A Starlink target state estimation method and system based on TLE

Abstract

The present invention provides a method for estimating the state of a Starlink target based on TLE, including obtaining a plurality of consecutive orbital elements of a Starlink target, solving the orbital height of the target at the epoch time, and obtaining a target height sequence; correcting the wild values ​​in the Starlink target height sequence; calculating the height change rate of the target under long and short cycles, and estimating the state of the target based on the height change rate. The advantages of the present invention are: using the orbital elements of consecutive days as input data, the data is easy to obtain, and the target height change rate is calculated by combining short and long cycles, which reduces the misjudgment rate, and can calculate the current state of the Starlink target in real time based on the accumulation of historical data.

Description

Technical Field

[0001] The present invention relates to the field of satellite state prediction technology, and in particular to a Starlink target state estimation method and system based on TLE. Background Art

[0002] In January 2015, SpaceX announced that it would launch a satellite internet broadband access project, the "Starlink" project. Since the launch of the network in May 2019, as of June 30, 2021, SpaceX has sent 1,740 "Starlink" satellites into orbit, and plans to launch about 12,000 satellites into low-Earth orbit by 2024 to build a giant three-layer satellite network. In the longer-term plan, this number will increase to 42,000. These satellites will connect points into lines and weave lines into a network in near-Earth space to create the next generation of satellite networks and lead the Earth into the era of space-based Internet.

[0003] As the number of low-orbit space satellites continues to increase, the risk of space target collisions continues to increase. At the current scale of the number of Starlink targets, Starlink satellites alone are involved in about 1,600 close encounters between spacecraft each week, and Starlink now accounts for half of the total number of encounters. Space target collisions can seriously endanger the safety of satellites and cause a surge in the number of space debris, thereby triggering the "Kessler effect" and causing a cascade reaction of space target collisions. At present, the main working orbit of Starlink targets is at an altitude of 550km, and the parking orbit is at an altitude of 300-400km. These two altitudes are commonly used altitudes for manned space activities and daily operations of space stations. Once a collision occurs, it will have a huge impact on the safe operation of manned spaceflight and space stations.

[0004] In order to achieve early warning of space target collision events, it is necessary to achieve accurate prediction of the target orbit. Some methods for predicting satellite orbits already exist in the prior art, such as a method for determining the orbital state of a GEO satellite through TLE data disclosed in the invention patent application with publication number CN109582029A, which proposes a method for determining the orbit of a satellite through TLE (two-line element) and making anomaly judgments.

[0005] However, Starlink targets have been in a small-scale electric propulsion orbit change state for a long time, so compared with traditional space targets, their orbit stability is poor and the prediction accuracy is low. In addition, since the Starlink target has a long orbit entry process, there is a long climbing and parking stage before orbit entry, and there is an active orbit reduction state after the end of its life. Therefore, in addition to the common working state and failure state, there are three new working states compared to conventional satellites: orbit raising, parking, and active orbit reduction. The traditional cataloging and orbit determination method has good adaptability and high accuracy to targets in the working state and failure state; but it has poor adaptability to targets in other states. In different states, different orbit determination strategies and different orbit determination parameters are needed to obtain better accuracy. Therefore, in order to improve the orbit determination accuracy of Starlink targets, it is necessary to first complete the real-time estimation of the Starlink target state, so as to further realize multiple application fields such as Starlink target cataloging and orbit determination, collision warning, and fall prediction. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a method for completing the altitude solution of the target based on the orbital elements, and then realizing the real-time estimation of the state of the Starlink target.

[0007] The present invention solves the above technical problems through the following technical solutions: a method for estimating a starlink target state based on TLE, comprising:

[0008] Obtain multiple consecutive orbital elements of the Starlink target, solve the orbital altitude of the target at the epoch time, and obtain the target altitude sequence;

[0009] Correction of outliers in the Starlink target altitude sequence;

[0010] The target's altitude change rate in long and short periods is calculated, and the target's state is estimated based on the altitude change rate.

[0011] The present invention uses the orbital elements of multiple consecutive days as input data. The data is easy to obtain and a combination of short and long cycles is used to calculate the target altitude change rate, which reduces the misjudgment rate. The current status of the Starlink target can be calculated in real time based on the accumulation of historical data.

[0012] Preferably, the method for calculating the orbital height of the target is:

[0013] Step i: Arrange the orbital elements in ascending order according to their epoch times to form an orbital element sequence {TLE1, TLE2, TLE3, ..., TLE n};

[0014] Step ii: For the i-th orbital element TLE i , get the epoch time x corresponding to the target i ,

[0015] Step iii: Use the SGP4 algorithm to calculate the TEM coordinates (X i , Y i , Z i ) TEME ;

[0016] Step iv: Transform the TEM coordinates (X i , Y i , Z i ) TEME Converted to the position in WGS84 coordinate system (Lon i , Lat i , Alt i ) WGS84 ;

[0017] Step v: Perform steps ii to iv for each orbital element to obtain the target original height sequence.

[0018] f0=(h1,h2,h3,...,h n )

[0019] Among them, each height point information h i =Alt i , represents the epoch time x i The target altitude value at the moment.

[0020] Preferably, in solving the Starlink target altitude sequence, at least 15 consecutive orbital elements are obtained.

[0021] Preferably, the method for correcting the outliers in the Starlink target altitude sequence includes:

[0022] Step I: Use a second-order polynomial function to calculate the height sequence of the Starlink target f0 = (h1, h2, h3, ..., h n ) is fitted, and the output expression of the second-order polynomial fitting is:

[0023]

[0024] Step II: Calculate the error between the fitting result and the original height sequence. The root mean square function of the error is,

[0025]

[0026] Step III: Using 3δ as the threshold value, the original height sequence is corrected to obtain a new height sequence. The correction function is:

[0027]

[0028] Step IV: Repeat steps I to III for a total of m times and output the corrected height sequence

[0029] Preferably, when correcting the wild values ​​in the Starlink target height sequence, the number of iterations m=3.

[0030] Preferably, the height change rate of each point in the long and short periods is calculated by sliding the window, and the method is:

[0031]

[0032]

[0033] Among them, D L and D S are the step sizes for long and short cycles respectively.

[0034] Preferably, D L =15,D S =3.

[0035] Preferably, the method for estimating the target state based on the height change rate is:

[0036] Step a: Construct the Starlink target state set State∈{active orbit reduction, failure, parking, working, orbit increase} and initialize the cumulative number of failures N Crt =0, i=1;

[0037] Step b: Distinguish the target state based on the target height change rate in a short period.

[0038]

[0039] Among them, R Rise is the altitude change threshold of the ascending orbit, R Decline is the altitude change threshold for active orbit lowering;

[0040] Step c: confirming the failure state of the target based on the height change rate of the target over a long period;

[0041]

[0042] Among them, R Invalid is the height change threshold for failure, N Invalid is the repetition cycle of failure determination;

[0043] Step d: Determine the target state according to the target height by:

[0044]

[0045] Among them, H Workis the height threshold of the working state, is the corrected height value;

[0046] Step e: If i<n, i=i+1, return to step b, otherwise output the target state sequence {State(x i )}.

[0047] The present invention also provides a TLE-based Starlink target state estimation system, comprising:

[0048] The altitude calculation module is used to obtain multiple consecutive orbital elements of the Starlink target, calculate the orbital altitude of the target at the epoch time, and obtain the target altitude sequence;

[0049] Data correction module, used to correct outliers in the Starlink target altitude sequence;

[0050] The state estimation module is used to calculate the target's altitude change rate in long and short periods, and estimate the target's state based on the altitude change rate.

[0051] The advantages of the Starlink target state estimation method and system based on TLE provided by the present invention are: the orbital elements of multiple consecutive days are used as input data, the data is easy to obtain, the target altitude change rate is calculated by combining short and long cycles, the misjudgment rate is reduced, and the current state of the Starlink target can be calculated in real time based on the accumulation of historical data. The sliding window method is used for processing to support the real-time estimation of the Starlink target state; the target altitude sequence cyclic fitting correction method is used to complete the correction of wild value points to avoid singular points from interfering with the target state judgment result; the target altitude change rate is calculated by combining short and long cycles, which not only realizes the timely detection of the two types of maneuvering states, namely orbit raising and active orbit lowering, but also reduces the misjudgment rate of the three types of states, namely failure, working and parking, through long-term accumulation, and realizes the subdivision of the target state. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 A flowchart of a Starlink target state estimation method based on TLE provided in an embodiment of the present invention;

[0053] Figure 2 A workflow diagram of the height solution of the TLE-based Starlink target state estimation method provided by an embodiment of the present invention;

[0054] Figure 3 A workflow diagram of the altitude sequence preprocessing of the TLE-based Starlink target state estimation method provided by an embodiment of the present invention;

[0055] Figure 4 A workflow diagram of state estimation of a Starlink target state estimation method based on TLE provided in an embodiment of the present invention;

[0056] Figure 5 A schematic diagram of the state estimation results of Starlink target 47576 from May 30 to July 8, 2021 using the Starlink target state estimation method based on TLE provided by an embodiment of the present invention;

[0057] Figure 6 A schematic diagram of the state estimation results of Starlink target 47985 from May 30 to July 8, 2021 using the Starlink target state estimation method based on TLE provided by an embodiment of the present invention;

[0058] Figure 7 A schematic diagram of a TLE-based Starlink target state estimation system provided for an embodiment of the present invention. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the technical solution of the present invention is clearly and completely described below in combination with specific embodiments and with reference to the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] like Figure 1 As shown, this embodiment provides a Starlink target state estimation method based on TLE, including:

[0061] Obtain multiple consecutive orbital elements of the Starlink target, solve the orbital altitude of the target at the epoch time, and obtain the target altitude sequence;

[0062] Correction of outliers in the Starlink target altitude sequence;

[0063] The target's altitude change rate in long and short periods is calculated, and the target's state is estimated based on the altitude change rate.

[0064] This embodiment uses the orbital roots of multiple consecutive days as input data. The data is easy to obtain and a combination of short and long cycles is used to calculate the target altitude change rate, which reduces the misjudgment rate. The current status of the Starlink target can be calculated in real time based on the accumulation of historical data.

[0065] Specifically, the Starlink target state estimation method based on TLE provided in this embodiment includes:

[0066] Obtain multiple consecutive orbital elements of the Starlink target, solve the orbital altitude of the target at the epoch time, and obtain the target altitude sequence;

[0067] When performing altitude calculation, at least 3 orbital elements are required. In order to improve the accuracy of calculation and estimation, it is preferred to collect at least 15 consecutive orbital elements. Figure 2 , the method for calculating the orbital height of the target is,

[0068] Step i: Arrange the orbital elements in ascending order according to their epoch times to form an orbital element sequence {TLE1, TLE2, TLE3, ..., TLE n};

[0069] Step ii: For the i-th orbital element TLE i , get the epoch time x corresponding to the target i ,

[0070] Step iii: Use the SGP4 algorithm (Simplified General Perturbations 4) to calculate the TEM coordinates (X i , Y i , Z i ) TEME ;

[0071] Step iv: Set the TEM (True Equator Mean Equinox) coordinate (X i , Y i , Z i ) TEME Converted to the position in WGS84 (World Geodetic System 1984) coordinate system (Lon i , Lat i , Alt i ) WGS84 ;

[0072] Step v: Perform steps ii to iv for each orbital element to obtain the target original height sequence.

[0073] f0=(h1,h2,h3,...,h n )

[0074] Among them, each height point information h i =Alt i Represents the epoch time x i The target altitude value at the moment.

[0075] Correction of outliers in the Starlink target altitude sequence;

[0076] refer to Figure 3 , the method for correcting the wild value adopted in this embodiment includes:

[0077] Step I: Use a second-order polynomial function to calculate the height sequence of the Starlink target f0 = (h1, h2, h3, ..., h n ) is fitted, and the output expression of the second-order polynomial fitting is:

[0078]

[0079] Step II: Calculate the error between the fitting result and the original height sequence. The root mean square function of the error is,

[0080]

[0081] Step III: Using 3δ as the threshold value, the original height sequence is corrected to obtain a new height sequence. The correction function is:

[0082]

[0083] Step IV: Repeat steps I to III for a total of m times. In this embodiment, the number of iterations is preferably set to m=3, and the corrected height sequence is output.

[0084] The target's altitude change rate in long and short periods is calculated, and the target's state is estimated based on the altitude change rate.

[0085] The height change rate of the i-th point in the long and short periods is calculated by sliding the window. The method is:

[0086]

[0087]

[0088] Among them, D L and D S are the step sizes for long and short cycles respectively, preferably set to D L =15,D S =3.

[0089] refer to Figure 4 , the method for estimating the target state based on the height change rate is:

[0090] Step a: Construct the Starlink target state set State∈{active orbit reduction, failure, parking, working, orbit increase} and initialize the cumulative number of failures N Crt =0, i=1;

[0091] Step b: Distinguish the target state based on the target height change rate in a short period.

[0092]

[0093] Among them, R Riseis the altitude change threshold of the ascending orbit, and the preferred value is 3; R Decline is the height change threshold for active orbit lowering, with a preferred value of -1;

[0094] Step c: confirming the failure state of the target based on the height change rate of the target over a long period;

[0095]

[0096] Among them, R Invalid is the failure height change threshold, the preferred value is -0.01; N Invalid is the repetition period of failure determination, the preferred value is 15;

[0097] Step d: Determine the target state according to the target height by:

[0098]

[0099] Among them, H Work is the height threshold of the working state, preferably set to 500, is the corrected height value;

[0100] Step e: If i<n, i=i+1, return to step b, otherwise output the target state sequence {State(x i )}.

[0101] This embodiment uses the orbital elements of multiple consecutive days as input. The orbital elements of the target can be downloaded directly from the Internet or generated through autonomous orbit determination, which is easy to obtain. The sliding window method is used for processing to support real-time estimation of the Starlink target state. The current state of the Starlink target can be calculated in real time based on the accumulation of historical data. The target altitude sequence cyclic fitting correction method is used to complete the correction of outlier points to avoid singular points interfering with the target state judgment result. The target altitude change rate is calculated by combining short and long cycles, which not only realizes the timely detection of the two types of maneuvering states, namely orbit raising and active orbit lowering, but also reduces the misjudgment rate of the three types of states, namely failure, working, and parking, through long-term accumulation, and realizes the subdivision of the target state.

[0102] Based on the method provided in this embodiment, the status of Starlink target 47576 from May 30 to July 8, 2021 is estimated, and the results are as follows: Figure 5 As shown in the figure, the middle axis corresponds to the target height change curve, and the right axis corresponds to the target working state estimation result. It can be seen from the figure that the target height change curve is divided into three obvious stages: horizontal, rising, and horizontal. The corresponding state estimation results are parking, orbit raising, and working. The estimation results are consistent with the actual state.

[0103] Figure 6This is the state estimation result of Starlink 47985 from May 30 to July 8, 2021. The left axis corresponds to the target altitude change curve, and the right axis corresponds to the target working state estimation result. It can be seen from the figure that the target altitude is stable and fluctuates between 356 and 358, and the corresponding state estimation result is parking. The estimation result is consistent with the actual state.

[0104] The state estimation results of the present invention are compared with the Starlink target states published on foreign websites, and the data from July 2 and July 5, 2021 are selected for comparative analysis. The consistency rate of the results on July 2 is 95.47%, and the consistency rate of the results on July 5 is 94.75%, indicating that the consistency rate of the state estimation results of the present invention and foreign websites is high, and has good application value. In the case that the relevant Starlink data is not disclosed or the data is biased, the method provided in this embodiment can autonomously obtain Starlink orbit data, which is of great significance to ensuring the safe operation of my country's satellites.

[0105] refer to Figure 7 , This embodiment also provides a TLE-based Starlink target state estimation system, including,

[0106] The altitude calculation module is used to obtain multiple consecutive orbital elements of the Starlink target, calculate the orbital altitude of the target at the epoch time, and obtain the target altitude sequence;

[0107] Data correction module, used to correct outliers in the Starlink target altitude sequence;

[0108] The state estimation module is used to calculate the target's altitude change rate in long and short periods, and estimate the target's state based on the altitude change rate.

[0109] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A Starlink target state estimation method based on TLE, characterized by: include, Obtain multiple consecutive orbital elements of the Starlink target, solve the orbital altitude of the target at the epoch time, and obtain the target altitude sequence; Correction of outliers in the Starlink target altitude sequence; Calculate the target's altitude change rate in long and short periods, and estimate the target's state based on the altitude change rate; The method for calculating the orbital height of the target is: Step i: Arrange the orbital elements in ascending order according to their epoch times to form an orbital element sequence {TLE1, TLE2, TLE3, ..., TLE n }; Step ii: For the i-th orbital element TLE i , get the epoch time x corresponding to the target i , Step iii: Use the SGP4 algorithm to calculate the TEM coordinates (X i , Y i , Z i ) TEME ; Step iv: Transform the TEM coordinates (X i , Y i , Z i ) TEME Converted to the position in WGS84 coordinate system (Lon i , Lat i , Alt i ) WGS84 ; Step v: Perform steps ii to iv for each orbital element to obtain the target original height sequence. f0=(h1,h2,h3,...,h n ) Among them, each height point information h i =Alt i , represents the epoch time x i The target altitude value at the moment.

2. The method for estimating a Starlink target state based on TLE according to claim 1, characterized in that: In solving the Starlink target altitude sequence, obtain at least 15 consecutive orbital elements.

3. The method for estimating a Starlink target state based on TLE according to claim 1, characterized in that: The method for correcting the outliers in the Starlink target altitude sequence includes: Step I: Use a second-order polynomial function to calculate the height sequence of the Starlink target f0 = (h1, h2, h3, ..., h n ) is fitted, and the output expression of the second-order polynomial fitting is: Step II: Calculate the error between the fitting result and the original height sequence. The root mean square function of the error is, Step III: Using 36 as the threshold value, correct the original height sequence to obtain a new height sequence. The correction function is: Step IV: Repeat steps I to III for a total of m times and output the corrected height sequence 4. The method for estimating a Starlink target state based on TLE according to claim 3, characterized in that: When correcting the outliers in the Starlink target height sequence, the number of iterations m=3.

5. The method for estimating a Starlink target state based on TLE according to claim 3, characterized in that: The height change rate of each point in long and short periods is calculated by sliding window, and the method is Among them, D L and D S are the step sizes for long and short cycles respectively.

6. The method for estimating a Starlink target state based on TLE according to claim 5, characterized in that: D L =15,D S =3。 7. The method for estimating a Starlink target state based on TLE according to claim 5, characterized in that: The method for estimating the target state based on the altitude change rate is: Step a: Construct the Starlink target state set State∈{active orbit reduction, failure, parking, working, orbit increase} and initialize the cumulative number of failures N Crt =0, i=1; Step b: Distinguish the target state based on the target height change rate in a short period. Among them, R Rise is the altitude change threshold of the ascending orbit, R Decline is the altitude change threshold for active orbit lowering; Step c: confirming the failure state of the target based on the height change rate of the target over a long period; Among them, R Invalid is the height change threshold for failure, N Invalid is the repetition period of failure determination; Step d: Determine the target state based on the target height by: Among them, H Work is the height threshold of the working state, is the corrected height value; Step e: If i<n, i=i+1, return to step b, otherwise output the target state sequence {State(x i )}.

8. A TLE-based Starlink target state estimation system, characterized by: include, The altitude calculation module is used to obtain multiple consecutive orbital elements of the Starlink target, calculate the orbital altitude of the target at the epoch time, and obtain the target altitude sequence; Data correction module, used to correct outliers in the Starlink target altitude sequence; The state estimation module is used to calculate the target's altitude change rate under long and short periods, and estimate the target's state based on the altitude change rate; The method for calculating the orbital height of the target is: Step i: Arrange the orbital elements in ascending order according to their epoch times to form an orbital element sequence {TLE1, TLE2, TLE3, ..., TLE n }; Step ii: For the i-th orbital element TLE i , get the epoch time x corresponding to the target i , Step iii: Use the SGP4 algorithm to calculate the TEM coordinates (X i , Y i , Z i ) TEME ; Step iv: Transform the TEM coordinates (X i , Y i , Z i ) TEME Converted to the position in WGS84 coordinate system (Lon i , Lat i , Alt i ) WGS84 ; Step v: Perform steps ii to iv for each orbital element to obtain the target original height sequence. f0=(h1,h2,h3,...,h n ) Among them, each height point information h i =Alt i , represents the epoch time x i The target altitude value at the moment.

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