A fitting method, device and medium for improving ephemeris orbit prediction accuracy based on TLE

Abstract

This invention discloses a fitting method, device, and medium for improving the accuracy of ephemeris orbit prediction based on TLE (Time-Based Echo) data. The method includes: reading the epoch times of a set of TLE elements in chronological order; determining the ephemeris prediction time interval for each TLE element; using the SGP4 / SDP4 analytical model to predict the ephemeris orbit and obtain ephemeris orbit parameters; selecting an orbit perturbation model to predict the original ephemeris orbit and using the least squares principle to estimate the ephemeris orbit parameters; using the estimated ephemeris orbit parameters to predict the ephemeris orbit and outputting the final result. This invention, by fusing TLE data and using the least squares principle to iteratively fit the orbit parameters, effectively reduces the prediction divergence problem caused by model errors (SGP4 / SDP4) and orbit determination errors in TLE data, and significantly improves the accuracy of orbit prediction.

Description

Technical Field

[0001] This invention relates to the field of ephemeris orbit prediction technology, and in particular to a fitting method, device and medium for improving the accuracy of ephemeris orbit prediction based on TLE. Background Technology

[0002] Two-line elements (TLE) are currently the most widely used ephemeris orbital elements. They employ the SGP4 / SDP4 analytical model, which primarily considers the perturbations of Earth's gravitational field, third bodies, and the atmosphere. When using TLE for forecasting, the sources of error are mainly twofold: first, the inherent error of the SGP4 / SDP4 analytical model itself. This model only considers second-order Earth oblateness perturbations, and the atmospheric model used is an exponential atmospheric model. Therefore, the forecast error increases significantly during years with low ephemeris orbital altitudes and high solar activity. Second, errors arising from orbit determination. These errors are caused by a combination of measurement errors from monitoring network equipment and model errors during the orbit determination process, and cannot be removed. Due to these errors, applications in scenarios requiring high ephemeris orbital accuracy (such as collision warning and remnant prediction) are limited.

[0003] Invention application No. 202310396010.0 discloses a method for predicting Starlink satellite orbits in a continuous maneuvering state based on TLE data. This method can achieve Starlink satellite orbit prediction in a continuous maneuvering state with dual-parameter compensation for orbital altitude and time offset, thus improving the orbit prediction accuracy of TLE data. However, this method also suffers from the following problems: errors inherent in the SGP4 / SDP4 analytical model itself, and insufficient consideration of Earth's oblateness perturbation.

[0004] Therefore, in order to improve the accuracy of TLE predictions, a fitting method based on TLE to improve the accuracy of ephemeris orbit predictions is needed. Summary of the Invention

[0005] To address the aforementioned problems, the present invention aims to provide a fitting method, device, and medium for improving the accuracy of ephemeris orbit prediction based on TLE, reducing the prediction divergence problem caused by model errors and orbit determination errors in TLE data, and improving orbit prediction accuracy.

[0006] This invention provides a fitting method, device, and medium for improving the accuracy of ephemeris orbit prediction based on TLE.

[0007] First aspect: A fitting method based on TLE to improve the accuracy of ephemeris orbit prediction, including:

[0008] S1. Select a target set of TLE roots and read the epoch times of this set of TLE roots in order of time;

[0009] S2. Based on the epoch time, determine the ephemeris prediction time interval for each TLE root;

[0010] S3. Use the SGP4 / SDP4 analytical model to predict ephemeris orbits and obtain ephemeris orbit parameters;

[0011] S4. Select an orbital perturbation model to predict the original ephemeris orbit, and use the least squares principle to estimate the ephemeris orbit parameters;

[0012] S5. Use the estimated ephemeris orbit parameters to predict the ephemeris orbit and output the final result.

[0013] Furthermore, the formula for determining the ephemeris prediction time interval for each TLE root is expressed as follows:

[0014] [(t1-t2) / 2+t1, (t2-t1) / 2+t1],

[0015] [(t2-t1) / 2+t1, (t3-t2) / 2+t2],

[0016] ...

[0017] [(t n-1 -t n-2 ) / 2+t n-2 ,(t n -t n-1 ) / 2+t n-1 ],

[0018] [(t n -t n-1 ) / 2+t n-1 ,(t n -t n-1 ) / 2+t n (1)

[0019] Among them, (t) i (i = 1, 2, ..., N) represents the epoch of the i-th TLE root.

[0020] Furthermore, the orbital perturbation model considers parameters such as Earth's non-spherical perturbation, solid tide perturbation, atmospheric drag perturbation (used for low-Earth orbit targets), lunar and solar gravitational perturbation, and solar radiation pressure perturbation (used for medium- and high-Earth orbit targets).

[0021] Furthermore, the estimation of ephemeris orbital parameters using the least squares principle is expressed by the following formula:

[0022] Δx j =(G T G) -1 G T ν j (2)

[0023] x kj+1 =x kj +Δx kj (3)

[0024] Where j is the number of ephemeris orbital parameters, Δx j Let G be the orbital correction for j parameters, G be the parameter differentiation matrix, k be the iteration number, and ν be the orbital correction for j parameters. j The ephemeris orbital residuals of the SGP4 / SDP4 analytical model and the orbital perturbation model when there are j parameters.

[0025] Furthermore, the ephemeris orbital residual ν of the SGP4 / SDP4 analytical model and the orbital perturbation model with j parameters... j The formula is expressed as:

[0026]

[0027] Where, ρ c To predict the original ephemeris orbit using a perturbation model, ρ o The ephemeris orbit is predicted by the SGP4 / SDP4 analytical model, where j is the number of ephemeris orbit parameters.

[0028] Furthermore, the parameter differentiation matrix G is expressed by the formula:

[0029]

[0030] The parameters in the parametric derivative matrix include the semi-major axis a of the ephemeris orbit, eccentricity e, inclination i, right ascension of the ascending node Ω, argument of perigee ω, and mean perigee M.

[0031] Furthermore, the parameter differentiation matrix G also includes the atmospheric drag coefficient, expressed by the formula:

[0032]

[0033] Among them, C D This is the atmospheric drag coefficient.

[0034] Second aspect: An electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, performs the steps of the method provided in the first aspect.

[0035] Third aspect: A non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method provided in the first aspect.

[0036] The beneficial effects of this invention are:

[0037] 1. This invention effectively reduces the forecast divergence caused by model errors (SGP4 / SDP4) and orbit determination errors in TLE data by fusing TLE data and using the least squares principle to iteratively fit orbit parameters. It is applicable to complex scenarios such as low-Earth orbit targets and years of high solar activity, and significantly improves orbit forecast accuracy.

[0038] 2. This invention dynamically selects the perturbation model based on the target orbital altitude (e.g., introducing atmospheric drag for low orbits and considering light pressure perturbation for medium and high orbits), specifically addressing the perturbation effects under different orbital environments, improving the universality, accuracy, and reliability of the method, and enhancing the model's adaptability.

[0039] 3. The method of this invention is based on publicly available TLE data and analytical models (SGP4 / SDP4), without relying on additional observation data or complex numerical integration. The program is simple to write and has low computational resource requirements, making it highly valuable for engineering applications. It is also simple and efficient to implement in engineering.

[0040] 4. This invention simultaneously compensates for inherent model errors (such as insufficient Earth oblateness order and simplification of atmospheric models) and orbit determination process errors. It systematically optimizes orbital elements through parameter estimation iteration, improves long-term forecast stability, and achieves collaborative optimization of multiple error sources.

[0041] 5. The improved forecast results of this invention can effectively support high-precision scenarios such as collision warning and impact prediction, make up for the limitations of direct forecasting with traditional TLE data, and expand the application scope of TLE data in professional fields.

[0042] 6. This invention adjusts the matrix dimension (e.g., by introducing an atmospheric drag coefficient C). D It can flexibly expand the solution parameters to adapt to the refined modeling needs under different perturbation conditions, and reserves interfaces for subsequent algorithm upgrades, thus improving the parameter expansion capability. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating the fitting method for improving the accuracy of ephemeris orbit prediction based on TLE according to the present invention.

[0044] Figure 2 This is a flowchart illustrating the principle of the fitting method for improving the accuracy of ephemeris orbit prediction based on TLE in this invention.

[0045] Figure 3 This is a schematic diagram of the structure of the electronic device of the present invention. Detailed Implementation

[0046] Embodiments of the present invention are described in detail below. Examples of these embodiments are illustrated in the accompanying drawings, wherein the same or similar symbols denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0047] Currently, when using TLE forecasts, the SGP4 / SDP4 analytical model is employed. However, the forecast error increases significantly during years with low ephemeris orbital altitudes and high solar activity, and the model will contain orbit determination errors during the orbit determination process.

[0048] To address the aforementioned problems, this invention provides a fitting method based on TLE to improve the accuracy of ephemeris orbit prediction. Figure 1 This is a flowchart illustrating the fitting method for improving ephemeris orbit prediction accuracy based on TLE, provided in an embodiment of the present invention. Figure 2 The following is a flowchart illustrating the principle of the fitting method provided in this embodiment of the invention. The method includes:

[0049] S1. Select a target set of TLE roots, sort them by time, and read the epoch time of this set of TLE roots.

[0050] Two-Line Element Set (TLE) is a standardized data format used to describe the ephemeris and orbit of artificial satellites or space targets. It is widely used in ephemeris and orbit prediction, collision warning, and reentry prediction.

[0051] TLE elements are published by NORAD and generated based on tracking data of space targets from its global surveillance network. TLE elements use the SGP4 / SDP4 analytical model to predict ephemeris orbits and are applicable to targets such as near-Earth ephemeris orbits (LEO), medium Earth ephemeris orbits (MEO), and geosynchronous ephemeris orbits (GEO).

[0052] The key parameters for TLE elements include the epoch time and the number of orbital elements, among which:

[0053] Epichronous time: The reference time point for TLE roots, usually the time of the most recent observation or update.

[0054] The orbital elements include: semi-major axis *a*, calculated through average motion, describing the size of the ephemeris orbit; eccentricity *e*, describing the shape of the ephemeris orbit (circle or ellipse); inclination *i*, the angle between the ephemeris orbital plane and the equatorial plane; right ascension of the ascending node *Ω*, the angle between the ascending node and the vernal equinox; argument of perigee *ω*, the angle between perigee and the ascending node; mean perigee *M*, describing the target's position on the ephemeris orbit; and atmospheric drag coefficient *C*. D This describes atmospheric drag corrections for low-Earth orbit targets, etc.

[0055] Select a spatial target, download the TLE root sequence within a certain time range from the TLE root release website, represented as: (TLE1, TLE2, TLE3, ..., TLE) N ).

[0056] Then, read the epoch of this set of TLE roots:

[0057] Using the format of TLE roots (publicly available information in the industry, not detailed here), the epoch time of each TLE root is parsed out, represented as (t i (i = 1, 2, ..., N).

[0058] S3. Based on the epoch time, determine the ephemeris prediction time interval for each TLE root.

[0059] The formula is expressed as:

[0060]

[0061] Among them, (t) i (i = 1, 2, ..., N) represents the epoch of the i-th TLE root.

[0062] S4. Use the SGP4 / SDP4 analytical model to predict ephemeris orbits and obtain ephemeris orbit parameters.

[0063] The SGP4 / SDP4 analytical models are classic analytical models for ephemeris orbit prediction, widely used in the calculation of space target ephemeris orbits based on TLE (Two-Line Element Set) elements. The SGP4 model is suitable for near-Earth ephemeris orbit (LEO) targets with an ephemeris orbit period of less than 225 minutes, while the SDP4 model is suitable for medium Earth ephemeris orbit (MEO) and geosynchronous ephemeris orbit (GEO) targets with an ephemeris orbit period of more than 225 minutes.

[0064] When using the SGP4 / SDP4 analytical model to predict ephemeris orbits, if the boundary points of the ephemeris prediction time intervals are repeated, the later ones will cover the earlier ones.

[0065] The ephemeris orbit generated by the SGP4 / SDP4 model based on the ephemeris time interval forecast is denoted as ρ. o .

[0066] S5. Select an orbital perturbation model to predict the original ephemeris orbit, and use the least squares principle to estimate the ephemeris orbit parameters.

[0067] A suitable orbital perturbation model is selected based on the ephemeris orbital altitude. The orbital perturbation model mainly considers factors such as the Earth's non-spherical perturbation, solid tide perturbation, atmospheric drag perturbation (used for low-Earth orbit targets), gravitational perturbation of the Sun and Moon, and solar radiation pressure perturbation (used for medium- and high-Earth orbit targets).

[0068] Using the orbital perturbation model, the predicted original ephemeris orbit is denoted as ρ. c .

[0069] Linear equations can be formed:

[0070]

[0071] In the formula, x is the orbital parameter, Δx is the correction amount of the initial value, and j is the number of orbital parameters.

[0072] Transform the original orbit to ρ o Calculate the difference in the coordinate system in which it is located, and denote it as the residual ν:

[0073] ν=ρ o -ρ c (4.2)

[0074] Therefore, equation (4.1) can be written as:

[0075] ν j =GΔx j (4.3)

[0076] Formation ν j expression:

[0077]

[0078] in

[0079]

[0080] Formula (5) is the parametric derivative matrix with m equal to 1. If ρ o The number of elements is m, and G is a 6m×6 matrix (this is the number of matrices without solving other parameters). The partial derivatives in the G matrix include the semi-major axis a of the ephemeris orbit, the eccentricity e, the inclination i, the right ascension of the ascending node Ω, the argument of perigee ω, and the mean perigee M.

[0081] If we calculate the atmospheric drag coefficient C D Then G is a 6m×7 matrix, expressed by the formula:

[0082]

[0083] Among them, C D This is the atmospheric drag coefficient; other cases are similar.

[0084] According to the least squares principle, we can obtain:

[0085] Δx j =(G T G) -1 G T ν j (2)

[0086] The optimal parameter correction, G, is obtained by minimizing the sum of squared residuals. T G is an n×n matrix (n is the number of parameters, such as 6 or 7). T If v is an n×1 vector, then:

[0087] x kj+1 =x kj +Δx kj (3)

[0088] j is the number of ephemeris orbital parameters, Δx j Let ν be the orbital correction for j-parameter ephemeris, G be the derivative matrix of the parameters, and ν be the orbital correction for the j-parameter ephemeris. j The orbital residuals of the SGP4 / SDP4 analytical model and the orbital perturbation model when there are j parameters, and k is the number of iterations; the iteration termination condition is: when the maximum number of iterations is reached (e.g., 10 times), it is determined whether the orbital residual value meets the requirements. If it does not meet the requirements, the selected TLE elements are adjusted and recalculated.

[0089] S6. Use the estimated ephemeris orbit parameters to predict the ephemeris orbit and output the final result.

[0090] The orbital parameters are iteratively corrected using the least squares principle, and an orbital perturbation model is employed to output ephemeris orbital predictions and write them to a file.

[0091] The present invention also provides an electronic device, Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention, such as... Figure 3 As shown, the electronic device may include a processor, a communications interface, memory, and a communication bus, wherein the processor, communications interface, and memory communicate with each other via the communication bus. The processor can invoke logical instructions from the memory, for example, to execute the following method:

[0092] S1. Select a target set of TLE roots and read the epoch times of this set of TLE roots in order of time;

[0093] S2. Based on the epoch time, determine the ephemeris prediction time interval for each TLE root;

[0094] S3. Use the SGP4 / SDP4 analytical model to predict ephemeris orbits and obtain ephemeris orbit parameters;

[0095] S4. Select an orbital perturbation model to predict the original ephemeris orbit, and use the least squares principle to estimate the ephemeris orbit parameters;

[0096] S5. Use the estimated ephemeris orbit parameters to predict the ephemeris orbit and output the final result.

[0097] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0098] This invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, is implemented to perform the methods provided in the above embodiments, including, for example:

[0099] S1. Select a target set of TLE roots and read the epoch times of this set of TLE roots in order of time;

[0100] S2. Based on the epoch time, determine the ephemeris prediction time interval for each TLE root;

[0101] S3. Use the SGP4 / SDP4 analytical model to predict ephemeris orbits and obtain ephemeris orbit parameters;

[0102] S4. Select an orbital perturbation model to predict the original ephemeris orbit, and use the least squares principle to estimate the ephemeris orbit parameters;

[0103] S5. Use the estimated ephemeris orbit parameters to predict the ephemeris orbit and output the final result.

[0104] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0105] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0106] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fitting method for improving the accuracy of ephemeris orbit prediction based on TLE, characterized in that, include: S1. Select a target set of TLE roots and read the epoch times of this set of TLE roots in order of time; S2. Based on the epoch time, determine the ephemeris prediction time interval for each TLE root; S3. Use the SGP4 / SDP4 analytical model to predict ephemeris orbits and obtain ephemeris orbit parameters; S4. Select an orbital perturbation model to predict the original ephemeris orbit, and use the least squares principle to estimate the ephemeris orbit parameters; S5. Use the estimated ephemeris orbit parameters to predict the ephemeris orbit and output the final result; The orbital perturbation model takes into account factors such as the Earth's non-spherical shape perturbation, solid tides and ocean tides, atmospheric drag perturbation, gravitational perturbation by the Sun and Moon, and solar radiation pressure perturbation. The formula for ephemeris orbit parameter estimation using the least squares principle is as follows: （2） （3） in, The number of ephemeris orbital parameters. For j parameters, the ephemeris orbital correction amount Find the derivative matrix for the parameters. For the number of iterations, The ephemeris orbital residuals of the SGP4 / SDP4 analytical model and the orbital perturbation model when there are j parameters; SGP4 / SDP4 analytical model and orbital perturbation model ephemeris orbital residuals with j parameters The formula is expressed as: （4） in, To predict the original ephemeris orbit for the perturbation model, Predicting ephemeris orbits using the SGP4 / SDP4 analytical model. This represents the number of ephemeris orbital parameters.

2. The fitting method according to claim 1, characterized in that, The formula for determining the ephemeris prediction time interval for each TLE root is expressed as follows: （1） in, Let be the epoch of the i-th TLE root.

3. The fitting method according to claim 1, characterized in that, The derivative matrix G of the parameters is expressed by the following formula: （5） The derivative parameters in the parametric derivative matrix include the semi-major axis of the ephemeris orbit. eccentricity ,inclination Right ascension of ascending node Perigeal argument , and the near point angle .

4. The fitting method according to claim 3, characterized in that, The parameter derivative matrix G also includes the atmospheric drag coefficient, expressed by the formula: （6） in, This is the atmospheric drag coefficient.

5. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the fitting method as described in any one of claims 1 to 4.

6. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the fitting method as described in any one of claims 1 to 4.

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