Autonomous orbit determination method and system for low-orbit navigation constellation under weak intersatellite topology

Abstract

The present disclosure provides a method and system for autonomous orbit determination of a low-orbit navigation constellation under a weak inter-satellite topology structure, which relates to the field of satellite orbit determination technology, including: obtaining various types of observation data of an inter-satellite link on a predetermined orbit, and pre-processing the various types of observation data; adopting a piecewise first-order polynomial satellite clock error modeling method to establish synchronous observation equations of orbit and clock error parameters, generate orbit, clock error and related error parameters of joint on-board GNSS and inter-satellite link data, and predict them; based on the error analysis results, extract multiple key features from the generated orbit, clock error and related error parameters as inputs of a parameter prediction model, and output four types of predicted parameter time series: relative weight, inter-satellite link hardware delay, low-orbit satellite clock error and unmodeled error; uploading the predicted parameter time series and broadcast ephemeris together to a main satellite, and the main satellite transmits them to each sub-satellite through an inter-satellite link, so as to realize distributed autonomous orbit determination of the sub-satellite operation.

Description

Technical Field

[0001] The present disclosure relates to the technical field of satellite orbit determination, and in particular to a method and system for autonomous orbit determination of a low-orbit navigation constellation under a weak inter-satellite topology. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] Low Earth Orbit (LEO) constellations offer advantages such as high ground-based signal strength, rapid geometric configuration changes, and the ability to complement medium- and high-orbit GNSS (Global Navigation Satellite System) constellations. These advantages significantly enhance GNSS navigation positioning, integrity, continuity, and availability, and have become a hot topic in the current satellite navigation field. LEO navigation augmentation satellites transmit navigation signals to Earth and simultaneously broadcast ephemeris. Accurate orbits are essential for users to enjoy reliable navigation and positioning services. Therefore, autonomous real-time orbit determination of LEO satellites is essential for ensuring the long-term, high-precision, and reliable autonomous operation of the constellation, providing technical support for the smooth implementation of high-precision scientific exploration missions.

[0004] Currently, observational data for autonomous orbit determination in low-orbit navigation constellations primarily consists of inter-satellite ranging information and onboard GNSS data. Onboard GNSS data provides a benchmark for the entire constellation, effectively controlling translational and rotational errors. Autonomous onboard orbit determination for low-orbit navigation constellations based on inter-satellite links can be categorized into two types: centralized and distributed. Centralized processing aggregates all observational information to a master satellite, which then calculates the orbits of all satellites in the constellation and distributes the results to each satellite. Distributed processing involves each satellite receiving and storing its own observational information and orbital information from associated satellites to calculate its own orbit and other parameters. Centralized processing can yield optimal orbit solutions, but places high demands on the master satellite's onboard storage, computing power, and data communication capabilities. Distributed models, due to their poor geometric robustness, produce suboptimal solutions, but they also place lower demands on the storage and computing power of each satellite. Therefore, given the large number of satellites in low-orbit navigation constellations, typically reaching thousands, distributed autonomous orbit determination is primarily employed. The specific subnet size is optimized and determined based on factors such as orbit determination accuracy requirements, inter-satellite link observation topology, number of links and inter-satellite data communication capabilities. The minimum subnet can be a single satellite or several satellites with local co-orbit or disparate orbits.

[0005] However, the following problems still exist in the distributed autonomous orbit determination of large LEO constellations:

[0006] 1) Due to the low altitude of satellite orbits and high atmospheric drag, intersatellite links are susceptible to space weather such as solar storms. Intersatellite link configurations change frequently, and weak intersatellite link structures may occur, making it difficult to guarantee the volume of intersatellite ranging data. However, autonomous orbit determination requires calculating satellite orbits, satellite clock errors, intersatellite link hardware delay bias, atmospheric drag parameters, and force model parameters. These numerous parameters can severely impact orbit determination results. Due to the high speed and short transit times of low-orbit satellites, the transmission of real-time GNSS and intersatellite link data to the ground will cause a certain time delay, which also increases the burden on the communication system. Furthermore, the real-time processing of large amounts of data on the ground requires certain computational efficiency requirements that ground processing systems may struggle to meet.

[0007] 2) Furthermore, autonomous orbit determination for LEO navigation-augmented constellations requires consideration of multiple error sources. Due to limited onboard computing power and resources, some errors can be calibrated on the ground to reduce the onboard processing burden. These errors include microwave and laser link noise, onboard GNSS data noise, intersatellite link hardware delay bias, GNSS pseudorange bias, multipath error, intersatellite link and GNSS antenna phase center offset (PCO) and variation (PCV), and other unmodeled errors such as multipath effects. Due to the numerous error sources considered for autonomous orbit determination of LEO satellites in various observation modes, as well as the low orbital altitude and complex observation environment of LEO satellites, intersatellite link establishment may not be as stable as that of navigation satellites, and the configuration may exhibit weak observation structures. In this case, the orbit determination equations are singular and the condition number is excessively large. Therefore, some unmodeled errors will remain in the residuals, affecting the accuracy of orbit determination. Summary of the Invention

[0008] To address the above-mentioned issues, the present disclosure proposes a method and system for autonomous orbit determination of a low-orbit navigation constellation under a weak inter-satellite topology. By receiving historical onboard GNSS and inter-satellite link data from the ground, satellite orbits, clock error parameters, and inter-satellite hardware delay bias parameters are obtained and predicted through post-processing. Then, key parameters to be estimated and their error levels are calibrated and predicted based on machine learning. These parameters are uploaded to the onboard processor for autonomous orbit determination and broadcast ephemeris generation. This allows robust orbit determination to be achieved even under a weak inter-satellite observation structure on board using parameters such as the orbit and clock error noted on the ground.

[0009] According to some embodiments, the present disclosure adopts the following technical solutions:

[0010] The autonomous orbit determination method for low-orbit navigation constellations under weak intersatellite topology includes:

[0011] Obtain various observation data of the intersatellite link on the predetermined orbit and pre-process the various observation data;

[0012] The synchronous observation equations for orbit and clock error parameters are established using a piecewise linear polynomial satellite clock error modeling method. The effects of clock error jumps are considered. Based on ground-uploaded data, weak constraints on prior orbit information and onboard GNSS reference constraints or GNSS rotation angle error constraints are imposed. Error analysis is performed on various preprocessed observation data to generate and predict the orbit, clock, and related error parameters of the combined onboard GNSS and inter-satellite link data.

[0013] Based on the error analysis results, several key features are extracted from the generated orbit, clock error, and related error parameters as input to the parameter prediction model. The output is the time series of error parameters for four categories of predictions: relative weight, inter-satellite link hardware delay, low-orbit satellite clock error, and unmodeled error.

[0014] The predicted error parameter time series and broadcast ephemeris are uploaded to the main satellite together, and the main satellite transmits them to each sub-satellite through inter-satellite links to realize distributed autonomous orbit determination of the sub-satellites.

[0015] According to some embodiments, the present disclosure adopts the following technical solutions:

[0016] The autonomous orbit determination system for low-orbit navigation constellations under a weak intersatellite topology structure includes:

[0017] The observation data acquisition module is used to obtain various observation data of the intersatellite link on the predetermined orbit and pre-process the various observation data;

[0018] The error analysis and calibration module is used to establish synchronous observation equations for orbit and clock error parameters using a piecewise linear polynomial satellite clock error modeling method. This module considers the effects of clock error jumps and applies weak constraints on prior orbit information and onboard GNSS reference constraints or GNSS rotation angle error constraints based on ground-uploaded data. It then performs error analysis on various preprocessed observation data, generates orbit, clock, and related error parameters for combined onboard GNSS and inter-satellite link data, and makes predictions.

[0019] The parameter prediction module is used to extract multiple key features from the generated orbit, clock error, and related error parameters based on the error analysis results as input to the parameter prediction model. The module outputs four types of error parameter time series: relative weight, inter-satellite link hardware delay, low-orbit satellite clock error, and unmodeled error.

[0020] The onboard orbit determination module is used to upload the predicted error parameter time series and broadcast ephemeris to the main satellite. The main satellite transmits them to each sub-satellite through inter-satellite links to realize distributed autonomous orbit determination of the sub-satellites.

[0021] According to some embodiments, the present disclosure adopts the following technical solutions:

[0022] A computer program product includes a computer program, which, when executed by a processor, implements the autonomous orbit determination method for a low-orbit navigation constellation under a weak inter-satellite topology.

[0023] According to some embodiments, the present disclosure adopts the following technical solutions:

[0024] A non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the method for autonomous orbit determination of a low-orbit navigation constellation under a weak inter-satellite topology is implemented.

[0025] According to some embodiments, the present disclosure adopts the following technical solutions:

[0026] An electronic device includes: a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to implement the method for autonomous orbit determination of a low-orbit navigation constellation under a weak inter-satellite topology.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] The disclosed method for automatic orbit determination of a low-orbit navigation constellation under a weak inter-satellite topology structure receives historical satellite-borne GNSS and inter-satellite link data from the ground, establishes synchronous observation equations for orbit and clock error parameters, solves and determines the satellite orbit, clock error and inter-satellite hardware delay deviation parameters, and then calibrates and predicts the key parameters to be estimated and their error levels based on machine learning and uploads them to the on-board processor. This method allows robust orbit determination to be achieved even under a weak inter-satellite observation structure on board the satellite through the orbit, clock error and other parameters injected on the ground, thereby obtaining reliable autonomous orbit determination results.

[0029] The disclosed method for automatic orbit determination of a low-orbit navigation constellation under a weak intersatellite topology effectively addresses the issue of low autonomous orbit determination accuracy under weak onboard intersatellite observation topologies. This method uses ground-based post-acquisition GNSS and intersatellite link data for precise processing to generate precise orbit, clock, and intersatellite hardware delay bias parameters. Key input variables influencing autonomous orbit determination, such as microwave and laser link noise, intersatellite link design delay, and unmodeled errors, are then configured. Machine learning methods are then used to accurately predict orbit, clock, and other parameters and inject them onto the satellite. Distributed autonomous orbit determination is performed onboard, and external priori parameter constraints are generally not required when the intersatellite observation topology is good. However, when a weak topology is present, robust orbit determination is achieved by applying certain priori constraints to the estimated parameters during autonomous orbit determination based on predicted relative weights, clock, hardware delay, and other parameters, as well as the error covariance matrix. This improves the accuracy of autonomous orbit determination under a distributed full-observation link structure, even when the intersatellite link observation structure is weak or observation data is insufficient.

[0030] The disclosed method for automatic orbit determination of low-orbit navigation constellations in a weak intersatellite topology establishes synchronous observation equations for orbit and clock parameters, taking into account the impact of clock jumps. It simultaneously obtains time series such as ground-based clock errors, link hardware delay deviations, weights of microwave / laser links relative to GNSS pseudoranges, and unmodeled errors, and performs an integrated solution for orbit, clock, and other parameters. Furthermore, based on actual conditions, onboard GNSS reference constraints, GNSS rotation angle error constraints, or weak constraints based on prior orbit information are applied to enhance the robustness of the results under the weak intersatellite observation structure. During execution, autonomous integrity monitoring is performed, i.e., autonomous satellite fault detection and integrity isolation processing are performed to prevent undetected faulty satellites from contaminating other satellites or even the entire constellation with gross or abnormal observations, thereby causing filter divergence.

[0031] The disclosed method for automated orbit determination of low-orbit navigation constellations in a weak intersatellite topology uses a predicted parameter time series, which can be uploaded to a master satellite along with broadcast ephemeris. The master satellite then transmits the data to each sub-satellite via intersatellite links, allowing the sub-satellites to perform distributed autonomous orbit determination. The predicted parameter series can be uploaded at a relatively frequent interval, which offers the advantage of reduced reliance on ground systems. For example, in special scenarios where ground control or uplink systems are compromised, robust autonomous orbit determination can be continued using the longer time series of predicted values ​​stored onboard. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The accompanying drawings, which constitute a part of the present disclosure, are used to provide a further understanding of the present disclosure. The exemplary embodiments of the present disclosure and their descriptions are used to explain the present disclosure and do not constitute an improper limitation to the present disclosure.

[0033] Figure 1Schematic diagram of the structure of an existing distributed autonomous orbit determination satellite solution system according to an embodiment of the present disclosure;

[0034] Figure 2 The Yunyao series satellite clock error time series and its adjustment operation according to the embodiment of the present disclosure;

[0035] Figure 3 Schematic diagram of an error analysis process taking into account low-orbit satellite clock error jumps according to an embodiment of the present disclosure;

[0036] Figure 4 Schematic diagram of the training process of the parameter prediction model based on deep learning according to an embodiment of the present disclosure;

[0037] Figure 5 This is a diagram showing the structure of the four parameter prediction training networks according to an embodiment of the present disclosure;

[0038] Figure 6 This is a flow chart of the overall method for autonomous orbit determination of a low-orbit navigation constellation under a weak inter-satellite topology structure according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0039] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0040] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present disclosure belongs.

[0041] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present disclosure. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0042] Example 1

[0043] In one embodiment of the present disclosure, a method for autonomous orbit determination of a low-orbit navigation constellation in a weak inter-satellite topology is provided, comprising the following steps:

[0044] Step 1: Obtain various observation data of the intersatellite link on the predetermined orbit and pre-process the various observation data;

[0045] Step 2: Use the piecewise linear polynomial satellite clock error modeling method to establish the synchronous observation equations of orbit and clock error parameters. Consider the influence of clock error jumps. Based on the ground-uploaded data, apply the prior orbit information weak constraints and the onboard GNSS reference constraints or GNSS rotation angle error constraints. Perform error analysis on the preprocessed observation data, generate the orbit, clock error and related error parameters of the combined onboard GNSS and inter-satellite link data, and make predictions.

[0046] Step 3: Based on the error analysis results, multiple key features are extracted from the generated orbit, clock error, and related error parameters as input to the parameter prediction model. The output is the time series of error parameters for four categories of predictions: relative weight, inter-satellite link hardware delay, low-orbit satellite clock error, and unmodeled error.

[0047] Step 4: The predicted error parameter time series and broadcast ephemeris are uploaded to the main satellite, which transmits them to each sub-satellite through inter-satellite links to realize distributed autonomous orbit determination of the sub-satellites.

[0048] As an example, conventional autonomous orbit determination observation data for low-orbit navigation constellations primarily includes inter-satellite ranging information and onboard GNSS information. Onboard GNSS data provides a benchmark for the entire constellation, effectively controlling its translational and rotational errors. Autonomous orbit determination onboard low-orbit constellations based on inter-satellite links can be categorized into two types: centralized and distributed. Centralized processing aggregates all observation information to a master satellite, which then calculates the orbits of all satellites in the constellation and distributes the results to each satellite. Distributed processing involves each satellite receiving and storing its own observations and orbital information from associated satellites to calculate its own orbit and other parameters. Centralized processing can yield optimal orbit solutions, but places high demands on the master satellite's onboard storage, computing power, and data communication capabilities. Distributed models, due to their poor geometric robustness, produce suboptimal results, but require less storage and computing power from each satellite. Therefore, given the large number of satellites in low-orbit navigation constellations, typically reaching thousands, distributed autonomous orbit determination is primarily employed. The specific subnet size is optimized and determined based on factors such as orbit determination accuracy requirements, inter-satellite link observation topology, number of links and inter-satellite data communication capabilities. The minimum subnet can be a single satellite or several satellites with local co-orbit or disparate orbits.

[0049] like Figure 1As shown in the figure, distributed autonomous orbit determination in the subnet utilizes parallel processing units. Information is transmitted between processing units via intersatellite communication. Constraints are established using observations from internal links within the processing unit, onboard GNSS observations, and information provided by external processing units to determine the orbits of satellites within the processing unit. However, the challenges faced by distributed autonomous orbit determination for large LEO constellations primarily stem from the low satellite orbit altitudes, high atmospheric drag, the susceptibility of intersatellite links to space weather such as solar storms, frequent changes in intersatellite link configurations, the potential for weak intersatellite link structures, and the difficulty in ensuring sufficient intersatellite ranging data. Autonomous orbit determination requires calculating satellite orbits, satellite clock errors, intersatellite link hardware delay bias, atmospheric drag parameters, and force model parameters. These numerous parameters significantly impact orbit determination results. Since low-orbit satellites move at high speeds and have short transit times, the transmission of real-time GNSS and inter-satellite link data to the ground will cause a certain time delay, and also increase the burden on the communication system. In addition, the real-time processing of large amounts of data on the ground has certain requirements for computational efficiency, which may be difficult for the ground processing system to meet. Therefore, the present disclosure proposes a method for autonomous orbit determination of low-orbit navigation constellations under a weak inter-satellite topology structure, which uses post-processing to obtain orbit and clock error parameters and inter-satellite hardware delay deviation parameters and predicts them, and then selects a suitable time slot to upload them to the satellite. Autonomous orbit determination generates broadcast ephemeris when the on-board distributed observation structure is robust, and when the on-board link structure is weak, the predicted orbit, clock error and inter-satellite hardware delay deviation parameters can be used as prior parameters to enhance orbit determination, thereby obtaining reliable autonomous orbit determination results. The specific implementation process of the disclosed method is as follows:

[0050] Step 1: Obtain various observation data of the intersatellite link on the predetermined orbit and pre-process the various observation data; specifically, the steps include:

[0051] Step 11: Multiple error sources need to be considered for autonomous orbit determination onboard the LEO navigation augmentation constellation. First, the various error sources in autonomous orbit determination of the LEO navigation constellation need to be analyzed, including the following:

[0052] The various types of observation data mainly include GNSS pseudorange and carrier phase observations involved in autonomous orbit determination of low-orbit navigation constellations, as well as microwave and laser link ranging values. It is necessary to analyze the error sources contained in these observation data:

[0053] (1) Satellite-related errors include GNSS broadcast ephemeris error, low-orbit satellite clock error, antenna phase center deviation, inter-satellite ranging hardware delay error, GNSS pseudorange, carrier phase, and inter-satellite ranging noise. GNSS broadcast ephemeris error will remain in the residual, while the low-orbit satellite clock error is estimated as an unknown parameter and can also be modeled. The phase center error of the antenna between the transmitter and the low-orbit satellite receiver and the distance deviation from the phase center of the inter-satellite ranging antenna to the center of mass and its variation are generally corrected by modeling ground calibration values ​​or post-processing estimates. The delay error of the inter-satellite ranging equipment is estimated by parameters and changes relatively slowly over a certain period of time, so it can be calibrated and predicted. The observation noise needs to be calibrated a priori. In standard filtering, the observation noise covariance matrix generally does not change, but the observation environment of the low-orbit satellite is complex. In order to optimally integrate the microwave / laser link and GNSS data, the relative weights need to be adaptively adjusted.

[0054] (2) Errors introduced by signal propagation are mainly ionospheric and tropospheric errors. The dual-frequency, two-way ranging combination of LEO satellite intersatellite links can eliminate the influence of ionospheric errors; however, for GNSS LEO satellite signals, an ionospheric-free combination is required to eliminate the first-order ionospheric effect. As for tropospheric errors, LEO satellite intersatellite observations do not consider tropospheric errors. The tropospheric errors of GNSS signals are accurately estimated using a model plus parameters.

[0055] (3) Other errors, such as relativistic effects and multipath errors. GNSS pseudoranges and carrier phases, as well as intersatellite ranging observations, all require relativistic model corrections. Multipath errors are generally difficult to eliminate, but some of their effects can be eliminated through hardware. Satellite-borne GNSS is primarily affected by near-field multipath errors, while in intersatellite links, antenna and signal design, attitude control, etc. can only eliminate approximately 30% of multipath errors. The multipath residual error of Ka-band microwave links is at the 5cm level. Therefore, multipath errors will primarily remain in unmodeled errors.

[0056] As an embodiment, the above-mentioned partial errors can be calibrated and predicted, and then used for onboard autonomous orbit determination. This can reduce the number of parameters for onboard autonomous orbit determination, or impose effective constraints on the parameters to be estimated to enhance the robustness of the normal equations in the case of weak observation structure.

[0057] Step 12: Intersatellite links are established to acquire observation data. The specific process involves: Generally, within a ranging frame, two satellites within the constellation that are visible to each other broadcast ranging code signals using microwave or laser dual-carrier frequencies within an allocated time slot. The remaining satellites receive signals and obtain a single measurement, completing one-way ranging. After traversing all satellites in the constellation, each satellite has effectively completed two-way ranging with the visible satellites, and the ranging frame ends. This is followed by the exchange of two-way navigation data between satellites. The intersatellite link then performs intersatellite data communication in the next cycle, enabling two-way data exchange between two satellites within the constellation that are visible to each other. The exchanged navigation data primarily includes intersatellite pseudoranges, satellite ephemeris and clock parameters, a priori error covariance matrices, and satellite integrity monitoring parameters.

[0058] Considering the balance between efficiency and accuracy of autonomous orbit determination, a distributed dynamic subnet processing strategy is adopted, and the subnet size is dynamically determined based on multiple factors such as accuracy. Regarding the selection of links, a stable polygonal network architecture is formed from a physical perspective based on the principles of proximity and maximum data utilization. The general principle of link formation is that permanent links can be formed within the same orbit, and the structure and scale of the satellite position state transfer matrix between each other generally do not change. The main reason for the difficulty of data exchange between ascending and descending orbits is that the movement between low-orbit satellites is too intense. Ascending orbits on different orbital planes can exchange data, and if the satellite orbits do not change significantly or other factors do not occur within a certain period of time, the relatively heterogeneous configuration can remain unchanged.

[0059] Step 13: After all satellites in the distributed subnet have completed ranging, the satellite equipped with the GNSS receiver is designated as the master satellite, providing the reference for the distributed subnet. The remaining satellites are designated as slave satellites. All intersatellite link data from all satellites in the subnet is ultimately transmitted to the master satellite for processing. The master satellite is equipped with dedicated data processing equipment and storage devices.

[0060] After the main satellite obtains various inter-satellite observation data within the subnet, it preprocesses the pseudo-range data, including ionospheric error, antenna phase center deviation and relativistic error correction, to obtain a clean distance measurement value after preprocessing.

[0061] Step 2: Use the piecewise linear polynomial satellite clock error modeling method to establish the synchronous observation equations of orbit and clock error parameters. Consider the influence of clock error jumps. Based on the ground-uploaded data, apply the prior orbit information weak constraints and the onboard GNSS reference constraints or GNSS rotation angle error constraints. Solve the various preprocessed observation data to generate the orbit, clock error and related error parameters of the combined onboard GNSS and inter-satellite link data, and make predictions. Specifically, it includes the following steps:

[0062] Step 21: First, the observation model for calculating orbital and clock parameters needs to be determined, including:

[0063] The low-orbit satellite equipped with a GNSS receiver, also known as the main satellite, synchronizes its clock by locking the navigation signal (the synchronization time difference is higher than that of the ground station, usually less than 1 , no more than 1 ), the rest of the low-orbit satellite clocks need to be synchronized through inter-satellite links. If the time for each satellite to receive and transmit signals between low-orbit satellites is , then the intersatellite pseudo-range observations obtained by each satellite are Or distributed on the time axis at integer multiple intervals, so each observation corresponds to the satellite clock error at different moments. For high-precision orbit determination and time synchronization, one satellite observes the other satellites at different times. When solving the joint solution, it is necessary to set the clock error parameters corresponding to different moments for this satellite. There are too many parameters and it is impossible to solve all the clock error parameters through adjustment. The traditional method is to perform epoch normalization on the inter-satellite link data to obtain at least two normalized pseudo-range observations observed simultaneously, so as to separate the orbit and clock error information and solve them separately. The present disclosure takes into account that the satellite clock error mainly changes linearly in a short period of time. Therefore, the present disclosure adopts a first-order polynomial to model the satellite clock error, so that the original one-way pseudo-range data and the onboard GNSS data observed non-simultaneously can be adjusted directly. The specific operation is to divide the continuous time axis into discrete non-overlapping time windows. Within a specific time window, at any moment The satellite clock error is expressed by a polynomial as:

[0064] (1)

[0065] in, For the The reference moment of the time window, The corresponding reference time The satellite clock error, is the clock error rate. Use the predicted clock speed information of the navigation message to correct the clock error rate in the above formula , then the intersatellite one-way pseudorange observations at different times in the same time window correspond to the same reference time clock difference.

[0066] Secondly, establish the inter-satellite one-way pseudo-range observation equation, assuming that the reference satellite At the time of observation Acquire the center satellite The interstellar observation quantity is , then a certain time window corresponds to its reference time The one-way pseudorange observation equation can be expressed as follows:

[0067] (2)

[0068] in, is the intersatellite pseudorange observation value, is the speed of light in a vacuum, Central Satellite At the time of observation Satellite clock error at time, Central Satellite The clock rate, It is a reference satellite With the central satellite The integrated hardware delay of intersatellite link transmission and reception, The unmodeled error means that the intersatellite one-way pseudorange measurements at different times in the same time window correspond to the same reference time. The clock error can be directly adjusted to determine the satellite orbit and clock error at the same time.

[0069] The above is the clock error parameter processing of the inter-satellite ranging data of a certain low-orbit satellite at different times, while the present disclosure needs to process the clock error parameters involved in the inter-satellite ranging data of a large number of different low-orbit satellites. In the distributed autonomous orbit determination system, the satellite clock error needs to be solved when the reference satellite establishes a link with other satellites through onboard GNSS data. When the ranging data in the system is transmitted to the central satellite one after another, the central satellite runs the autonomous orbit determination algorithm. However, the inter-satellite ranging moments of the sub-satellites are often not synchronized, which poses a challenge to data processing. The central satellite has two options: one is to introduce a large number of clock error parameters that correspond one-to-one to the sub-satellite moments; the other is to extrapolate the sub-satellite coordinates to the coordinates of the central satellite at the time of link establishment through a dynamic model, but this will result in a decrease in coordinate accuracy. Therefore, the present disclosure uses a first-order polynomial to model the clock error of the reference satellite and the central satellite, and synchronizes the clock error parameters of all sub-satellites participating in the distributed orbit determination to the time of autonomous orbit determination of the central satellite. In this way, if the reference satellite pseudo-range link moment is used, is the reference time, then the reference satellite and central satellite The inter-satellite link clock error synchronization equation can be expressed as:

[0070] (3)

[0071] The inter-satellite link clock error synchronization equation between the central satellite and the sub-satellite can be expressed as:

[0072] (4)

[0073] in, Central Satellite and sub-satellites The intersatellite distance measurement observations between Sub-satellite To the central satellite The inter-satellite one-way link establishment time, the above epoch reference time is unified to the reference satellite. Central Satellite and sub-satellites The calculated inter-satellite pseudorange value, It is a central satellite and sub-satellites The hardware latency of the integrated intersatellite link transmission and reception is reduced. Clock error modeling not only allows the clock errors of sub-satellites to be unified with the central satellite's reference time for processing, but also enables the clock errors of distributed system satellites to be unified with the reference time. The advantage of this processing method is that it facilitates the transfer of the master satellite's reference to the sub-satellites, facilitating the synchronous processing of observation data at different times, significantly reducing the number of unknown clock error parameters, and thus improving the system's computational efficiency.

[0074] However, the disclosed method and the traditional epoch normalization method will produce large clock error calculation and orbit determination errors when encountering clock error jumps. When analyzing the clock error of a domestic meteorological occultation satellite, Yunyao satellite, it was found that the clock error of Yunyao constellation satellites will jump at certain specific moments, such as Figure 2 The figure shows the changing clock error of Yunyao YY18. This is primarily due to the rapid drift of the clock error, which necessitates adjustments to the atomic clock at approximately 10:00 AM each day. For rapidly changing satellite clock errors, since each time window defaults to only one clock error parameter and one clock rate parameter for each satellite, the calculated clock error and rate may deviate, significantly impacting orbit determination results.

[0075] Step 22: Considering the impact of clock error jumps, based on the ground-uploaded data, apply a priori orbit information weak constraints and onboard GNSS reference constraints or GNSS rotation angle error constraints, solve the preprocessed observation data, generate the orbit, clock error and related error parameters of the combined onboard GNSS and inter-satellite link data, and make predictions as follows:

[0076] This method constructs an intersatellite piecewise linear polynomial clock error observation equation, taking into account the effects of clock error jumps. It simultaneously obtains time series such as the clock error recorded on the ground, link hardware delay bias, the weight of the microwave / laser link relative to the GNSS pseudorange, and unmodeled errors, and performs an integrated solution for orbit and clock parameters. Furthermore, based on actual conditions, it applies onboard GNSS reference constraints, GNSS rotation angle error constraints, or weak constraints based on prior orbit information to enhance the robustness of the results under weak intersatellite observation structures.

[0077] Among them, the prior orbit information weak constraint refers to the constraint on the satellite orbit inclination only. m and right ascension of the ascending node By performing a priori weak constraints, the overall rotation error of the constellation can be constrained from growing too fast. However, due to the complexity of the perturbation force of low-orbit satellites and the systematic and long-term nature of such errors, the role of predicted constraints in the autonomous orbit determination process will gradually weaken with the passage of time. The onboard GNSS reference constraint refers to the use of onboard GNSS data of some satellites (master satellites) and inter-satellite link ranging data of the remaining satellites (slave satellites) to perform joint adjustment to solve the precise orbit and dynamic parameters of the master and slave satellites. The GNSS data of the master satellite can accurately determine its own coordinates as a reference benchmark to constrain the orbit determination process of other satellites (such as slave satellites). The GNSS rotation angle error constraint refers to the consideration that the rotation angle changes of satellites in the same orbital plane are basically the same, and it is much more convenient to transmit the rotation angle changes and their errors in the same orbital plane. Therefore, the onboard GNSS of the reference satellite in the same orbital plane and the inter-satellite ranging data provided by the distributed orbit determination can be used. Angle is used to calibrate the overall or local rotation error of the current low-orbit navigation constellation to constrain the rotation error of all satellites in the orbital plane.

[0078] The present disclosure proposes a method for predicting the solved orbit and clock error to detect clock jumps. Specifically, the previous window predicts the clock error value of the reference time of the current window based on the solved clock error and clock speed. If the error of a certain star is too large, it means that the clock error of the star in the current window has jumped, and it is marked at the same time, but the jump time cannot be determined. At this time, the prior clock speed and clock error can be well utilized to predict the clock error value of each epoch in the current window, and at the same time, the predicted orbit and inter-satellite hardware delay deviation parameters are combined to obtain the inter-satellite ranging value of each paired satellite group in each epoch in the current window, and the difference is made with the observed value. If the residual is greater than 3 times the inter-satellite noise, it means that the clock error of the satellite group has jumped, and the calculation is terminated at this time. Combined with the previously determined satellite number, it can be determined which satellite has had a clock jump and when. At this time, the linear polynomial model of the current window is set to piecewise linear to perform orbit determination, and the result is subjected to the residual sum of squares ( ) test, if the piecewise linear estimate is detected This is significantly better than the value before segmentation, indicating that the result is correct. Considering the real-time nature, this disclosure does not use algorithms such as gradient descent or traversal iteration to find the optimal time point, because iteration will cause the current window calculation to be very time-consuming.

[0079] Step 3: Based on the error analysis results, multiple key features are extracted from the generated orbit, clock error, and related error parameters as input to the parameter prediction model. The output is the time series of four types of predicted parameters: relative weight, inter-satellite link hardware delay, low-orbit satellite clock error, and unmodeled error.

[0080] Given that machine learning plays an important role in modeling and predicting various nonlinear errors, this paper proposes to use machine learning methods to predict the relevant errors involved in onboard autonomous orbit determination, and to increase the robustness of the normal equations by calibrating some parameter errors in advance.

[0081] Specifically, machine learning is introduced into the autonomous orbit determination method of low-orbit satellite constellations, and a nonlinear model is established by learning from massive data. The present invention constructs a parameter prediction model, which is a neural network architecture. During the neural network training process, based on the error analysis of autonomous orbit determination observations, 9 key features are selected as the input of the neural network. The neural network architecture is as follows: Figure 6 As shown, the network consists of four layers, namely a The input layer inputs 9 feature vectors ; Six fully connected layers, namely 、 、 、 、 、 , the input feature vector is expanded to 64, 128, 256, and finally reduced to 4, and four output prediction values ​​are obtained. Since there may be a large number of low-orbit satellites, the number of inter-satellite hardware delay deviation parameters involved may be large, and the input feature value is expanded to ,The dimension can be expanded according to actual needs. ,The iteration threshold is set to 10 times.

[0082] Furthermore, the nine key eigenvectors selected as neural network inputs are microwave and laser link noise, GNSS pseudorange and carrier phase noise, GNSS altitude angle to low-orbit satellites, geometric dilution of precision (GDOP) of low-orbit satellite inter-satellite links, inter-satellite link hardware delay bias, low-orbit satellite clock error, and observation residual sequence. Among them, GNSS uses ionospheric-free combined pseudorange and carrier phase observations. The prior noise of the carrier and pseudorange observations is first set, and the prior noise of the laser and microwave ranging values ​​is also set. The observation noise array generally does not change in the filtering calculation. In order to reduce complexity and computational complexity, a weight coefficient is directly given to the GNSS system (ionospheric-free combination of pseudorange and carrier phase) and a weight coefficient is directly given to the inter-satellite ranging system (microwave or laser data or both). The final weight coefficient is determined by Helmert variance component estimation, and then the ratio of the two is the relative weight ratio. The GDOP value of the intersatellite link reflects the geometric structure of the intersatellite link and is constrained by the constellation configuration and antenna beam angle. Generally, when the constellation configuration and antenna scheme are determined, the GDOP is determined. However, due to the instability of low-orbit satellite links, the GDOP value often changes, affecting the orbit determination results. These 9 features are defined as the input feature vector of the neural network. Each network defines 600 rounds of training, and each round of training traverses the observation data.

[0083] Based on neural network, build relative weight , intersatellite link hardware delay , low-orbit satellite clock error , unmodeled error For the parameter prediction model, the root mean square error (RMSE) is selected as the loss function:

[0084] (5)

[0085] in, is the loss function, is the sequence of orbital clock error and other parameters solved afterwards, is the predicted parameter sequence, let For distance observations calculated based on prior values, the program implementation uses the backpropagation process to obtain the partial derivative of the final loss with respect to the predicted value. The chain derivation method is used to calculate the gradient of the predicted value:

[0086] , , , , (6)

[0087] The parameter prediction network predicts four types of parameter time series at the same time. The activation function of the first three layers of the network is ReLU, and the branch that outputs the weight uses Sigmoid control range. The four output parameters are relative weight ratio , intersatellite link hardware delay , low-orbit satellite clock error , unmodeled error .

[0088] As an embodiment, the network training goal is to determine the parameter set that minimizes the loss function , as shown in Equation (7). Equation (8) shows the process of solving the gradient, and then Equation (9) is used to update the parameters, where Represents the learning rate.

[0089] (7)

[0090] in, Represents the true value of the model calculated after the test, which is compared with the model prediction value to find the minimum value of the loss function; is a performance function based on the Extended Kalman Filter (EKF) estimation technique; Indicates the distance value calculated by the variable parameters input during each iteration, and the distance value calculated by the prior Compare and obtain the parameter set that minimizes the loss function .

[0091] The training process is as follows:

[0092] (8)

[0093] (9)

[0094] Predict these four parameters through the trained network:

[0095] (10)

[0096] Finally, the predicted value is used in the orbit determination solution to obtain the optimized orbit determination result:

[0097] (11)

[0098] The ReLU activation function is introduced into the network, and the nonlinear nature of the ReLU activation function is used to improve the learning ability of the system's complex model. The activation function of the first three layers is ReLU, and the branch that outputs the weight uses the Sigmoid activation function to ensure that the output value is consistent with the weight in the range of 0 to 1. The network structure of these four types of parameter prediction training is as follows Figure 6 shown.

[0099] Step 4: Upload the predicted parameter time series and broadcast ephemeris to the main satellite, which transmits them to each sub-satellite through inter-satellite links to achieve distributed autonomous orbit determination of the sub-satellites.

[0100] Specifically, the predicted parameter time series can be uploaded to the main satellite along with the broadcast ephemeris. The main satellite then transmits the data to each sub-satellite via intersatellite links, allowing the sub-satellites to perform distributed autonomous orbit determination. The predicted parameter series can be uploaded at a relatively frequent interval, resulting in a method with reduced reliance on ground systems. For example, in the event of a wartime disruption to ground control or uplink systems, robust autonomous orbit determination can be continued using the long-term prediction series stored onboard.

[0101] As an embodiment, the algorithm performs autonomous integrity monitoring during execution, that is, autonomous satellite fault detection and integrity isolation processing, to prevent undetected faulty satellites from contaminating other satellites or even the entire constellation with gross errors or abnormal observations, causing filter divergence.

[0102] As an embodiment, due to the large number of error sources considered in the autonomous orbit determination of low-orbit satellites under various observation modes, and the low orbit altitude and complex observation environment of low-orbit satellites, the inter-satellite link establishment may not be as stable as that of navigation satellites, and the configuration may have a weak observation structure. At this time, the orbit determination equation is singular and the condition number is too large, so some unmodeled errors will remain in the residual, so this application first accurately calibrates the parameter errors. In view of the important role played by machine learning in the modeling and prediction of various nonlinear errors, it is proposed here to use machine learning methods to predict the relevant errors involved in the autonomous orbit determination of the satellite, and to increase the robustness of the equation by calibrating some parameter errors in advance. Therefore, the problems solved by this disclosure include (1) the characteristics of the microwave link, laser link and various errors of the onboard GNSS in the autonomous orbit determination of the low-orbit navigation enhanced constellation, providing a reference for machine learning to construct reasonable input characteristic parameters in distributed autonomous orbit determination; (2) the modeling, analysis and prediction method of the relevant error parameters of the distributed autonomous orbit determination of the low-orbit navigation constellation based on machine learning, as well as the network training structure and model of machine learning in orbit determination.

[0103] Example 2

[0104] In one embodiment of the present disclosure, a low-orbit navigation constellation autonomous orbit determination system in a weak inter-satellite topology is provided, comprising:

[0105] The observation data acquisition module is used to obtain various observation data of the intersatellite link on the predetermined orbit and pre-process the various observation data;

[0106] The error analysis and calibration module is used to establish synchronous observation equations for orbit and clock error parameters using a piecewise linear polynomial satellite clock error modeling method. This module considers the effects of clock error jumps and applies weak constraints on prior orbit information and onboard GNSS reference constraints or GNSS rotation angle error constraints based on ground-uploaded data. It then solves various preprocessed observation data to generate and predict orbit, clock, and related error parameters for combined onboard GNSS and inter-satellite link data.

[0107] The parameter prediction module is used to extract multiple key features from the generated orbit, clock error, and related error parameters based on the error analysis results as input to the parameter prediction model. The output is a time series of four types of predicted parameters: relative weight, inter-satellite link hardware delay, low-orbit satellite clock error, and unmodeled error.

[0108] The onboard orbit determination module is used to upload the predicted parameter time series and broadcast ephemeris to the main satellite. The main satellite transmits them to each sub-satellite through inter-satellite links to realize distributed autonomous orbit determination of the sub-satellites.

[0109] Example 3

[0110] In one embodiment of the present disclosure, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the method for autonomous orbit determination of a low-orbit navigation constellation in a weak inter-satellite topology is implemented.

[0111] Example 4

[0112] In one embodiment of the present disclosure, a non-transitory computer-readable storage medium is provided, wherein the non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the method for autonomous orbit determination of a low-orbit navigation constellation under a weak inter-satellite topology is implemented.

[0113] Example 5

[0114] In one embodiment of the present disclosure, an electronic device is provided, comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device implements the method for autonomous orbit determination of a low-orbit navigation constellation under a weak inter-satellite topology structure.

[0115] The present disclosure is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present disclosure. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0116] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0117] Although the above describes the specific implementation methods of the present disclosure in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present disclosure. Those skilled in the art should understand that on the basis of the technical solution of the present disclosure, various modifications or variations that can be made by those skilled in the art without creative work are still within the scope of protection of the present disclosure.

Claims

1. An autonomous orbit determination method for a low-orbit navigation constellation in a weak intersatellite topology, characterized by: include: Obtain various types of observation data of the inter-satellite link on the predetermined orbit and pre-process various types of observation data; the process of establishing a link between the inter-satellite links to obtain observation data includes: within a ranging frame, two satellites that are visible to each other in the constellation broadcast a ranging code signal using microwave or laser dual-carrier frequency within the allocated time interval, and the remaining satellites are in a signal receiving state, obtaining a measurement data and completing one-way ranging. After traversing all satellites in the constellation, each satellite completes two-way ranging with the visible satellite, and the ranging frame ends; then, inter-satellite two-way navigation data exchange is carried out. The inter-satellite link performs inter-satellite data communication in the next cycle, and two-way data exchange is realized between two satellites that are visible to each other in the constellation. The exchanged navigation data includes inter-satellite measurement pseudorange, satellite ephemeris and clock parameters, prior error covariance matrix, and satellite integrity monitoring parameters; After obtaining various intersatellite observation data, the pseudo-range data is preprocessed, including ionospheric error, antenna phase center deviation and relativistic error correction, to obtain a clean distance measurement value after preprocessing; The synchronous observation equations for orbit and clock error parameters are established using a piecewise linear polynomial satellite clock error modeling method. The effects of clock error jumps are considered. Based on ground-uploaded data, weak constraints on prior orbit information and onboard GNSS reference constraints or GNSS rotation angle error constraints are imposed. Error analysis is performed on various preprocessed observation data to generate and predict the orbit, clock, and related error parameters of the combined onboard GNSS and inter-satellite link data. Based on the error analysis results, several key features are extracted from the generated orbit, clock error, and related error parameters as input to the parameter prediction model. The output is the time series of error parameters for four categories of predictions: relative weight, inter-satellite link hardware delay, low-orbit satellite clock error, and unmodeled error. The predicted error parameter time series and broadcast ephemeris are uploaded to the main satellite together, and the main satellite transmits them to each sub-satellite through inter-satellite links to realize distributed autonomous orbit determination of the sub-satellites.

2. The autonomous orbit determination method for a low-orbit navigation constellation in a weak inter-satellite topology structure according to claim 1, wherein: Low-orbit satellites equipped with GNSS receivers synchronize their clocks by locking onto navigation signals, and the clocks of other low-orbit satellites are synchronized through inter-satellite links. Each observation data corresponds to the satellite clock error at a different time. A linear polynomial is used to model the satellite clock error, and the original one-way pseudo-range data and onboard GNSS data that are not observed simultaneously are directly adjusted. The specific process is to divide the continuous time axis into discrete non-overlapping time windows. Within a specific time window, the satellite clock error at any time is represented by a polynomial, and an inter-satellite one-way pseudo-range observation equation is established. A linear polynomial is used to model the clock errors of the reference satellite and the central satellite, and the clock error parameters of all sub-satellites participating in distributed orbit determination are synchronized to the time of autonomous orbit determination of the central satellite.

3. The autonomous orbit determination method for a low-orbit navigation constellation in a weak inter-satellite topology structure according to claim 1, wherein: Clock jumps are detected by predicting the solved orbit and clock error. The clock error value of the reference time of the current window is predicted based on the solved clock error and clock rate in the previous window. If the error of a certain satellite is too large, it means that the clock error of the satellite in the current window has jumped. The clock error value of each epoch in the current window is predicted using the prior clock rate and clock error. At the same time, the predicted orbit and inter-satellite hardware delay bias parameters are combined to calculate the inter-satellite ranging value of each paired satellite group in each epoch in the current window. The difference between the residual and the observed value is taken. If the residual is greater than 3 times the inter-satellite noise, it means that the clock error of the satellite group has jumped, and the calculation is terminated.

4. The autonomous orbit determination method for a low-orbit navigation constellation in a weak intersatellite topology structure according to claim 1, wherein: Based on the error analysis of autonomous orbit determination observations, nine key features are selected as the input of the parameter prediction model, namely microwave link noise, laser link noise, GNSS pseudorange, carrier phase noise, GNSS altitude angle to low-orbit satellites, low-orbit satellite inter-satellite link geometric precision factor, inter-satellite link hardware delay bias, low-orbit satellite clock error and observation value residual sequence, and four types of parameter time series are predicted and output.

5. An autonomous orbit determination system for a low-orbit navigation constellation under a weak inter-satellite topology, specifically implementing the autonomous orbit determination method for a low-orbit navigation constellation under a weak inter-satellite topology according to any one of claims 1 to 4, characterized in that: include: The observation data acquisition module is used to obtain various observation data of the intersatellite link on the predetermined orbit and pre-process the various observation data; The error analysis and calibration module is used to establish synchronous observation equations for orbit and clock error parameters using a piecewise linear polynomial satellite clock error modeling method. This module considers the effects of clock error jumps and applies weak constraints on prior orbit information and onboard GNSS reference constraints or GNSS rotation angle error constraints based on ground-uploaded data. It then performs error analysis on various preprocessed observation data, generates orbit, clock, and related error parameters for combined onboard GNSS and inter-satellite link data, and makes predictions. The parameter prediction module is used to extract multiple key features from the generated orbit, clock error, and related error parameters based on the error analysis results as input to the parameter prediction model. The module outputs four types of error parameter time series: relative weight, inter-satellite link hardware delay, low-orbit satellite clock error, and unmodeled error. The onboard orbit determination module is used to upload the predicted error parameter time series and broadcast ephemeris to the main satellite. The main satellite transmits them to each sub-satellite through inter-satellite links to realize distributed autonomous orbit determination of the sub-satellites.

6. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the method for autonomous orbit determination of a low-orbit navigation constellation under a weak inter-satellite topology structure according to any one of claims 1 to 4 is implemented.

7. A non-transitory computer-readable storage medium, characterized in that The non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by the processor, the method for autonomous orbit determination of a low-orbit navigation constellation under a weak inter-satellite topology structure according to any one of claims 1 to 4 is implemented.

8. An electronic device, characterized in that: include: A processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to implement the method for autonomous orbit determination of a low-orbit navigation constellation under a weak inter-satellite topology structure as described in any one of claims 1 to 4.

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