Calculation method and system for converting orbit Kepler number into double-row number

Abstract

The invention belongs to the technical field of spaceflight measurement and control, and particularly relates to a calculation method and system for converting an orbit Kepler number into a double-row element, and the method comprises the steps: converting the orbit Kepler number of a space object at a specified epoch moment into an orbit quantity in the double-row element through iterative calculation by employing an SGP4 / SDP4 model; fitting and calculating an orbit semi-major axis correction and a resistance term in the double-row elements by using an extrapolation ephemeris with a certain time length; and correcting the orbit semi-major axis in the double-row elements, and generating a double-row element orbit parameter set. According to the method, conversion calculation is simple and convenient, the efficiency is higher compared with orbit determination calculation, and a method for issuing the TLE parameters through the Kepler number or the position velocity vector can be provided for commercial spaceflight users.

Description

Technical Field

[0001] The invention belongs to the field of aerospace measurement and control technology, and in particular relates to a calculation method and system for converting orbit Kepler roots into double-row roots. Background Art

[0002] Kepler roots are a set of parameters that describe the spatial motion state of a space object at a certain moment, and the space object includes satellites, space debris, etc. It is usually expressed by the semi-major axis of the orbit, eccentricity, orbit inclination, right ascension of the ascending node, argument of perigee and mean anomaly. The Kepler roots at a certain moment can be converted to the position velocity vector. Usually, the orbit calculation method based on Kepler roots or position velocity vectors usually uses two methods: analytical method and numerical method. The analytical method is a method of calculating the orbit by solving the differential equations of the satellite orbit motion and establishing an analytical model. It is characterized by high calculation efficiency, but low accuracy and difficulty in improvement. The numerical method is a method of solving the differential equations of the satellite orbit motion by ordinary differential numerical methods to calculate the orbit. It is characterized by high accuracy but low calculation efficiency.

[0003] Two-line Element (TLE) is a set of parameters proposed abroad to describe the orbital motion of space objects. It was first used for cataloging and tracking measurements of space objects. TLE is matched with a dedicated orbit calculation model (SGP4 / SDP4 model, a simplified analytical method. SGP4 (Simplified General Perturbations) is a simplified general perturbation model. The SGP4 model is suitable for orbit calculation of near-Earth spacecraft. The SDP4 model is an extension of the SGP4 model and is suitable for deep space targets. SGP4 can accurately predict the orbit of space targets with a period of less than 225 minutes. SDP4 mainly predicts the orbit of high-orbit and deep-space targets. ) is used for rapid orbit prediction, characterized by high calculation efficiency but low accuracy. Since the SGP4 / SDP4 model has a very mature general software algorithm and has mature applications in space target monitoring and cataloging, some domestic commercial aerospace companies use TLE for satellite orbit calculation and prediction in order to reduce costs and technical difficulties, and because TLE data can be obtained free of charge from relevant websites.

[0004] There are two main sources of TLE parameters. One is from the catalog orbital information of space targets released by relevant foreign institutions. The other is obtained by converting other forms of orbital state parameters of space objects. At present, there is uncertainty about whether the data from relevant foreign institutions can be obtained. The conversion of orbital state parameters based on other forms is to generate ephemeris with orbital prediction, and then use the SGP4 / SDP4 model to calculate TLE parameters through orbit determination. This method has the problem of complex calculation and low efficiency. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects of the prior art and propose a calculation method for converting orbital Kepler roots into double row roots.

[0006] In view of this, the present invention proposes a method for calculating the orbital Kepler root number to the double row root number, comprising:

[0007] Step A: Using the SGP4 / SDP4 model, the Kepler roots of the space object orbit at the specified epoch are converted into orbital quantities in the double row roots through iterative calculation;

[0008] Step B: Using the extrapolated ephemeris of a certain length, fit and calculate the orbital semi-major axis correction and the drag term in the double-row elements;

[0009] Step C: Correct the orbital semi-major axis in the double-row element to generate a double-row element orbital parameter set.

[0010] Preferably, the step A comprises:

[0011] Step A1: Get the epoch to be converted Kepler root number of time , and the mass and cross-sectional area of ​​the space object; wherein the epoch Kepler root number of time , The orbital semi-major axis, orbital eccentricity, orbital inclination, right ascension of ascending node, argument of perigee and mean anomaly, which represent Kepler roots respectively;

[0012] Defining epochs The orbital elements are defined as follows: ,in, The orbital semi-major axis, orbital eccentricity, orbital inclination, right ascension of ascending node, argument of perigee and mean anomaly of the double row elements are represented respectively;

[0013] Set epoch The double row root of the moment defines the orbital root equal , resistance term is 0;

[0014] Step A2: Using the SGP4 / SDP4 model, Calculating epochs Kepler root number approximation of time ;

[0015] Step A3: Calculation and The difference ;

[0016] Step A4: Assign to , thus make corrections;

[0017] Step A5: and They are converted into position and velocity vectors respectively, and the position difference between the two is calculated. If the absolute value of the position difference is less than the set threshold or the number of iterations reaches the set value, the iteration is stopped, otherwise the number of iterations is increased by 1 and the process goes to step A2.

[0018] Preferably, the step B comprises:

[0019] Step B1: Using orbital dynamics method, based on Predict extrapolated ephemeris, the extrapolated time interval is The extrapolated sampling interval is ,in, is the start time of the extrapolated time interval, is the end time of the extrapolated time interval, ; The jth extrapolated sampling time , The ephemeris at that time is recorded as ;in, Respectively The orbital semi-major axis, orbital eccentricity, orbital inclination, right ascension of ascending node, argument of perigee and mean anomaly of Kepler roots at the moment;

[0020] Step B2: Using the SGP4 / SDP model, based on Extrapolation calculation Ephemeris of the moment ;in, Respectively The orbital semi-major axis, orbital eccentricity, orbital inclination, right ascension of ascending node, argument of perigee and mean anomaly of the double row elements at the moment;

[0021] Step B3: Calculate the orbit semi-major axis difference and phase difference at each sampling moment;

[0022] Step B4: Using the phase difference and semi-major axis difference as observation quantities, calculate the orbit semi-major axis correction in the double row elements using the least squares method based on the observation model. and resistance .

[0023] Preferably, the step B3 comprises: according to the following formula:

[0024]

[0025] Calculate each Time orbit semi-major axis difference and phase difference .

[0026] Preferably, the observation model of step B4 is:

[0027]

[0028] in, is the atmospheric drag perturbation parameter, for Angular position deviation at the moment, is the average angular velocity, satisfying the following formulas:

[0029]

[0030]

[0031] ,

[0032]

[0033]

[0034]

[0035] in, is the Earth's gravitational constant, is the parameter related to atmospheric resistance, is the perigee height, is the equatorial radius of the Earth.

[0036] Preferably, step C comprises:

[0037] Step C1: Correct the semi-major axis in the double row root , and calculate the number of circles NR per day in the double row root;

[0038] Step C2: Combine the obtained ephemeris data and , and obtain the final double-row element orbit parameter set .

[0039] Preferably, the step C1 comprises:

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] in, is the semi-major axis of the orbit, and are the orbital semi-major axis and mean angular velocity defined by the SGP4 model, , , is the middle value, is the circumference of a circle, is the geodynamic oblateness term.

[0048] In another aspect, the present invention provides a system for calculating the conversion of orbital Kepler roots to double row roots, comprising:

[0049] Iterative calculation module, used to convert the Kepler roots of the orbit of the space object at the specified epoch time into the orbital quantity in the double row roots by iterative calculation using the SGP4 / SDP4 model;

[0050] The fitting calculation module is used to fit and calculate the orbital semi-major axis correction and the drag term in the double-row elements using the extrapolated ephemeris of a certain length of time;

[0051] The correction calculation module is used to correct the orbital semi-major axis in the double-row element and generate the double-row element orbital parameter set.

[0052] Compared with the prior art, the advantages of the present invention are:

[0053] The present invention adopts a simple calculation method for converting Kepler roots to double-row roots by combining single-point conversion and numerical fitting. First, the Kepler roots at the epoch are converted into orbital quantities in the double-row roots by iterative calculation using the SGP4 / SDP4 model. Then, the orbital semi-major axis and the drag term in the double-row roots are fitted and corrected using the extrapolated ephemeris of a certain length to generate the double-row roots. The double-row roots given by this method can achieve the same orbit calculation accuracy as the double-row roots given by relevant foreign institutions (see Figure 4 ), but the conversion calculation is relatively simple and more efficient than orbit determination calculation, which can provide commercial aerospace users with a method to publish TLE parameters using Kepler roots or position velocity vectors. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a basic processing block diagram of the calculation method of converting orbit Kepler roots to double row roots of the present invention;

[0055] Figure 2It is a specific flow chart of the calculation method of converting orbital Kepler roots to double row roots of the present invention;

[0056] Figure 3 is the accuracy of the TLE extrapolated orbit given by this method;

[0057] Figure 4 This is a comparison of the TLE extrapolated orbit accuracy given by this method and the TLE given by relevant foreign institutions. DETAILED DESCRIPTION

[0058] Aiming at the problem of converting Kepler roots described by Kepler roots (position velocity vectors can be converted into Kepler roots first) into TLE parameters, the present invention proposes a conversion method combining single-point conversion and numerical fitting to achieve fast TLE conversion calculation with guaranteed accuracy.

[0059] This method first uses the SGP4 / SDP4 model to convert the Kepler at the specified epoch into the orbital quantity in the TLE parameters through iterative calculation, and then uses the Kepler root number and TLE parameters to perform orbital extrapolation, and uses the least squares method to fit the orbital semi-major axis and drag term for the deviation of the extrapolated orbit, corrects the orbital semi-major axis in the TLE, and generates TLE parameters. Finally, the conversion from Kepler root number to TLE is realized to meet some orbital calculation needs when the TLE parameters officially released by relevant institutions cannot be obtained, as well as the needs of users to publish TLE parameters.

[0060] like Figure 1 Therefore, the main process of the method for calculating the Kepler root number to the double row root number proposed by the present invention is as follows:

[0061] (1) Through single-point iterative calculation, the input Kepler root number is converted into TLE parameters. The input Kepler root number is denoted as , the number of orbital elements under TLE definition is , the resistance term is , where a is the semi-major axis of the orbit, e is the orbit eccentricity, and i is the orbit inclination. is the right ascension of the ascending node, is the argument of perigee, M is the mean anomaly, the subscript "k" indicates the Kepler root number, the subscript "TLE" indicates the TLE parameter, and the "0" in the subscript corresponds to the orbital epoch In addition, the length unit is meter and the angle unit is radian. The specific iteration process is as follows:

[0062] 1) , , iterations = 1;

[0063] 2) Using the SGP4 / SDP4 model, calculate Approximate value of Kepler root number at time , the superscript “TLE” indicates the parameters calculated by the SGP4 / SDP4 model through the number of TLE roots;

[0064] 3) ;

[0065] 4) Use Correction : ;

[0066] 5) and Convert them into position and velocity vectors respectively, calculate the position difference between the two, if the absolute value of the position difference is less than the given threshold (which can be set according to the accuracy requirement) or the number of iterations reaches the maximum value, stop the iteration, otherwise increase the number of iterations by one and return to step 2);

[0067] (2) Use and Extrapolate the calculated ephemeris and calculate it based on the difference between the calculated ephemeris The correction amount and resistance , the steps are as follows:

[0068] 1) Using traditional orbital dynamics methods, based on Predict extrapolated ephemeris, the extrapolated time interval is , the extrapolated sampling interval is ,in, is the start time of the extrapolated time interval, is the end time of the extrapolated time interval, ; Extrapolated sampling time , The ephemeris at that time is recorded as The extrapolation time interval here can be determined according to the accuracy requirements. Generally, 3 days can be used. The sampling interval Then you can take 900 seconds;

[0069] 2) Using the SGP4 / SDP model, based on Extrapolate the ephemeris, and the extrapolation time interval is , the extrapolated sampling interval is ; The ephemeris at that time is recorded as ;

[0070] 3) According to the following formula:

[0071]

[0072] Calculate the orbital semi-major axis difference and phase difference at each sampling moment;

[0073] 4) Using the phase difference and semi-major axis difference generated in step 3) as the observed quantities, the least squares method is used to fit and calculate based on the following observation model: and :

[0074]

[0075] in, is the atmospheric drag perturbation parameter, for Angular position deviation at the moment, is the average angular velocity, satisfying the following formulas:

[0076]

[0077]

[0078] ,

[0079]

[0080]

[0081]

[0082] in, is the Earth's gravitational constant, is the parameter related to atmospheric resistance, is the perigee height, is the Earth's equatorial radius, They represent the orbital semi-major axis, right ascension of ascending node, argument of perigee and mean anomaly of Kepler roots at the corresponding time.

[0083] (3) Correction of the semi-major axis in TLE , calculate the number of revolutions per day NR in the TLE parameter, and the comprehensive process step (1) given and process step (2) gives , the final TLE orbit parameter set can be obtained :

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091] in, is the semi-major axis of the orbit, and are the orbital semi-major axis and mean angular velocity defined by the SGP4 model, , , is the middle value, is the circumference of a circle, is the geodynamic oblateness term.

[0092] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0093] Example 1

[0094] like Figure 2 As shown, embodiment 1 of the present invention provides a method for calculating the conversion of orbital Kepler roots to double row roots, comprising the following steps:

[0095] (1) Initialization: Obtain the Kepler root number of the orbit of the space object to be converted and the corresponding epoch , as well as the mass and cross-sectional area of ​​space objects.

[0096] (2) Order , , iterations = 1;

[0097] (3) Using the SGP4 / SDP4 model, Calculate Kepler orbital elements at time ;

[0098] (4) ;

[0099] (5) Use Correction : ;

[0100] (6) and Convert them into position and velocity vectors respectively, and calculate the position difference between the two. If the absolute value of the position difference is less than a given threshold (here 10m) or the number of iterations reaches the maximum number of iterations, stop iterating and proceed to the next step. Otherwise, increase the number of iterations by 1 and return to step (3).

[0101] (7) Using traditional orbital dynamics methods, based on Predict extrapolated ephemeris, the extrapolated time interval is The extrapolated sampling interval is 900 seconds, and the extrapolated sampling time is , The ephemeris at that time is recorded as ;

[0102] (8) Using the SGP4 / SDP model, based on Extrapolation calculation Ephemeris of the moment ;

[0103] (9) According to the following formula:

[0104]

[0105] Calculate the orbital semi-major axis difference and phase difference at each sampling moment;

[0106] (10) Taking the phase difference and the semi-major axis difference as the observed quantities, the least squares method is used to fit the following model: and :

[0107]

[0108] in:

[0109]

[0110]

[0111] ,

[0112]

[0113]

[0114]

[0115] (11) Use the following formula to correct the semi-major axis in TLE: , and calculate the number of laps per day in the TLE parameter NR, combined with the previously obtained and , and obtain the final TLE orbital parameter set :

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123] Example 2

[0124] Embodiment 2 of the present invention provides a calculation system for converting orbital Kepler roots to double row roots, which is implemented based on the method of embodiment 1 and includes:

[0125] Iterative calculation module, used to convert the Kepler roots of the orbit of the space object at the specified epoch time into the orbital quantity in the double row roots by iterative calculation using the SGP4 / SDP4 model;

[0126] The fitting calculation module is used to fit and calculate the orbital semi-major axis correction and the drag term in the double-row elements using the extrapolated ephemeris of a certain length of time;

[0127] The correction calculation module is used to correct the orbital semi-major axis in the double-row element and generate the double-row element orbital parameter set.

[0128] It is worth noting that in the embodiment of the above system, the modules included are only divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be achieved; in addition, the specific names of the functional modules are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of the present invention.

[0129] like Figure 3 Shown is the accuracy of the TLE extrapolated orbit given by this method; Figure 4 This is a comparison of the TLE extrapolated orbit accuracy given by this method and the TLE given by relevant foreign institutions.

[0130] The main innovative features of the present invention are:

[0131] (1) An iterative calculation method for converting the single-point Kepler root number to TLE was designed;

[0132] (2) A method for improving the semi-major axis and resistance term of TLE parameters by least squares fitting was designed, achieving short-term prediction of the kilometer level (see Figure 3 ) accuracy.

[0133] 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 the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention and should be included in the scope of the claims of the present invention.

Claims

1. A method for calculating the conversion of orbital Kepler elements to double-row elements, comprising: Step A: Using the SGP4 / SDP4 model, the Kepler roots of the space object orbit at the specified epoch are converted into orbital quantities in the double row roots through iterative calculation; Step B: Using the extrapolated ephemeris of a certain length, fit and calculate the orbital semi-major axis correction and the drag term in the double-row elements; Step C: Correct the orbital semi-major axis in the double-row element to generate a double-row element orbital parameter set.

2. The method for calculating the orbital Kepler elements to double row elements according to claim 1, characterized in that: The step A comprises: Step A1: Get the epoch to be converted Kepler root number of time , and the mass and cross-sectional area of ​​the space object, where the epoch Kepler root number of time , The orbital semi-major axis, orbital eccentricity, orbital inclination, right ascension of ascending node, argument of perigee and mean anomaly, which represent Kepler roots respectively; Defining epochs The orbital elements are defined as follows: ,in, The orbital semi-major axis, orbital eccentricity, orbital inclination, right ascension of ascending node, argument of perigee and mean anomaly of the double row elements are represented respectively; Set epoch The double row root of the moment defines the orbital root equal , resistance term is 0; Step A2: Using the SGP4 / SDP4 model, Calculating epochs Kepler root number approximation of time ; Step A3: Calculation and The difference ; Step A4: Assign to , thus make corrections; Step A5: and They are converted into position and velocity vectors respectively, and the position difference between the two is calculated. If the absolute value of the position difference is less than the set threshold or the number of iterations reaches the set value, the iteration is stopped, otherwise the number of iterations is increased by 1 and the process goes to step A2.

3. The method for calculating the orbital Kepler elements to double row elements according to claim 2, characterized in that: The step B comprises: Step B1: Using orbital dynamics method, based on Predict extrapolated ephemeris, the extrapolated time interval is The extrapolated sampling interval is ,in, is the start time of the extrapolated time interval, is the end time of the extrapolated time interval, epoch time ; The jth extrapolated sampling time , The ephemeris at that time is recorded as ;in, Respectively The orbital semi-major axis, orbital eccentricity, orbital inclination, right ascension of ascending node, argument of perigee and mean anomaly of Kepler roots at the moment; Step B2: Using the SGP4 / SDP model, based on Extrapolation calculation Ephemeris of the moment ;in, Respectively The orbital semi-major axis, orbital eccentricity, orbital inclination, right ascension of ascending node, argument of perigee and mean anomaly of the double row elements at the moment; Step B3: Calculate the orbit semi-major axis difference and phase difference at each sampling moment; Step B4: Using the phase difference and semi-major axis difference as observation quantities, calculate the orbit semi-major axis correction in the double row elements using the least squares method based on the observation model. and resistance .

4. The method for calculating the orbital Kepler elements to double row elements according to claim 3, characterized in that: The step B3 comprises: according to the following formula: Calculate each Time orbit semi-major axis difference and phase difference .

5. The method for calculating the orbital Kepler elements to double-row elements according to claim 4, characterized in that: The observation model of step B4 is: ； in, is the atmospheric drag perturbation parameter, for Angular position deviation at the moment, is the average angular velocity, satisfying the following formulas: ； ； , ； ； ； ； in, is the Earth's gravitational constant, is the parameter related to atmospheric resistance, is the perigee height, is the equatorial radius of the Earth.

6. The method for calculating the orbital Kepler elements to double-row elements according to claim 5, characterized in that: The step C comprises: Step C1: Correct the semi-major axis in the double row root , and calculate the number of circles NR per day in the double row root; Step C2: Combine the obtained ephemeris data and , and obtain the final double-row element orbit parameter set .

7. The method for calculating the orbital Kepler elements to double row elements according to claim 6, characterized in that: The step C1 comprises: ； ； ； ； ； ； ； in, is the semi-major axis of the orbit, and are the orbital semi-major axis and mean angular velocity defined by the SGP4 model, , , is the middle value, is the circumference of a circle, is the geodynamic oblateness term.

8. A calculation system for converting orbital Kepler roots to double-row roots, characterized in that: include: Iterative calculation module, used to convert the Kepler roots of the orbit of the space object at the specified epoch time into the orbital quantity in the double row roots by iterative calculation using the SGP4 / SDP4 model; The fitting calculation module is used to fit and calculate the orbital semi-major axis correction and the drag term in the double-row elements using the extrapolated ephemeris of a certain length of time; and The correction calculation module is used to correct the orbital semi-major axis in the double-row element and generate the double-row element orbital parameter set.

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