ELFO satellite and beidou satellite combined autonomous orbit determination method and system

Abstract

This invention relates to a method and system for joint autonomous orbit determination of ELFO and BeiDou satellites. The method includes: generating inertial frame position and velocity prediction information for BeiDou and ELFO satellites based on a high-precision orbital dynamics model; collecting bidirectional link measurement information between BeiDou satellites, between BeiDou and ELFO satellites, and between ELFO satellites; correcting the bidirectional link measurement information to generate corrected measurement information; and performing state prediction and covariance prediction using an extended Kalman filter algorithm, using the corrected measurement information to perform filtering correction on the state prediction information and covariance prediction information, and outputting the joint autonomous orbit determination result of BeiDou and ELFO satellites. The method proposed in this invention incorporates the transfer matrix under the gravitational asymmetry caused by the strong gravitational pull of the moon into the filtering solution process, effectively suppressing inertial frame orientation and rotation errors.

Description

Technical Field

[0001] This invention relates to the field of high-precision autonomous orbit determination technology for navigation satellites and lunar spacecraft, specifically to a method and system for joint autonomous orbit determination of elliptical frozen orbit (ELFO) satellites and BeiDou satellites. Through high-precision ranging via Ka-band bidirectional links between BeiDou satellites, between BeiDou and ELFO satellites, and between ELFO satellites, combined with the constraint of the asymmetric gravitational forces of the Earth-Moon three-body system, long-term, high-precision autonomous orbit determination of BeiDou and ELFO satellites in inertial frames is achieved. Background Technology

[0002] Traditionally, the accuracy of BeiDou satellites' autonomous orbit determination based on inter-satellite links has been declining over time. The main source of this error is the overall rotation error of the satellite, which cannot be effectively observed and corrected through inter-satellite links. The overall rotation error of the satellite includes two aspects: First, because the satellite cannot communicate with the ground in autonomous orbit determination mode, the Earth Rotation Parameters (ERPs) cannot be updated and uploaded to the satellite. Orbit determination results based solely on ERP predictions will have a rotational direction deviation in the Earth-fixed coordinate system. Effective means to reduce this error are to improve the prediction accuracy of ERPs and to establish a satellite-to-ground communication ranging method based on anchored stations.

[0003] Second, due to the unpredictable nature of the right ascension of the ascending node in the inertial frame for autonomous orbit determination based on inter-satellite ranging, the orientation and rotation errors generated by the satellite in the inertial frame cannot be corrected. Currently, the most common method for correcting this error in navigation satellites is to suppress the orientation and rotation errors based on the satellite's orbital orientation prediction parameters. However, the orientation parameters in the predicted orbit diverge slowly over time, becoming more pronounced when the satellite enters the Earth's shadow region, making long-term high-precision suppression difficult.

[0004] Currently, countries are accelerating their lunar exploration efforts, constructing lunar navigation constellations covering the near-lunar region and the lunar surface to provide precise position and timing information for complex exploration missions. Zhang proposed a lunar space navigation constellation based on L1 and L2 orbits, with lunar orbiting satellites achieving a navigation and positioning accuracy of 20 meters. Sirbu proposed a lunar navigation constellation based on ELFO (Elastic Elastic Floating-Field) satellites, with four ELFO satellites achieving a positioning accuracy of 200 meters. Considering the pressure on ground-based tracking and control from numerous future deep-space missions, and the invisibility issues arising from regional tracking and control networks or lunar obstruction, the autonomous orbit determination after the lunar navigation constellation is established is particularly important.

[0005] Hill's analysis shows that, due to the asymmetric three-body gravitational pull on the Earth-Moon satellite, introducing an inter-satellite link for autonomous orbit determination can effectively observe and suppress directional rotational deviations in the inertial frame. Gao, Xu, and Song also verified the feasibility of autonomous orbit determination for the Earth-Moon satellite based on inter-satellite link ranging through simulations. Existing technologies have the following specific shortcomings: Defect 1: When traditional BeiDou satellites autonomously determine their orbits based solely on inter-satellite links, the right ascension information of the ascending node in the inertial frame is not readily available, and the overall rotation error of the constellation cannot be effectively observed and corrected through inter-satellite ranging, resulting in a continuous degradation of orbit determination accuracy over time.

[0006] Defect 2: In existing autonomous orbit determination methods, the Earth rotation parameters (ERP) cannot be updated in real time. The orbit determination results based solely on the predicted ERP will produce a rotation direction deviation in the Earth-fixed coordinate system. Moreover, this deviation accumulates over time and cannot be effectively constrained and corrected by inter-satellite link measurements within the constellation.

[0007] Deficiency 3: Existing research on autonomous orbit determination of lunar navigation constellations is based solely on simulation data and does not use real on-orbit measured inter-satellite link data for verification. Therefore, it is impossible to accurately evaluate the performance of joint autonomous orbit determination in actual on-orbit environments, and there is a lack of joint orbit determination technology solutions with Earth navigation satellites.

[0008] Considering the future deployment of lunar navigation satellites and the realization of inter-satellite link ranging communication between Earth navigation satellites and lunar navigation satellites, based on the asymmetry of satellite forces caused by the gravitational influence of the three bodies on the moon, it will be possible to achieve long-term, high-precision autonomous determination of orbital information between Earth navigation satellites and lunar navigation satellites in an inertial frame.

[0009] Therefore, there is an urgent need for a method that can effectively solve the problem of joint autonomous orbit determination technology between ELFO satellites and Beidou satellites. Summary of the Invention

[0010] The objective of this invention is to provide a method and system for joint autonomous orbit determination of ELFO satellites and BeiDou satellites. This method and / or system addresses the problems of existing BeiDou constellation satellites' inability to effectively suppress overall constellation rotation errors caused by the unobservable right ascension information of the ascending node in the inertial frame during autonomous orbit determination based on inter-satellite links, and the lack of a joint autonomous orbit determination scheme between existing lunar navigation constellations and Earth navigation constellations. By utilizing the strong gravitational pull of the ELFO satellite from the moon to generate strong gravitational asymmetry, the invention aims to suppress directional rotational deviations of BeiDou satellites in the inertial frame and achieve high-precision orbit determination for the ELFO satellite.

[0011] In a first aspect of the invention, the aforementioned task is accomplished by a joint autonomous orbit determination method using ELFO satellites and BeiDou satellites, the method comprising the following steps: Based on a high-precision orbital dynamics model, inertial frame position and velocity prediction information for BeiDou and ELFO satellites is generated. Collect bidirectional link measurement information between BeiDou satellites, between BeiDou satellites and ELFO satellites, and between ELFO satellites; The bidirectional link measurement information is corrected to generate corrected measurement information; and The extended Kalman filter algorithm is used to perform state prediction and covariance prediction. The corrected measurement information is used to perform filtering correction on the state prediction information and covariance prediction information, and the joint autonomous orbit determination results of Beidou satellite and ELFO satellite are output.

[0012] In one embodiment of the present invention, the high-precision orbital dynamics model simultaneously considers both BeiDou satellites and ELFO satellites: For BeiDou satellites: the Earth's non-spherical gravity was calculated using the EGM 2008 12×12 order non-spherical gravity model; the gravitational force of the Sun, Moon, and Human Planets was calculated using the JPL DE430 lunar and solar ephemeris; and the solar radiation pressure perturbation force was calculated using the ECOM5 parametric model; and For the ELFO satellite: the non-spherical gravity of the Moon was calculated using the GRGM900c 4×4 order non-spherical gravity model, the gravity of the Sun, Moon and Sun was calculated using the JPL DE430 lunar ephemeris, and the solar radiation pressure perturbation was calculated using the spherical radiation pressure model.

[0013] In one embodiment of the present invention, collecting bidirectional link measurement information between BeiDou satellites, between BeiDou satellites and ELFO satellites, and between ELFO satellites includes: At the current time t0, the ELFO satellite transmits Ka-band inter-satellite link information, which is received by the BeiDou satellite, generating a measurement message; and The BeiDou satellite sends Ka-band inter-satellite link information, which is received by the ELFO satellite and generates another measurement information.

[0014] In one embodiment of the present invention, performing correction on the bidirectional link measurement information includes: Corrections are performed on the phase eccentricity error, relativistic effect error, transmit / receive delay error, bidirectional link reduction error, and clock error of the Earth-Moon satellite involved in the bidirectional link measurement information.

[0015] In one embodiment of the present invention, the method for correcting the phase eccentricity error is as follows: Based on the antenna's location in the star system attitude matrix of the Earth-Moon satellite body coordinate system relative to the inertial coordinate system Obtain the position of the antenna phase center relative to the satellite's center of mass in the inertial coordinate system. , This refers to the phase eccentricity error. The calculation formula is as follows: Where T represents the transpose of the matrix; The phase center deviation in the pointing direction is determined based on the projection of the phase eccentricity error in the inertial coordinate system onto the pointing direction. , in, This represents the vector information pointing between the AB binary stars in the inertial coordinate system. Calculated according to the following formula, in, These represent the position vectors of the AB binary stars, respectively.

[0016] In one embodiment of the present invention, The method for correcting the relativistic error is as follows: calculating the relativistic error of gravitational time delay and time dilation effects; and / or The transmit / receive delay error is a constant error, determined based on the satellite transmit / receive delay recorded on the ground; and / or The bidirectional link reduction error is calculated by using short-time orbit prediction to reduce the bidirectional link measurement information between the BeiDou satellite and the ELFO satellite to the current time t0, respectively. ; and / or The clock error is eliminated by summing and averaging the measurement information reduced to time t0. The calculation formula is as follows: .

[0017] In one embodiment of the present invention, the extended Kalman filter algorithm is used to perform state prediction and covariance prediction. The corrected measurement information is used to perform filtering correction on the state prediction information and covariance prediction information, and the output of the joint autonomous orbit determination results of Beidou satellite and ELFO satellite includes: Iterative solutions are performed using the extended Kalman filter algorithm to perform state prediction and covariance prediction. in, Indicates the previous moment, Indicates the current time; Indicates from the previous moment up to the current moment The orbital state transition matrix; This represents state variables, including the predicted position and velocity corrections for BeiDou and ELFO satellites; Indicates the current time State variables; Represents state variables Covariance solution; Represents state variables The noise covariance matrix; T denotes the transpose of the matrix; According to the following formula, the corrected measurement information is used to perform filtering correction on the state prediction information and covariance prediction information. in, For the current moment The observation matrix Calculated using the following formula, Where M represents the number of constellation satellites involved in the solution; in, This represents the gain matrix of the Kalman filter algorithm; Represents the observation noise matrix. Represents the identity matrix; Represents the observation residual. Calculated using the following formula, in, This indicates the corrected measurement information. They represent The forecast.

[0018] In a second aspect of the invention, the aforementioned task is also addressed by a joint autonomous orbit determination system for ELFO and BeiDou satellites, which is applied to the joint autonomous orbit determination method for ELFO and BeiDou satellites. The system includes: The orbit prediction module is configured to generate inertial frame position and velocity prediction information for BeiDou and ELFO satellites based on a high-precision orbit dynamics model. The bidirectional link measurement information collection module is configured to collect bidirectional link measurement information between BeiDou satellites, between BeiDou satellites and ELFO satellites, and between ELFO satellites. The measurement information correction module is configured to correct the bidirectional link measurement information and generate corrected measurement information; and The autonomous orbit determination module is configured to use the extended Kalman filter algorithm to perform state prediction and covariance prediction, and to use the corrected measurement information to perform filtering correction on the state prediction information and covariance prediction information, and output the joint autonomous orbit determination results of Beidou satellite and ELFO satellite.

[0019] In a third aspect, the present invention also provides an electronic device comprising: A processor, configured to execute machine-readable instructions; A graphics card with an artificial intelligence chip is configured to train the ELFO satellite and the BeiDou satellite joint autonomous orbit determination method; and A memory configured to store machine-readable instructions that, when executed by a processor and / or graphics card, perform the steps of the ELFO satellite and BeiDou satellite joint autonomous orbit determination method.

[0020] In a fourth aspect, the present invention also provides a computer-readable storage medium storing computer-readable instructions thereon, which, when executed by a processor, perform the steps of the ELFO satellite and BeiDou satellite joint autonomous orbit determination method.

[0021] The technical solution provided by this invention has the following advantages: 1. The proposed method and system for joint autonomous orbit determination of ELFO satellite and BeiDou satellite, by introducing ELFO satellite and BeiDou satellite for autonomous orbit determination, utilizes the gravitational force of the Earth-Moon tri-body on the ELFO satellite as a constraint on rotational error drift. The BeiDou MEO satellite (Medium Earth Orbit Satellite) can sustainably maintain extremely high orbit determination accuracy, significantly improving the stability of long-term autonomous orbit determination accuracy.

[0022] 2. The ELFO satellite and BeiDou satellite joint autonomous orbit determination method and system proposed in this invention continuously suppresses the orientation rotation deviation of BeiDou satellite in the inertial frame by introducing the transfer matrix under the gravitational asymmetry caused by the strong gravitational force of the ELFO satellite under the strong gravitational force of the moon into the filtering solution process. This results in the overall rotational drift error of the constellation being constrained to the sub-meter range for a long time, effectively suppressing the orientation rotation error of the inertial frame.

[0023] 3. The ELFO satellite and BeiDou satellite joint autonomous orbit determination method and system proposed in this invention, by constructing a joint calculation architecture for two-way ranging information of BeiDou satellite and ELFO satellite, the system not only completes high-precision self-calibration of the Earth navigation constellation, but also realizes high-precision orbit determination of ELFO satellite, providing reliable spatiotemporal reference support for future lunar navigation constellation deployment and autonomous operation of deep space missions. Attached Figure Description

[0024] To further illustrate the above and other advantages and features of the various embodiments of the present invention, a more specific description of the various embodiments of the present invention will be presented with reference to the accompanying drawings. It is to be understood that these drawings depict only typical embodiments of the invention and are therefore not intended to limit its scope. In the drawings, identical or corresponding parts will be indicated by identical or similar reference numerals for clarity.

[0025] Figure 1A flowchart illustrating a method for joint autonomous orbit determination using ELFO and BeiDou satellites according to an embodiment of the present invention is shown. Figure 2 A schematic diagram of the ELFO1–ELFO4 satellite distribution according to an embodiment of the present invention is shown; Figure 3 The diagram illustrates the deviations between the PRN25 BeiDou satellite's autonomous orbit determination orbit and the precise reference orbit in the R, T, and N directions, as well as the corresponding URE (User Range Error). Figure 4 This diagram illustrates the URE statistical analysis of 24 BeiDou satellites according to an embodiment of the present invention. Figure 5 The diagram illustrates the deviations of the ELFO1-ELFO4 satellites in the R, T, and N directions, and the resulting three-dimensional deviation schematic, according to an embodiment of the present invention. Figure 6 The diagram shows the deviations of the autonomous orbit of the PRN25 Beidou satellite, which is determined solely based on measured data from the Beidou inter-satellite link, from the precise reference orbit in the R, T, and N directions, as well as the corresponding URE diagrams. Figure 7 This diagram illustrates the URE statistical analysis of 24 BeiDou satellites based solely on measured data from BeiDou inter-satellite links; and... Figure 8 A schematic diagram of an ELFO satellite and BeiDou satellite joint autonomous orbit determination system according to an embodiment of the present invention is shown. Detailed Implementation

[0026] In the following description, the invention is described with reference to various embodiments. However, those skilled in the art will recognize that the embodiments may be practiced without one or more specific details or with other alternatives and / or additional methods or components. In other instances, well-known structures or operations are not shown or described in detail so as not to obscure the inventive points of the invention. Similarly, for illustrative purposes, specific numbers and configurations are set forth to provide a comprehensive understanding of embodiments of the invention. However, the invention is not limited to these specific details.

[0027] In this specification, references to "an embodiment" or "this embodiment" mean that a particular feature, structure, or characteristic described in connection with that embodiment is included in at least one embodiment of the invention. The phrase "in one embodiment" appearing throughout this specification does not necessarily refer to the same embodiment in all instances.

[0028] It should be noted that the embodiments of the present invention describe the method steps in a specific order; however, this is only for illustrating the specific embodiment and not for limiting the order of the steps. On the contrary, in different embodiments of the present invention, the order of the steps can be adjusted according to actual needs.

[0029] In this invention, the modules of the system according to the invention can be implemented using software, hardware, firmware, or a combination thereof. When a module is implemented using software, its function can be implemented through computer program flow. For example, the module can be implemented using code segments (such as code segments in languages ​​like C and C++) stored in a storage device (such as a hard disk, memory, etc.), wherein the corresponding function of the module can be implemented when the code segment is executed by a processor. When a module is implemented using hardware, its function can be implemented by setting a corresponding hardware structure. For example, the module's function can be implemented by hardware programming a programmable device such as a field-programmable gate array (FPGA), or by designing an application-specific integrated circuit (ASIC) that includes multiple transistors, resistors, capacitors, and other electronic devices. When a module is implemented using firmware, the module's function can be written into a read-only memory such as an EPROM or EEPROM in the form of program code, and the corresponding function of the module can be implemented when the program code is executed by a processor. In addition, some functions of the module may need to be implemented by separate hardware or by working in cooperation with the hardware. For example, the detection function is implemented by a corresponding sensor (such as a proximity sensor, accelerometer, gyroscope, etc.), the signal transmission function is implemented by a corresponding communication device (such as a Bluetooth device, infrared communication device, baseband communication device, Wi-Fi communication device, etc.), the output function is implemented by a corresponding output device (such as a display, speaker, etc.), and so on.

[0030] Compared to evaluation and analysis based solely on simulation data, this invention obtains post-hoc BeiDou satellite orbit information, and uses real, on-orbit measured inter-satellite link data. Therefore, it can accurately assess the current autonomous orbit determination performance of BeiDou satellites and more accurately evaluate the improvement in autonomous orbit determination accuracy after the addition of lunar satellites. Furthermore, based on literature analysis and comparison of lunar navigation constellations, if navigation coverage to the lunar south pole is a primary consideration, the ELFO constellation appears to be a more ideal choice. Therefore, this invention, following the literature, uses a lunar constellation consisting of four ELFO satellites to analyze and evaluate the autonomous orbit determination accuracy in conjunction with the BeiDou constellation.

[0031] Figure 1 A flowchart illustrating a method for joint autonomous orbit determination using ELFO and BeiDou satellites according to an embodiment of the present invention is shown below. Figure 1 This paper describes the proposed method for joint autonomous orbit determination of ELFO satellites and BeiDou satellites. For example... Figure 1 As shown, the joint autonomous orbit determination method of ELFO satellite and Beidou satellite includes the following steps: Step 101: Based on the high-precision orbital dynamics model, generate inertial frame position and velocity prediction information for BeiDou satellites and ELFO satellites.

[0032] In one embodiment of the present invention, the high-precision orbital dynamics model simultaneously considers both BeiDou satellites and ELFO satellites: For BeiDou satellites: the Earth's non-spherical gravity was calculated using the EGM 2008 12×12 order non-spherical gravity model; the gravitational force of the Sun, Moon, and Human Planets was calculated using the JPL DE430 lunar and solar ephemeris; and the solar radiation pressure perturbation force was calculated using the ECOM5 parametric model; and For the ELFO satellite: the non-spherical gravity of the Moon was calculated using the GRGM900c 4×4 order non-spherical gravity model, the gravity of the Sun, Moon and Sun was calculated using the JPL DE430 lunar ephemeris, and the solar radiation pressure perturbation was calculated using the spherical radiation pressure model.

[0033] It should be noted that the BeiDou satellite mentioned in this invention can be a BeiDou MEO satellite (Medium Earth Orbit Satellite).

[0034] It should be noted that the BeiDou satellite in step 101 can be a BeiDou constellation satellite, and the ELFO satellite can be an ELFO constellation satellite. Figure 2 This is a schematic diagram showing the distribution of the ELFO constellation satellites, which include ELFO1, ELFO2, ELFO3, and ELFO4. Figure 2 The "Moon" in the name refers to the moon. The ELFO1, ELFO2, ELFO3, and ELFO4 satellites provide coverage of the lunar south pole.

[0035] Step 102: Collect bidirectional link measurement information between BeiDou satellites, between BeiDou satellites and ELFO satellites, and between ELFO satellites.

[0036] Specifically, at the current time t0, in the first 1.5 seconds, the ELFO satellite sends Ka-band inter-satellite link information, which is received by the BeiDou satellite, generating a measurement message; and In the next 1.5 seconds, the BeiDou satellite sends Ka-band inter-satellite link information, which is received by the ELFO satellite and generates another measurement information.

[0037] Step 103: Correct the bidirectional link measurement information to generate corrected measurement information.

[0038] Correcting bidirectional link measurement information includes: Corrections are performed on the phase eccentricity error, relativistic effect error, transmission and reception delay error, two-way link reduction error, and clock error of the Earth-Moon satellite involved in the two-way link measurement information (i.e., ranging information based on Ka inter-satellite links).

[0039] The methods for correcting phase eccentricity error include: First, based on the antenna's position in the star-fixed system. attitude matrix of the Earth-Moon satellite body coordinate system relative to the inertial coordinate system Obtain the position of the antenna phase center relative to the satellite's center of mass in the inertial coordinate system. , This refers to the phase eccentricity error. The calculation formula is as follows: in, express transpose, Represents the attitude matrix The inverse matrix.

[0040] Secondly, based on the projection of the phase eccentricity error in the inertial coordinate system onto the pointing direction, the phase center deviation in the pointing direction is determined. , in, This represents the vector information pointing between the AB binary stars in the inertial coordinate system. Calculated according to the following formula, in, These represent the position vectors of the AB binary stars, respectively.

[0041] The method for correcting relativistic error is to calculate the relativistic error of gravitational time delay and time dilation effects.

[0042] The transmission and reception delay error can be regarded as a constant error, so the satellite transmission and reception delay error can be determined based on the satellite transmission and reception delay recorded on the ground.

[0043] The two-way link reduction error can be reduced to the current time t0 by using short-time orbit prediction to calculate the two-way link measurement information between Beidou satellites and ELFO satellites. .

[0044] Clock error can be eliminated by summing and averaging the measurement information reduced to time t0. The calculation formula is as follows: , This refers to the observed values ​​after preprocessing the two-way ranging information.

[0045] Step 104: Use the extended Kalman filter algorithm to perform state prediction and covariance prediction. Use the corrected measurement information to perform filtering correction on the state prediction information and covariance prediction information, and output the joint autonomous orbit determination result of Beidou satellite and ELFO satellite. The orbit determination result mentioned here is the satellite orbital position and velocity information.

[0046] Specifically, the Extended Kalman Filter (EKF) algorithm is used to perform iterative solutions. The state variables obtained are the corrections to the position and velocity information of all satellites in the constellation (including BeiDou and ELFO satellites). The one-step prediction method for the corrections and their covariance information is as follows: in, Indicates the previous moment, Indicates the current time; Indicates from the previous moment up to the current moment The orbital state transition matrix; This represents state variables, including the predicted position and velocity corrections for BeiDou and ELFO satellites; Indicates the current time State variables; Represents state variables Covariance solution; Represents state variables The noise covariance matrix; T represents the transpose of the matrix; the superscript - indicates the forecast information.

[0047] According to the following formula, the corrected measurement information is used to perform filtering correction on the state prediction information and covariance prediction information. in, For the current moment The observation matrix. For inter-satellite link ranging observations of any binary system AB with M satellites, it is represented as one row of the observation matrix, specifically calculated using the following formula: in, Represents the Kalman filter gain matrix; Represents the observation noise matrix. Represents the identity matrix; Represents the observation residual. Calculated using the following formula, in, This represents the corrected measurement information, which is the original measurement information after being corrected for phase center deviation, relativistic effect error, time delay error, bidirectional link reduction error, and clock error.

[0048] It should be noted that the filtering parameter setting principle only considers the measurement accuracy of noise in long-distance inter-satellite observations, and the link establishment takes into account factors such as Earth obstruction and the visibility range of the BeiDou Ka payload.

[0049] It should be noted that by using joint orbit determination of Earth and lunar satellites, and introducing filtering into the transfer matrix under the strong asymmetric gravity of the moon, the rotation error correction is ultimately achieved.

[0050] The following example illustrates the effectiveness of the ELFO satellite and BeiDou satellite joint autonomous orbit determination method provided by this invention.

[0051] The experiment was scheduled to run from 00:00 on October 15, 2020 to 00:00 on December 14, 2020, lasting 60 days. The experimental scenario consisted of 24 BeiDou-3 MEO satellites and 4 lunar ELFO satellites. The orbital parameters of the 24 MEO satellites were generated post-hoc with precise orbits, and the orbital parameters of the ELFO satellites in the lunar inertial frame were as described in the previous high-precision orbital dynamics model. The set cycle for a single autonomous orbit determination was 5 minutes.

[0052] The experimental data consists of measured data from the BeiDou inter-satellite link and simulated ranging data from the inter-satellite link between the Earth-Moon ELFO satellite and the BeiDou satellite, as well as the inter-satellite link between the Earth-Moon ELFO satellite and the BeiDou satellite.

[0053] With the introduction of the ELFO satellite, a joint autonomous orbit determination system was implemented using the Earth-Moon ELFO satellite and the BeiDou MEO satellite. The gravitational pull of the Earth, Moon, and Earth bodies acting on the ELFO satellite served as a constraint on rotational error drift, allowing the MEO satellite to maintain extremely high orbit determination accuracy. Taking the PRN25 BeiDou satellite as an example again, such as... Figure 3 As shown, the orbit determination error oscillates stably between 0.18m and 2.5m in the T and N directions, while the accuracy in the R direction remains better than 0.20m. Therefore, the maximum URE of the satellite orbit over 60 days does not exceed 0.64m. Meanwhile, Figure 4 The daily root mean square (RMS) and standard deviation (STD) values ​​of the URE (Uniqueness) for 24 BeiDou satellites are displayed. The maximum daily URE for the 60-day constellation satellites is 0.61m. The URE of each satellite exhibits stable oscillation, and the standard deviation of the URE for the constellation satellites is 0.08m.

[0054] Four ELFO satellites, together with 24 BDS-3 MEO satellites, participated in joint AOD (Autonomous Orbit Determination) calculations based on inter-satellite links. With the overall rotational deviation of the BDS-3 MEO satellites effectively suppressed, the four ELFO satellites also achieved high-precision AOD results. Figure 5 The diagram illustrates the deviations of the ELFO1–ELFO4 satellites in the R, T, and N directions, and the resulting three-dimensional deviations. Accuracy analysis in the Earth RTN coordinate system shows that, compared to a precise reference orbit, the maximum deviations of the AOD results for the four ELFO satellites in the R, T, and N directions do not exceed 0.16 meters, 1.66 meters, and 1.83 meters, respectively. Therefore, the maximum three-dimensional position deviation does not exceed 2.26 meters.

[0055] Based solely on measured data from the BeiDou inter-satellite link, accuracy still shows a gradual degradation over time. For the PRN25 BeiDou satellite, the deviation of its autonomous orbit from the precise reference orbit remains stable at 0.20m in the radial (R) direction, but exhibits slow drift in the tangential (T) and normal (N) directions, with maximum deviations of 2.9m and 2.0m respectively. The satellite's user distance error (URE) diverges to 0.65m on day 60. Figure 6 As shown. The statistical performance of the entire constellation is summarized in... Figure 7 The root mean square (RMS) values ​​and standard deviations of the URE for all 24 satellites are given. On day 60, the constellation's average URE is 0.60m, with a corresponding standard deviation of 0.07m.

[0056] The ELFO satellite and BeiDou satellite joint autonomous orbit determination method provided by this invention utilizes the strong gravitational pull of the moon on the ELFO satellite to generate strong gravitational asymmetry, thereby suppressing the directional rotation deviation under the inertial frame of the BeiDou satellite and achieving high-precision orbit determination of the ELFO satellite.

[0057] In one embodiment of the present invention, the present invention also provides a joint autonomous orbit determination system for ELFO satellites and BeiDou satellites, used in the aforementioned joint autonomous orbit determination method for ELFO satellites and BeiDou satellites, such as... Figure 8 As shown, the system includes: The orbit prediction module 201 is configured to generate inertial frame position and velocity prediction information for BeiDou and ELFO satellites based on a high-precision orbit dynamics model.

[0058] The bidirectional link measurement information collection module 202 is configured to collect bidirectional link measurement information between BeiDou satellites, between BeiDou satellites and ELFO satellites, and between ELFO satellites.

[0059] The measurement information correction module 203 is configured to correct the bidirectional link measurement information and generate corrected measurement information.

[0060] The autonomous orbit determination module 204 is configured to use the extended Kalman filter algorithm to perform state prediction and covariance prediction, and to use the corrected measurement information to perform filtering correction on the state prediction information and covariance prediction information, and output the joint autonomous orbit determination results of Beidou satellite and ELFO satellite.

[0061] The proposed method and system for joint autonomous orbit determination of ELFO and BeiDou satellites utilizes the transfer matrix under the gravitational asymmetry caused by the strong gravitational pull of the ELFO satellite on the moon to continuously suppress the directional rotation deviation of the BeiDou satellite in the inertial frame during the filtering and calculation process. This keeps the overall rotational drift error of the constellation within the sub-meter range for a long time, effectively suppressing the directional rotation error of the inertial frame. By constructing a joint calculation architecture for two-way ranging information from BeiDou and ELFO satellites, the system not only completes high-precision self-calibration of the Earth navigation constellation but also achieves high-precision orbit determination of the ELFO satellite, providing reliable spatiotemporal reference support for the future deployment of the lunar navigation constellation and the autonomous operation of deep space missions.

[0062] In one embodiment of the present invention, an electronic device is also provided, comprising: a processor, a graphics card with an artificial intelligence chip, and a memory. The memory is configured to store machine-readable instructions, the graphics card is configured to train the joint autonomous orbit determination method of the ELFO satellite and the BeiDou satellite, and the processor is configured to execute the machine-readable instructions. When the processor and / or the graphics card executes the machine-readable instructions, the following processing steps are implemented: generating inertial frame position and velocity prediction information of the BeiDou satellite and the ELFO satellite based on a high-precision orbital dynamics model; collecting bidirectional link measurement information between BeiDou satellites, between BeiDou satellites and the ELFO satellite, and between ELFO satellites; performing correction on the bidirectional link measurement information to generate corrected measurement information; and performing state prediction and covariance prediction using an extended Kalman filter algorithm, performing filtering correction on the state prediction information and covariance prediction information using the corrected measurement information, and outputting the joint autonomous orbit determination result of the BeiDou satellite and the ELFO satellite.

[0063] The graphics card used can preferably be a model with a GPU computing power higher than 5.0. Since the amount of data to be trained is large, providing a graphics card configuration can significantly improve the training speed.

[0064] The memory includes various media capable of storing machine-readable instructions, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0065] It is understood that, in addition to the memory and processor mentioned above, the computer system described above also includes other hardware and software components not listed in this specification. The specific components can be determined according to the model of the specific data processing equipment in different application scenarios, and will not be listed and described in detail in this specification.

[0066] In one embodiment of the present invention, a computer-readable storage medium is also provided, on which computer-readable instructions are stored. When executed by a processor, the computer-readable instructions perform the following processing steps: generating inertial frame position and velocity prediction information for BeiDou satellites and ELFO satellites based on a high-precision orbital dynamics model; collecting bidirectional link measurement information between BeiDou satellites, between BeiDou satellites and ELFO satellites, and between ELFO satellites; performing correction on the bidirectional link measurement information to generate corrected measurement information; and performing state prediction and covariance prediction using an extended Kalman filter algorithm, using the corrected measurement information to perform filtering correction on the state prediction information and covariance prediction information, and outputting the joint autonomous orbit determination result of BeiDou satellites and ELFO satellites.

[0067] Although various embodiments of the present invention have been described above, it should be understood that they are presented by way of example only and not as limitations. It will be apparent to those skilled in the art that various combinations, modifications, and alterations can be made without departing from the spirit and scope of the invention. Therefore, the breadth and scope of the invention disclosed herein should not be limited by the exemplary embodiments disclosed above, but should be defined according to the technical solutions of the invention and their equivalents.

Claims

1. A method for joint autonomous orbit determination using ELFO satellite and BeiDou satellite, characterized in that, Includes the following steps: Based on a high-precision orbital dynamics model, inertial frame position and velocity prediction information for BeiDou and ELFO satellites is generated. Collect bidirectional link measurement information between BeiDou satellites, between BeiDou satellites and ELFO satellites, and between ELFO satellites; The bidirectional link measurement information is corrected to generate corrected measurement information; as well as The extended Kalman filter algorithm is used to perform state prediction and covariance prediction. The corrected measurement information is used to perform filtering correction on the state prediction information and covariance prediction information, and the joint autonomous orbit determination results of Beidou satellite and ELFO satellite are output.

2. The ELFO satellite and BeiDou satellite joint autonomous orbit determination method according to claim 1, characterized in that, The high-precision orbital dynamics model takes into account both BeiDou and ELFO satellites: For BeiDou satellites: the Earth's non-spherical gravity was calculated using the EGM 2008 12×12 order non-spherical gravity model; the gravitational force of the Sun, Moon, and Human Planets was calculated using the JPL DE430 lunar and solar ephemeris; and the solar radiation pressure perturbation force was calculated using the ECOM5 parametric model; and For the ELFO satellite: the non-spherical gravity of the Moon was calculated using the GRGM900c 4×4 order non-spherical gravity model, the gravity of the Sun, Moon and Sun was calculated using the JPL DE430 lunar ephemeris, and the solar radiation pressure perturbation was calculated using the spherical radiation pressure model.

3. The ELFO satellite and BeiDou satellite joint autonomous orbit determination method according to claim 1, characterized in that, The collection of bidirectional link measurement information between BeiDou satellites, between BeiDou satellites and ELFO satellites, and between ELFO satellites includes: At the current time t0, the ELFO satellite transmits Ka-band inter-satellite link information, which is received by the BeiDou satellite, generating a measurement message; and The BeiDou satellite sends Ka-band inter-satellite link information, which is received by the ELFO satellite and generates another measurement information.

4. The ELFO satellite and BeiDou satellite joint autonomous orbit determination method according to claim 1, characterized in that, Performing corrections on the bidirectional link measurement information includes: Corrections are performed on the phase eccentricity error, relativistic effect error, transmit / receive delay error, bidirectional link reduction error, and clock error of the Earth-Moon satellite involved in the bidirectional link measurement information.

5. The ELFO satellite and BeiDou satellite joint autonomous orbit determination method according to claim 4, characterized in that, The method for correcting the phase eccentricity error is as follows: Based on the antenna's location in the star system attitude matrix of the Earth-Moon satellite body coordinate system relative to the inertial coordinate system Obtain the position of the antenna phase center relative to the satellite's center of mass in the inertial coordinate system. , This refers to the phase eccentricity error. The calculation formula is as follows: Where T represents the transpose of the matrix; The phase center deviation in the pointing direction is determined based on the projection of the phase eccentricity error in the inertial coordinate system onto the pointing direction. , in, This represents the vector information pointing between the AB binary stars in the inertial coordinate system. Calculated according to the following formula, in, Let represent the position vectors of the AB binary star system inertial frames, respectively.

6. The ELFO satellite and BeiDou satellite joint autonomous orbit determination method according to claim 4, characterized in that, The method for correcting the relativistic error is as follows: calculating the relativistic error of gravitational time delay and time dilation effects; and / or The transmit / receive delay error is a constant error, determined based on the satellite transmit / receive delay recorded on the ground; and / or The bidirectional link reduction error is calculated by using short-time orbit prediction to reduce the bidirectional link measurement information between the BeiDou satellite and the ELFO satellite to the current time t0, respectively. ; and / or The clock error is eliminated by summing and averaging the measurement information reduced to time t0. The calculation formula is as follows: 。 7. The ELFO satellite and BeiDou satellite joint autonomous orbit determination method according to claim 1, characterized in that, The extended Kalman filter algorithm is used to perform state prediction and covariance prediction. The corrected measurement information is used to filter and correct the state prediction information and covariance prediction information. The joint autonomous orbit determination results of BeiDou satellite and ELFO satellite are output, including: Iterative solutions are performed using the extended Kalman filter algorithm to perform state prediction and covariance prediction. in, Indicates the previous moment, Indicates the current time; Indicates from the previous moment up to the current moment The orbital state transition matrix; This represents state variables, including the predicted position and velocity corrections for BeiDou and ELFO satellites; Indicates the current time State variables; Represents state variables Covariance solution; Represents state variables The noise covariance matrix; T denotes the transpose of the matrix; According to the following formula, the corrected measurement information is used to perform filtering correction on the state prediction information and covariance prediction information. in, For the current moment The observation matrix Calculated using the following formula, Where M represents the number of constellation satellites involved in the solution; in, This represents the gain matrix of the Kalman filter algorithm; Represents the observation noise matrix. Represents the identity matrix; Represents the observation residual. Calculated using the following formula, in, This indicates the corrected measurement information. They represent The forecast.

8. A joint autonomous orbit determination system for ELFO satellites and BeiDou satellites, used in the joint autonomous orbit determination method for ELFO satellites and BeiDou satellites as described in any one of claims 1-7, characterized in that, include: The orbit prediction module is configured to generate inertial frame position and velocity prediction information for BeiDou and ELFO satellites based on a high-precision orbit dynamics model. The bidirectional link measurement information collection module is configured to collect bidirectional link measurement information between BeiDou satellites, between BeiDou satellites and ELFO satellites, and between ELFO satellites. The measurement information correction module is configured to correct the bidirectional link measurement information and generate corrected measurement information. as well as The autonomous orbit determination module is configured to use the extended Kalman filter algorithm to perform state prediction and covariance prediction, and to use the corrected measurement information to perform filtering correction on the state prediction information and covariance prediction information, and output the joint autonomous orbit determination results of Beidou satellite and ELFO satellite.

9. An electronic device, characterized in that, include: A processor, configured to execute machine-readable instructions; A graphics card with an artificial intelligence chip is configured to train the ELFO satellite and the Beidou satellite joint autonomous orbit determination method; as well as A memory configured to store machine-readable instructions that, when executed by a processor and / or a graphics card, perform the steps of the method according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, It stores computer-readable instructions that, when executed by a processor, perform the steps of the method according to any one of claims 1-7.

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