Satellite orbit forecasting method and device considering maneuvering acceleration

Abstract

The invention discloses a satellite orbit forecasting method and device considering maneuvering acceleration, and belongs to the field of communication navigation remote sensing, and the method comprises the steps: carrying out the initial value calculation of a satellite orbit before orbit maneuvering, and obtaining an initial value calculation result; the initial value calculation result comprises six Kepler numbers at an initial moment and a sunlight pressure parameter; taking the orbit maneuvering acceleration as a random pulse, and introducing the random pulse and the initial value resolving result into a motion equation to obtain a simplified motion equation considering the maneuvering acceleration; wherein the starting moment, the ending moment and the numerical value of the orbit maneuvering acceleration are known parameters; the starting and ending moments determine the width of the random pulse; and performing numerical integration on the simplified motion equation under the constraint of a plurality of perturbative force models to obtain a satellite orbit forecasting result subjected to simplified dynamic constraint at any moment. According to the method, the track forecasting precision and the calculation load can be effectively balanced, and efficient and high-precision track forecasting is realized.

Description

Technical Field

[0001] The present invention belongs to the field of communication, navigation and remote sensing, and in particular relates to a satellite orbit prediction method and device taking maneuvering acceleration into consideration. Background Art

[0002] Satellite orbit prediction is crucial for spacecraft operations and constellation configuration maintenance. High-precision predicted satellite orbits provide accurate parameters for ground data transmission stations and ground tracking and control stations, reducing the resource burden on ground stations tracking satellites. Furthermore, ground tracking and control stations can use these high-precision orbit predictions to rationally plan and reduce unnecessary satellite maneuvers, thereby avoiding intersatellite collisions and interference and extending satellite service life.

[0003] During satellite orbital operations, atmospheric drag and other perturbations can cause the satellite's orbit to deviate from its intended trajectory, necessitating maneuvers to maintain the satellite's orbit. During and after orbital maneuvers, ground stations are also required to track the satellite and transmit data. Therefore, high-precision orbit prediction that takes into account orbital maneuvers is essential. A common approach involves incorporating a maneuver model into the orbit determination model, incorporating thrust magnitude and direction, and utilizing measurement data from maneuvers to determine and predict the orbit. Alternatively, numerical dynamics integration or simplified polynomials can be used for orbit prediction.

[0004] While orbit determination and prediction using measured data during maneuvers is generally highly accurate, its accuracy is affected by the volume and quality of the data measured during the maneuver, resulting in slower timeliness. Prediction using dynamic numerical integration involves calculating multiple perturbations, resulting in high accuracy but a high computational load. Orbit prediction using simplified polynomials is fast but limited in accuracy. Therefore, an efficient and highly accurate orbit prediction solution is urgently needed. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a satellite orbit prediction method and device taking maneuvering acceleration into consideration.

[0006] The technical problem to be solved by the present invention is achieved through the following technical solutions: A satellite orbit prediction method considering maneuvering acceleration includes: Performing an initial value solution on the satellite orbit before the orbital maneuver to obtain an initial value solution result; the initial value solution result includes six Kepler roots and a solar pressure parameter at an initial moment; The orbital maneuver acceleration is used as a random pulse and introduced into the motion equation together with the initial value solution result to obtain a simplified motion equation that takes the maneuver acceleration into account; wherein the start and end times and values ​​of the orbital maneuver acceleration are known parameters; the start and end times determine the width of the random pulse; The simplified motion equation is numerically integrated under the constraints of multiple perturbation dynamic models to obtain a satellite orbit prediction result under simplified dynamic constraints at any time.

[0007] Optionally, when the orbital maneuvering acceleration is introduced into the motion equation as a random pulse together with the initial value solution result, the step size of the motion equation is changed as the width of the random pulse changes.

[0008] Optionally, the step size of the motion equation is varied as the width of the random pulse varies, comprising: When the width of the random pulse is less than 3 minutes, the step length of the motion equation is set to be equal to the width of the random pulse; When the width of the random pulse is greater than 3 minutes, the step size of the motion equation is set to be equal to the maximum divisor or approximate value of the width of the random pulse within 3 minutes.

[0009] Optionally, the multiple perturbation force models include: gravity field model, N-body perturbation, solid tide, ocean tide, earth rotation parameters, precession model and nutation model.

[0010] The present invention also provides a satellite orbit prediction device taking into account maneuvering acceleration, comprising: An initial value solution module is used to perform an initial value solution on the satellite orbit before the orbital maneuver to obtain an initial value solution result; the initial value solution result includes the six Kepler roots and the solar pressure parameter at the initial moment; Simplified motion equation; the simplified motion equation is a motion equation that takes maneuvering acceleration into account, obtained by introducing orbital maneuvering acceleration as a random pulse together with the initial value solution result; The orbit prediction module is used to numerically integrate the simplified motion equation under the constraints of multiple perturbation dynamic models to obtain the satellite orbit prediction result under the simplified dynamic constraints at any time.

[0011] Optionally, when the orbital maneuvering acceleration is introduced into the motion equation as a random pulse together with the initial value solution result, the step size of the motion equation is changed as the width of the random pulse changes.

[0012] Optionally, the step size of the motion equation is varied as the width of the random pulse varies, comprising: When the width of the random pulse is less than 3 minutes, the step length of the motion equation is set to be equal to the width of the random pulse; When the width of the random pulse is greater than 3 minutes, the step size of the motion equation is set to be equal to the maximum divisor or approximate value of the width of the random pulse within 3 minutes.

[0013] Optionally, the multiple perturbation force models include: gravity field model, N-body perturbation, solid tide, ocean tide, earth rotation parameters, precession model and nutation model.

[0014] The present invention provides a satellite orbit prediction method that takes maneuver acceleration into account. The method performs an initial value calculation on the satellite orbit before the orbital maneuver, obtaining six Kepler roots and a solar pressure parameter as the initial value solution results. The orbital maneuver acceleration is then used as a random pulse and introduced into the equation of motion along with the initial value solution results to obtain a simplified equation of motion that takes into account the maneuver acceleration. The simplified equation of motion is then numerically integrated under the constraints of multiple perturbation force models to obtain a satellite orbit prediction result under simplified dynamic constraints at any time, achieving high-precision simplified dynamic fitting and prediction. The present invention does not require the use of measurement data during the maneuver for orbit determination and prediction, thus having high timeliness. Secondly, compared to the prior art that uses dynamic numerical integration to predict multiple perturbations, the present invention simplifies the equation of motion and then numerically integrates the simplified equation of motion to achieve orbit prediction, effectively balancing orbit prediction accuracy and computational load. This significantly reduces the amount of computation while maintaining high accuracy, achieving efficient and high-precision orbit prediction.

[0015] The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 1 is a flow chart of a satellite orbit prediction method taking maneuvering acceleration into account provided by an embodiment of the present invention; Figure 2 The figure is a schematic structural diagram of a satellite orbit prediction device taking maneuvering acceleration into consideration provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0017] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0018] In order to achieve efficient and high-precision orbit prediction, the embodiment of the present invention provides a satellite orbit prediction method taking into account maneuvering acceleration, such as Figure 1 As shown, the method includes the following steps: S10. Performing an initial value solution on the satellite orbit before the orbital maneuver to obtain an initial value solution result; the initial value solution result includes six Kepler roots and a solar pressure parameter at the initial moment.

[0019] Specifically, the initial value of the satellite orbit before the orbital maneuver is calculated by fitting and solving the satellite's motion equations. The least squares method can be used to solve the six Kepler roots and the solar pressure parameter at the initial time. Here, the initial time refers to the initial time within the measurement interval before the orbital maneuver.

[0020] The satellite's motion equation is expanded in the J2000.0 coordinate system as follows: ; ; ; ; in, is the satellite's position vector, for A partial derivative with respect to time, for Second partial derivative with respect to time. is the gravitational constant, is the number of celestial bodies, Number the celestial bodies. is the mass of the celestial body. is the time variable, represents the initial moment, for After a period of time, is the step size of the equation of motion, for The variable upper limit of , . is the semi-major axis, is the eccentricity, is the orbital inclination, is the right ascension of the ascending node, is the argument of perigee, is the argument of latitude, and the six Kepler root numbers are . There are 9 light pressure parameters, including constant terms, Sin periodic terms and Cos periodic terms in the radial (R), tangential (S) and normal (W) directions. It represents the acceleration of the satellite caused by various perturbation factors. In the above motion equation, various perturbation factors include . For the initial moment The satellite's position vector, for A partial derivative with respect to time.

[0021] S20. The orbital maneuvering acceleration is taken as a random pulse and introduced into the motion equation together with the initial value solution result to obtain a simplified motion equation taking into account the maneuvering acceleration.

[0022] A random pulse is a mathematical concept used to simulate instantaneous, random disturbances, typically manifesting as random forces or momentum changes applied over a short period of time. The core idea is to approximate the uncertainty or noise effects in real systems through discrete random shocks. In this paper, orbital maneuver acceleration is treated as a random pulse, with its start and end times and value as known parameters. This pulse, along with the initial value solution, is introduced into the equation of motion, resulting in a simplified equation of motion that accounts for maneuver acceleration. Its expansion in the J2000.0 coordinate system is as follows: ; ; ; ; in, are the orbital maneuver accelerations in radial, tangential and normal directions respectively. Note that in the simplified motion equations proposed in this invention, the accelerations caused by the various perturbation factors affecting the satellite are In addition to being Affected by The meanings of the remaining parameters refer to the above.

[0023] In the present invention, when the orbital maneuver acceleration is introduced into the motion equation as a random pulse, it can be introduced into the motion equation based on the known orbital maneuver start and end times, so that acceleration correction can be performed in the predetermined direction and arc segment. Here, the orbital maneuver start and end times determine the width of the random pulse. Assuming that the orbital maneuver start and end times are 、 , then the width of the random pulse is to This period of time.

[0024] Preferably, when the orbital maneuvering acceleration is introduced into the motion equation as a random pulse together with the initial value solution result, the step size of the motion equation can be changed as the width of the random pulse changes.

[0025] It can be understood that the step size of the motion equation reflects the minimum characteristic time scale of the dynamic system. Changing the step size of the motion equation with the width of the random pulse can optimize the program running time while ensuring the accuracy of orbit prediction.

[0026] Exemplarily, in one implementation, varying the step length of the motion equation with the width of the random pulse may include: when the width of the random pulse is less than 6 minutes, varying the step length of the motion equation equal to the width of the random pulse; and when the width of the random pulse is greater than 6 minutes, varying the step length of the motion equation equal to the maximum divisor or approximate value of the width of the random pulse within 6 minutes. This process is expressed as follows: ; in, is the pulse width of orbital maneuver acceleration, is the maximum divisor or approximate value of the pulse width of orbital maneuver acceleration within 6 minutes, is a set of positive integers whose element values ​​satisfy .

[0027] In another implementation, varying the step length of the motion equation with the width of the random pulse may include: when the width of the random pulse is less than 3 minutes, varying the step length of the motion equation equal to the width of the random pulse; and when the width of the random pulse is greater than 3 minutes, varying the step length of the motion equation equal to the maximum divisor or approximate value of the width of the random pulse within 3 minutes. This process is expressed as follows: ; It should be noted that the criteria for determining whether the step size of the equation of motion is equal to the width of the random pulse is not limited to the 3 minutes or 6 minutes shown above. In practice, it can be optimized and adjusted based on the final satellite orbit prediction results. The inventors of the present invention have discovered through experiments that using 3 minutes as the basis for determining whether the step size of the equation of motion is equal to the width of the random pulse produces more stable experimental results than using 6 minutes. In other words, the final satellite orbit prediction results obtained based on this method can be more accurate and stable.

[0028] S30. Numerically integrate the simplified motion equations under the constraints of multiple perturbation dynamic models to obtain satellite orbit prediction results under simplified dynamic constraints at any time.

[0029] The multiple perturbation models here include: gravity field model, N-body perturbation, earth tide, ocean tide, Earth rotation parameters, precession model, and nutation model. Of course, the solar pressure parameters and orbital maneuver acceleration included in the initial value solution also belong to the perturbation model.

[0030] For example, each perturbation force model may be set with reference to Table 1, but is certainly not limited thereto.

[0031] Table 1

[0032] In step S30, the Collocation multi-step method can be used to numerically integrate the simplified motion equation, and finally obtain the predicted orbit at any time in the integration interval, that is, the satellite orbit prediction result under simplified dynamic constraints at any time.

[0033] In summary, the present invention proposes an orbit prediction method that takes orbital maneuver acceleration into account. This method is based on simplified dynamics, and introduces orbital maneuver acceleration as a random pulse into the motion equation for numerical integration, thereby achieving efficient and high-precision orbit prediction that takes orbital maneuver acceleration into account. Specifically, the present invention performs an initial value solution on the satellite orbit before the orbital maneuver, obtains 6 Kepler roots and solar pressure parameters as the initial value solution results, and then introduces the orbital maneuver acceleration as a random pulse together with the initial value solution results into the motion equation to obtain a simplified motion equation that takes maneuver acceleration into account. The simplified motion equation is then numerically integrated under the constraints of multiple perturbation force models, and the satellite orbit prediction result constrained by simplified dynamics at any time can be obtained, thereby achieving high-precision simplified dynamic fitting and prediction. Among them, the present invention does not need to use the measurement data during the maneuver for orbit determination and prediction, so it has high timeliness. Secondly, compared with the existing technology that uses dynamic numerical integration to predict the orbit, which involves the calculation of various perturbations, the present invention simplifies the motion equations and then numerically integrates the simplified motion equations to achieve orbit prediction. It can effectively balance the orbit prediction accuracy and computational load, greatly reducing the amount of calculation while maintaining high accuracy, and achieving efficient and high-precision orbit prediction.

[0034] In order to verify the effectiveness of the present invention, the inventors selected the Sentinel-3B satellite for testing on February 16, 2023. The satellite's maneuvering arc on that day was 10:34:46.000-10:35:14.000, during which its acceleration in the radial, tangential, and normal directions was constant at 0.17931071×10 -7 km / s 2 (kilometers per second squared), 0.60405877×10 -6 km / s 2 、-0.11236769×10 -7 km / s 2 Using the satellite's precise satellite orbit and orbital maneuver acceleration for a total of 3 hours from 07:00 to 10:00 on February 16, 2023, an orbit prediction was performed starting at 10:00 on February 16, 2023. The differences between the satellite orbit prediction results and the actual precise satellite orbit 1 hour, 3 hours, 6 hours, 12 hours, and 24 hours after the maneuver are shown in Table 2: Table 2

[0035] In Table 2, 3D RMS stands for three-dimensional root mean square, which is used to quantify the overall magnitude of error, noise, or bias in three-dimensional space. It combines errors in three orthogonal directions (such as the X, Y, and Z axes) into a comprehensive metric and is widely used in the navigation field. The data in Table 2 demonstrates that the satellite orbits predicted using the method of the present invention have high accuracy.

[0036] The method provided in the embodiments of the present invention can be applied to electronic devices. Specifically, the electronic devices can be desktop computers, portable computers, smart mobile terminals, servers, etc. This is not limited here; any electronic device that can implement the present invention falls within the scope of protection of the present invention.

[0037] Based on the same inventive concept, corresponding to the above-mentioned satellite orbit prediction method considering maneuvering acceleration, the present invention also provides a satellite orbit prediction device considering maneuvering acceleration, such as Figure 2 As shown, the device includes: An initial value calculation module 201 is used to perform an initial value calculation on the satellite orbit before the orbital maneuver to obtain an initial value calculation result; the initial value calculation result includes the six Kepler roots and the solar pressure parameter at the initial moment; Simplified equation of motion 202; the simplified equation of motion is obtained by introducing orbital maneuvering acceleration as a random pulse together with the initial value solution result into the equation of motion, taking maneuvering acceleration into account; The orbit prediction module 203 is used to perform numerical integration on the simplified motion equations under the constraints of multiple perturbation dynamic models to obtain the satellite orbit prediction results under the simplified dynamic constraints at any time.

[0038] Optionally, when the orbital maneuvering acceleration is introduced into the motion equation as a random pulse together with the initial value solution result, the step size of the motion equation is changed as the width of the random pulse changes.

[0039] Optionally, the step size of the equation of motion can be varied with the width of the random pulse, including: When the width of the random pulse is less than 3 minutes, let the step size of the motion equation be equal to the width of the random pulse; When the width of the random pulse is greater than 3 minutes, let the step size of the motion equation be equal to the maximum divisor or approximation of the width of the random pulse within 3 minutes.

[0040] Optionally, multiple perturbation force models include: gravity field model, N-body perturbation, solid tide, ocean tide, earth rotation parameters, precession model and nutation model.

[0041] It should be noted that, for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple. For relevant matters, please refer to the partial description of the method embodiment, and the device embodiment can obtain the same beneficial effects as the method embodiment.

[0042] It should be noted that the terms "first," "second," and the like are used to distinguish similar objects and are not necessarily used to describe a particular order or precedence. It should be understood that the terms used in this manner are interchangeable where appropriate, so that the embodiments of the present invention described herein can be implemented in sequences other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Instead, they are merely examples of devices and methods consistent with some aspects of the present invention.

[0043] In the description of this specification, the reference terms "one embodiment," "some embodiments," "example," "specific example," or "some examples" mean that the specific features or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described can be combined in any suitable manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification.

[0044] Although the present invention is described herein in conjunction with various embodiments, in the process of implementing the claimed invention, those skilled in the art can understand and implement other variations of the disclosed embodiments by viewing the drawings and the disclosed content. In the description of the present invention, the word "comprising" does not exclude other components or steps, "one" or "a" does not exclude multiple situations, and "multiple" means two or more, unless otherwise clearly and specifically defined. In addition, certain measures are recorded in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0045] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, devices (equipment), or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or a combination of software and hardware embodiments, all of which are collectively referred to herein as "modules" or "systems." Furthermore, the present invention may 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 computer program may be stored / distributed in a suitable medium, provided together with other hardware or as part of the hardware, or may be distributed in other forms, such as via the Internet or other wired or wireless telecommunications systems.

[0046] The present invention is described with reference to the flowcharts and / or block diagrams of the methods, apparatus (devices) and computer program products of the embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as the combination of processes and / or blocks in the flowcharts 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, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0047] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0048] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0049] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A satellite orbit prediction method considering maneuvering acceleration, characterized in that: include: Performing an initial value solution on the satellite orbit before the orbital maneuver to obtain an initial value solution result; the initial value solution result includes six Kepler roots and a solar pressure parameter at an initial moment; The orbital maneuver acceleration is used as a random pulse and introduced into the motion equation together with the initial value solution result to obtain a simplified motion equation that takes the maneuver acceleration into account; wherein the start and end times and values ​​of the orbital maneuver acceleration are known parameters; the start and end times determine the width of the random pulse; The simplified motion equation is numerically integrated under the constraints of multiple perturbation dynamic models to obtain a satellite orbit prediction result under simplified dynamic constraints at any time.

2. The satellite orbit prediction method considering maneuvering acceleration according to claim 1, characterized in that: When the orbital maneuvering acceleration is taken as a random pulse and introduced into the motion equation together with the initial value solution result, the step size of the motion equation is changed as the width of the random pulse changes.

3. The satellite orbit prediction method considering maneuvering acceleration according to claim 2, characterized in that: The step size of the motion equation is changed as the width of the random pulse changes, including: When the width of the random pulse is less than 3 minutes, the step length of the motion equation is set to be equal to the width of the random pulse; When the width of the random pulse is greater than 3 minutes, the step size of the motion equation is set to be equal to the maximum divisor or approximate value of the width of the random pulse within 3 minutes.

4. The satellite orbit prediction method considering maneuvering acceleration according to claim 1, characterized in that: The multiple perturbation force models include: gravity field model, N-body perturbation, solid tide, ocean tide, earth rotation parameters, precession model and nutation model.

5. A satellite orbit prediction device taking into account maneuvering acceleration, characterized in that: Includes: An initial value solution module is used to perform an initial value solution on the satellite orbit before the orbital maneuver to obtain an initial value solution result; the initial value solution result includes the six Kepler roots and the solar pressure parameter at the initial moment; Simplified motion equation; the simplified motion equation is a motion equation that takes maneuvering acceleration into account, obtained by introducing orbital maneuvering acceleration as a random pulse together with the initial value solution result; The orbit prediction module is used to numerically integrate the simplified motion equation under the constraints of multiple perturbation dynamic models to obtain the satellite orbit prediction result under the simplified dynamic constraints at any time.

6. The satellite orbit prediction device considering maneuvering acceleration according to claim 5, characterized in that: When the orbital maneuvering acceleration is taken as a random pulse and introduced into the motion equation together with the initial value solution result, the step size of the motion equation is changed as the width of the random pulse changes.

7. The satellite orbit prediction device considering maneuvering acceleration according to claim 6, characterized in that: The step size of the motion equation is changed as the width of the random pulse changes, including: When the width of the random pulse is less than 3 minutes, the step length of the motion equation is set to be equal to the width of the random pulse; When the width of the random pulse is greater than 3 minutes, the step size of the motion equation is set to be equal to the maximum divisor or approximate value of the width of the random pulse within 3 minutes.

8. The satellite orbit prediction device considering maneuvering acceleration according to claim 5, characterized in that: The multiple perturbation force models include: gravity field model, N-body perturbation, solid tide, ocean tide, earth rotation parameters, precession model and nutation model.

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