TLE-based fitting method and equipment for improving ephemeris orbit prediction precision, and medium

Abstract

The invention discloses a TLE-based fitting method and device for improving ephemeris orbit prediction precision, and a medium. The method comprises the following steps: reading epoch moments of a group of TLE elements according to a time sequence; determining an ephemeris forecast time interval of each TLE element; performing ephemeris orbit forecasting by using the SGP4 / SDP4 analytical model to obtain ephemeris orbit parameters; selecting an orbit perturbation model to forecast an original ephemeris orbit, and performing ephemeris orbit parameter estimation by using a least square principle; and performing ephemeris orbit forecasting by using the estimated ephemeris orbit parameters and outputting a final result. According to the method, TLE data are fused, iteration fitting is carried out on the orbit parameters through the least square principle, the problem of prediction divergence caused by model errors (SGP4 / SDP4) and orbit determination errors of the TLE data is effectively solved, and the orbit prediction precision is remarkably improved.

Description

Technical Field

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

[0002] The Two-Line Elements (TLE) is a currently widely used type of ephemeris orbit elements. The ephemeris orbit model it adopts is the SGP4 / SDP4 analytical model, and the model mainly considers the perturbation effects of the Earth's gravitational field, third bodies, and the atmosphere, etc. When using TLE for prediction, there are mainly two sources of prediction errors: one is the error of the SGP4 / SDP4 analytical model itself. This model only considers the second-order Earth oblateness perturbation, and the atmosphere model also uses the exponential atmosphere model. Therefore, the prediction error will increase significantly when the ephemeris orbit altitude is low and in the high solar activity years; the other is the error generated by orbit determination, which is jointly caused by the measurement error of the monitoring network equipment and the model error in the orbit determination process and cannot be removed. Due to the existence of the above errors, it restricts the application of some scenarios that require high ephemeris orbit accuracy (such as collision warning, fall prediction, etc.).

[0003] The invention application with the application number 202310396010.0 discloses a method for predicting the orbit of Starlink satellites in a continuously maneuvering state based on TLE data. Using this solution, it is possible to realize the prediction of the orbit of Starlink satellites in a continuously maneuvering state with dual-parameter compensation of orbit altitude and time offset, and the orbit prediction accuracy of TLE data can be improved. However, there are also problems in its solution: the problem of the error of the SGP4 / SDP4 analytical model itself, and the problem of not fully considering the Earth oblateness perturbation.

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

[0005] Aiming at the above existing problems, the purpose of the present invention is to provide a fitting method, device and medium for improving the accuracy of ephemeris orbit prediction based on TLE, reduce the problem of prediction divergence caused by model error and orbit determination error of TLE data, and improve the orbit prediction accuracy.

[0006] The embodiments of the present invention provide a fitting method, device and medium for improving the accuracy of ephemeris orbit prediction based on TLE.

[0007] First aspect: A fitting method for improving the accuracy of ephemeris orbit prediction based on TLE, comprising:

[0008] S1. Select a group of target TLE elements, and read the epoch time of this group of TLE elements in time order;

[0009] S2. Determine the ephemeris prediction time interval for each set of TLE elements based on the epoch time;

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

[0011] S4. Select an orbit 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 perform ephemeris orbit prediction and output the final result.

[0013] Further, the formula for determining the ephemeris prediction time interval for each set of TLE elements is expressed as:

[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] where (t i , i = 1, 2,..., N) is the epoch time of the i-th set of TLE elements.

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

[0021] Further, the formula for using the least squares principle to estimate the ephemeris orbit parameters is expressed as:

[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 orbit parameters, and Δx j is the ephemeris orbit correction of j parameters, G is the parameter derivative matrix, k is the number of iterations, and ν j is the ephemeris orbit residual between the SGP4 / SDP4 analytical model and the orbit perturbation model when there are j parameters.

[0025] Furthermore, the ephemeris orbit residual ν between the SGP4 / SDP4 analytical model and the orbit perturbation model when there are j parameters j , is expressed by the formula:

[0026]

[0027] where ρ c is the predicted original ephemeris orbit of the perturbation model, ρ o is the predicted ephemeris orbit of the SGP4 / SDP4 analytical model, and j is the number of ephemeris orbit parameters.

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

[0029]

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

[0031] Furthermore, the parameters of the parameter derivative matrix G also include the atmospheric drag coefficient, which is expressed by the formula:

[0032]

[0033] where C D is the atmospheric drag coefficient.

[0034] Second aspect: An electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps of the method provided in the first aspect are implemented.

[0035] Third aspect: A non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the method provided in the first aspect are implemented.

[0036] Advantageous effects of the present invention:

[0037] 1. The present invention effectively reduces the problem of forecast divergence of TLE data caused by model errors (SGP4 / SDP4) and orbit determination errors by fusing TLE data and performing iterative fitting on orbit parameters using the least squares principle. It is applicable to complex scenarios such as low-earth orbit targets and high solar activity years, and significantly improves the orbit forecast accuracy.

[0038] 2. The present invention dynamically selects perturbation models according to the target orbit altitude (such as introducing atmospheric drag for low-earth orbits and considering radiation pressure perturbation for medium and high orbits), specifically solves the perturbation effects in different orbit environments, improves the universality and accuracy reliability of the method, and enhances the model adaptability.

[0039] 3. The method of the present invention is based on publicly available TLE data and analytical models (SGP4 / SDP4), without relying on additional observational data or complex numerical integration. The program is simple to write and has low computational resource requirements, with high engineering application value and simple and efficient engineering implementation.

[0040] 4. The present invention compensates for both the inherent errors of the model (such as insufficient order of the Earth's oblateness and simplification of the atmospheric model) and the errors in the orbit determination process, systematically optimizes the orbital elements through parameter estimation iteration, improves the long-term forecast stability, and realizes the collaborative optimization of multiple error sources.

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

[0042] 6. The present invention can flexibly expand the solution parameters by adjusting the matrix dimension (for example, introducing the atmospheric drag coefficient C D ), adapt to the refined modeling requirements under different perturbation conditions, reserve an interface for subsequent algorithm upgrade, and improve the parameter expansion ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is a schematic flow chart of the fitting method for improving the ephemeris orbit forecast accuracy based on TLE of the present invention;

[0044] Figure 2 is a schematic principle flow chart of the fitting method for improving the ephemeris orbit forecast accuracy based on TLE of the present invention;

[0045] Figure 3 is a schematic structural diagram of the electronic device of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0046] The following describes embodiments of the present invention in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar symbols throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present invention and are not to be construed as limiting the present invention.

[0047] Currently, when TLE prediction is used, the SGP4 / SDP4 analytical model is used. The prediction error will increase significantly when the ephemeris orbit altitude is low and in years with high solar activity, and the model will have orbit determination errors during the orbit determination process.

[0048] In view of the above problems, the present invention provides a fitting method based on TLE to improve the accuracy of ephemeris orbit prediction. Figure 1 A flow chart of a fitting method for improving the accuracy of ephemeris orbit prediction based on TLE provided in an embodiment of the present invention is provided. Figure 2 The principle flow chart of the fitting method provided in an embodiment of the present invention includes:

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

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

[0051] The TLE element number is published by NORAD and is generated based on tracking data of space targets through its global surveillance network. The TLE element number uses the SGP4 / SDP4 analytical model to predict ephemeris orbits and is applicable to targets such as Low Earth Ephemeris Orbit (LEO), Medium Earth Ephemeris Orbit (MEO), and Geosynchronous Ephemeris Orbit (GEO).

[0052] The key parameters of the TLE elements include the epoch time and the orbital elements, where:

[0053] Epoch time: The reference time point of the TLE element number, usually the time of the most recent observation or update.

[0054] The orbital elements include: semi-major axis a, calculated by the mean motion, describing the size of the ephemeris orbit; eccentricity e, describing the shape of the ephemeris orbit (circular or elliptical); inclination i, the angle between the ephemeris orbit plane and the equatorial plane; right ascension Ω, the angle between the ascending node of the ephemeris orbit and the vernal equinox; argument of perigee ω, the angle between the perigee and the ascending node; mean anomaly M, describing the position of the target on the ephemeris orbit; atmospheric drag coefficient C D , describing the atmospheric drag correction for low-orbit targets, etc.

[0055] Select a space target and download the TLE root number sequence within a certain time range from the TLE root number release website, which is expressed as: (TLE1, TLE2, TLE3, ..., TLE N ).

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

[0057] The format of TLE root number (public content in the industry, no longer detailed here) is used to parse the epoch time of each TLE root number, expressed as (t i ,i=1,2,...,N).

[0058] S3. Determine the ephemeris prediction time interval for each TLE element according to the epoch time.

[0059] The formula is:

[0060]

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

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

[0063] The SGP4 / SDP4 analytical model is a classic analytical model for ephemeris orbit prediction and is widely used in the calculation of ephemeris orbits of space targets based on TLE (Two-LineElementSet) elements. The SGP4 model is suitable for Low 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 greater than 225 minutes.

[0064] When using the SGP4 / SDP4 analytical model for ephemeris orbit prediction, if the boundary points of the ephemeris prediction time interval are repeated, the latter one will overwrite the former one.

[0065] The ephemeris orbit generated by the SGP4 / SDP4 model according to the ephemeris time interval prediction 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] Select a suitable orbit perturbation model according to the ephemeris orbital altitude. The orbit perturbation model mainly considers factors such as the non-spherical perturbation of the Earth, the solid tide and ocean tide perturbation, the atmospheric drag perturbation (for low-orbit targets), the solar and lunar gravitational perturbation, and the solar radiation pressure perturbation (for medium- and high-orbit targets).

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

[0069] A linear equation 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] Convert the original orbit to the coordinate system where ρ o is located and calculate the difference, denoted as the residual ν:

[0073] ν = ρ o - ρ c (4.2)

[0074] Thus, equation (4.1) can be denoted as:

[0075] ν j = GΔx j (4.3)

[0076] Form the ν j expression:

[0077]

[0078] Among them

[0079]

[0080] Formula (5) is the derivative matrix of the parameter when m equals 1. If the number of ρ o is m, G is a 6m×6 matrix (this is the number of matrices in the case of not solving other parameters). The partial derivatives in the G matrix include the semi-major axis a, eccentricity e, inclination i, right ascension of the ascending node Ω, argument of perigee ω, and mean anomaly M of the ephemeris orbit.

[0081] If the atmospheric drag coefficient C D is solved, then G is a 6m×7 matrix, and the formula is expressed as:

[0082]

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

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

[0085] Δx j =(G T G) -1 G T ν j (2)

[0086] By minimizing the residual sum of squares, the optimal parameter correction is obtained, G 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 orbit parameters, Δx j is the j parameter ephemeris orbit correction, G is the parameter derivative matrix, ν j The ephemeris orbit residuals of the SGP4 / SDP4 analytical model and the orbit 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 (such as 10) is reached, it is judged whether the orbit residual value meets the requirements. If not, the number of TLE elements selected is adjusted and recalculated.

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

[0090] The orbit parameters are iteratively corrected using the least squares principle, and the orbit perturbation model is used to output the ephemeris orbit prediction and write it into a file.

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

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

[0093] S2. Determine the ephemeris prediction time interval for each TLE element based on the epoch time;

[0094] S3. Use the SGP4 / SDP4 analytical model to predict the ephemeris orbit and obtain the 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 perform ephemeris orbit prediction and output the final result.

[0097] In addition, the logical instructions in the above-mentioned memory can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art or the part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, and other media that can store program code.

[0098] An embodiment of the present invention further provides a non-transitory computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method provided in each of the above embodiments is implemented, for example, including:

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

[0100] S2. Determine the ephemeris prediction time interval for each TLE element based on the epoch time;

[0101] S3. Use the SGP4 / SDP4 analytical model to predict the ephemeris orbit and obtain the 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 perform ephemeris orbit prediction 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 separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art can understand and implement it without creative work.

[0105] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on such an understanding, the essence of the above technical solution, 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 for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment 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 are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features. And these modifications or replacements do not make the essence of the corresponding technical solutions 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 prediction accuracy of ephemeris orbit based on TLE, characterized in that include: S1. Select a target group of TLE roots and read the epoch time of this group of TLE roots in time order; S2. Determine the ephemeris prediction time interval for each TLE element based on the epoch time; S3. Use the SGP4 / SDP4 analytical model to predict the ephemeris orbit and obtain the 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 perform ephemeris orbit prediction and output the final result.

2. The fitting method according to claim 1, characterized in that The formula for determining the ephemeris prediction time interval for each TLE number is expressed as: Among them, (t i ,i=1,2,...,N) is the epoch time of the i-th TLE root number.

3. The fitting method according to claim 1, characterized in that The orbital perturbation model takes into account the factors of the non-spherical perturbation of the earth, the perturbation of solid tides and ocean tides, the perturbation of atmospheric resistance, the perturbation of the gravitational force of the sun and the moon, and the perturbation of solar light pressure.

4. The fitting method according to claim 1, characterized in that The least squares principle is used to estimate the ephemeris orbit parameters, and the formula is expressed as: Δx j =(G T G) -1 G T ν j (2) x kj+1 = x kj + Δx kj (3) where j is the number of ephemeris orbit parameters, Δx j is the ephemeris orbit correction of j parameters, G is the parameter derivative matrix, k is the number of iterations, ν j is the ephemeris orbit residual between the SGP4 / SDP4 analytical model and the orbit perturbation model when there are j parameters.

5. The fitting method according to claim 4, characterized in that, Ephemeris orbit residuals ν of the SGP4 / SDP4 analytical model and the orbit perturbation model with j parameters j , which is expressed by the formula as follows: where ρ c is the predicted ephemeris orbit of the original satellite by the perturbation model, and ρ o is the predicted ephemeris orbit by the SGP4 / SDP4 analytical model, and j is the number of ephemeris orbit parameters.

6. The fitting method according to claim 1, wherein The parameter derivative matrix G is expressed as follows: Among them, the derivative parameters in the parameter derivative matrix include the semi-major axis a of the ephemeris orbit, the eccentricity e, the inclination i, the right ascension Ω of the ascending node, the argument of perigee ω, and the mean anomaly M.

7. The fitting method according to claim 6, characterized in that The parameter derivative matrix G also includes the atmospheric drag coefficient, which is expressed as follows: Among them, C D is the atmospheric drag coefficient.

8. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, the steps of the fitting method according to any one of claims 1 to 7 are implemented.

9. A non-transitory computer-readable storage medium storing a computer program thereon, characterized in that, When the computer program is executed by a processor, the steps of the fitting method according to any one of claims 1 to 7 are implemented.

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