Moon satellite formation autonomous navigation method based on inter-satellite ranging information

Abstract

The invention provides a lunar satellite formation autonomous navigation method based on inter-satellite ranging information. The lunar satellite formation autonomous navigation method comprises three parts of orbit dynamics model establishment, collaborative observation model establishment and navigation filtering algorithm data fusion. The invention provides an autonomous navigation method based on inter-satellite distance measurement and angle measurement information, which establishes a high-precision dynamic model containing 165-order moon non-spherical perturbation for moon satellite formation. The system can operate independently of a ground station, and high-precision autonomous navigation of the lunar satellite formation is realized only by using on-orbit observation data.

Description

Technical Field

[0001] The invention relates to the field of aerospace, and in particular to an autonomous navigation method for a lunar satellite formation based on inter-satellite ranging information. Background Art

[0002] As a frontier research field that countries around the world have focused on in recent years, lunar exploration has seen the emergence of many influential projects, such as the US "Artemis" program, China's "Chang'e Project" and Europe's "Moon Village" concept. In the lunar exploration mission system, the lunar satellite formation plays an indispensable and key supporting role, providing high-precision navigation and positioning services, efficient mission re-planning capabilities, and a stable and reliable communication network, effectively ensuring the redundancy and reliability of the entire exploration system.

[0003] During the lunar satellite formation mission, the core operations such as the stable maintenance of the formation configuration, the coordinated control between satellites, and the scientific and reasonable mission planning are highly dependent on the precise orbital position and velocity data of the satellites. Therefore, high-precision orbit determination technology has become one of the core elements to ensure the normal and efficient operation of the lunar satellite formation.

[0004] However, compared with the near-Earth space environment, lunar satellite formation navigation faces more complex technical challenges. First, the lunar gravitational field is more uneven than the Earth's gravitational field, which directly leads to the poor long-term stability of the lunar satellite orbit and requires more frequent orbit correction operations to maintain the normal operation of the satellite. Second, there is a large communication delay between the moon and the earth, especially in the far side of the moon. Since its direct communication link with the earth is completely blocked, it is difficult to effectively control the lunar satellite in real time, which greatly increases the difficulty and complexity of satellite control. Third, due to the limited ground measurement and control resources, when managing multiple lunar satellites at the same time, the complexity and execution frequency of measurement and control tasks will increase significantly, causing the load of ground measurement and control stations to increase sharply, seriously affecting the efficiency and quality of measurement and control. Summary of the invention

[0005] The present invention establishes a high-precision dynamic model including 165-order lunar non-spherical perturbations for a lunar satellite formation, and proposes an autonomous navigation method for a lunar satellite formation based on inter-satellite ranging information, which is characterized by comprising: In the lunar center inertial coordinate system J2000, the dynamic model of the lunar satellite formation is established; Obtaining orbit prediction information of the satellite formation through the dynamic model; In the formation flying mission, the satellite observes the intersatellite distance and optical angle of the main satellite, thereby obtaining observation information including azimuth, pitch angle and distance; By collaboratively calculating the observation information, a collaborative observation model of the lunar satellite formation is established; Acquiring collaborative observation information of the lunar satellite formation through the collaborative observation model; The orbit prediction information and the collaborative observation information are fused through the UKF algorithm to obtain the absolute orbit state and relative orbit error of each satellite in the formation, and then correct the orbit error.

[0006] In one embodiment of the present invention, in the lunar center inertial coordinate system J2000, establishing the dynamic model of the lunar satellite formation includes: establishing the following motion equations of each single satellite in the dynamic model: ; in, is the three-dimensional position of the satellite; is the three-dimensional velocity of the satellite; is the lunar gravitational acceleration, including the effects of the lunar center gravity and non-spherical perturbations; It is the acceleration of the three bodies of the Sun and the Earth; is the solar pressure acceleration; It is the acceleration caused by general relativistic motion.

[0007] In another embodiment of the present invention, the lunar gravitational acceleration is expressed as: ; in, is the lunar gravitational constant; is the radius of the Moon; are the order and degree respectively, when When , it means that only the central gravity of the moon is considered; N is the highest order of non-spherical perturbation, N=165; are the normalized spherical harmonic coefficients; is the normalized Legendre function; are the satellite’s fixed-link longitude and latitude respectively; The acceleration caused by the gravity of the three bodies of the Sun and the Earth is expressed as: ; in, are the gravitational constants of the Earth and the Sun, respectively; are the position vectors of the Earth and the Sun relative to the Moon; The acceleration caused by the solar pressure perturbation It is expressed as: ; in, is the solar pressure coefficient; A is the effective illumination cross-sectional area; is the reflection coefficient; m is the mass of the satellite; is the unit vector of the satellite pointing toward the sun; and The acceleration caused by the general relativistic perturbation It is expressed as: ; Where c is the speed of light.

[0008] In another embodiment of the present invention, the satellite observes the intersatellite distance and optical angle of the primary satellite, including: establishing the following optical angle observation equation: ; The following inter-satellite distance observation equation is established: ; in, is the azimuth information between the ith satellite and the main satellite; is the pitch angle information between the ith satellite and the main satellite; represents the optical observation error, ; Represents the ranging error between the ith satellite and the main satellite.

[0009] In another embodiment of the present invention, establishing a collaborative observation model for a lunar satellite formation includes: establishing the following collaborative observation model: ; in, .

[0010] The present invention establishes a high-precision dynamic model for the lunar satellite formation including 165-order lunar non-spherical perturbations, and proposes an autonomous navigation method based on inter-satellite ranging and angle measurement information. In formation flight, the distance range between adjacent satellites is between 10 and 100 km, the ranging accuracy of the inter-satellite low-gain link can reach 1 m, and the optical angle measurement accuracy can reach 1 m. The method can operate independently of the ground station and realize high-precision autonomous navigation of the lunar satellite formation using only on-orbit observation data. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 The flow chart of the method for autonomous navigation of lunar satellite formation based on inter-satellite ranging information of the present invention is shown; Figure 2 A flow chart of a lunar satellite formation autonomous navigation method based on inter-satellite ranging information in one embodiment of the present invention is shown; Figure 3 A schematic diagram of the absolute position error of a satellite formation in one embodiment of the present invention is shown; Figure 4 A schematic diagram showing the absolute velocity error of a satellite formation in one embodiment of the present invention is shown; and Figure 5 A schematic diagram of the relative orbit error of a satellite formation in one embodiment of the present invention is shown. DETAILED DESCRIPTION

[0012] In the following description, the present invention is described with reference to various embodiments. However, those skilled in the art will recognize that various embodiments may be implemented without one or more specific details or with other replacement and / or additional methods, materials or components. In other cases, well-known structures, materials or operations are not shown or described in detail to avoid obscuring the inventive point of the present invention. Similarly, for the purpose of explanation, specific quantities, materials and configurations are set forth to provide a comprehensive understanding of embodiments of the present invention. However, the present invention is not limited to these specific details.

[0013] In this specification, reference to "one embodiment" or "the embodiment" means that a particular feature, structure, or characteristic described in conjunction with the embodiment is included in at least one embodiment of the present invention. The phrase "in one embodiment" appearing in various places in this specification does not necessarily all refer to the same embodiment.

[0014] In the present invention, each embodiment is only intended to illustrate the aspects of the present invention and should not be construed as limiting.

[0015] In addition, the numbering of the steps of the methods of the present invention does not limit the execution order of the method steps. Unless otherwise specified, the method steps can be executed in different orders.

[0016] The present invention will be further described below in conjunction with specific embodiments with reference to the accompanying drawings.

[0017] Figure 1 The flowchart of the method for autonomous navigation of a lunar satellite formation based on inter-satellite ranging information of the present invention is shown.

[0018] As shown in the figure, the lunar satellite formation autonomous navigation method based on inter-satellite ranging information of the present invention includes: (1) Establishment of dynamic model of lunar satellite formation10 In the lunar-centered inertial coordinate system J2000, a high-precision orbital dynamics model of the lunar satellite formation is established, which includes the effects of 165-order high-order lunar non-spherical perturbations, solar-terrestrial gravitational perturbations, solar radiation pressure perturbations and relativistic perturbations.

[0019] In the orbital dynamics model, the equation of motion of a single star is expressed as: (1-1) in, is the three-dimensional position of the satellite; is the three-dimensional velocity of the satellite; is the lunar gravitational acceleration, including the effects of the lunar center gravity and non-spherical perturbations; It is the acceleration of the three bodies of the Sun and the Earth; is the solar pressure acceleration; It is the acceleration caused by general relativistic motion.

[0020] (2) Obtain orbital prediction information of the satellite formation 20 The dynamic model of the lunar satellite formation not only comprehensively considers the perturbation factors, but also introduces the synergistic effect of formation flying. Using precise dynamic equations and numerical integration methods, the model can accurately predict the orbital evolution of the formation satellites, thereby obtaining orbital prediction information for the satellite formation.

[0021] (3) Obtain observation information of the satellite on the primary star 30 In the formation flying mission system, the satellite bears the key observation responsibility for the main satellite. With the help of specific observation methods, the satellite conducts precise observation of the intersatellite distance and optical angle of the main satellite, and then obtains three important observation information: azimuth, pitch angle and distance.

[0022] Among them, the optical angle observation is expressed as: (2-1) The inter-satellite distance observation is expressed as: (2-2) in, is the azimuth information between the ith satellite and the main satellite; is the pitch angle information between the ith satellite and the main satellite; represents the optical observation error, ; Represents the ranging error between the ith satellite and the main satellite.

[0023] (4) Establishing a collaborative observation model for the lunar satellite formation40 Based on the principle of inter-satellite angle and distance measurement, the collaborative observation model of the satellite formation is established as follows: (2-3) in, .

[0024] (5) Obtaining collaborative observation information of the lunar satellite formation 50 In the actual operation process, multiple satellites will synchronously observe the optical angle information of the main satellite. At the same time, each satellite will also conduct intersatellite measurements with the main satellite to obtain the corresponding distance information. The collaborative observation information of the lunar satellite formation is obtained through the collaborative observation model.

[0025] (6) Correction of orbit error 60 In the operation system of the lunar satellite formation, in order to achieve high-precision orbit determination, it is necessary to fully rely on two key models. The first is a high-precision dynamics model, which carefully describes the motion laws of the lunar satellite formation under the complex lunar gravitational field and other space environment forces; the second is a collaborative observation model, which accurately describes the mechanism and data correlation characteristics of collaborative observation between satellites.

[0026] Based on the above two models, this solution adopts the Unscented Kalman Filter (UKF) navigation filtering algorithm. The core advantage of this algorithm is that it can efficiently integrate orbit prediction data with real-time satellite observation data. Through orbit prediction, the orbit state in the future can be estimated based on the satellite's dynamic characteristics and known orbital parameters; and the on-orbit observation data comes from various observation equipment carried by the satellite, which truthfully reflects the actual current operating status of the satellite. The UKF algorithm uses a unique nonlinear filtering strategy to deeply integrate and optimize these two types of data.

[0027] Through the effective operation of this algorithm, the absolute orbital state and relative orbital error of each satellite in the formation are obtained, and then the orbital error is corrected.

[0028] Figure 2 A flow chart of a lunar satellite formation autonomous navigation method based on inter-satellite ranging information in one embodiment of the present invention is shown.

[0029] The autonomous navigation method of the lunar satellite formation in the present invention is mainly divided into three parts: establishment of a high-precision orbital dynamics model, establishment of a collaborative observation model and navigation filter algorithm data fusion.

[0030] (1) Orbital dynamics model establishment 101 In the lunar center inertial coordinate system J2000, a high-precision orbital dynamics model of the lunar satellite formation is established, including the effects of 165-order high-order lunar non-spherical perturbations, solar-terrestrial gravitational perturbations, solar light pressure perturbations, and relativistic perturbations. In the orbital dynamics model, the motion equation of a single star is expressed as: (1-1) in, is the three-dimensional position of the satellite; is the three-dimensional velocity of the satellite; is the lunar gravitational acceleration, including the effects of the lunar center gravity and non-spherical perturbations; It is the acceleration of the three bodies of the Sun and the Earth; is the solar pressure acceleration; It is the acceleration caused by general relativistic motion.

[0031] Lunar gravitational acceleration It is expressed as: (1-2) in, is the lunar gravitational constant; is the radius of the Moon; are the order and degree respectively, when When , it means that only the central gravity of the moon is considered; N is the highest order of non-spherical perturbation. In one embodiment of the present invention, N=165; are the normalized spherical harmonic coefficients; is the normalized Legendre function; are the satellite's fixed-link longitude and latitude, respectively.

[0032] The acceleration caused by the gravity of the three bodies of the Sun and the Earth is expressed as: (1-3) in, are the gravitational constants of the Earth and the Sun, respectively; are the position vectors of the Earth and the Sun relative to the Moon, respectively.

[0033] Acceleration caused by solar pressure perturbation It is expressed as: (1-4) in, is the solar pressure coefficient; A is the effective illumination cross-sectional area; is the reflection coefficient; m is the mass of the satellite; is the unit vector of the satellite pointing towards the sun.

[0034] The acceleration caused by general relativistic perturbation is expressed as: (1-5) Where c is the speed of light.

[0035] Based on the single-satellite motion equations shown in formulas (1-1)-(1-5), the state model of the lunar satellite formation is established as follows: .

[0036] (2) Establishment of collaborative observation model 102 During the formation flight mission, the satellite observes the intersatellite distance and optical angle of the main satellite, and obtains three types of observation information: azimuth, pitch angle and distance. By collaboratively calculating these observation information, a collaborative observation model for the lunar satellite formation was established.

[0037] Among them, the optical angle observation is expressed as: (2-1) The inter-satellite distance observation is expressed as: (2-2) in, is the azimuth information between the ith satellite and the main satellite; is the pitch angle information between the ith satellite and the main satellite; represents the optical observation error, ; Represents the ranging error between the ith satellite and the main satellite.

[0038] Based on the principle of inter-satellite angle and distance measurement, the collaborative observation model of the satellite formation is established as follows: (2-3) in, .

[0039] (3) Navigation filtering algorithm data fusion 103 Based on the high-precision dynamic model of the lunar satellite formation and the collaborative observation model shown in formula (2-3), the Unscented Kalman Filter (UKF) navigation filtering algorithm is used to fuse orbit prediction and on-orbit observation data to realize autonomous orbit determination of the satellite formation. The orbit error is corrected by the UKF algorithm to obtain the absolute orbital state and relative orbital error of each satellite in the formation, thereby ensuring the stability of the formation and the successful execution of the mission, improving the autonomy of the lunar flight formation and reducing the pressure of ground-based measurement and control.

[0040] The technical effects of the present invention will be described below with reference to specific embodiments.

[0041] Figure 3 FIG. 4 shows a schematic diagram of the absolute position error of a satellite formation in one embodiment of the present invention, and Figure 4 A schematic diagram of the absolute velocity error of a satellite formation in one embodiment of the present invention is shown.

[0042] In one embodiment of the present invention, in the lunar center inertial coordinate system J2000, the initial position error of the satellite formation is 1km, and the speed error is 1m / s. The inter-satellite distance error during the measurement process is 1m ( ), the angle error is After autonomous navigation simulation, the absolute orbit error of the satellite formation is as follows: Figure 3 and Figure 4 The navigation algorithm can converge quickly. After convergence, the three-dimensional position error is about 800m and the three-axis speed error is 0.2m / s.

[0043] Figure 5 A schematic diagram of the relative orbit error of a satellite formation in one embodiment of the present invention is shown.

[0044] In this embodiment, the relative orbit error of the satellite formation is as follows: Figure 5 In formation flying, the relative position error is better than 0.5m, and the relative speed error is better than 6.6977×10 -3 m / s.

[0045] The above simulation results show that the lunar satellite formation autonomous navigation method proposed in the present invention has accurate and stable orbit determination performance, can effectively maintain the formation configuration, and provide technical support for various exploration missions.

[0046] Although various embodiments of the present invention are described above, it should be understood that they are presented as examples only and not as limitations. It is obvious to those skilled in the relevant art that various combinations, deformations and changes can be made thereto without departing from the spirit and scope of the present invention. Therefore, the breadth and scope of the present invention disclosed herein should not be limited by the exemplary embodiments disclosed above, but should only be defined according to the attached claims and their equivalents.

Claims

1. A lunar satellite formation autonomous navigation method based on inter-satellite ranging information, characterized in that: include: In the lunar center inertial coordinate system J2000, the dynamic model of the lunar satellite formation is established; Obtaining orbit prediction information of the satellite formation through the dynamic model; In the formation flying mission, the satellite observes the intersatellite distance and optical angle of the main satellite, thereby obtaining observation information including azimuth, pitch angle and distance; By collaboratively calculating the observation information, a collaborative observation model of the lunar satellite formation is established; Acquiring collaborative observation information of the lunar satellite formation through the collaborative observation model; The orbit prediction information and the collaborative observation information are fused through the UKF algorithm to obtain the absolute orbit state and relative orbit error of each satellite in the formation, and then correct the orbit error.

2. The lunar satellite formation autonomous navigation method according to claim 1, characterized in that: In the lunar center inertial coordinate system J2000, establishing the dynamic model of the lunar satellite formation includes: establishing the following motion equations of each single satellite in the dynamic model: ； in, is the three-dimensional position of the satellite; is the three-dimensional velocity of the satellite; is the lunar gravitational acceleration, including the effects of the lunar center gravity and non-spherical perturbations; It is the acceleration of the three bodies of the Sun and the Earth; is the solar pressure acceleration; It is the acceleration caused by general relativistic motion.

3. The lunar satellite formation autonomous navigation method according to claim 2, characterized in that: The lunar gravitational acceleration It is expressed as: ； in, is the lunar gravitational constant; is the radius of the Moon; are the order and degree respectively, when When , it means that only the central gravity of the moon is considered; N is the highest order of non-spherical perturbation, N=165; are the normalized spherical harmonic coefficients; is the normalized Legendre function; are the satellite’s fixed-link longitude and latitude respectively; The Sun-Earth three-body acceleration It is expressed as: ； in, are the gravitational constants of the Earth and the Sun, respectively; are the position vectors of the Earth and the Sun relative to the Moon; The acceleration caused by the solar pressure perturbation It is expressed as: ； in, is the solar pressure coefficient; A is the effective illumination cross-sectional area; is the reflection coefficient; m is the mass of the satellite; is the unit vector of the satellite pointing toward the sun; and The acceleration caused by the general relativistic perturbation It is expressed as: ； Where c is the speed of light.

4. The lunar satellite formation autonomous navigation method according to claim 1, characterized in that: The observation of the interstellar distance and optical angle of the primary star by the secondary star includes: establishing the following optical angle observation equation: ； The following inter-satellite distance observation equation is established: ； in, is the azimuth information between the ith satellite and the main satellite; is the pitch angle information between the ith satellite and the main satellite; represents the optical observation error, ; Represents the ranging error between the ith satellite and the main satellite.

5. The lunar satellite formation autonomous navigation method according to claim 1, characterized in that: Establishing a collaborative observation model for the lunar satellite formation includes establishing the following collaborative observation model: ； in, .

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