Constellation satellite autonomous positioning method based on inter-satellite measurement and GNSS local availability, storage medium and equipment

Abstract

The invention discloses a constellation satellite autonomous positioning method based on inter-satellite measurement and local available GNSS, a storage medium and equipment, belongs to the technical field of satellite positioning, and aims to solve the problems that a satellite cannot be effectively positioned under the condition that a GNSS signal is locally invisible and the satellite positioning precision needs to be improved under the condition that the signal is visible. Under the condition that the GNSS is visible, establishing a state prediction model based on a satellite orbit kinetic equation containing J2 perturbation, fusing GNSS observation data by using extended Kalman filtering, and correcting a positioning error by using a nonlinear observation equation; the inter-satellite link measurement information is fused through a weighted least square method, and positioning of a satellite to be positioned is achieved; under the condition that GNSS signals are locally invisible, the satellites to be positioned in an area are connected with adjacent GNSS visible satellites through inter-satellite links, relative positioning is carried out by fusing a C-W equation and volume Kalman filtering, and positioning of the satellites to be positioned is achieved.

Description

Technical Field

[0001] This invention belongs to the field of satellite positioning technology, specifically relating to a low-Earth orbit constellation satellite positioning method, storage medium, and device based on GNSS and inter-satellite links. Background Technology

[0002] In recent years, with the rapid development of aerospace technology and the booming rise of commercial spaceflight, the Giant Star constellation system has demonstrated enormous application potential in global communications, Earth observation, and navigation enhancement. Typically composed of hundreds to thousands, or even tens of thousands, of satellites, Giant Star offers global coverage, high revisit rates, and low-latency services, making it a crucial area of ​​competition in national space infrastructure and commercial spaceflight. Against this backdrop, achieving high-precision, high-reliability autonomous positioning for satellites within the constellation has become a key technological requirement for ensuring coordinated constellation operation and enhancing system service capabilities.

[0003] However, in the field of low-Earth orbit (LEO) satellite positioning, traditional methods relying on centralized processing architectures and satellite-to-ground links have inherent limitations, such as the risk of single-point failure at the central node, large satellite-to-ground transmission delays, and limited link bandwidth. These limitations severely restrict the system's real-time performance, robustness, and autonomy. Especially under extreme conditions such as GNSS (Global Navigation Satellite System) denial or satellite-to-ground link interruption, existing methods struggle to maintain high-precision spatial references and cannot meet the urgent needs of large-scale constellations in complex space environments for distributed, interference-resistant, and low-latency positioning capabilities.

[0004] Therefore, developing a high-precision autonomous positioning method that can integrate multi-source information, adapt to different visibility conditions, and possess distributed collaborative capabilities has become a key issue for achieving long-term stable operation of constellation systems and improving overall navigation performance, and is of great strategic significance for promoting the intelligent development of my country's space infrastructure. Summary of the Invention

[0005] This invention aims to address the problem of ineffective satellite positioning when GNSS signals are partially invisible, and the need to improve the satellite positioning accuracy of existing methods when GNSS signals are visible.

[0006] An autonomous positioning method for constellation satellites based on inter-satellite measurements and locally available GNSS includes:

[0007] In GNSS-visible conditions, absolute positioning is achieved based on GNSS observation information and inter-satellite ranging information. First, a state prediction model is established based on the satellite orbital dynamics equations with J2 perturbation, and a priori state estimates are generated through numerical integration. Then, extended Kalman filtering is used to fuse GNSS observation data, and nonlinear observation equations are used to correct positioning errors. Finally, inter-satellite link measurement information is fused using the weighted least squares method to achieve positioning of the satellite to be located.

[0008] In situations where GNSS signals are partially invisible, the satellite to be positioned within the region establishes a connection with nearby visible GNSS satellites via inter-satellite links; relative positioning is achieved by fusing CW equations and commensurate Kalman filtering, realizing the chained transmission and sharing of absolute spatial references, thus enabling the satellite to be positioned to indirectly achieve absolute positioning.

[0009] Furthermore, the process of establishing a state prediction model based on the satellite orbital dynamics equations containing J2 perturbations includes:

[0010] A state prediction model is established based on the following satellite orbital dynamics equations containing J2 perturbations. Vector The vector pointing from the Earth's center to the satellite. These are the coordinate components of the satellite in the three axes of the ECI coordinate system. for The second derivative; Earth's gravitational constant, a scalar The distance from the satellite to the Earth's center. This is the J2 perturbation term.

[0011] Furthermore, the process of fusing GNSS observation data using the Extended Kalman Filter (EKF) and correcting positioning errors using nonlinear observation equations includes:

[0012] Observation equations , For GNSS noise measurement, An observation function describing the true geometric relationship between satellites and GNSS satellites; linearize the observation function and calculate the Jacobian matrix. ;

[0013] Then, based on the state prediction model and the observation equation, the extended Kalman filter is used to obtain the positioning information of the satellite to be positioned after correcting the positioning error.

[0014] Furthermore, the process of autonomously fusing and evaluating the space reference of low-Earth orbit constellation satellites through weighted least squares fusion of inter-satellite link measurement information and three-stage collaborative optimization includes:

[0015] Establish a relative position observation model between satellite i and neighboring satellite j: , The relative position measurement between satellite i and neighboring satellite j; The nonlinear observation function describing the relative positional relationship between two satellites has a theoretical value derived from the satellite state. and Calculated; The inter-satellite measurement noise is assumed to be zero-mean white noise, and its covariance matrix is: ;

[0016] Observation is defined as the difference between the actual measured value and the theoretical predicted value: By analyzing the nonlinear observation function Perform a first-order Taylor expansion and linearize to obtain , It is the Jacobian matrix of the observation function with respect to the satellite i state vector, i.e., the observation matrix. It is the state correction quantity to be solved;

[0017] Stacking the observation equations of J neighboring satellites for satellite i yields a linear system: , It is the observation residual matrix; ; The noise vectors of all neighboring satellites are given; the position correction is solved using the weighted least squares method. This enables satellite positioning.

[0018] Furthermore, the position correction is solved using the weighted least squares method. , The weight matrix is ​​typically the inverse of the measurement noise covariance matrix, i.e. .

[0019] Furthermore, the process of relative positioning by fusing the CW equation with capacitive Kalman filtering includes:

[0020] The state vector is constructed by selecting the relative position and relative velocity of the satellite to be positioned relative to the reference satellite. , These represent the relative position and relative velocity in the radial, circumferential, and normal directions, respectively; for the state vector... A state prediction model is established based on the CW equation. ;

[0021] The observation vector is determined as ; The distance is relative. It is the azimuth angle. The elevation angle, , , For three-dimensional relative velocity; based on the observation vector With state vector The transformation relationship determines the observation equation ;

[0022] Based on the state prediction model and observation equations, the relative positioning of the satellite to be positioned is achieved by using capacitive Kalman filtering.

[0023] Furthermore, regarding the state vector A state prediction model is established based on the CW equation. as follows:

[0024]

[0025] in, This is the orbital angular velocity of the reference star.

[0026] Furthermore, the observation equation as follows:

[0027]

[0028] In the formula, Noise for relative distance measurement; Noise in azimuth measurement; Noise in azimuth measurement; , , Noise is measured for relative velocity in the corresponding direction.

[0029] A computer storage medium storing at least one instruction, which is loaded and executed by a processor to implement the aforementioned autonomous positioning method for constellation satellites based on inter-satellite measurements and locally available GNSS.

[0030] An autonomous positioning device for constellation satellites based on inter-satellite measurement and locally available GNSS, the device comprising a processor and a memory, the memory storing at least one instruction, the at least one instruction being loaded and executed by the processor to implement the aforementioned autonomous positioning method for constellation satellites based on inter-satellite measurement and locally available GNSS.

[0031] Beneficial effects:

[0032] In summary, this invention successfully achieves a low-Earth orbit constellation satellite space reference fusion evaluation adapted to different GNSS visibility conditions based on GNSS observation and inter-satellite links. It achieves absolute positioning when GNSS is visible by using extended Kalman filtering and weighted least squares method, and relative positioning by combining CW equations and commensurate Kalman filtering when GNSS is invisible. Thus, it can achieve high-precision and robust autonomous satellite positioning under different visibility conditions, and can achieve accurate satellite positioning when GNSS signals are partially invisible. At the same time, it also improves the satellite positioning accuracy when GNSS signals are visible. Attached Figure Description

[0033] Figure 1 This represents the three-dimensional position trajectory and three-axis position components of satellite 1.

[0034] Figure 2 This is a diagram showing the absolute positioning error of the constellation satellites (90 satellites are selected).

[0035] Figure 3 This is a schematic diagram of a test scenario where some satellite GNSS signals are unavailable.

[0036] Figure 4 This is a diagram showing the indirect absolute positioning error of satellites where GNSS signals are unavailable. Detailed Implementation

[0037] This invention primarily considers low-Earth orbit (LEO) satellite constellations against the backdrop of the Giants constellation. Based on GNSS observation information and inter-satellite ranging information, it achieves distributed satellite positioning adaptable to varying GNSS visibility conditions. When an LEO satellite is visible to GNSS, it uses GNSS observation information and inter-satellite ranging information to perform absolute positioning through extended Kalman filtering and weighted least squares method. When GNSS signals are locally invisible, the satellite in that area uses inter-satellite ranging information and, with the aid of the CW equation and commensurate Kalman filtering, establishes a chain navigation connection with nearby visible GNSS satellites, thereby indirectly achieving absolute positioning.

[0038] The positioning method has the following main features and advantages: by fusing GNSS observation information, inter-satellite ranging information and dynamic models and other multi-source data through a distributed architecture, it overcomes the problems of single point of failure and heavy computational burden in the traditional centralized architecture, realizes distributed spatial benchmark fusion evaluation that can adapt to different GNSS visibility conditions, and does not require satellite-to-ground link support, thus having stronger robustness and autonomy. Specific implementation method one:

[0040] This embodiment describes a constellation-based autonomous positioning method for satellites using inter-satellite measurements and locally available GNSS, comprising:

[0041] (1) Absolute positioning of low-Earth orbit constellation satellites in GNSS visibility conditions:

[0042] In GNSS-visible scenarios, this invention performs absolute positioning based on GNSS observation information and inter-satellite ranging information. First, a state prediction model is established based on the satellite orbital dynamics equations with J2 perturbation, and a priori state estimates are generated through numerical integration. Then, GNSS observation data is fused using extended Kalman filtering (EKF), and nonlinear observation equations are used to correct positioning errors. Finally, inter-satellite link measurement information is fused using weighted least squares method to complete the autonomous fusion evaluation of the low-Earth orbit constellation satellite space reference.

[0043] 1) Establish a state prediction model based on the following satellite orbital dynamics equations containing J2 perturbations:

[0044] ,

[0045] In the formula, vector The vector pointing from the Earth's center to the satellite. These are the coordinate components of the satellite in the three axes of the ECI coordinate system. for The second derivative; Earth's gravitational constant, a scalar The distance from the satellite to the Earth's center. The J2 perturbation term has the following expression:

[0046] ,

[0047] In the formula, is a dimensionless band harmonic coefficient (second order). The radius of the Earth's equator;

[0048] Prior state estimates are generated by numerical integration of the state prediction model, which are then used for state prediction in extended Kalman filtering.

[0049] 2) Positioning correction is performed based on GNSS observation information using extended Kalman filtering.

[0050] The observation equation can be described as a combination of a geometric distance function and noise:

[0051]

[0052] In the formula, GNSS noise measurement; This is the observation function representing the true geometric relationship between the satellite to be located and the GNSS satellite. The input is the satellite state vector, and the output is the error-free theoretical distance truth value.

[0053] Linearize the observation function and calculate the Jacobian matrix: ;

[0054] The extended Kalman filter update is performed in two steps. The first step is the prediction phase, which predicts the current state and error covariance based on the state prediction model and the process noise covariance, as follows:

[0055]

[0056] In the formula, This is the state prediction result (prior estimate) based on the state at time k-1. Let f(·) be the optimal result (posterior estimate) of the state at time k-1, and f(·) be the state prediction model. It is a quantity that changes over time; , for , covariance, The Jacobian matrix of the state prediction matrix. Let be the process noise covariance matrix.

[0057] The second stage is the correction phase, where the observation information is fused using Kalman gain, and the state estimate and covariance are updated as follows:

[0058]

[0059] In the formula, For the observation equation, This is the actual observed value (distance); As a unit array, To observe the Jacobian matrix; The Kalman gain matrix can be obtained using the following formula:

[0060]

[0061] in, To observe the noise covariance matrix;

[0062] 3) Based on the low-orbit constellation satellite positioning results obtained in 2), further refinement is achieved using inter-satellite ranging information.

[0063] The relative position observation model between satellite i and its neighboring satellite j is established as follows:

[0064]

[0065] In the formula, The relative position measurement between satellite i and neighboring satellite j; The nonlinear observation function describing the relative positional relationship between two satellites has a theoretical value derived from the satellite state. and Calculated; The inter-satellite measurement noise is assumed to be zero-mean white noise, and its covariance matrix is: .

[0066] Observation is defined as the difference between the actual measured value and the theoretical predicted value:

[0067]

[0068] By analyzing the nonlinear observation function Linearizing the result using a first-order Taylor expansion, we obtain:

[0069]

[0070] in, It is the Jacobian matrix (i.e., the observation matrix) of the observation function with respect to the state vector of satellite i. It is the state correction quantity to be solved.

[0071] The equations for observing J neighboring satellites of satellite i are stacked to form the linear system shown below:

[0072]

[0073] In the formula, It is the observation residual matrix, representing the difference between the actual measured values ​​and the theoretical predicted values; It is the Jacobian matrix of the observation function with respect to the state vector (i.e., the observation matrix). It is the state correction quantity to be solved; This is the noise vector for all neighboring satellites.

[0074] The position correction is solved using the weighted least squares (WLS) method:

[0075]

[0076] In the formula, The weight matrix is ​​typically the inverse of the measurement noise covariance matrix, i.e. .

[0077] (2) Relative positioning of low-Earth orbit constellation satellites in the case of GNSS invisibility:

[0078] In situations where GNSS signals are partially invisible, this invention enables satellites within that area (referred to as the satellites to be positioned) to establish connections with nearby visible GNSS satellites (referred to as reference satellites) via inter-satellite links. By fusing the CW equations and commensurate Kalman filtering (CKF), relative positioning is achieved, thereby realizing the chained transmission and sharing of the absolute spatial reference. This allows the satellites to be positioned to indirectly achieve absolute positioning, thus maintaining a unified high-precision spatiotemporal reference across the entire constellation.

[0079] 1) Establish a satellite relative motion model based on the CW equation.

[0080] A relative coordinate system is established with the orbital plane of the reference star as the reference. By using the simplified circular orbit assumption, the CW equation is used to describe the near-distance relative motion of the satellite to be positioned relative to the reference star, providing a theoretical framework for state estimation.

[0081] The relative position and relative velocity of the satellite to be positioned relative to the reference satellite are selected to form the state vector, which is defined as follows:

[0082]

[0083] in, These are the relative positions and relative velocities in the radial, circumferential, and normal directions, respectively.

[0084] A state prediction model is established based on the CW equation. as follows:

[0085]

[0086] in, This is the orbital angular velocity of the reference star.

[0087] 2) Relative state estimation based on capacitive Kalman filtering:

[0088] The observation vector is determined as .in, The distance is relative. It is the azimuth angle. The elevation angle, , , The three-dimensional relative velocity (measured directly by inter-satellite velocimetry equipment, and in the state vector) correspond).

[0089] Based on the observation vector With state vector The transformation relationship can determine the observation equation. as follows:

[0090]

[0091] In the formula, Noise for relative distance measurement; Noise in azimuth measurement; Noise in azimuth measurement; , , Noise is measured for relative velocity in the corresponding direction.

[0092] Next, capacitive Kalman filtering is performed. First, the initial state estimate is determined based on the initial inter-satellite observations and initial accuracy settings. and initial error covariance Then, based on the posterior state at time k and error covariance Generate 2n sampling points (n is the dimension of the state vector, here n=6):

[0093]

[0094] Substitute each sampling point into the state prediction equation The predicted sampling points are as follows:

[0095]

[0096] in, The wavelength is the filtering time.

[0097] The prior state estimate and prior error covariance are calculated as follows:

[0098]

[0099]

[0100] in, The process noise covariance matrix is ​​determined by the modeling error of the CW equation, the orbital perturbation residual, etc. It is a diagonal matrix, and the diagonal elements are the process noise variances of each state component.

[0101] Next, state correction is performed, substituting the prior sampling points into the observation equation. Calculate the sampling observation points:

[0102]

[0103] The calculated observed predictions, observation error covariance, and state-observation cross-covariance are as follows:

[0104]

[0105]

[0106]

[0107] in, The noise covariance matrix is ​​determined by the accuracy of the ranging, angle measuring, and velocity measuring equipment. It is a diagonal matrix, with the diagonal elements being the noise variance of each observed component.

[0108] Therefore, the posterior state estimate and posterior error covariance can be obtained as follows:

[0109]

[0110]

[0111] Among them, Kalman gain .

[0112] By fusing the optimal relative state obtained from the posterior state estimation with the absolute state of the reference satellite, the absolute state of the satellite to be located can be obtained.

[0113] In summary, this invention successfully achieves a low-Earth orbit constellation satellite space reference fusion evaluation adapted to different GNSS visibility conditions based on GNSS observation and inter-satellite links. It achieves absolute positioning when GNSS is visible by using extended Kalman filtering and weighted least squares method, and relative positioning when GNSS is not visible by combining CW equations and commensurate Kalman filtering. Thus, it can achieve high-precision and robust autonomous satellite positioning under different visibility conditions.

[0114] To verify and demonstrate the effectiveness of the low-Earth orbit constellation satellite space reference fusion evaluation algorithm designed in this invention, this invention uses a low-Earth orbit constellation consisting of 9,000 satellites as a background to conduct space reference fusion evaluation simulation verification, demonstrating the space reference fusion evaluation effect based on multi-source space measurement information filtering processing.

[0115] In the mission environment, the Walker constellation consists of 9,000 satellites across 100 orbital planes, with 90 satellites on each plane. The orbital altitude is 650 km, the inclination is 60°, the phase factor is 1, and the eccentricity is 0.00103. Simultaneously, five high-orbit satellites (three in equatorial orbit and two in inclined orbit) are introduced into the mission environment to provide GNSS signals to the low-orbit constellation satellites.

[0116] When all satellites in the constellation can receive GNSS signals, the satellites perform absolute positioning based on the GNSS signals and error-refined inter-satellite ranging values. For example... Figure 1-2 The figure shows the absolute positioning results when all satellites in the constellation can receive GNSS signals. Figure 1 It is the three-dimensional position trajectory and three-axis position components of satellite 1 during one cycle. Figure 2 This represents the absolute positioning error of the constellation satellites. Due to the large number of satellites in the constellation, only the positioning results of 90 satellites are shown here. In the figure, the blue bars represent the positioning error when using only GNSS signals for absolute positioning, and the red bars represent the positioning error when using GNSS signals and inter-satellite ranging information for absolute positioning.

[0117] When some satellites in a constellation can receive GNSS signals while others cannot, the satellites that can receive GNSS signals perform absolute positioning normally, while the satellites that cannot receive GNSS signals use nearby satellites capable of absolute positioning as a reference for relative positioning, thus indirectly achieving absolute positioning. For example... Figure 3 The diagram shown illustrates this scenario. The Sat1 satellite can acquire GNSS signals normally for absolute positioning, while the Sat2 satellite cannot acquire GNSS signals and can only achieve absolute positioning indirectly by relying on the Sat1 satellite for relative positioning.

[0118] Figure 4 This represents the absolute position error between the reference satellite Sat1, which can perform absolute positioning normally, and the satellite Sat2, which cannot acquire GNSS signals, in this scenario. As can be seen from the figure, Sat2 indirectly achieves its own absolute positioning by using the relative positioning based on Sat1. Although the positioning error increases slightly, it still remains within 2m. Specific Implementation Method Two:

[0120] This embodiment is a computer storage medium that stores at least one instruction. The at least one instruction is loaded and executed by a processor to implement the aforementioned autonomous positioning method for constellation satellites based on inter-satellite measurements and locally available GNSS.

[0121] It should be understood that the instructions include computer program products, software, or computerized methods corresponding to any method described in this invention; the instructions can be used to program computer systems or other electronic devices. Computer storage media may include readable media on which instructions are stored, and may include, but are not limited to, magnetic storage media, optical storage media; magneto-optical storage media include read-only memory (ROM), random access memory (RAM), erasable programmable memory (e.g., EPROM and EEPROM), and flash memory layers, or other types of media suitable for storing electronic instructions. Specific implementation method three:

[0123] This embodiment is an autonomous positioning device for constellation satellites based on inter-satellite measurement and local GNSS availability. The device includes a processor and a memory. It should be understood that this includes any device described in this invention that includes a processor and a memory. The device may also include other units and modules that perform display, interaction, processing, control, and other functions through signals or instructions.

[0124] The memory stores at least one instruction, which is loaded and executed by the processor to implement the aforementioned autonomous positioning method for constellation satellites based on inter-satellite measurements and locally available GNSS.

[0125] Those skilled in the art will understand that at least one stored instruction constitutes a computer program product corresponding to a method or system. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0126] This application is described with reference to flowchart illustrations and / or block diagrams of methods, systems, and computer program products according to embodiments of this application, and can also be used with corresponding devices. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0127] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0128] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0129] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0130] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

[0131] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A constellation-based autonomous positioning method for satellites based on inter-satellite measurements and locally available GNSS, characterized in that, include: In GNSS-visible conditions, absolute positioning is achieved based on GNSS observation information and inter-satellite ranging information. First, a state prediction model is established based on the satellite orbital dynamics equations with J2 perturbation, and a priori state estimate is generated through numerical integration. Then, GNSS observation data is fused using extended Kalman filtering, and nonlinear observation equations are used to correct positioning errors. Finally, inter-satellite link measurement information is fused using weighted least squares method to achieve positioning of the satellite to be located. In situations where GNSS signals are partially invisible, the satellite to be positioned within the region establishes a connection with nearby visible GNSS satellites via inter-satellite links; relative positioning is achieved by fusing CW equations and commensurate Kalman filtering, realizing the chained transmission and sharing of absolute spatial references, thus enabling the satellite to be positioned to indirectly achieve absolute positioning.

2. The constellation satellite autonomous positioning method based on inter-satellite measurement and locally available GNSS as described in claim 1, characterized in that, The process of establishing a state prediction model based on the satellite orbital dynamics equations with J2 perturbation includes: A state prediction model is established based on the following satellite orbital dynamics equations containing J2 perturbations. Vector The vector pointing from the Earth's center to the satellite. These are the coordinate components of the satellite in the three axes of the ECI coordinate system. for The second derivative; Earth's gravitational constant, a scalar The distance from the satellite to the Earth's center. This is the J2 perturbation term.

3. The constellation satellite autonomous positioning method based on inter-satellite measurement and locally available GNSS as described in claim 1, characterized in that, The process of fusing GNSS observation data using the Extended Kalman Filter (EKF) and correcting positioning errors using nonlinear observation equations includes: Observation equations , For GNSS noise measurement, An observation function describing the true geometric relationship between satellites and GNSS satellites; linearize the observation function and calculate the Jacobian matrix. ; Then, based on the state prediction model and the observation equation, the extended Kalman filter is used to obtain the positioning information of the satellite to be positioned after correcting the positioning error.

4. The constellation satellite autonomous positioning method based on inter-satellite measurement and locally available GNSS as described in claim 1, characterized in that, The process of autonomously fusing and evaluating the space reference of low-Earth orbit constellation satellites by fusing inter-satellite link measurement information using the weighted least squares method and through three-stage collaborative optimization includes: Establish a relative position observation model between satellite i and neighboring satellite j: , The relative position measurement between satellite i and neighboring satellite j; The nonlinear observation function describing the relative positional relationship between two satellites has a theoretical value derived from the satellite state. and Calculated; The inter-satellite measurement noise is assumed to be zero-mean white noise, and its covariance matrix is: ; Observation is defined as the difference between the actual measured value and the theoretical predicted value: By analyzing the nonlinear observation function Perform a first-order Taylor expansion and linearize to obtain , It is the Jacobian matrix of the observation function with respect to the satellite i state vector, i.e., the observation matrix. It is the state correction quantity to be solved; Stacking the observation equations of J neighboring satellites for satellite i yields a linear system: , It is the observation residual matrix; ; The noise vectors of all neighboring satellites are given; the position correction is solved using the weighted least squares method. This enables satellite positioning.

5. The constellation satellite autonomous positioning method based on inter-satellite measurement and locally available GNSS as described in claim 4, characterized in that, The position correction is solved using the weighted least squares method. , The weight matrix is ​​typically the inverse of the measurement noise covariance matrix, i.e. .

6. A constellation satellite autonomous positioning method based on inter-satellite measurement and locally available GNSS, as described in any one of claims 1 to 5, characterized in that, The process of relative positioning by fusing the CW equation with capacitive Kalman filtering includes: The state vector is constructed by selecting the relative position and relative velocity of the satellite to be positioned relative to the reference satellite. , These represent the relative position and relative velocity in the radial, circumferential, and normal directions, respectively; for the state vector... A state prediction model is established based on the CW equation. ; The observation vector is determined as ; The distance is relative. It is the azimuth angle. The elevation angle, , , For three-dimensional relative velocity; based on the observation vector With state vector The transformation relationship determines the observation equation ; Based on the state prediction model and observation equations, the relative positioning of the satellite to be positioned is achieved by using capacitive Kalman filtering.

7. The constellation satellite autonomous positioning method based on inter-satellite measurement and locally available GNSS as described in claim 6, characterized in that, For the state vector A state prediction model is established based on the CW equation. as follows: ， in, This is the orbital angular velocity of the reference star.

8. The constellation satellite autonomous positioning method based on inter-satellite measurement and locally available GNSS as described in claim 6, characterized in that, The observation equation as follows: ， In the formula, Noise for relative distance measurement; Noise in azimuth measurement; Noise in azimuth measurement; , , Noise is measured for relative velocity in the corresponding direction.

9. A computer storage medium, characterized in that, The storage medium stores at least one instruction, which is loaded and executed by a processor to implement the autonomous positioning method for constellation satellites based on inter-satellite measurements and locally available GNSS as described in any one of claims 1 to 8.

10. A constellation-based autonomous positioning device based on inter-satellite measurements and locally available GNSS, characterized in that, The device includes a processor and a memory, the memory storing at least one instruction, which is loaded and executed by the processor to implement the autonomous positioning method for constellation satellites based on inter-satellite measurement and locally available GNSS as described in any one of claims 1 to 8.

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