Satellite precise orbit determination method and device based on along-track error, equipment and medium
By optimizing the precise satellite orbit determination method based on track error, constructing a partial derivative matrix and an objective function, the problem of insufficient track error correction in satellite orbit determination is solved, and higher precision satellite orbit determination is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-03-11
- Publication Date
- 2026-06-12
AI Technical Summary
Existing technologies for precise satellite orbit determination do not adequately correct for errors along the track, resulting in insufficient accuracy in orbit prediction, especially since errors along the track direction are difficult to eliminate completely.
A precise satellite orbit determination method based on track error is adopted. This method involves constructing an initial state vector, generating a reference orbit, calculating the track observation residuals, constructing a partial derivative matrix and an objective function, minimizing the track direction residuals, and optimizing the state vector to improve accuracy.
It significantly improves the accuracy of satellite orbits along the track direction, achieving higher-precision satellite orbit determination, and is easy to integrate into existing orbit determination software processes without significantly increasing computational complexity.
Smart Images
Figure CN122192343A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of spacecraft orbital dynamics technology, and relates to a method, apparatus, equipment and medium for precise satellite orbit determination based on track error. Background Technology
[0002] When using spaceborne observation data (such as GNSS) for precise satellite orbit determination, a state vector is typically constructed that includes the satellite's position, velocity, and key mechanical model parameters (such as atmospheric damping coefficient). The closest existing technology employs a "three-dimensional residual global minimization" strategy: in each iteration, the residuals between the observed and predicted values in three-dimensional space (radial, along the track, and normal) are calculated, and the state vector is adjusted using a least squares algorithm to minimize the sum of squares of the three-dimensional residuals, thereby simultaneously determining the optimal orbit and model parameters.
[0003] Of the three directions of orbit determination error, the track-along error is usually the most significant and has the greatest impact on orbit prediction. Traditional methods incorporate the residuals in the three directions into the same objective function for minimization, treating them "equally" or with fixed weights. This essentially uses a comprehensive index to guide the optimization, causing the optimization process to be dominated by relatively easy-to-converge components such as the radial and normal directions. Consequently, sufficient "optimization attention" is not focused on accurately correcting the most critical and significant track-along residuals. As a result, systematic errors in the track-along direction are difficult to eliminate sufficiently, becoming a bottleneck restricting the final orbit determination accuracy.
[0004] The root cause of this defect is that, under the condition of limited parameters and observation data, attempting to simultaneously and optimally solve multiple (three) coupled but different problems (error corrections in three directions) with a single objective function will inevitably lead to insufficient solutions to the key sub-problems. Summary of the Invention
[0005] To address the problem of insufficient correction of errors along the track direction caused by the overall minimization of three-dimensional residuals in the existing technology, this invention proposes a satellite precision orbit determination method, apparatus, equipment, and medium based on track error, which can more effectively correct systematic errors along the track direction, thereby directly and significantly improving the accuracy of the final orbit product in the track direction.
[0006] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions: On the one hand, a precise satellite orbit determination method based on trajectory error is provided, including the following steps: Step 1: Construct an initial state vector based on the satellite's precise orbital data, space environment data, and surface-to-mass ratio data.
[0007] Step 2: Based on the satellite dynamics model, space environment data, and surface-to-mass ratio data, use the initial state vector as the initial value to predict the orbit and generate a reference orbit.
[0008] Step 3: Compare the reference orbit with the precise orbit data to obtain the observation residuals. Project the observation parameters along the track direction to obtain the track observation residuals.
[0009] Step 4: Based on the initial state vector and the reference orbit, construct the partial derivative matrix using the state numerical perturbation method.
[0010] Step 5: Based on the partial derivative matrix, construct the objective function with the goal of minimizing the observation residuals along the track.
[0011] Step 6: Solve the objective function to obtain the optimal correction amount for the initial state vector.
[0012] Step 7: Update the initial state vector using the optimal correction amount and output the precise orbit determination result.
[0013] On the other hand, a satellite precise orbit determination device based on track error is also provided, comprising: The initial state vector construction module is used to construct the initial state vector based on the satellite's precise orbital data, space environment data, and surface-to-mass ratio data.
[0014] The track observation residual determination module is used to predict the orbit based on the satellite dynamics model, space environment data, and surface-to-mass ratio data, using the initial state vector as the initial value, and generate a reference orbit. The reference orbit is compared with the precise orbit data to obtain the observation residual. The observation parameters are then projected along the track direction to obtain the track observation residual.
[0015] The partial derivative matrix construction module is used to construct the partial derivative matrix based on the initial state vector and the reference orbit using the state numerical perturbation method.
[0016] The objective function construction module is used to construct an objective function based on the partial derivative matrix, with the goal of minimizing the observation residuals along the track.
[0017] The optimal correction determination module is used to solve the objective function and obtain the optimal correction of the initial state vector.
[0018] The precision orbit determination module is used to update the initial state vector using the optimal correction amount and output the precision orbit determination result.
[0019] In another aspect, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the satellite precise orbit determination method based on the path error described above.
[0020] Furthermore, a computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements the steps of the above-mentioned satellite precise orbit determination method based on track error.
[0021] One of the above technical solutions has the following advantages and beneficial effects: The aforementioned satellite precise orbit determination method, apparatus, equipment, and medium based on track error shifts the optimization objective from minimizing the overall three-dimensional residual to prioritizing the minimization of the track-direction residual during the state vector estimation process. This guides the solution process to concentrate resources on overcoming the most critical accuracy bottleneck, ultimately achieving higher-precision satellite orbit determination and improving the accuracy of the final orbit product in the track direction. This method requires no changes to the basic structure of the state vector or the core estimator; it can be implemented simply by adjusting the definition of the optimization objective function. It is easily integrated into existing orbit determination software workflows, with no significant increase in computational complexity, and possesses strong engineering practicality. Attached Figure Description
[0022] To more clearly illustrate the technical solutions in the embodiments of this application or the conventional technology, the drawings used in the description of the embodiments or the conventional technology will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0023] Figure 1 This is a flowchart illustrating a satellite precise orbit determination method based on track error in one embodiment. Detailed Implementation
[0024] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.
[0025] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.
[0026] It should be noted that, in this document, the reference to "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The presentation of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. Those skilled in the art will understand that the embodiments described herein can be combined with other embodiments. The term "and / or" as used herein refers to any combination of one or more of the associated listed items, and all possible combinations, including such combinations.
[0027] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
[0028] In one embodiment, such as Figure 1 As shown, a precise satellite orbit determination method based on path error is provided, which may include the following processing steps 1 to 7: Step 1: Construct an initial state vector based on the satellite's precise orbital data, space environment data, and surface-to-mass ratio data.
[0029] Specifically, the initial state vector usually refers to the vector at a certain reference epoch. At what moment, the satellite's position in the inertial coordinate system and speed A six-dimensional vector.
[0030] In precise orbit determination or long-arc segment prediction, the state vector may also contain dynamic parameters to be estimated (such as atmospheric drag coefficient). Solar radiation pressure coefficient (etc.), forming an extended state vector.
[0031] Precise orbit data typically provides high-precision position / velocity of satellites over a period of time (such as GPS precise ephemeris, post-hoc precise orbit). The orbital state at a reference time is extracted from the precise orbit data and used as the source of initial values.
[0032] Space environment data includes solar radiation flux, geomagnetic index, and sometimes parameters required for atmospheric density models. It is used to construct non-conservative force models (atmospheric drag, solar radiation pressure), and is dynamically used during orbital integration. It does not directly enter the state vector, but it does affect the accuracy of the dynamic equations.
[0033] The surface-to-mass ratio data is the cross-sectional area of the satellite. With quality The ratio ( (This may also distinguish the effective area in different directions.) Used to calculate atmospheric drag acceleration. And solar radiation pressure acceleration. The surface-to-mass ratio is usually treated as a fixed parameter, while... , It may be a parameter to be estimated.
[0034] The specific steps for constructing the initial state vector are as follows: Step 1.1: Select Reference Era Then, position and velocity are extracted. Specifically, a suitable initial moment (e.g., the start of an orbital arc or a specific epoch) is selected from the precise orbital data. If the precise orbital data is not directly provided at that moment, the position and velocity can be obtained through interpolation. During orbital prediction, the coordinate system of the data is converted to an inertial frame.
[0035] Step 1.2: Process the dough-to-texture ratio data. Specifically, this includes: adjusting the dough-to-texture ratio... As a known constant. If it is necessary to estimate the drag coefficient, then... Add the state vector, and multiply the surface-to-mass ratio as a known quantity.
[0036] If changes in satellite attitude lead to changes in drag area, a more refined satellite surface model may be needed. In this case, the surface-to-mass ratio is a function of attitude, but the initial state vector still only contains position and velocity.
[0037] Step 1.3: Utilization of Space Environment Data. Space environment data is not directly added to the state vector, but it must be accessed in real-time during orbital integration.
[0038] Step 1.4: Construct the extended state vector (optional). Specifically: If parameter estimation (such as precise orbit determination) is required, the dynamic parameters (such as...) can be... , Add the initial value to the state vector. , It can be set based on experience (e.g.) (This is followed by updates using least squares).
[0039] Step 2: Based on the satellite dynamics model, space environment data, and surface-to-mass ratio data, use the initial state vector as the initial value to predict the orbit and generate a reference orbit.
[0040] Step 3: Compare the reference orbit with the precise orbit data to obtain the observation residuals. Project the observation parameters along the track direction to obtain the track observation residuals.
[0041] Specifically, because the optimization process is explicitly directed to minimize the track residual, the algorithm can more effectively correct systematic errors along the track direction, thereby directly and significantly improving the accuracy of the final track product in the track direction.
[0042] Step 4: Based on the initial state vector and the reference orbit, construct the partial derivative matrix using the state numerical perturbation method.
[0043] Specifically, the state vector is changed sequentially. For each parameter in the algorithm, orbit prediction is performed for each state. The predicted orbit is compared with the initial orbit, and the partial derivative matrix is calculated. This matrix is one of the core parameters for solving the orbit determination problem using the least squares method.
[0044] The specific steps for constructing the partial derivative matrix are as follows: Step 4.1: Using actual orbital parameters ( Using the initial value as an example, extrapolate the trajectory to obtain an initial trajectory; Step 4.2: Change With all other parameters remaining unchanged, extrapolation of the orbit is performed to obtain the second orbit. Step 4.3: Change the remaining orbital parameters in sequence to perform orbital extrapolation and obtain the remaining orbits; Step 4.4: Based on the extrapolated trajectory and the initial trajectory, calculate the radial error R, the trajectory error T, and the normal error N, and construct the partial derivative matrix. The expression for the partial derivative matrix is as follows: .
[0045] Step 5: Based on the partial derivative matrix, construct the objective function with the goal of minimizing the observation residuals along the track.
[0046] Specifically, this method improves upon the traditional standard of "minimizing the overall three-dimensional error" in orbit determination, and proposes and implements a precise orbit determination method under the condition of "minimizing the residual along the track". By reconstructing the objective function, within the framework of a general estimation algorithm, it cleverly achieves the optimization of resource allocation towards the track error direction, with simple and effective technical means.
[0047] Step 6: Solve the objective function to obtain the optimal correction amount for the initial state vector.
[0048] Step 7: Update the initial state vector using the optimal correction amount and output the precise orbit determination result.
[0049] Specifically, the initial state vector is updated using the optimal correction amount, and the updated state vector is used as the solution result to output parameters such as the precise orbital ephemeris and the optimized atmospheric damping coefficient.
[0050] The aforementioned satellite precise orbit determination method based on track error shifts the optimization objective from minimizing the overall three-dimensional residual to prioritizing the minimization of the track-direction residual during the state vector estimation process. This guides the solution process to concentrate resources on overcoming the most critical accuracy bottleneck, ultimately achieving higher-precision satellite orbit determination and improving the accuracy of the final orbit product along the track direction. This method does not require changes to the basic structure of the state vector or the core estimator; it can be implemented simply by adjusting the definition of the optimization objective function. It is easily integrated into existing orbit determination software workflows, with no significant increase in computational complexity, and possesses strong engineering practicality.
[0051] In one embodiment, step 4 includes: sequentially applying small perturbations to each component of the initial state vector to generate a perturbation initial state; performing orbit prediction based on each perturbation initial state to obtain the corresponding perturbation prediction orbit; and calculating the partial derivatives of the tracking error with respect to each component of the initial state vector based on the difference in tracking error between each perturbation orbit and the reference orbit at each observation time to form a partial derivative matrix.
[0052] In one embodiment, step 5 includes: constructing an objective function based on the partial derivative matrix, with the goal of minimizing the observation residuals along the track: ; in, Let be the objective function. This is the current trail residual vector. This is the initial state correction amount. It is a partial derivative matrix. This is the weight matrix.
[0053] In one embodiment, step 6 includes: using the minimum residual of observation along the track as the criterion, solving the objective function by least squares to obtain the optimal correction amount of the initial state vector.
[0054] In one embodiment, the state vector includes: satellite position, velocity, and atmospheric damping coefficient.
[0055] It should be understood that, although the above Figure 1 The steps are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise explicitly stated in this document, there is no strict order in which these steps are executed; they can be performed in other orders. Furthermore, the above... Figure 1 At least some of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.
[0056] In one embodiment, a satellite precise orbit determination device based on trajectory error is also provided, comprising: The initial state vector construction module is used to construct the initial state vector based on the satellite's precise orbital data, space environment data, and surface-to-mass ratio data.
[0057] The track observation residual determination module is used to predict the orbit based on the satellite dynamics model, space environment data, and surface-to-mass ratio data, using the initial state vector as the initial value, and generate a reference orbit. The reference orbit is compared with the precise orbit data to obtain the observation residual. The observation parameters are then projected along the track direction to obtain the track observation residual.
[0058] The partial derivative matrix construction module is used to construct the partial derivative matrix based on the initial state vector and the reference orbit using the state numerical perturbation method.
[0059] The objective function construction module is used to construct an objective function based on the partial derivative matrix, with the goal of minimizing the observation residuals along the track.
[0060] The optimal correction determination module is used to solve the objective function and obtain the optimal correction of the initial state vector.
[0061] The precision orbit determination module is used to update the initial state vector using the optimal correction amount and output the precision orbit determination result.
[0062] In one embodiment, the partial derivative matrix construction module is further used to sequentially apply small perturbations to each component of the initial state vector to generate a perturbation initial state; perform orbit prediction based on each perturbation initial state to obtain the corresponding perturbation prediction orbit; and calculate the partial derivatives of the tracking error with respect to each component of the initial state vector based on the difference in tracking error between each perturbation orbit and the reference orbit at each observation time to form a partial derivative matrix.
[0063] In one embodiment, the optimal correction determination module is further configured to construct an objective function based on the partial derivative matrix, with the goal of minimizing the residual of observations along the track: ; in, Let be the objective function. This is the current trail residual vector. This is the initial state correction amount. It is a partial derivative matrix. This is the weight matrix.
[0064] In one embodiment, the optimal correction determination module is further configured to solve the objective function using least squares with the criterion of minimizing the residual of observation along the track, thereby obtaining the optimal correction of the initial state vector.
[0065] In one embodiment, the state vector in the initial state vector construction module includes: satellite position, velocity, and atmospheric damping coefficient.
[0066] It is understood that for a detailed explanation of the satellite precise orbit determination device based on track error, please refer to the corresponding explanations of the various embodiments of the satellite precise orbit determination method based on track error above, which will not be repeated here. Each module in the above-mentioned satellite precise orbit determination device based on track error can be implemented entirely or partially through software, hardware, or a combination thereof. Each module can be embedded in hardware or independently of a device with data processing capabilities, or it can be stored in software in the memory of the aforementioned device, so that the processor can call and execute the operations corresponding to each module. The aforementioned device can be, but is not limited to, various types of data processing computer devices already existing in the art.
[0067] In one embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above method embodiments.
[0068] It is understood that, in addition to the memory and processor mentioned above, the computer equipment described above also includes other hardware and software components not listed in this specification. The specific components can be determined according to the model of the image processing computer in different application scenarios, and will not be listed and described in detail in this specification.
[0069] In one embodiment, a computer storage medium is also provided, on which a computer program is stored, which, when executed by a processor, implements the steps in the above method embodiments.
[0070] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), memory bus DRAM (RDRAM), and interface DRAM (DRDRAM), etc.
[0071] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0072] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of protection of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and all such modifications and improvements fall within the scope of protection of this application.
Claims
1. A precise satellite orbit determination method based on path error, characterized in that, Including the following steps: Step 1: Construct an initial state vector based on the satellite's precise orbital data, space environment data, and surface-to-mass ratio data; Step 2: Based on the satellite dynamics model, the space environment data, and the surface-to-mass ratio data, use the initial state vector as the initial value to predict the orbit and generate a reference orbit; Step 3: Compare the reference orbit with the precise orbit data to obtain the observation residuals, and project the observation parameters along the track direction to obtain the track observation residuals; Step 4: Based on the initial state vector and the reference orbit, construct the partial derivative matrix using the state numerical perturbation method; Step 5: Based on the partial derivative matrix, construct an objective function with the goal of minimizing the observation residuals along the track; Step 6: Solve the objective function to obtain the optimal correction amount for the initial state vector; Step 7: Update the initial state vector using the optimal correction amount and output the precise orbit determination result.
2. The satellite precise orbit determination method based on path error according to claim 1, characterized in that, Step 4 includes: Small perturbations are applied sequentially to each component of the initial state vector to generate a perturbed initial state; Based on each of the initial states of the disturbance, a trajectory prediction is performed to obtain the corresponding predicted trajectory of the disturbance; Based on the tracking error of each of the perturbed orbits relative to the reference orbit at each observation time, the partial derivatives of the tracking error with respect to each component of the initial state vector are calculated to form a partial derivative matrix.
3. The satellite precise orbit determination method based on track error according to claim 1, characterized in that, Step 5 includes: Based on the partial derivative matrix, constructing an objective function with the goal of minimizing the observation residuals along the track as follows: ； in, Let be the objective function. This is the current trail residual vector. This is the initial state correction amount. It is a partial derivative matrix. This is the weight matrix.
4. The satellite precise orbit determination method based on path error according to claim 1, characterized in that, Step 6 includes: using the minimum residual of observation along the track as the criterion, solving the objective function using least squares to obtain the optimal correction amount of the initial state vector.
5. The satellite precise orbit determination method based on path error according to claim 1, characterized in that, The state vector includes: satellite position, velocity, and atmospheric damping coefficient.
6. A satellite precise orbit determination device based on track error, characterized in that, include: The initial state vector construction module is used to construct the initial state vector based on the satellite's precise orbital data, space environment data, and surface-to-mass ratio data. The track observation residual determination module is used to predict the orbit and generate a reference orbit based on the satellite dynamics model, the space environment data, and the surface-to-mass ratio data, with the initial state vector as the initial value. The reference orbit is compared with the precise orbit data to obtain the observation residual. The observation parameters are then projected along the track direction to obtain the track observation residual. The partial derivative matrix construction module is used to construct the partial derivative matrix based on the initial state vector and the reference orbit using the state numerical perturbation method. The objective function construction module is used to construct an objective function based on the partial derivative matrix, with the goal of minimizing the observation residuals along the track; The optimal correction quantity determination module is used to solve the objective function and obtain the optimal correction quantity of the initial state vector; The precision orbit determination module is used to update the initial state vector using the optimal correction amount and output the precision orbit determination result.
7. The satellite precise orbit determination device based on track error according to claim 1, characterized in that, The partial derivative matrix construction module is also used to sequentially apply small perturbations to each component of the initial state vector to generate perturbed initial states; perform orbit prediction based on each perturbed initial state to obtain the corresponding perturbed predicted orbit; and calculate the partial derivatives of the track error with respect to each component of the initial state vector based on the difference in track error between each perturbed orbit and the reference orbit at each observation time to form a partial derivative matrix.
8. The satellite precise orbit determination device based on track error according to claim 1, characterized in that, The optimal correction determination module is also used to construct an objective function based on the partial derivative matrix, with the goal of minimizing the observation residuals along the track: ； in, Let be the objective function. This is the current trail residual vector. This is the initial state correction amount. It is a partial derivative matrix. This is the weight matrix.
9. A computer device, comprising a memory and a processor, characterized in that, The memory stores a computer program, and when the processor executes the computer program, it implements the steps of the satellite precise orbit determination method based on track error as described in any one of claims 1 to 5.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the satellite precise orbit determination method based on track error as described in any one of claims 1 to 5.