A Method for Improving the Orbital Accuracy of Lunar Probes Based on Reflecting Prism Constraints

Abstract

This invention discloses a method for improving the orbital accuracy of a lunar probe based on reflective prism constraints. The method first utilizes laser ranging data obtained from a known reflective prism on the lunar surface using an onboard laser altimeter, and constructs an error equation set by combining this data with a dynamic orbital model. Next, a high-resolution camera is used to perform multiple imaging operations on the lunar reflective prism from different orbits and perspectives. Using the bundle adjustment principle, the observed image point coordinates are combined with the dynamic model to construct the error equation set. Finally, laser ranging observations from the reflective prism and multi-temporal photogrammetry observations are used as two different types of geometric constraints to construct a joint adjustment model of multi-source observation data. The high-precision orbital parameters are then calculated using a least-squares algorithm. This invention uses laser ranging data and an optical image database to add new constraints to the estimated orbit, ultimately correcting and further improving the orbital accuracy of the lunar probe.

Description

Technical Field

[0001] This invention belongs to the field of deep space navigation and exploration, and particularly relates to precise orbit determination of deep space probes, lunar geodesy, lunar photogrammetry, and laser ranging. Specifically, it is a method for improving the orbital accuracy of lunar probes based on reflective prism constraints. Background Technology

[0002] Precise orbit determination for lunar probes typically involves numerically integrating the probe's orbit using a set of force models to obtain calculated values ​​(i.e., expected measurements). These calculated values ​​are then subtracted from the actual observations obtained from ground-based tracking stations to obtain residuals. The least squares method is then used for iterative calculations to minimize the sum of squared residuals, resulting in the final precise orbit. However, with the increasing number of Earth-Moon system satellites and deep space exploration missions, traditional ground-based tracking methods face challenges such as busy tracking workloads and an insufficient number of ground stations to meet the ever-expanding tracking demands. Furthermore, the unique geographical location of the far side of the moon makes direct ground communication for orbit tracking impossible, significantly limiting traditional ground-based measurement methods (such as ground-based ranging / velocity measurement and VLBI measurements). When traditional ground-based measurement methods fail due to lunar self-obstruction, the probe's orbit on the far side lacks constraints, affecting overall orbital accuracy. Besides space-based tracking systems, autonomous navigation methods such as inertial navigation (INS) and celestial navigation can also be used for orbit determination. However, these methods have limited accuracy, and both inertial and celestial navigation can only obtain relative navigation information. Therefore, there is an urgent need to find new tracking and control methods to reduce the tracking and control burden on ground tracking stations and to obtain the invisible arc segment on the far side of the moon. This would reduce mission costs, improve mission efficiency, and simultaneously constrain the overall orbit, thereby improving orbital accuracy. This is one of the challenges currently facing the field of precision orbit determination, and also a difficult problem in the field of deep space navigation and exploration.

[0003] Currently, three laser reflectors have been deployed on the lunar surface by the Apollo 11, Apollo 14, and Apollo 15 missions, and Lunakhod 1 and Lunakhod 2 by the Luna 17 and Luna 21 missions. All of these laser reflectors have known, high-precision lunar surface coordinates. In addition, there is a laser reflector deployed on the far side of the moon by the CE-06 mission. Some usable prisms are shown in Table 1. How to effectively utilize the high-precision coordinates of the reflecting prisms and their reflection physics characteristics, and integrate them into the precise orbit determination of lunar probes to improve orbital accuracy, is another challenge currently facing the field of precise orbit determination.

[0004] Table 1. Coordinates of the lunar reflecting prism

[0005] . Summary of the Invention

[0006] The purpose of this invention is to address the problem of missing lunar far-side arc segments in current precise orbit determination of lunar probes, reduce the pressure on ground stations, and further improve orbit determination accuracy. This invention proposes a method for improving the orbit accuracy of lunar probes based on reflective prism constraints. This method utilizes known high-precision lunar reflective prism coordinates, combined with the probe's laser ranging data and optical image database, to add new constraints to the estimated orbit, ultimately correcting it and obtaining a more precise orbit.

[0007] According to one aspect of the present invention, a method for improving the orbital accuracy of a lunar probe based on reflective prism constraint is provided, comprising:

[0008] Based on the reflecting prism, laser ranging data and multi-temporal photogrammetry data of the lunar probe were acquired;

[0009] A first set of error equations is constructed based on the laser ranging data;

[0010] A second set of error equations is constructed based on the multi-temporal photogrammetry data;

[0011] A joint set of error equations is constructed based on the first and second sets of error equations, and a weight matrix is ​​introduced to handle the accuracy differences of different observations.

[0012] The joint error equations are solved based on the least squares principle to obtain the corrections to the orbital parameters. The orbital parameters are then iteratively updated until convergence, resulting in a precise orbit.

[0013] As a further technical solution, laser ranging data from the lunar probe is acquired based on a reflecting prism, including:

[0014] The spaceborne laser altimeter is controlled to emit laser pulses toward a lunar surface reflecting prism and receive the reflected signals, thus obtaining the round-trip time of the laser pulse from emission to reception. According to the formula The instantaneous absolute slant distance S between the lunar probe and the reflecting prism was calculated, where c is the speed of light.

[0015] As a further technical solution, based on a reflecting prism, multi-temporal photogrammetric data of the lunar probe can be obtained, including:

[0016] The spaceborne high-resolution camera is controlled to take multiple images of the lunar surface region containing the reflecting prisms at different times and in different orbits, and the image plane coordinates of each reflecting prism are extracted from each image by the ground processing system. .

[0017] As a further technical solution, a first set of error equations is constructed based on the laser ranging data as follows:

[0018] ,

[0019] in It is the laser ranging residual vector, and each residual is represented by a corresponding vector. Instantaneous absolute slant distance measurement between the lunar probe and the reflecting prism The theoretical distance calculated from the lunar probe's position obtained by integrating the reference orbit and the known coordinates of the reflecting prism Subtracting them gives the result; This is the overall design matrix for laser ranging, and each design matrix consists of corresponding... Distance observation model at time The partial derivative with respect to the orbital parameter p yields the observation model. Defined as The Euclidean distance between the satellite's position, determined by the orbital dynamics model, and the known coordinates of the reflecting prism; The correction vector for the parameters to be determined; It is a vector of laser ranging constants, with subscripts 1, 2, ..., m indicating the 1st, 2nd, ..., mth variables.

[0020] As a further technical solution, a second set of error equations is constructed based on the multi-temporal photogrammetry data:

[0021] ,

[0022] in It is a photogrammetric residual vector, where each residual is calculated from the theoretical image point coordinates and corresponding coordinates using the collinearity condition equation. The measured coordinates of the image point of the i-th reflecting prism at time i Subtracting them gives the result; It is a photogrammetric overall design matrix, and each design matrix consists of corresponding... The partial derivative of the image point coordinate observation model with respect to the orbital parameters at time t is obtained; The correction vector for the parameters to be determined; It is a vector of photogrammetric constants, with subscripts 1, 2, ..., n indicating the 1st, 2nd, ..., nth variables.

[0023] As a further technical solution, a joint error equation set is constructed based on the first and second error equation sets as follows:

[0024] ,

[0025] in The result is a joint residual vector that integrates the residual vectors from laser ranging and photogrammetry. This is a joint design matrix that integrates both laser ranging and photogrammetry design matrices. It is a joint constant vector that simultaneously integrates laser ranging and photogrammetry.

[0026] As a further technical solution, the method also includes:

[0027] The joint normal equation is expressed as follows:

[0028] ,

[0029] Using the initial reference orbit calculate and Then, the correction vector of the orbital parameters is obtained by solving the equations. ;get Then, update the orbital parameters; re-perform numerical integration of the orbit, and recalculate the theoretical observations and design matrix. Construct new normal equations and solve for new corrections. This iterative process continues until the preset convergence condition is met; the final converged orbital parameter estimates are obtained. This refers to the optimal precision track obtained after adding constraints from both reflective prism laser ranging and multi-temporal photogrammetry data. Represents the weight array.

[0030] According to one aspect of the present invention, a lunar probe orbit accuracy improvement system based on reflective prism constraint is provided, for implementing the method, comprising:

[0031] The data acquisition module is used to acquire laser ranging data and multi-temporal photogrammetry data of the lunar probe based on the reflecting prism;

[0032] The first construction module is used to construct a first set of error equations based on the laser ranging data;

[0033] The second construction module is used to construct a second set of error equations based on the multi-temporal photogrammetry data;

[0034] The third construction module is used to construct a joint error equation set based on the first and second error equation sets, and to introduce a weight matrix to handle the accuracy differences of different observations.

[0035] The solution update module is used to solve the joint error equations based on the least squares principle to obtain the corrections of the orbital parameters, iteratively update the orbital parameters until convergence, and obtain the precise orbit.

[0036] According to one aspect of the present invention, a device for improving the orbital accuracy of a lunar probe based on a reflective prism constraint is provided, comprising a memory and a processor, wherein the memory stores program instructions that are executed by the processor, and the processor invokes the program instructions to execute the method for improving the orbital accuracy of a lunar probe based on a reflective prism constraint.

[0037] According to one aspect of the present invention, a non-transitory computer-readable storage medium is provided, the non-transitory computer-readable storage medium storing computer instructions that cause the computer to execute the described method for improving the orbital accuracy of a lunar probe based on a reflective prism constraint.

[0038] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0039] This invention addresses the problem of missing lunar far-side arc segments in current precise orbit determination for lunar probes, the need to reduce the burden on ground stations, and the requirement to further improve orbit determination accuracy. It proposes a method for improving the orbital accuracy of low-Earth orbit lunar probes based on lunar surface reflecting prism constraints. This method utilizes laser ranging and optical image databases from the lunar probe. It calculates the image-side coordinates and relative distance to the probe using the reflecting prism, and then introduces high-precision known coordinates of the lunar surface reflecting prism to achieve joint adjustment of multi-source data. Finally, it combines a detailed force model to add new constraints to the estimated orbit, ultimately correcting the trajectory and further improving the orbital accuracy of the lunar probe, providing fundamental orbital support for the scientific data of the lunar probe. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 A flowchart illustrating a method for improving the orbital accuracy of a lunar probe based on reflective prism constraints, provided in an embodiment of the present invention;

[0042] Figure 2 A schematic diagram illustrating the principle of the lunar probe orbit accuracy improvement method based on reflective prism constraint provided in this embodiment of the invention;

[0043] Figure 3 This is a schematic diagram illustrating the process of constructing a multi-temporal photogrammetric image database based on a lunar surface reflecting prism, as provided in an embodiment of the present invention. Detailed Implementation

[0044] To address the issues of missing lunar far-side arc segments in current precise orbit determination for lunar probes, the need to reduce the burden on ground stations, and the requirement to further improve orbit determination accuracy, this invention proposes a technical solution. Using an orbital dynamics model as a unified framework, it constructs a multi-source observation data joint adjustment model by treating laser ranging observations from a reflecting prism and multi-temporal photogrammetry observations as two different types of geometric constraints. The high-precision orbital parameters are then calculated using a least-squares algorithm.

[0045] This invention aims to utilize the laser ranging and optical image database data of the lunar probe, calculate the image-side coordinates and relative distance of the reflecting prism, and then introduce the high-precision known coordinates of the lunar reflecting prism to achieve joint adjustment of multi-source data. Finally, by combining a detailed force model, new constraints are added to the estimated orbit, thereby further improving the orbital accuracy of the lunar probe and providing basic orbital support for the scientific data of the lunar probe.

[0046] 1. Constructing an error equation set for laser ranging based on a reflecting prism.

[0047] The core of this process lies in using a spaceborne laser altimeter to actively emit laser pulses to measure the distance to a reflecting prism with known high-precision coordinates on the lunar surface. This yields direct and accurate observations of the distance between the moon and the stars. These observations are then used as strong constraints, combined with a detailed dynamic orbital model, to optimize the orbit and thus precisely correct it.

[0048] This invention breaks down the method into three main steps, as shown in the appendix. Figure 1 As shown. This includes:

[0049] (1) System composition and observation acquisition

[0050] The orbiter needs to carry a precision laser altimeter. As the orbiter flies over the lunar reflector prism, a precision pointing control system aligns the laser altimeter's emission axis with the target prism. The laser altimeter then emits a short laser pulse towards the prism; this pulse is reflected by the prism and received by the orbiter's receiving telescope. The precise round-trip time of the laser pulse from emission to reception is measured. And based on the speed of light c, the instantaneous absolute slant distance S between the orbiter and the reflecting prism can be calculated in real time:

[0051] ,

[0052] This distance observation S is independent of the orbital dynamics model and is a high-precision direct geometric observation.

[0053] (2) Establishment of the observation model

[0054] Let the known coordinates of the reflecting prism in the lunar-fixed coordinate system be... These coordinates have been precisely measured to millimeter-level accuracy using long-term lunar laser ranging. Let... The position of the satellite in the same coordinate system at any given time is determined by the orbital dynamics model. The theoretical observation model for laser ranging is:

[0055] ,

[0056] The observation equation is: ,in This is the actual measured distance. This represents the observation error.

[0057] (3) Construct a system of error equations

[0058] Satellite position It is not an independent parameter, but rather a set of orbital parameters. It is obtained through numerical integration of the orbital dynamics model, i.e. Parameter vector It typically includes the initial orbital state vector (position, velocity) and the dynamic parameters to be estimated (solar radiation pressure coefficient, empirical acceleration, etc.).

[0059] To achieve orbital constraints, the nonlinear observation equations need to be applied to the reference orbit. Linearization. Let To use reference parameters The calculated theoretical distance. The linearized error equation is then:

[0060] ,

[0061] in, The parameter correction vector to be determined. This represents the higher-order terms of the linearized error equation. During adjustment, a first-order linearized error equation is typically used, and higher-order terms are omitted. Partial derivatives It can be calculated using the chain rule:

[0062] ,

[0063] First item It is the partial derivative of the distance with respect to the satellite's position; in essence, it is the unit line-of-sight vector from the satellite to the reflecting prism. The negative transpose of can be expressed as:

[0064] ,

[0065] Second item It is the partial derivative of the satellite's position with respect to its orbital parameters, i.e. This matrix is ​​obtained through the integral orbital variational equation, describing the time... How the satellite position changes orbital parameters at time The changes include a detailed orbital dynamics model.

[0066] In summary, for single-shot laser ranging, its design matrix... for:

[0067] .

[0068] Finally, in actual orbital missions, multiple laser ranging measurements can be performed on multiple different orbital arcs and multiple different reflecting prisms. The error equations from all m observations are then combined to form a total error equation system:

[0069] ,

[0070] in:

[0071] It is the residual vector;

[0072] It is the overall design matrix;

[0073] It is a constant term vector, where the subscripts 1,2,...,m represent the 1st, 2nd,...,mth variables (residuals, overall design matrix, constant terms), and m represents the number of variables.

[0074] 2. An error equation set is constructed based on multi-temporal photogrammetry.

[0075] The core of this method lies in using the high-resolution camera on the orbiter to take multiple images of the reflecting prism with known high-precision coordinates on the lunar surface from different orbits and from different perspectives. Through the rigorous bundle adjustment principle, the image point coordinate observations are combined with the orbital dynamics model to calculate high-precision orbital parameters.

[0076] This invention breaks down the process into three main steps, as shown in the appendix. Figure 1 As shown. This includes:

[0077] (1) System composition and acquisition of multi-temporal observations

[0078] The orbiter needs to carry a high-resolution space camera. During the long-term operation of the orbiter, the ground-based and on-board tracking and control systems need to arrange for the camera to take multiple pictures of the lunar surface region containing the same set of reflecting prisms at different times and in different orbits, so as to obtain a series of images with different perspectives.

[0079] Using a ground-based image processing system, the image plane coordinates of each reflecting prism are extracted from each image. This results in a series of image point coordinates of the same target obtained from different spatial geometric relationships, constituting multi-temporal photogrammetric observations.

[0080] (2) Establishment of the observation model

[0081] The fundamental mathematical model of photogrammetry is the collinearity condition equation, which expresses the rigorous geometric relationship that the object point, the photographic center, and the image point are collinear. The known coordinates of the reflecting prism in the lunar-fixed coordinate system are... Set time The satellite's position in the same coordinate system is The camera's attitude is determined by three attitude angles. Defined rotation matrix (Its elements are) The collinearity condition equation then gives the image point coordinates. Theoretical calculation values:

[0082] ,

[0083] in, To accurately calibrate known camera interior orientation elements via ground calibration, where The coordinates of the principal point are given, and f is the focal length.

[0084] For the i-th reflecting prism in the j-th image, its observation equation can be written as:

[0085] ,

[0086] in, These are the actual measured coordinates of the image point. For observation error, For a moment Camera pose, , These represent the theoretically calculated values ​​of the image point's x and y coordinates, respectively.

[0087] (3) Construct a system of error equations

[0088] Similar to laser ranging methods, the instantaneous position of the satellite and posture It is not an independent parameter, but rather a set of orbital parameters. The following is obtained through numerical integration of the orbital dynamics model:

[0089] ,

[0090] , These represent the position state equation and the attitude state equation, respectively.

[0091] To achieve orbital constraints, the nonlinear collinearity condition equations need to be applied to the reference orbit. Linearization. Let To use reference parameters The calculated theoretical image point coordinates are then used. The linearized error equation is:

[0092] .

[0093] Based on the multi-temporal photogrammetric observation equations for the reflecting prism, the partial derivatives... and It can be represented as:

[0094] ,

[0095] The first item The partial derivative of the image point coordinates with respect to the satellite position reflects how changes in the satellite position cause image point displacement on the image plane; the second term... It is the partial derivative of the satellite's position with respect to its orbital parameters, i.e., the state transition matrix. ; Third item The partial derivative of the image point coordinates with respect to the camera pose reflects the influence of changes in camera pose on the image point coordinates; the fourth term It is the partial derivative of the satellite's attitude with respect to the orbital parameters, i.e., the state transition matrix. .

[0096] Therefore, for a single image point observation, its merged design matrix is:

[0097] ,

[0098] The theoretical calculation equation representing the combined coordinates (x, y) of the image point is (the theoretical calculation value derived from the collinearity condition equation above).

[0099] Finally, in actual orbital missions, observations from multiple temporal image points can be obtained. The error equations for all n image point observations are then combined to form a system of total error equations:

[0100] ,

[0101] in:

[0102] It is the residual vector;

[0103] It is the overall matrix;

[0104] It is a constant term vector, where the subscripts 1, 2, ..., n represent the 1st, 2nd, ..., nth variables (residuals, photogrammetric overall design matrix, constant terms), and n expresses the number of variables.

[0105] 3. Joint adjustment and trajectory determination of multi-source data.

[0106] By combining all m laser ranging measurements and n image point observations, a system of overall error equations is formed:

[0107] ,

[0108] in:

[0109] For the joint residual vector;

[0110] For joint design matrix;

[0111] This is a vector of joint constant terms.

[0112] Considering the different accuracies of the two types of observations, a weighting matrix is ​​introduced. The weight matrix is ​​a diagonal matrix, and its diagonal elements are the reciprocals of the weights of each observation. The weights are determined based on the prior precision of the observations.

[0113] According to the least squares principle Construct the joint normal equation:

[0114] .

[0115] Solving this normal equation yields the optimal corrections to the orbital parameters:

[0116] ,

[0117] Parameters are continuously updated through an iterative process. The process continues until convergence, ultimately yielding the optimal orbital parameter estimates. .

[0118] In summary, this invention utilizes known high-precision lunar surface reflecting prism coordinates, combined with the probe's laser ranging data and optical image database, to add new constraints to the estimated orbit, ultimately correcting it and obtaining a more precise orbit.

[0119] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form new technical solutions. Such combinations are not bound by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0120] This invention addresses the issues of missing lunar far-side arc segments in current precise orbit determination for lunar probes, the need to reduce the burden on ground stations, and the requirement to further improve orbit determination accuracy. It proposes a method for improving the orbital accuracy of lunar probes based on reflective prism constraints. Specifically, it utilizes laser ranging and optical image data from the probe, combined with a dynamic model, to construct error equations, achieving joint adjustment of multi-source data. Ultimately, this corrects the orbital parameters and yields a more precise orbit. A flowchart is attached. Figure 1 As shown.

[0121] This invention will comprehensively describe a method for improving the orbital accuracy of a low-Earth orbit lunar probe based on lunar surface reflective prism constraints, using specific mission parameters and data from the Lunar Reconnaissance Orbiter (LRO). Since its launch in 2009, the LRO mission has continuously acquired massive amounts of high-resolution images and laser altimetry data, and its orbit has undergone long-term, precise measurement, providing an ideal platform for validating this method.

[0122] 1. Acquire and preprocess laser ranging data and optical image data.

[0123] The laser ranging data comes from the Lunar Orbiter Laser Altimeter (LOLA) aboard the LRO. LOLA is a multi-beam laser altimeter system. When the LRO flies over a known lunar reflector prism (such as the Apollo 15 reflector prism), the control system adjusts the probe's attitude to ensure that LOLA's emission optical axis is precisely pointed towards the target prism. LOLA emits nanosecond-level short-pulse lasers towards the prism and receives signals returned from the corner reflector prism, as shown in the attached diagram. Figure 2 As shown. By precisely measuring the round-trip time of the laser pulse from emission to reception. According to the formula The instantaneous absolute slant range S between the detector and the reflecting prism is directly calculated. This raw observation value requires preprocessing, including internal delay correction and a unified time system. Furthermore, using precise ephemeris data, the range value is corrected from the instrument's phase center to the detector's center of mass. Finally, a series of high-precision instantaneous slant range observations with the center of mass as the reference are obtained. Its single-shot ranging accuracy is determined by LOLA's performance specifications.

[0124] Multi-temporal photogrammetry data comes from the high-resolution camera system onboard the LRO, primarily from the narrow-angle camera LROC NAC. LROC NAC possesses extremely high spatial resolution (up to 0.5 meters at an orbital altitude of 50 km), enabling it to clearly capture and distinguish the Apollo 15 isotropic reflector prism on the lunar surface at different times and angles, as shown in the attached image. Figure 2 and attached Figure 3 As shown in the attached image. When implementing this invention, it is necessary to select multiple images from the LRO image database taken at different times and from different orbits of the same area containing a reflecting prism (such as the Apollo 15 landing site), as shown in the attached image. Figure 3 As shown. These images should have different viewpoints, with significant differences in the satellite's position and attitude at corresponding times, to form strong geometric constraints. After acquiring the raw images, rigorous photogrammetric preprocessing is required. The first step is radiometric calibration, converting the raw DN values ​​into physical quantities; the second step is initial geometric correction, using the coarse attitude and orbital parameters provided by the satellite to eliminate most systematic errors. The key step is to use ground processing software to manually or automatically identify and measure the image plane coordinates of the target reflecting prism on each preprocessed image with sub-pixel accuracy. This process also requires the use of a high-precision digital terrain model (such as GLD100 generated by LOLA) as an aid to eliminate image point displacement caused by terrain undulations. Ultimately, a sequence of image point coordinate observations across multiple time phases and images is obtained.

[0125] 2. Construct a system of error equations.

[0126] After obtaining and preprocessing the two types of observation data mentioned above, it is necessary to construct error equation sets separately to prepare for joint adjustment and orbital constraints. First, a unified orbital dynamics framework needs to be constructed. This is based on the lunar-fixed coordinate system and the lunar-centered celestial coordinate system defined in the planetary and lunar ephemeris published by JPL (such as DE430). The initial reference orbit of the LRO is obtained from the JPL precise ephemeris. including the initial time Position and velocity vector in the lunar celestial coordinate system The force models employed include: lunar non-spherical gravitational perturbations (using the GRGM660PRIM high-order model, truncated to order 440), third-body perturbations (DE430 ephemeris), solar radiation pressure (combined with the LRO multi-sail model), and tidal perturbations. Based on this force model, the reference orbit... Numerical integration is performed to obtain the result at any given time. satellite position and state transition matrix .

[0127] Next, error equations are constructed for the two types of observations. For laser ranging observations, the preprocessed slant range observations are used... Position obtained by integrating with the reference orbit and known prism coordinates (For example, the theoretical distance calculated from the coordinates of Apollo 15 in the DE430 PA coordinate system) By comparison, the residuals are obtained. According to the formula The design matrix is ​​obtained, where This is the unit line-of-sight vector pointing from the detector to the prism. For photogrammetric observations, this refers to the measured image point coordinates. The theoretical value calculated using the collinearity condition equation A comparison is needed. The calculation of the collinearity condition equation requires satellite positions. The camera's attitude matrix in the J2000 coordinate system (Aptitude ephemeris data can be obtained from LROC NAC), and precise in-camera orientation elements. (Determined by ground-based laboratory calibration). The specific form of the collinearity condition equation is:

[0128] .

[0129] For each image point observation, the residual is and The design matrix must follow the formula. Calculation. Among them, and It can be obtained by differentiating the collinear equation; It is the attitude state transition matrix, which describes the relationship between attitude parameters and the initial state of the orbit. Its calculation also requires integrating the attitude variational equation.

[0130] 3. Joint adjustment of multi-source data and trajectory determination.

[0131] After constructing the error equations for all laser ranging and photogrammetric observations separately, they were combined into a joint set of error equations:

[0132] ,

[0133] in:

[0134] It is the joint residual vector;

[0135] It is a joint design matrix;

[0136] It is a vector of joint constant terms;

[0137] Because the two types of observations have different levels of precision, a weighting matrix must be introduced. To handle this difference. Weight matrix It is usually taken as a diagonal matrix, and its diagonal elements are the reciprocals of the variances of the observations. Prior variance of laser ranging observations The prior variance of the image point coordinate observations can be set according to the calibration accuracy of LOLA. The setting is based on the measurement accuracy. The weighting matrix unifies observations of different categories into the same adjustment system.

[0138] Finally, the least squares iterative solution process is entered. To minimize the sum of squared residuals, the joint normal equations are constructed:

[0139] ,

[0140] In the first iteration, the initial reference orbit is used. calculate and Then, the correction vector of the orbital parameters is obtained by solving the equations. .get Then, update the orbital parameters. Based on the updated parameters As a new reference orbit, numerical integration of the orbit is performed again, and the satellite position, velocity, and state transition matrix at all times are recalculated. In turn, the theoretical observations and design matrices are recalculated. Construct new normal equations and solve for new corrections. This iterative process continues until a preset convergence condition is met. The convergence condition is typically set as the norm of the correction vector between two consecutive iterations. Less than a certain threshold. The final converged orbital parameter estimate. This refers to the optimal LRO precision track obtained after adding constraints from both reflective prism laser ranging and multi-temporal photogrammetry data.

[0141] Through the above-described specific implementation process, the method of the present invention can utilize the abundant data resources and high-precision control points on the lunar surface of the LRO mission to add new geometric constraints to the lunar probe orbit, especially the arc segment on the far side of the moon that cannot be covered by ground-based telemetry and control. This improves the overall orbit determination accuracy of LRO and provides more reliable basic orbital support for the production of its scientific products.

[0142] The implementation of the various embodiments of the present 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 the present invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of the present invention provide a lunar probe orbit accuracy improvement system based on a reflecting prism constraint. This system is used to execute a lunar probe orbit accuracy improvement method based on a reflecting prism constraint from the above method embodiments.

[0143] The system includes: a data acquisition module for acquiring laser ranging data and multi-temporal photogrammetry data of the lunar probe based on a reflecting prism; a first construction module for constructing a first set of error equations based on the laser ranging data; a second construction module for constructing a second set of error equations based on the multi-temporal photogrammetry data; a third construction module for constructing a joint set of error equations based on the first and second set of error equations, and introducing a weight matrix to handle the accuracy differences of different observations; and a solution and update module for solving the joint set of error equations based on the least squares principle to obtain the corrections to the orbital parameters, iteratively updating the orbital parameters until convergence, and obtaining a precise orbit.

[0144] This invention provides a lunar probe orbit accuracy improvement system based on reflecting prism constraints. Addressing the current problem of missing lunar far-side arc segments in precise lunar probe orbit determination, and the need to reduce the burden on ground stations and further improve orbit determination accuracy, this system employs several modules. Utilizing known high-precision lunar reflecting prism coordinates, combined with the probe's laser ranging data and optical image database, it adds new constraints to the estimated orbit, ultimately correcting it and obtaining a more precise orbit.

[0145] It should be noted that the system embodiments provided by the present invention are used not only to implement the methods in the above method embodiments, but also to implement the methods in other method embodiments provided by the present invention. The only difference is that corresponding functional modules are set. The principle is basically the same as that of the above system embodiments provided by the present invention. As long as those skilled in the art can improve the modules in the above system embodiments by referring to the specific technical solutions in other method embodiments and combining technical features to obtain corresponding technical means and technical solutions composed of these technical means, on the basis of the above system embodiments, and on the premise of ensuring the practicality of the technical solutions, they can obtain corresponding system-like embodiments for implementing the methods in other method-like embodiments.

[0146] Based on the same inventive concept as any of the foregoing embodiments, this embodiment of the invention also provides a lunar probe orbit accuracy improvement device based on reflective prism constraint, including a memory and a processor. The memory stores program instructions that are executed by the processor, and the processor calls the program instructions to execute the lunar probe orbit accuracy improvement method based on reflective prism constraint.

[0147] Based on the same inventive concept as any of the foregoing embodiments, this embodiment of the invention also provides a non-transitory computer-readable storage medium storing computer instructions that cause the computer to execute the method for improving the orbital accuracy of a lunar probe based on a reflective prism constraint.

[0148] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0149] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0150] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0151] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0152] In summary, this invention discloses a method for improving the orbital accuracy of a lunar probe based on reflective prism constraints. The method first utilizes laser ranging data obtained from a known lunar reflective prism using an onboard laser altimeter, and constructs an error equation set by combining this data with a dynamic orbital model. Next, a high-resolution camera is used to image the lunar reflective prism multiple times from different orbits and perspectives. Using the bundle adjustment principle, the image point coordinate observations are combined with the dynamic model to construct the error equation set. Finally, laser ranging observations from the reflective prism and multi-temporal photogrammetry observations are used as two different types of geometric constraints to construct a joint adjustment model of multi-source observation data. The high-precision orbital parameters are then calculated using a least-squares algorithm. This invention uses laser ranging data and an optical image database to add new constraints to the estimated orbit, ultimately correcting and further improving the orbital accuracy of the lunar probe.

[0153] The terms “comprising” and “having”, and any variations thereof, in the specification, claims, and accompanying drawings of this invention are intended to cover a non-exclusive inclusion, such as a process, method, system, product, or apparatus that includes a series of steps or units, not necessarily limited to those explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0154] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A method for improving the accuracy of a lunar probe's orbit based on the constraint of a reflecting prism, characterized in that, The method comprises the following steps: acquiring laser ranging data and multi-temporal photogrammetry data of a lunar probe based on a reflecting prism; constructing a first error equation set based on the laser ranging data; constructing a second error equation set based on the multi-temporal photogrammetry data; constructing a joint error equation set based on the first error equation set and the second error equation set, and introducing a weight matrix to process accuracy differences of different observation values; solving the joint error equation set based on a least square principle to obtain correction numbers of orbit parameters, iteratively updating the orbit parameters until convergence is achieved, and obtaining a precise orbit.

2. The method of claim 1, wherein the method is characterized by: acquiring laser ranging data of a lunar probe based on a reflecting prism, comprising the following steps: The spaceborne laser altimeter transmits laser pulses to the lunar surface reflection prism and receives the reflected signals to obtain the round-trip time of the measurement laser pulse from transmission to reception , the instantaneous absolute slant range S between the lunar probe and the reflection prism is calculated according to the formula , wherein c is the speed of light.

3. The method of claim 1, wherein the method is characterized by: acquiring multi-temporal photogrammetry data of a lunar probe based on a reflecting prism, comprising the following steps: The control of the high-resolution camera on the satellite to take multiple images of the lunar surface area containing the reflecting prisms at different times and different orbits, and the ground processing system extracts the image plane coordinates of each reflecting prism on each image .

4. The method of claim 2, wherein the method is characterized by, constructing a first error equation set based on the laser ranging data is: ， where is the laser ranging residual vector, each residual is given by the difference between the measured range and the theoretical range computed from the lunar probe position and known coordinates of the reflecting prism at the time instant is the laser ranging design matrix, each design matrix is given by the difference between the measured range and the theoretical range computed from the lunar probe position and known coordinates of the reflecting prism at the time instant is the Euclidean distance between the satellite position determined by the orbit dynamics model and the known coordinates of the reflecting prism at the time instant is the parameter correction vector to be determined is the laser ranging constant vector, the subscripts 1, 2,..., m indicate the 1st, 2nd,..., mth variable.​​ 5. The method of claim 3, wherein the method is characterized by: constructing a second error equation set based on the multi-temporal photogrammetry data is: ， wherein is the photogrammetric residual error vector, each residual error is calculated by the theoretical image point coordinates through the collinearity condition equation and the corresponding is the measured value of the image point coordinates of the i-th reflecting prism at the time instant is obtained by subtraction; is the photogrammetric overall design matrix, each design matrix is calculated by the corresponding is obtained by the partial derivative of the image point coordinate observation model at the time instant to the orbital parameters; is the parameter correction vector to be solved; is the photogrammetric constant term vector, the subscripts 1, 2,..., n represent the 1st, 2nd,..., n-th variable.

6. The method of claim 1, wherein the method is based on a reflective prism constraint. constructing a joint error equation set based on the first error equation set and the second error equation set is: ， wherein is a combined residual vector, which combines the residual vectors of laser ranging and photogrammetry; is a combined design matrix, which combines the design matrices of laser ranging and photogrammetry; is a combined constant term vector, which combines the constant term vectors of laser ranging and photogrammetry; is a correction number vector of the orbit parameters.

7. The method of claim 6, wherein the method is characterized by, The method further comprises: constructing a joint method equation expression is: ， Using initial reference orbit Compute And Then solve the normal equation to obtain the correction vector of orbit parameters ; Obtain After that, update the orbit parameters; re-carry out the numerical integration of the orbit, and calculate the theoretical observation value and the design matrix again , construct a new normal equation and solve a new correction ; This iteration process is repeated until the preset convergence condition is met; the final converged orbit parameter estimate , that is, the optimal precise orbit obtained after adding the common constraints of the retro-reflective prism laser ranging and multi-temporal photogrammetry data, wherein represents the weight matrix.

8. A lunar probe orbit accuracy enhancement system based on reflection prism constraint, for implementing the method of any one of claims 1 to 7, characterized in that, The method comprises the following steps: a data acquisition module is configured to acquire laser ranging data and multi-temporal photogrammetry data of a lunar probe based on a reflecting prism; a first construction module is configured to construct a first error equation set based on the laser ranging data; a second construction module is configured to construct a second error equation set based on the multi-temporal photogrammetry data; a third construction module is configured to construct a joint error equation set based on the first error equation set and the second error equation set, and introduce a weight matrix to process accuracy differences of different observation values; a solution and update module is configured to solve the joint error equation set based on a least square principle to obtain correction numbers of orbit parameters, iteratively update the orbit parameters until convergence is achieved, and obtain a precise orbit.

9. A lunar probe orbit accuracy enhancement device based on reflection prism constraint, characterized in that, The non-transitory computer readable storage medium stores computer instructions, and the computer instructions cause the computer to execute the method for improving orbit precision of a lunar probe based on a reflecting prism constraint according to any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium, comprising: The non-transitory computer readable storage medium stores computer instructions, and the computer instructions cause the computer to execute the method for improving orbit precision of a lunar probe based on a reflecting prism constraint according to any one of claims 1 to 7.

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