions based on the joint partial derivative matrix and the lunar distance calculated according to the joint lunar measurement model of LRR and LLR, using nonlinear least squares to obtain the lunar libration parameters.

7. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the high-precision calculation method for lunar libration parameters using the combined LRR and LLR technologies as described in any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the high-precision calculation method for lunar libration parameters using the combined LRR and LLR technologies as described in any one of claims 1 to 5.

Images