Astronomical orientation parameter solving method and system based on inverse VLBI interferometry and medium

Through the inverse VLBI interferometry measurement mode, a celestial body rotation orientation physical model and a differential measurement model were established, theoretical observation values ​​and partial derivatives were calculated, signal propagation errors were eliminated, and high-precision orientation parameter solution of extraterrestrial objects was achieved, solving the problem of insufficient accuracy of traditional VLBI measurements and improving the accuracy of astrophysical models.

CN119199723BActive Publication Date: 2025-10-17SHANGHAI SATELLITE ENG INST
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Patent Information

Application Number
CN202411137245.9
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-08-19
Publication Date
2025-10-17
Estimated Expiration
2044-08-19

AI Technical Summary

Technical Problem

The existing traditional VLBI measurement mode has the problem of insufficient accuracy in measuring the orientation parameters of extraterrestrial objects, and it is difficult to meet the requirements of deep space exploration missions for high-precision orientation parameters.

Method used

Using the inverse VLBI interferometry measurement mode, by establishing a celestial body rotation orientation physical model and an inverse VLBI differential measurement model, calculating theoretical observation values ​​and partial derivatives, and using the least squares method to fit ground observation values, the position vector of the lander and the orientation parameters of the celestial body are solved, signal propagation errors are eliminated, and high-precision positioning and orientation parameter solution are achieved.

Benefits of technology

It has improved the accuracy of solving the orientation parameters of extraterrestrial objects, provided information on the internal structure and surface mass distribution of celestial bodies, and significantly improved the perfection of astrophysical models.

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Abstract

The application provides a celestial body orientation parameter solving method and system based on inverse VLBI interferometry and a medium. The method comprises the following steps: firstly, a rotation orientation physical model of a celestial body and an inverse VLBI differential measurement model are established, a lander coordinate and a celestial body orientation parameter are introduced into the model by combining the conversion between a non-inertial system and an inertial system coordinate. High-precision differential measurement tracking data of inverse VLBI are obtained, and based on the principle of the least square method, a lander position and a celestial body orientation model parameter are determined, so that the residual square sum between the calculated theoretical observation value of inverse VLBI and the ground observation value is minimum, and high-precision extraterrestrial celestial body orientation parameters are obtained. The application can realize precise positioning of a lander and solving of celestial body orientation parameters, the obtained data are high in precision, high-precision inverse VLBI differential measurement data can significantly improve the solving precision of the celestial body orientation model parameters, and then information about the internal structure and surface mass distribution change of the celestial body is provided, and additional constraints for the improvement of the celestial body physical model are provided.
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Description

TECHNICAL FIELD

[0001] The present application relates to the field of landing probe precise positioning and deep space exploration, and in particular, to a landing probe precise positioning and extraterrestrial high-precision directional parameter solving method and system based on inverse VLBI measurement mode and a medium. BACKGROUND

[0002] The transformation of celestial body rotation contains important information of its internal structure and surface mass distribution, and the determination of high-precision directional parameters helps to provide additional constraints for the improvement of celestial body physical model, so as to reveal the internal structure of the celestial body. At present, the high-precision measurement of lunar directional parameters is based on lunar laser ranging based on lunar reflector, and the high-precision measurement of Mars directional parameters is based on two-way ranging and speed measurement based on Mars lander radio tracking, while other celestial bodies have low precision of directional parameters due to insufficient exploration data. Generally speaking, new deep space exploration missions and more tracking observation data can effectively improve the physical model of celestial body rotation.

[0003] The traditional Very Long Baseline Interferometry (VLBI) is to receive electromagnetic waves radiated by radio sources through two antennas on the ground, and then measure the time delay and time delay rate. This measurement method is used to study the rotation of the earth, as shown in FIG. 1. For the study of extraterrestrial objects, the traditional VLBI has limitations. Figure 3

[0004] The implementation of new measurement modes such as inverse VLBI is an effective means to further improve the precision of directional parameters. Inverse VLBI measurement is to receive signals simultaneously emitted from different positions on other celestial bodies by a ground antenna, and to study the rotation of extraterrestrial objects by virtue of the feature that the geometric path difference of electromagnetic waves reaching the ground antenna is constantly changing due to the rotation of extraterrestrial objects, as shown in FIG. 2. Figure 2

[0005] In summary, we need a landing probe precise positioning and extraterrestrial high-precision directional parameter solving method and system based on inverse VLBI measurement mode, which can break through the limitations of traditional measurement. SUMMARY

[0006] In view of the defects in the prior art, the purpose of the present application is to realize the precise positioning of the lander and the directional parameter solving of the celestial body, so as to obtain high-precision data.

[0007] According to the celestial directional parameter solving method based on inverse VLBI interferometric measurement provided by the present application, the following steps are included:

[0008] Step S1: For the research target, a rotation directional physical model of the celestial body and an inverse VLBI differential measurement model are established; ​​

[0009] Step S2: based on the self-orientation physical model and the inverse VLBI differential measurement model, calculating the theoretical observation value of the inverse VLBI differential measurement, and the partial derivative of the theoretical observation value to the coordinate of the landing vehicle to be estimated and the orientation parameter of the celestial body;

[0010] Step S3: according to the theoretical observation value and the partial derivative, fitting the ground observation value of the inverse VLBI differential measurement, solving the correction value of the position vector of the landing vehicle and the orientation parameter of the celestial body, and adding the correction value to the estimated parameter to obtain the optimal estimation value;

[0011] Wherein, repeating the step S2 and the step S3 until the difference between the optimal estimation values before and after the correction is less than the convergence condition.

[0012] Preferably, the step S1 comprises the following sub-steps:

[0013] S1.1, establishing a self-orientation physical model of the moon;

[0014] S1.2, establishing an inverse VLBI differential measurement model.

[0015] Preferably, in the step S1.1, the conversion relationship of the self-orientation physical model of the moon from the moon-centered celestial coordinate system to the moon-centered moon-fixed coordinate system is as follows:

[0016]

[0017] Wherein, r bf and r icrs are the moon-fixed coordinate and the moon celestial coordinate respectively, R (x,y,z) represents the rotation matrix around the x, y, z three axes, and the three Euler angles are calculated by the following formula:

[0018]

[0019] θ=90°-δ0

[0020] ψ=W

[0021] Wherein, α0, δ0 and W define the direction of the rotation axis of the celestial body and the position of the initial meridian.

[0022] Preferably, in the step S1.2, the inverse VLBI differential measurement system comprises: a plurality of celestial landing vehicles, a relay satellite and a ground receiving antenna, the ground receiving antenna is used to receive the information emitted by the plurality of landing vehicles at the same time, measure the receiving delay to obtain the ground observation value, the ground observation value includes time delay and time delay rate data; the relay satellite is used for bidirectional time synchronization between the plurality of landing vehicles;

[0023] The time delay measurement model is as follows:

[0024] Tivlbi = τ g + Δτ t + Δτ p

[0025] where τ g is the geometric delay, Δτ t is the inter-lander time difference correction, Δτ p is the propagation path delay correction.

[0026] Preferably, in step S2,

[0027] The formula for calculating the theoretical observation value of the inverse VLBI differential measurement is as follows:

[0028]

[0029] where R1 and R2 are the distances from the two landers to the ground antenna, c is the speed of light, RLT is the gravitational delay in the signal propagation process, t1 and t2 represent the times when the ground receives the signals from the two landers, respectively, since the ground antenna records the observation value in the UTC time scale, the latter part is the correction for converting the time scale from UTC to TDB;

[0030] The formula for calculating the partial derivative is as follows:

[0031]

[0032]

[0033] where (x, y, z) represents the position vector of the lander in the lunar fixed system, are three Euler angle parameters describing the orientation of the lunar rotation.

[0034] Preferably, step S3 includes the following sub-steps:

[0035] S3.1, fitting the ground observation value of the inverse VLBI differential measurement according to the theoretical observation value;

[0036] S3.2, solving the correction values of the position vector of the lander and the orientation parameters of the celestial body according to the partial derivative;

[0037] S3.3, adding the correction values to the to-be-estimated parameters to obtain the optimal estimation value.

[0038] Preferably, in step S3.2, the normal equation is constructed according to the partial derivative, that is, the least squares method principle is used to determine the lander position and the orientation model parameters of the celestial body, so that the residual sum of squares between the theoretical observation value and the ground observation value is minimized, and based on the lander position and the orientation model parameters of the celestial body, the correction values of the position vector of the lander and the orientation parameters of the celestial body are solved.

[0039] Preferably, in step S3, a convergence condition is determined, and the multiple iterations are performed to obtain the optimal estimation of the lander position vector and the celestial body orientation parameter model.

[0040] The application also provides a celestial body orientation parameter solving system based on inverse VLBI interferometry, comprising:

[0041] A model establishing module: for a research target, a rotation orientation physical model of a celestial body and an inverse VLBI differential measurement model are established;

[0042] A theoretical observation value and partial derivative calculation module: based on the rotation orientation physical model and the inverse VLBI differential measurement model, a theoretical observation value of the inverse VLBI differential measurement and partial derivatives of the theoretical observation value with respect to a coordinate of a lander to be estimated and orientation parameters of the celestial body are calculated;

[0043] An optimal estimation value generation module: based on the theoretical observation value and the partial derivatives, ground observation values of the inverse VLBI differential measurement are fitted, and correction values of the lander position vector and the celestial body orientation parameters are solved and added to the to-be-estimated parameters respectively to obtain optimal estimation values; the theoretical observation value and partial derivative calculation module and the optimal estimation value generation module are repeatedly triggered to work until a difference between the optimal estimation values before and after the correction is less than a convergence condition.

[0044] The application also provides a computer readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-mentioned celestial body orientation parameter solving method based on inverse VLBI interferometry.

[0045] Compared with the prior art, the application has the following beneficial effects:

[0046] The application is based on an inverse VLBI measurement mode to carry out a deep space exploration task, and uses inverse VLBI differential measurement data to realize precise positioning of a lander and solving of celestial body orientation parameters.

[0047] Inverse VLBI measurement eliminates most errors in signal propagation between a star and the earth through differential means, and the obtained data is high in precision; high-precision inverse VLBI differential measurement data can significantly improve the solving precision of celestial body orientation model parameters, and further provide information about internal structure and surface mass distribution changes of a celestial body, thereby providing additional constraints for improvement of a celestial body physical model.

[0048] The application applies the inverse VLBI measurement mode to solving of rotation orientation parameters of an extraterrestrial celestial body; high-precision inverse VLBI differential measurement data is sensitive to the celestial body orientation parameters, high-quality data contains transformation information of the celestial body rotation, can significantly constrain the celestial body rotation physical model, improve the solving precision of the orientation parameters, and further reveal the internal structure and material composition of the celestial body. BRIEF DESCRIPTION OF DRAWINGS

[0049] Other features, objects, and advantages of the application will become more apparent from the following detailed description of non-limiting embodiments thereof, when read in conjunction with the accompanying drawings:

[0050] Figure 1 A reference frame for defining the orientation of a celestial body in an embodiment of the application;

[0051] Figure 2 A schematic diagram of a reverse VLBI differential measurement model in an embodiment of the application;

[0052] Figure 3 A schematic diagram of a conventional VLBI measurement model;

[0053] Figure 4 A schematic diagram of a reverse VLBI differential measurement model and a physical model of the rotation of an extraterrestrial body. DETAILED DESCRIPTION

[0054] The application is applicable to the field of deep space exploration, and considers joint reverse VLBI measurement experiments on the surface of a landing celestial body by multiple probes, two-way time synchronization with the assistance of a relay satellite, and the return of radio signals to the same ground station. The application is based on a method for solving high-precision positioning information of a lander and celestial orientation parameters based on differential time delay data in a reverse VLBI interferometric measurement mode. The method eliminates most errors in the propagation of signals between planets by means of differential data processing, and then provides high-precision reverse VLBI measurement time delay and time delay rate data, so as to achieve high-precision positioning of the lander and high-precision calculation of the celestial orientation parameters. First, a reverse VLBI interferometric measurement mode and a mathematical and physical model of the rotation of a celestial body are established, and the lander coordinates and the celestial orientation parameters are introduced into the model in combination with the conversion between the non-inertial system and the inertial system coordinates. Based on the principle of the least square method, a lander position and a celestial orientation model parameter are determined by means of high-precision differential measurement tracking data of the reverse VLBI, so that the residual sum of squares between the calculated theoretical observation values of the reverse VLBI and the ground observation values is minimized, and high-precision extraterrestrial celestial orientation parameters are inversely calculated.

[0055] The application will be described in detail below with specific embodiments. The following embodiments will help those skilled in the art to further understand the application, but do not limit the application in any form. It should be pointed out that, for those skilled in the art, without departing from the concept of the application, a number of changes and improvements can be made. These all belong to the protection scope of the application.

[0056] Embodiment 1:

[0057] The application utilizes the inverse VLBI interferometric measurement mode, removes the influence of signal interplanetary propagation error through differential means, and obtains high-precision differential tracking measurement data between landers.

[0058] The embodiment of the application provides a celestial body orientation parameter solving method based on inverse VLBI interferometric measurement, and comprises the following steps:

[0059] Step S1: For a research target, a rotation orientation physical model of a celestial body and an inverse VLBI differential measurement model are established.

[0060] The rotation orientation mathematical physical model of the extraterrestrial celestial body is established, the position coordinate conversion matrix between the inertial system and the non-inertial system of the lander is obtained, the time and space frames are unified, and the relationship between the measurement values and the model parameters is established.

[0061] Long-time tracking measurement is performed on signals simultaneously emitted by multiple landers, the geometric path difference of the signals reaching the ground antenna is calculated, and the differential inverse VLBI measurement values containing the rotation orientation physical change information of the extraterrestrial celestial body are obtained.

[0062] In the embodiment, the high-precision orientation parameter solving of the moon is taken as an example.

[0063] Step S1 comprises the following sub-steps:

[0064] S1.1, a rotation orientation physical model of the moon is established.

[0065] In the classical Newtonian space-time frame, the coordinate system is divided into the inertial coordinate system and the non-inertial coordinate system, and the rotation orientation physical model of the extraterrestrial celestial body is used for the conversion between the two coordinate systems. Generally, different celestial bodies have their respective non-inertial systems. For example, the moon, the conversion model of the rotation orientation physical model of the moon needs to consider the influence of the libration of the moon, and the conversion model is generally represented by three Euler angles. The conversion relationship is as follows:

[0066]

[0067] Wherein, r bf and r icrs are the moon-fixed coordinate and the moon-sky coordinate, R (x,y,z) represents the rotation matrix around the x, y and z axes, and the three Euler angles are calculated by the following formula:

[0068]

[0069] θ=90°-δ0

[0070] ψ=W

[0071] Among them, α0, δ0 and W define the direction of the celestial body's rotation axis and the position of the prime meridian.

[0072] Figure 1 Schematic diagram of a reference system for defining the orientation of a celestial body in an embodiment of the present invention.

[0073] like Figure 1 As shown in the figure, the celestial north pole is represented by the right ascension α0 and declination δ0 of the axis of rotation projected onto the celestial sphere. W is the angle between the ascending node of the celestial body's mean equator and the Earth's mean equator, from west to east, to the prime meridian, describing the rotation of the celestial body. However, due to factors such as precession and nutation of the celestial body's rotation axis, the parameters α0, δ0, and W vary over time. Therefore, further corrections using observational data are needed to obtain high-precision rotation orientation parameter values ​​for extraterrestrial objects.

[0074] S1.2, establish an inverse VLBI differential measurement model.

[0075] Figure 2 Schematic diagram of an inverse VLBI differential measurement model in an embodiment of the present invention, Figure 4 Schematic diagram of the physical model of extraterrestrial rotation and inverse VLBI differential measurement.

[0076] In this embodiment, Figure 2 、 4 As shown in Figure 1, the inverse VLBI differential measurement system consists of three parts: two or more celestial landers, a relay satellite and a ground receiving antenna.

[0077] The specific measurement mode is: use the ground receiving antenna to receive the information sent simultaneously by the lander, measure the receiving delay, and obtain ground observation values, which include time delay and delay rate data; the role of the relay satellite is to perform two-way time synchronization between the landers to eliminate factors that cause time drift.

[0078] The specific delay measurement model is as follows:

[0079] τ ivlbi =τ g +Δτ t +Δτ p

[0080] Among them, τ g is the geometric delay, Δτ t is the time difference correction between landers, Δτ p is the propagation path delay correction. Specifically, τ gIt is the main body of the inverse VLBI differential measurement, which is the geometric distance difference between the lander and the ground receiving antenna. Because the clocks on the landers are not necessarily completely stable and synchronized, the clocks between the landers are synchronized in both directions through the relay satellite, and the resulting time difference correction Δτ t At the same time, the propagation process of electromagnetic waves is affected by many factors, and it is necessary to correct the propagation time change Δτ caused by the relativistic effect in the solar system. p .

[0081] Step S2: Based on the rotation orientation physical model and the inverse VLBI differential measurement model, calculate the theoretical observation value of the inverse VLBI differential measurement and the partial derivatives of the observation value with respect to the coordinates of the lander to be estimated and the orientation parameters of the celestial body.

[0082] The calculation formula of the theoretical observation value of inverse VLBI differential measurement is as follows:

[0083]

[0084] Where R1 and R2 are the distances from the two landers to the ground antenna, c is the speed of light, RLT is the gravitational delay during signal propagation, and t1 and t2 represent the times when the ground receives the signals from the two landers. Since ground antennas generally record observations in UTC, the corresponding time scale needs to be corrected. The second half is the correction to convert the time scale from UTC to TDB.

[0085] It is worth noting that the inverse VLBI differential observation data contains the relative position changes between the landers, so the positions of the two landers cannot be solved at the same time. Therefore, the inverse VLBI differential measurement only determines the partial derivatives of the position vector and lunar orientation parameters of a certain lander.

[0086] The calculation formula of partial derivative is as follows:

[0087]

[0088]

[0089] Where (x, y, z) represents the position vector of the lander in the lunar fixed system. These are the three Euler angle parameters that describe the rotation orientation of the moon. Depending on the accuracy of the observation values, these three Euler angles can be further subdivided into J2000 values, change rates, and correction terms.

[0090] Step S3: Based on the theoretical observations and partial derivatives, the ground observations of the inverse VLBI differential measurement are fitted to calculate the correction values ​​of the lander's position vector and the orientation parameters of the celestial body. The correction values ​​are added to the parameters to be estimated to obtain the optimal estimate.

[0091] Step S3 includes the following sub-steps:

[0092] S3.1. Fit the ground-based observations from the inverse VLBI differential measurement to the theoretical observations.

[0093] S3.2. Calculate the correction values ​​of the lander's position vector and the celestial body's orientation parameters based on the partial derivatives.

[0094] Specifically, based on the partial derivatives, the normal equation is constructed, that is, the principle of least squares method is used to determine the position of the lander and the orientation model parameters of the moon, so that the sum of squared residuals between the theoretical observation values ​​and the ground observation values ​​is minimized. Based on the lander position and the orientation model parameters of the celestial body, the correction values ​​of the lander's position vector and the orientation parameters of the celestial body are solved.

[0095] S3.3, add the correction value to the parameter to be estimated to obtain the optimal estimate.

[0096] Here, step S2 and step S3 are repeated until the difference between the two optimal estimation values ​​before and after correction is less than the convergence condition.

[0097] Specifically, the convergence conditions are determined and multiple iterations are performed to obtain the best estimates of the position vector of the lander and the orientation parameter model of the celestial body.

[0098] Example 2:

[0099] The present invention also provides a celestial body orientation parameter solution system based on inverse VLBI interferometry. The celestial body orientation parameter solution system based on inverse VLBI interferometry can be implemented by executing the process steps of the celestial body orientation parameter solution method based on inverse VLBI interferometry. That is, those skilled in the art can understand the celestial body orientation parameter solution method based on inverse VLBI interferometry as a preferred implementation of the celestial body orientation parameter solution system based on inverse VLBI interferometry.

[0100] An embodiment of the present invention provides a celestial body orientation parameter calculation system based on inverse VLBI interferometry, comprising:

[0101] Model building module: Based on the research objectives, establish the celestial body's rotation orientation physical model and inverse VLBI differential measurement model;

[0102] Theoretical observation value and partial derivative calculation module: Based on the rotation orientation physical model and the inverse VLBI differential measurement model, it calculates the theoretical observation values ​​of the inverse VLBI differential measurement, as well as the partial derivatives of the theoretical observation values ​​with respect to the coordinates of the lander to be estimated and the orientation parameters of the celestial body;

[0103] Optimal estimate generation module: Based on theoretical observations and partial derivatives, it fits the ground observations of inverse VLBI differential measurement, calculates the correction values ​​of the lander's position vector and the celestial body's orientation parameters, and adds them to the parameters to be estimated to obtain the optimal estimate;

[0104] The theoretical value and partial derivative calculation module and the optimal estimate value generation module are repeatedly triggered to work until the difference between the optimal estimate values ​​before and after correction is less than the convergence condition.

[0105] Example 3:

[0106] An embodiment of the present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the computer program implements the steps of the above-mentioned method for solving celestial body orientation parameters based on inverse VLBI interferometry.

[0107] Those skilled in the art will appreciate that, in addition to implementing the system and its various devices, modules, and units provided by the present invention in purely computer-readable program code, it is entirely possible to implement the same functions of the system and its various devices, modules, and units provided by the present invention in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; the devices, modules, and units for implementing various functions can also be considered as both software modules implementing the method and structures within the hardware component.

[0108] In the description of this application, it should be understood that the terms "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on this application.

[0109] The above describes specific embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. The embodiments of this application and the features in the embodiments may be combined with each other in any manner unless there is a conflict.

Claims

1. A method for calculating celestial body orientation parameters based on inverse VLBI interferometry, characterized in that: The steps include: Step S1: Establish a rotation orientation physical model and an inverse VLBI differential measurement model for the celestial body according to the research target; Step S2, calculating theoretical observation values ​​of inverse VLBI differential measurement and partial derivatives of the theoretical observation values ​​with respect to the coordinates of the lander to be estimated and the orientation parameters of the celestial body based on the rotation orientation physical model and the inverse VLBI differential measurement model; Step S3, fitting the ground observations of the inverse VLBI differential measurement based on the theoretical observations and the partial derivatives, calculating the correction values ​​of the position vector of the lander and the orientation parameters of the celestial body, and adding the correction values ​​to the parameters to be estimated to obtain the optimal estimate; Here, step S2 and step S3 are repeated until the difference between the two optimal estimation values ​​before and after correction is less than the convergence condition.

2. The method for calculating celestial body orientation parameters based on inverse VLBI interferometry according to claim 1, characterized in that: The step S1 includes the following sub-steps: S1.1, establish a physical model of the lunar rotation orientation; S1.2, establish an inverse VLBI differential measurement model.

3. The method for calculating celestial body orientation parameters based on inverse VLBI interferometry according to claim 2, characterized in that: In step S1.1, the conversion relationship of the lunar rotation orientation physical model from the lunar center celestial coordinate system to the lunar center lunar fixed coordinate system is as follows: Among them, r bf and r icrs are the lunar solid coordinates and lunar celestial coordinates, R (x,y,z) Represents the rotation matrix around the x, y, and z axes, three Euler angles Calculated by the following formula: θ=90°-δ0 ψ=W Among them, α0, δ0 and W define the direction of the celestial body's rotation axis and the position of the prime meridian.

4. The method for calculating celestial body orientation parameters based on inverse VLBI interferometry according to claim 2, wherein: In step S1.2, the inverse VLBI differential measurement system includes: multiple celestial landers, a relay satellite, and a ground receiving antenna, wherein the ground receiving antenna is used to receive information simultaneously transmitted by the multiple celestial landers, measure reception delay, and obtain the ground observation value, wherein the ground observation value includes time delay and time delay rate data; the relay satellite is used to perform two-way time synchronization between the multiple celestial landers; The delay measurement model is as follows: t ivlbi =t g +Δt t +Δt p Among them, τ g is the geometric delay, Δτ t is the time difference correction between landers, Δτ p is the propagation path delay correction.

5. The method for calculating celestial body orientation parameters based on inverse VLBI interferometry according to claim 4, characterized in that: In the step S2, The calculation formula of the theoretical observation value of the inverse VLBI differential measurement is as follows: Where R1 and R2 are the distances from the two landers to the ground antenna, c is the speed of light, RLT is the gravitational delay during signal propagation, t1 and t2 are the times when the ground receives the signals from the two landers, respectively. Since the observations recorded by the ground antenna are given in UTC time, the second half is the correction to convert the time scale from UTC to TDB time scale. The calculation formula of the partial derivative is as follows: Where (x, y, z) represents the position vector of the lander in the lunar fixed system. are the three Euler angle parameters that describe the rotation orientation of the moon.

6. The method for calculating celestial body orientation parameters based on inverse VLBI interferometry according to claim 5, characterized in that: The step S3 includes the following sub-steps: S3.1, fitting ground observations obtained by inverse VLBI differential measurement based on the theoretical observations; S3.2, calculating a position vector of the lander and a correction value of an orientation parameter of the celestial body based on the partial derivatives; S3.3, adding the correction value to the parameter to be estimated to obtain the optimal estimated value.

7. The method for calculating celestial body orientation parameters based on inverse VLBI interferometry according to claim 6, characterized in that: In step S3.2, a normal equation is constructed based on the partial derivatives, that is, the principle of the least squares method is used to determine the lander position and the orientation model parameters of the celestial body, so that the sum of squared residuals between the theoretical observation values ​​and the ground observation values ​​is minimized. Based on the lander position and the orientation model parameters of the celestial body, the correction values ​​of the lander position vector and the orientation parameters of the celestial body are solved.

8. The method for calculating celestial body orientation parameters based on inverse VLBI interferometry according to claim 1, characterized in that: In step S3, the convergence condition is determined, and multiple iterations are performed to obtain the best estimated values ​​of the lander position vector and the orientation parameter model of the celestial body.

9. A celestial body orientation parameter calculation system based on inverse VLBI interferometry, characterized in that: include: Model building module: Based on the research objectives, establish the celestial body's rotation orientation physical model and inverse VLBI differential measurement model; A theoretical observation value and partial derivative calculation module is configured to calculate theoretical observation values ​​of inverse VLBI differential measurement and partial derivatives of the theoretical observation values ​​with respect to the coordinates of the lander to be estimated and the orientation parameters of the celestial body based on the rotation orientation physical model and the inverse VLBI differential measurement model. The optimal estimate generation module fits the ground observation values ​​of the inverse VLBI differential measurement based on the theoretical observation values ​​and the partial derivatives, calculates the correction values ​​of the lander's position vector and the orientation parameters of the celestial body, and adds them to the parameters to be estimated to obtain the optimal estimate. The theoretical observation value and partial derivative calculation module and the optimal estimate generation module are repeatedly triggered until the difference between the optimal estimates before and after the correction is less than the convergence condition.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method for solving celestial body orientation parameters based on inverse VLBI interferometry according to any one of claims 1 to 8 are implemented.

Citation Information

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