A method and system for correcting a navigation satellite constellation coordinate frame based on inter-satellite observations

Abstract

The application discloses a navigation satellite constellation coordinate frame correction method and system based on inter-satellite observation, which firstly determines a seven-parameter time sequence of a navigation satellite constellation coordinate frame relative to an international terrestrial reference frame, and respectively establishes a trend and a periodic signal model for each parameter in the seven-parameter time sequence, then fits parameters of the trend and the periodic signal model, and determines whether to correct the navigation satellite constellation coordinate frame based on systematic deviation of the parameters. The application can quantitatively detect frame origin offset and scale drift, predict evolution trend of frame parameters, realize prospective correction, and can maintain a closed loop of the frame, thereby improving long-term stability of the navigation satellite constellation coordinate frame.

Description

Technical Field

[0001] This invention relates to the field of satellite geodesy and navigation satellite system technology, and in particular to a method and system for correcting the coordinate frame of a navigation satellite constellation based on inter-satellite observation. Background Technology

[0002] The coordinate frame of a navigation satellite constellation is the foundation of satellite navigation and positioning. The accuracy and stability of the coordinate frame's origin, scale, and orientation directly affect the positioning accuracy at the user end. The International Geodetic Reference Frame (ITRF) is established and maintained by the International Association of Geodesy (IAG) by integrating observational data from four space geodetic techniques: VLBI, SLR, GNSS, and DORIS. Its origin accuracy reaches the sub-millimeter level, and its scale accuracy reaches the 0.1 ppb level, making it the most accurate global geocentric reference frame currently available.

[0003] The coordinate framework of navigation satellite constellations such as GPS, GLONASS, Galileo, and BeiDou is typically established through a precise orbit determination process using a network of ground monitoring stations. The origin of the framework is indirectly defined by the coordinate constraints of the ground stations, while the framework scale is constrained by the ranging model and the definition of the speed of light. However, most ground stations are located on land in the Northern Hemisphere and are extremely unevenly distributed, leading to systematic deviations in the origin and scale of the framework. Furthermore, as regional frameworks such as CGCS2000 gradually deviate from their actual geocentric positions due to plate tectonics and crustal deformation, the long-term maintenance of the framework faces challenges.

[0004] Inter-satellite links are a key technical feature of next-generation navigation satellites. The BeiDou-3 satellite constellation is fully equipped with Ka-band inter-satellite links, enabling two-way ranging and time-frequency transmission. Inter-satellite link observations provide the constellation with an autonomous space observation method independent of ground station networks, theoretically allowing for the autonomous establishment and maintenance of the constellation's coordinate framework using pure inter-satellite observations. However, pure inter-satellite observations suffer from a "rank deficiency" problem; inter-satellite distance observations cannot determine the constellation's absolute position, absolute direction, and absolute scale. External constraints or collaboration with ground observations are required to fully define the coordinate framework.

[0005] In existing technologies, inter-satellite links are mainly used to assist ground station networks in precise orbit determination or for short-term autonomous navigation under conditions without ground support. However, a systematic method is lacking for long-term monitoring and autonomous correction of the constellation coordinate frame origin and scale. How to utilize inter-satellite observations to monitor the offset trend of frame parameters relative to the ITRF and perform autonomous correction based on an autonomously defined internal frame is a key issue in improving the long-term stability of navigation satellite constellation frames. Summary of the Invention

[0006] To address some or all of the problems in existing technologies, and to solve the issues of over-reliance on ground station networks and lack of long-term autonomous monitoring and correction capabilities for the coordinate frame of navigation satellite constellations, the first aspect of this invention provides a method for correcting the coordinate frame of navigation satellite constellations based on inter-satellite observations, comprising: Determine the seven-parameter time series of the navigation satellite constellation coordinate frame relative to the International Terrestrial Reference Frame (ITRF); For each parameter in the seven-parameter time series, a trend and periodic signal model is established respectively; The parameters of the trend and periodic signal model are fitted, and based on the systematic deviation of the parameters, it is determined whether to correct the navigation satellite constellation coordinate frame.

[0007] Furthermore, the time series of seven parameters for determining the navigation satellite constellation coordinate frame relative to the International Earth Reference Frame includes; Select several satellites from the navigation satellite constellation and establish a transformation model based on their coordinates in the navigation satellite constellation coordinate frame and the international earth reference frame, wherein the number of satellites is no less than 4. Linearize the transformation model; Using a specified duration as a solution unit, the seven parameters and their covariance are estimated to obtain the seven-parameter time series.

[0008] Furthermore, the seven parameters and their covariances are estimated using weighted least squares.

[0009] Furthermore, the specified duration is one day or one week.

[0010] Furthermore, the parameters of the trend and periodic signal model are fitted using the least squares method.

[0011] Furthermore, determining whether to correct the navigation satellite constellation coordinate frame based on the systematic deviation of the parameters includes: Based on the systematic deviation of the parameters, the cumulative deviation is determined; If the accumulated deviation exceeds a preset threshold, a correction is triggered.

[0012] Furthermore, the modification includes: The correction amount is determined based on the seven-parameter estimates of the current epoch; The correction amount and its uncertainty estimate are published through navigation message parameters, on-board injection parameters, or ground product documents; Based on the aforementioned correction amount and uncertainty estimate, the coordinate frame of the navigation satellite constellation is corrected to align it with the International Earth Reference Frame.

[0013] Furthermore, the initial navigation satellite constellation coordinate framework is obtained during the autonomous orbit determination process based on inter-satellite observations by applying constellation centroid constraints, net rotation constraints, and net scale constraints.

[0014] Based on the correction method described above, a second aspect of the present invention provides a correction system for the coordinate frame of a navigation satellite constellation based on inter-satellite observations, comprising: The frame parameter monitoring module is used to determine the seven-parameter time series of the navigation satellite constellation coordinate frame relative to the International Earth Reference Frame, and to establish trend and periodic signal models. The correction and maintenance module is used to determine whether to correct the navigation satellite constellation coordinate frame based on the systematic deviation of the parameters, and to correct the navigation satellite constellation coordinate frame.

[0015] Furthermore, the correction system also includes: The constellation autonomous orbit determination module is used to construct inter-satellite observation equations and perform joint constellation orbit determination. The frame definition module is used to apply centroid constraints, net rotation constraints, and net scale constraints during the joint orbit determination process of the constellation to determine the initial navigation satellite constellation coordinate frame.

[0016] This invention provides a method and system for correcting the coordinate frame of a navigation satellite constellation based on inter-satellite observations. It utilizes inter-satellite link observation data for autonomous constellation orbit determination and applies internal constraints to define the frame, reducing reliance on the uniformity of ground station network distribution. Through Helmert seven-parameter transformation, it achieves precise alignment and parameter monitoring between the constellation's internal frame and the ITRF (Inter-Independent Parameter Radiometer), thereby quantitatively detecting frame origin shift and scale drift. By establishing trend and periodic signal models for the seven-parameter time series, it predicts the evolution trend of frame parameters, achieving forward-looking correction. Furthermore, when the cumulative deviation of translation or scale parameters exceeds a threshold, it autonomously generates and publishes correction values, achieving closed-loop maintenance of the frame and improving the long-term stability of the navigation satellite constellation coordinate frame. Attached Figure Description

[0017] 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.

[0018] Figure 1 This diagram illustrates a method for correcting the coordinate frame of a navigation satellite constellation based on inter-satellite observations, according to an embodiment of the present invention. Figure 2This diagram illustrates the alignment and transformation of the navigation satellite constellation coordinate frame and the ITRF frame according to an embodiment of the present invention. Figure 3 This diagram illustrates the structure of a correction system for a navigation satellite constellation coordinate frame based on inter-satellite observations, according to an embodiment of the present invention. Detailed Implementation

[0019] 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 in conjunction 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. Furthermore, it should be understood that the embodiments shown in the drawings are illustrative representations and are not necessarily drawn to scale.

[0020] 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.

[0021] 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.

[0022] To address the problem of existing navigation satellite constellation coordinate frames over-reliance on ground station network distribution and the difficulty in maintaining long-term benchmarks, and to overcome the rank deficiency bottleneck of pure inter-satellite observation, this invention provides a method and system for correcting navigation satellite constellation coordinate frames based on inter-satellite observation. It establishes a long-term autonomous monitoring and correction mechanism for the frame that does not rely on massive ground infrastructure. It fully utilizes inter-satellite link data and applies internal constraints, significantly reducing dependence on the uniform distribution of ground station networks. Simultaneously, it accurately isolates and quantitatively detects the frame's origin offset (geocentric motion) and scale drift using Helmert seven parameters, and introduces trend and periodic signal models to fit the parameter time series, achieving the ability to predict the evolution trend of frame errors. Furthermore, it possesses a threshold triggering mechanism that can autonomously generate and publish correction values, achieving closed-loop maintenance of the frame and significantly improving the long-term stability of the coordinate frame.

[0023] The technical solution of the present invention will be further described below with reference to the accompanying drawings of the embodiments.

[0024] Figure 1 This diagram illustrates a flowchart of a method for correcting the coordinate frame of a navigation satellite constellation based on inter-satellite observations, according to an embodiment of the present invention. Figure 1 As shown, a method for correcting the coordinate frame of a navigation satellite constellation based on inter-satellite observations includes: First, in step 101, the seven-parameter time series is determined. The seven-parameter time series of the navigation satellite constellation coordinate frame relative to the International Terrestrial Reference Frame (ITRF) is determined. In one embodiment of the invention, the navigation satellite constellation coordinate frame is obtained during the autonomous orbit determination process based on inter-satellite observations by applying constellation centroid constraints, no net rotation constraints, and no net scale constraints.

[0025] Navigation satellite constellations, such as the BeiDou-3 MEO constellation, are typically equipped with Ka-band microwave inter-satellite links. Satellites communicate with each other via these links for two-way ranging and time-frequency transmission. The inter-satellite link establishment strategy involves each satellite establishing a link with the remaining satellites in the constellation one by one within one orbital period, achieving ranging accuracy better than 1 cm and time-frequency transmission accuracy better than 0.3 ns. When equipped with an inter-satellite laser ranging terminal, laser ranging data with an accuracy better than 1 mm can also be obtained.

[0026] The observation equation for inter-satellite two-way ranging is expressed as: , in, For satellite With satellite Inter-satellite ranging observations; The speed of light in a vacuum; , Satellites ,satellite Clock difference; The hardware delay of the inter-satellite link equipment is largely eliminated in bidirectional observation; Correction for relativistic effects; To account for observation noise and residual unmodeled errors; Interstellar geometric distance: , in , Satellites ,satellite Position coordinates in the geocentric inertial coordinate system.

[0027] The inter-satellite observation equations for all satellites in the constellation are linearized to construct normal equations, and joint orbit determination is performed using the least squares method or Kalman filtering. The parameters to be estimated include: the initial orbital state vector of each satellite, satellite clock bias and clock drift parameters, solar radiation pressure model parameters, etc., where the initial orbital state vector includes six components each for position and velocity. The orbit determination arc is typically taken as 1 to 3 days.

[0028] The normal equations for pure inter-satellite observations are rank deficient. Specifically, inter-satellite distance observations cannot determine the absolute translation, absolute rotation, and absolute scale of the constellation in inertial space. The absolute translation includes 3 degrees of freedom, the absolute rotation includes 3 degrees of freedom, and the absolute scale includes 1 degree of freedom, totaling 7 rank deficient degrees of freedom. To determine the coordinate frame of the navigation satellite constellation, in one embodiment of the present invention, a constellation centroid constraint is applied to define the frame origin, a net rotation constraint is applied to define the frame orientation, and a net scale constraint is applied to define the frame scale.

[0029] The constellation centroid constraint is as follows: , in The number of satellites participating in orbit determination, For the first A satellite in the era The position vector, These are the coordinates of the constellation's geometric centroid. The constellation centroid constraint defines the frame origin at the constellation's geometric centroid. Since the constellation's geometric centroid is not the Earth's centroid, there is an offset between the origin of the navigation satellite constellation coordinate frame and the ITRF geocenter.

[0030] The net rotation constraint is as follows: , in For the first The prior coordinates of the satellite, This is the coordinate correction amount. The absence of net rotation constraint ensures that the frame orientation remains consistent between adjacent epochs, preventing overall rotation.

[0031] The absence of net dimensional constraints is as follows: , The absence of net scale constraints ensures that the frame scale and the overall radial scaling of the constellation remain constant across epochs.

[0032] By employing the constellation's centroid constraints, net rotation constraints, and net scale constraints, rank-deficient degrees of freedom can be eliminated, making the normal equations solvable at full rank. The orbit determination output is the precise orbit of each satellite within the navigation satellite constellation coordinate framework.

[0033] Based on this, in one embodiment of the invention, such as Figure 2 As shown, using ITRF framework products, ITRF2020 station coordinates and velocity fields, IGS precise orbit products, or ILRS SLR products as references, the Helmert seven-parameter transformation between the navigation satellite constellation coordinate frame and ITRF is calculated. Specifically, at least four satellites in the constellation are selected, and their reference coordinates under ITRF are used. Coordinates within the navigation satellite constellation coordinate framework Establish the Helmert transform model: , in, These are three translation parameters, in millimeters, representing the offset of the origin of the navigation satellite constellation coordinate frame relative to the geocenter of the ITRF; is a scale parameter, with units of ppb, which characterizes the deviation of the navigation satellite constellation coordinate frame scale from the ITRF scale; For three tiny rotation parameters The rotation matrix formed is in units of mas (milliar seconds) and represents the orientation deviation.

[0034] When the rotation angle is a small amount, the rotation matrix can be linearized as follows: , After linearizing the Helmert transform equations, the seven parameters and their covariances are estimated using weighted least squares, where the weight matrix is ​​the inverse of the satellite coordinate covariance matrix. Using daily, weekly, or other specified durations as a solution unit, the time series of the seven parameters is obtained: , in The time series represents the length of the time series. The time series of the three translation parameters reflect the motion of the constellation frame origin relative to the ITRF geocenter, i.e., geocentric motion, which includes annual and semi-annual variations of the Earth's center of mass due to atmospheric, oceanic, and terrestrial water loads, with amplitudes of approximately several millimeters, as well as possible long-term drift. The time series of the scale parameters reflects the stability of the frame scale.

[0035] Next, in step 102, trend and cycle signal models are established. For each parameter in the seven-parameter time series, a trend and cycle signal model is established, where the trend and cycle signal model includes constant, linear trend, annual cycle, and semi-annual cycle. Taking the translation parameter as an example, the model is expressed as follows: , in, For reference epochs, This is a constant offset, reflecting the systematic deviation of the frame origin. The coefficient for the linear trend term reflects the long-term drift rate (mm / yr) of the origin. , The annual signal amplitude coefficient, The day is a yearly cycle. , This is the half-year signal amplitude coefficient. A day is a half-year cycle.

[0036] Next, in step 103, the model parameters are fitted. The parameters of the trend and periodic signal model are fitted using methods such as least squares. By fitting the parameters using least squares, the systematic bias and drift rate of the frame parameters can be obtained, which can be used to determine whether the frame needs to be corrected. At the same time, the fitted model can be used to make short-term forecasts of the frame parameters, which can provide a basis for real-time correction, and the fitted residual sequence can be obtained to evaluate the random fluctuation level of the frame parameters.

[0037] Next, in step 104, it is determined whether correction is needed. Based on the systematic deviation of the parameters, it is determined whether to correct the navigation satellite constellation coordinate frame. In one embodiment of the present invention, the systematic deviation and drift rate of the frame parameters are obtained, and the cumulative deviation is determined. The cumulative deviation is compared with a preset threshold. If it exceeds the preset threshold, then proceed to step 105 to correct the navigation satellite constellation coordinate frame. In one embodiment of the present invention, the cumulative deviation of the translation parameters is defined as... .when Exceeding the preset translation threshold When this occurs, origin correction is triggered, where the preset translation threshold ranges from 1mm to 10mm. In one embodiment of the invention, the cumulative deviation of the scale parameter is defined as... .when Exceeding the preset scale threshold When the scale correction is triggered, the preset scale threshold ranges from 0.1ppb to 1.0ppb.

[0038] In step 105, the navigation satellite constellation coordinate frame is corrected. A correction amount is determined based on the seven-parameter estimates for the current epoch. This correction amount and its uncertainty estimate are published via navigation message parameters, on-board injection parameters, or ground product documents. Based on the correction amount and uncertainty estimate, the navigation satellite constellation coordinate frame is corrected to align with the International Geodetic Reference Frame. In one embodiment of the invention, the correction amount is the negative of the seven-parameter estimates for the current epoch. .

[0039] To illustrate the accuracy of the aforementioned method, estimations were performed based on typical parameters of the BeiDou-3 MEO constellation, using the method described above. The BeiDou-3 MEO constellation comprises 24 satellites, with a Ka-band inter-satellite link ranging accuracy of approximately 1 cm. Under typical 1-day arc-segment orbit determination conditions, the orbital accuracy of autonomous constellation orbit determination is approximately 5 to 10 cm radially, the daily solution accuracy of the Helmert translation parameters is approximately 3 to 5 mm, and the daily solution accuracy of the scale parameters is approximately 0.3 to 0.5 ppb. For the translation parameter time series, the annual signal amplitude of the tx and ty components of geocentric motion is approximately 2 to 5 mm, and the annual signal amplitude of the tz component is approximately 3 to 6 mm, consistent with independent SLR and GNSS results. The linear trend term is on the order of 0.1 to 0.5 mm / yr, corresponding to the long-term drift rate of the frame origin. If the translation threshold is set to 5 mm, then under normal operating conditions, the trigger frequency for frame origin correction is approximately once every 1 to 3 months. If equipped with an inter-satellite laser ranging system with an accuracy of 1 mm, the daily solution accuracy of Helmert translation parameters can be improved to 1 to 2 mm, and the sensitivity of frame monitoring can be improved by 2 to 3 times accordingly.

[0040] Based on the correction method described above Figure 3 This diagram illustrates the structure of a correction system for a navigation satellite constellation coordinate frame based on inter-satellite observations, according to an embodiment of the present invention. Figure 3 As shown, a correction system for the coordinate frame of a navigation satellite constellation based on inter-satellite observations includes a frame parameter monitoring module 301 and a correction and maintenance module 302. The frame parameter monitoring module 301 is used to determine the seven-parameter time series of the navigation satellite constellation coordinate frame relative to the International Earth Reference Frame and establish a trend and periodic signal model. The correction and maintenance module 302 is used to determine whether to correct the navigation satellite constellation coordinate frame based on the systematic deviation of the parameters, and then corrects the navigation satellite constellation coordinate frame accordingly.

[0041] In one embodiment of the present invention, the correction system further includes a constellation autonomous orbit determination module 303 and a frame definition module 304. The constellation autonomous orbit determination module 303 is used to construct inter-satellite observation equations and perform joint constellation orbit determination. The inter-satellite observation equations are constructed based on the inter-satellite link two-way ranging and time-frequency transfer data output by the inter-satellite observation processing module 001. The inter-satellite observation processing module 001 is also used to preprocess the inter-satellite link two-way ranging and time-frequency transfer data, including gross error removal, equipment delay correction, and relativistic correction. The frame definition module 304 is used to apply centroid constraints, net rotation constraints, and net scale constraints during the joint constellation orbit determination process to determine the initial navigation satellite constellation coordinate frame.

[0042] Based on the correction method described above, this invention also provides an autonomous orbit determination method, which corrects the coordinate frame using the correction method described above, constructs inter-satellite observation equations based on inter-satellite observations, and then performs joint orbit determination using least squares and Kalman filtering.

[0043] Although various embodiments of the 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 solely by the appended claims and their equivalents.

Claims

1. A method for correcting the coordinate frame of a navigation satellite constellation based on inter-satellite observations, characterized in that, include: Determine the time series of seven parameters of the navigation satellite constellation coordinate frame relative to the International Earth Reference Frame; For each parameter in the seven-parameter time series, a trend and periodic signal model is established respectively; The parameters of the trend and periodic signal model are fitted, and the cumulative deviation is determined based on the systematic deviation of the parameters. If the cumulative deviation exceeds a preset threshold, the correction amount is determined based on the seven-parameter estimate of the current epoch. The correction amount and its uncertainty estimate are published through navigation message parameters, on-board injection parameters, or ground product documents. Based on the correction amount and uncertainty estimate, the coordinate frame of the navigation satellite constellation is corrected to align it with the International Earth Reference Frame.

2. The correction method as described in claim 1, characterized in that, The seven-parameter time series for determining the coordinate frame of the navigation satellite constellation relative to the International Earth Reference Frame includes: Select several satellites from the navigation satellite constellation and establish a transformation model based on their coordinates in the navigation satellite constellation coordinate frame and the international earth reference frame, wherein the number of satellites is no less than 4. Linearize the transformation model; Using a specified duration as a solution unit, the seven parameters and their covariance are estimated to obtain the seven-parameter time series.

3. The correction method as described in claim 2, characterized in that, The seven parameters and their covariances are estimated using weighted least squares.

4. The correction method as described in claim 2, characterized in that, The specified duration is one day or one week.

5. The correction method as described in claim 1, characterized in that, The parameters of the trend and periodic signal model are fitted using the least squares method.

6. The correction method as described in claim 1, characterized in that, The initial navigation satellite constellation coordinate framework is obtained during the autonomous orbit determination process based on inter-satellite observations by applying constellation centroid constraints, net rotation constraints, and net scale constraints.

7. A correction system for the coordinate frame of a navigation satellite constellation based on inter-satellite observations, characterized in that, include: The frame parameter monitoring module is configured to determine the seven-parameter time series of the navigation satellite constellation coordinate frame relative to the International Earth Reference Frame and to establish trend and periodic signal models. The correction and maintenance module is configured to determine the cumulative deviation based on the systematic deviation of the parameters. If the cumulative deviation exceeds a preset threshold, a correction amount is determined based on the seven-parameter estimate of the current epoch. The correction amount and its uncertainty estimate are published through navigation message parameters, on-board injection parameters, or ground product documents. Based on the correction amount and uncertainty estimate, the coordinate frame of the navigation satellite constellation is corrected to align it with the International Earth Reference Frame.

8. The correction system as described in claim 7, characterized in that, Also includes: The constellation autonomous orbit determination module is configured to construct inter-satellite observation equations and perform joint constellation orbit determination. The frame definition module is configured to apply centroid constraints, net rotation constraints, and net scale constraints during the joint orbit determination process of the constellation to determine the initial navigation satellite constellation coordinate frame.

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