An autonomous navigation method for lunar satellite formation based on inter-satellite ranging information

Abstract

The present invention provides a method for autonomous navigation of a lunar satellite formation based on inter-satellite ranging information, which includes three parts: establishment of an orbital dynamics model, establishment of a cooperative observation model, and data fusion of a navigation filtering algorithm. The present invention establishes a high-precision dynamics model for the lunar satellite formation, including the 165th-order lunar non-spherical perturbation, and proposes an autonomous navigation method based on inter-satellite ranging and angle measurement information. It can operate independently of the ground station and achieve high-precision autonomous navigation of the lunar satellite formation only by using on-orbit observation data.

Description

Technical Field

[0001] The present 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 has been intensively carried out by various countries in recent years, lunar exploration has seen the emergence of many influential projects, such as the United States' "Artemis" program, China's "Chang'e Project", and the European "Lunar Village" concept. In the lunar exploration mission system, the lunar satellite formation plays an indispensable and crucial supporting role, capable of providing high-precision navigation and positioning services, efficient mission replanning capabilities, and a stable and reliable communication network, effectively ensuring the redundancy and reliability of the entire exploration system.

[0003] During the mission execution of the lunar satellite formation, core operations such as maintaining the stability of the formation configuration, coordinated control among satellites, and scientific and reasonable mission planning all highly rely on the accurate orbital position and velocity data of the satellites. Thus, it can be seen that 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, the navigation of the lunar satellite formation faces more complex technical challenges. Firstly, the lunar gravitational field shows stronger inhomogeneous characteristics compared to the Earth's gravitational field, which directly leads to poor long-term stability of the lunar satellite orbit and requires more frequent orbit correction operations to maintain the normal operating orbit of the satellite. Secondly, 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 achieve real-time control of the lunar satellite, greatly increasing the difficulty and complexity of satellite control. Thirdly, limited by the finiteness of ground measurement and control resources, when managing multiple lunar satellites simultaneously, the complexity and execution frequency of the measurement and control tasks will increase significantly, resulting in a sharp increase in the load of the ground measurement and control station and seriously affecting the measurement and control efficiency and quality. Summary of the Invention

[0005] The present invention establishes a high-precision dynamic model for the lunar satellite formation that includes 165-degree lunar non-spherical perturbations, and proposes an autonomous navigation method for the lunar satellite formation based on inter-satellite ranging information, which is characterized by including:

[0006] Establish a dynamic model of the lunar satellite formation in the lunar-centered inertial coordinate system J2000;

[0007] Obtain the orbit prediction information of the satellite formation through the dynamic model;

[0008] In the formation flight mission, the slave satellite observes the inter-satellite distance and optical angle of the master satellite to obtain the observation information including azimuth, elevation angle, and distance;

[0009] By collaboratively calculating the observation information, a collaborative observation model of the lunar satellite formation is established;

[0010] The collaborative observation information of the lunar satellite formation is obtained through the collaborative observation model;

[0011] 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 the orbit error is corrected.

[0012] In an embodiment of the present invention, in the geocentric inertial coordinate system J2000, establishing the dynamic model of the lunar satellite formation includes: establishing the following motion equations for each single satellite in the dynamic model:

[0013] ;

[0014] Among them, is the three-dimensional position of the satellite;

[0015] is the three-dimensional velocity of the satellite;

[0016] is the lunar gravitational acceleration, including the influence of the lunar central gravity and non-spherical perturbation;

[0017] is the sun-earth three-body acceleration;

[0018] is the solar radiation pressure acceleration;

[0019] is the acceleration caused by general relativistic motion.

[0020] In another embodiment of the present invention, the lunar gravitational acceleration is expressed as:

[0021] ;

[0022] Among them, is the lunar gravitational constant;

[0023] is the radius of the moon;

[0024] are the order and degree respectively. When it means only considering the central gravity of the moon;

[0025] N is the highest order of non-spherical perturbation, N = 165;

[0026] are the normalized spherical harmonic coefficients respectively;

[0027] is the normalized Legendre function;

[0028] are the longitude and latitude of the satellite's body-fixed coordinate system respectively;

[0029] The acceleration caused by the sun-earth-moon three-body gravity is expressed as:

[0030] ;

[0031] where, are the gravitational constants of the earth and the sun respectively;

[0032] are the position vectors of the earth and the sun relative to the moon respectively;

[0033] The acceleration caused by the solar radiation pressure perturbation is expressed as:

[0034] ;

[0035] where, is the solar radiation pressure coefficient;

[0036] A is the effective illuminated cross-sectional area;

[0037] is the reflection coefficient;

[0038] m is the mass of the satellite;

[0039] is the unit vector of the satellite pointing to the sun; and

[0040] The acceleration caused by the general relativity perturbation is expressed as:

[0041] ;

[0042] where c is the speed of light.

[0043] In another embodiment of the present invention, the inter-satellite distance and optical angle observations by the slave satellite on the master satellite include: establishing the following optical angle observation equation:

[0044] ;

[0045] Establishing the following inter-satellite distance observation equation:

[0046] ;

[0047] Among them, is the azimuth angle information between the i-th sub-star and the main star;

[0048] is the elevation angle information between the i-th sub-star and the main star;

[0049] represents the optical observation error, ;

[0050] represents the ranging error between the i-th sub-star and the main star.

[0051] In another embodiment of the present invention, establishing a cooperative observation model for a lunar satellite formation includes: establishing the following cooperative observation model:

[0052] ;

[0053] Among them, .

[0054] The present invention has established a high-precision dynamic model for a lunar satellite formation that includes 165-order lunar non-spherical perturbations, and proposed an autonomous navigation method based on inter-satellite ranging and angle measurement information. During 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. This method can operate independently of the ground station and achieve high-precision autonomous navigation of the lunar satellite formation only by using on-orbit observation data. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 shows a flowchart of the autonomous navigation method for a lunar satellite formation based on inter-satellite ranging information according to the present invention;

[0056] Figure 2 shows a flowchart of the autonomous navigation method for a lunar satellite formation based on inter-satellite ranging information in an embodiment of the present invention;

[0057] Figure 3 shows a schematic diagram of the absolute position error of a satellite formation in an embodiment of the present invention;

[0058] Figure 4 shows a schematic diagram of the absolute velocity error of a satellite formation in an embodiment of the present invention; and

[0059] Figure 5 shows a schematic diagram of the relative orbit error of a satellite formation in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0060] In the following description, the present invention is described with reference to the embodiments. However, those skilled in the art will recognize that the embodiments can be implemented without one or more of the specific details or in combination with other alternative and / or additional methods, materials, or components. In other instances, well-known structures, materials, or operations have not been shown or described in detail to avoid obscuring the inventive aspects of the present invention. Similarly, for purposes of explanation, specific quantities, materials, and configurations are set forth in order to provide a thorough understanding of the embodiments of the present invention. However, the present invention is not limited to these specific details.

[0061] In this specification, the reference to "one embodiment" or "the embodiment" means that the specific features, structures, or characteristics described in connection with that embodiment are included in at least one embodiment of the present invention. The phrase "in one embodiment" appearing throughout this specification does not necessarily all refer to the same embodiment.

[0062] In the present invention, the embodiments are merely intended to illustrate the solutions of the present invention and should not be construed as restrictive.

[0063] 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 a different order.

[0064] The present invention will be further elaborated below in conjunction with the specific embodiments with reference to the accompanying drawings.

[0065] Figure 1 The flowchart of the autonomous navigation method for a lunar satellite formation based on inter-satellite ranging information of the present invention is shown.

[0066] As shown in the figure, the autonomous navigation method for a lunar satellite formation based on inter-satellite ranging information of the present invention includes:

[0067] (1) Establish the dynamic model 10 of the lunar satellite formation

[0068] Under the geocentric inertial coordinate system J2000, a high-precision orbital dynamic model of the lunar satellite formation is established, including the influence of high-order lunar non-spherical perturbations up to the 165th order, solar and terrestrial gravitational perturbations, solar radiation pressure perturbations, and relativistic perturbations.

[0069] In the orbital dynamic model, the motion equation of a single satellite is expressed as:

[0070] (1-1)

[0071] Among them, is the three-dimensional position of the satellite;

[0072] is the three-dimensional velocity of the satellite;

[0073] is the lunar gravitational acceleration, including the effects of the gravitational force at the lunar center and non-spherical perturbations;

[0074] is the three-body acceleration of the sun-earth system;

[0075] is the solar radiation pressure acceleration;

[0076] is the acceleration caused by general relativistic motion.

[0077] (2)Obtain the orbit prediction information of the satellite formation 20

[0078] The dynamic model of the lunar satellite formation not only comprehensively considers the perturbation factors, but also introduces the cooperative effect of formation flight. Using accurate dynamic equations and numerical integration methods, this model can accurately predict the orbit evolution of the formation satellites, thereby obtaining the orbit prediction information of the satellite formation.

[0079] (3)Obtain the observation information of the slave satellite to the master satellite 30

[0080] In the formation flight mission system, the slave satellite undertakes the key observation responsibility for the master satellite. The slave satellite uses specific observation means to carry out precise observation operations on the master satellite for the inter-satellite distance and optical angle, and then obtains three important observation information: azimuth angle, elevation angle and distance.

[0081] Among them, the optical angle observation is expressed as:

[0082] (2-1)

[0083] The inter-satellite distance observation is expressed as:

[0084] (2-2)

[0085] Among them, is the azimuth angle information between the i-th slave satellite and the master satellite;

[0086] is the elevation angle information between the i-th slave satellite and the master satellite;

[0087] represents the optical observation error, ;

[0088] represents the ranging error between the i-th slave satellite and the master satellite.

[0089] (4)Establish the cooperative observation model of the lunar satellite formation 40

[0090] Based on the principles of inter-satellite angle and distance measurement, the cooperative observation model of the satellite formation is established as:

[0091] (2 - 3)

[0092] Among them, .

[0093] (5) Obtain the collaborative observation information 50 of the lunar satellite formation

[0094] During the actual operation process, multiple sub - satellites will synchronously carry out the observation operation of the main satellite's optical angle information. At the same time, each sub - satellite will also conduct inter - satellite measurement 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.

[0095] (6) Correct the orbit error 60

[0096] In the operation system of the lunar satellite formation, to achieve high - precision orbit determination, two key models need to be fully relied on. One is the high - precision dynamics model, which carefully depicts the motion law of the lunar satellite formation under the action of the complex lunar gravitational field and other space environmental forces; the other is the collaborative observation model, which accurately describes the mechanism of collaborative observation between satellites and the characteristics of data association.

[0097] 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 fuse the orbit prediction data and the satellite's on - orbit real - time observation data. Through orbit prediction, according to the dynamic characteristics of the satellite and the known orbit parameters, the orbit state in the future period can be estimated; while the on - orbit observation data comes from various observation devices carried by the satellite, which truly reflects the current actual operation state of the satellite. The UKF algorithm uses a unique non - linear filtering strategy to deeply fuse and optimize these two types of data.

[0098] Through the effective operation of this algorithm, the absolute orbit state and relative orbit error of each satellite in the formation are obtained, and then the orbit error is corrected.

[0099] Figure 2 Shows the flowchart of the autonomous navigation method for the lunar satellite formation based on inter - satellite ranging information in an embodiment of the present invention.

[0100] The autonomous navigation method for the lunar satellite formation in the present invention mainly includes three parts: establishing a high - precision orbit dynamics model, establishing a collaborative observation model, and data fusion of the navigation filtering algorithm.

[0101] (1) Establish the orbit dynamics model 101

[0102] In the lunar-centered inertial coordinate system J2000, a high-precision orbital dynamics model of the lunar satellite formation is established, including the effects of high-order lunar non-spherical perturbations up to 165 orders, solar-terrestrial gravitational perturbations, solar radiation pressure perturbations, and relativistic perturbations. In the orbital dynamics model, the motion equation of a single satellite is expressed as:

[0103] (1-1)

[0104] where, is the three-dimensional position of the satellite;

[0105] is the three-dimensional velocity of the satellite;

[0106] is the lunar gravitational acceleration, including the effects of the lunar central gravity and non-spherical perturbations;

[0107] is the solar-terrestrial three-body acceleration;

[0108] is the solar radiation pressure acceleration;

[0109] is the acceleration caused by general relativistic motion.

[0110] The lunar gravitational acceleration is expressed as:

[0111] (1-2)

[0112] where, is the lunar gravitational constant;

[0113] is the radius of the moon;

[0114] are the degree and order respectively. When it means only considering the central gravity of the moon;

[0115] N is the highest order of non-spherical perturbations. In an embodiment of the present invention, N = 165;

[0116] are the normalized spherical harmonic coefficients respectively;

[0117] is the normalized Legendre function;

[0118] are the longitude and latitude of the satellite's body-fixed frame respectively.

[0119] The acceleration caused by the solar-terrestrial three-body gravity is expressed as:

[0120] (1 - 3)

[0121] Wherein, are respectively the gravitational constants of the earth and the sun;

[0122] are respectively the position vectors of the earth and the sun relative to the moon.

[0123] The acceleration caused by solar radiation pressure perturbation is expressed as:

[0124] (1 - 4)

[0125] Wherein, is the solar radiation pressure coefficient;

[0126] A is the effective light - receiving cross - sectional area;

[0127] is the reflection coefficient;

[0128] m is the mass of the satellite;

[0129] is the unit vector of the satellite pointing to the sun.

[0130] The acceleration caused by general relativity perturbation is expressed as:

[0131] (1 - 5)

[0132] Wherein, c is the speed of light.

[0133] 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:

[0134] .

[0135] (2) Establishment of cooperative observation model 102

[0136] In the formation - flight mission, the slave satellite observes the inter - satellite distance and optical angle of the master satellite, obtaining three kinds of observation information: azimuth angle, elevation angle and distance. By cooperatively calculating these observation information, the cooperative observation model of the lunar satellite formation is established.

[0137] Wherein, the optical angle observation is expressed as:

[0138] (2 - 1)

[0139] The inter - satellite distance observation is expressed as:

[0140] (2 - 2)

[0141] wherein, is the azimuth angle information between the i-th sub-star and the main star;

[0142] is the elevation angle information between the i-th sub-star and the main star;

[0143] represents the optical observation error, ;

[0144] represents the ranging error between the i-th sub-star and the main star.

[0145] Based on the inter-satellite angle and distance measurement principle, the cooperative observation model of the satellite formation is established as:

[0146] (2-3)

[0147] wherein, .

[0148] (3) Navigation Filter Algorithm Data Fusion 103

[0149] Based on the high-precision dynamic model of the lunar satellite formation and the cooperative observation model shown in formula (2-3), the Unscented Kalman Filter (UKF) navigation filter algorithm is used to fuse the orbit prediction and on-orbit observation data, realize the autonomous orbit determination of the satellite formation, and correct the orbit error through the UKF algorithm to obtain the absolute orbit state and relative orbit error of each satellite in the formation, so as to ensure the formation stability and the successful execution of the mission, improve the autonomy of the lunar flight formation and reduce the ground-based measurement and control pressure.

[0150] The technical effects of the present invention will be described below with reference to specific embodiments.

[0151] Figure 3 shows the absolute position error diagram of the satellite formation in an embodiment of the present invention, and Figure 4 shows the absolute velocity error diagram of the satellite formation in an embodiment of the present invention.

[0152] In an embodiment of the present invention, in the geocentric inertial coordinate system J2000, the initial position error of the satellite formation is 1 km, and the velocity error is 1 m / s. The inter-satellite distance error in the measurement process is 1 m ( ), and the angle error is . After the autonomous navigation simulation, the absolute orbit error of the satellite formation is as shown in Figure 3 and Figure 4 . The navigation algorithm can converge quickly. After convergence, the three-dimensional position error is about 800 m, and the three-axis velocity error is 0.2 m / s.

[0153] Figure 5 The schematic diagram of the relative orbit error of the satellite formation in an embodiment of the present invention is shown.

[0154] In this embodiment, the relative orbit error of the satellite formation is as Figure 5 shown. During formation flight, the relative position error is better than 0.5 m, and the relative velocity error is better than 6.6977×10 -3 m / s.

[0155] The above simulation results show that the autonomous navigation method for lunar satellite formation proposed by the present invention has accurate and stable orbit determination performance, can effectively maintain the formation configuration, and provides technical support for various exploration tasks.

[0156] Although the embodiments of the present invention have been described above, it should be understood that they are presented only as examples and not as limitations. It will be apparent 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 width and scope of the present invention disclosed herein should not be limited by the above-disclosed exemplary embodiments, but should be defined only by the appended claims and their equivalents.

Claims

1. An autonomous navigation method for a lunar satellite formation based on inter-satellite ranging information, characterized in that Including: Establish a dynamic model of a lunar satellite formation in the lunar-centered inertial coordinate system J2000; Obtain the orbit prediction information of the satellite formation through the dynamic model; During the formation flight mission, the slave satellite observes the inter-satellite distance and optical angle of the master satellite, so as to obtain the observation information including azimuth, elevation angle and distance; Establish a cooperative observation model of the lunar satellite formation by cooperatively calculating the observation information; Obtain the cooperative observation information of the lunar satellite formation through the cooperative observation model; Fuse the orbit prediction information and the cooperative observation information 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 autonomous navigation method for a lunar satellite formation according to claim 1, wherein Establishing a dynamic model of a lunar satellite formation in the lunar-centered inertial coordinate system J2000 includes: establishing the following motion equations for each single satellite in the dynamic model: ； Among them, 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 central lunar gravity and non-spherical perturbations; is the acceleration of the Earth-Sun three-body system; is the solar radiation pressure acceleration; is the acceleration caused by general relativistic motion.

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

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