Method for calculating satellite impulse orbit transfer based on phase difference

Abstract

The application discloses a satellite impulse orbit change quantity calculation method based on phase difference, and the method comprises the following steps: S1, deriving the relationship between the orbit change quantity, impulse and phase difference; S2, calculating the phase difference; S3, detecting the target maneuvering orbit change event and calculating the orbit change quantity; and S4, detecting and calculating the orbit maneuvering. The method can find the space target orbit change within 1 hour by using the initial TLE root number and observation data, and can provide the orbit change quantity and time within 3 hours; the error of the orbit change quantity is controlled within 4%, and the error of the orbit change time is controlled within 30 minutes.

Description

TECHNICAL FIELD

[0001] The present application relates to a satellite pulse calculation method, in particular to a satellite pulse orbit transfer quantity calculation method based on phase difference. BACKGROUND

[0002] When a space target is maneuvered, high-speed material is mainly ejected to generate a counter-thrust acceleration, so as to change the speed of the target and realize the change of the target orbit. In terms of thrust size and duration, there are mainly two ways of orbit transfer: impulse counter-thrust orbit transfer and ion fuel electric thrust orbit transfer. Impulse counter-thrust orbit transfer has short transfer time and large thrust, and can realize large orbit transfer in a short time. Electric thrust maneuvering transfer has small thrust, long duration and high efficiency, and the orbit transfer is relatively slow.

[0003] It is known that the published CN2020101531200, a TLE-based on-orbit spacecraft orbit transfer detection method, calculates the time of on-orbit spacecraft orbit transfer and the change of semi-major axis within a given time period through TLE information, including the following steps:

[0004] Step one: within a given time period [t0, t1] (t1-t0≥30 days), sort the TLEs of the same target in time sequence;

[0005] Step two: calculate the semi-major axis difference of adjacent two TLE roots according to the semi-major axis sequence ai in step one;

[0006] Step three: calculate the average value and variance of the absolute value of Δai(i=1,2,…k-1) in step two;

[0007] Step four: set the detection threshold by different altitudes;

[0008] Step five: calculate the orbit transfer time and orbit transfer quantity by detecting the two roots before and after the orbit transfer.

[0009] This method only relies on TLE information to detect orbit transfer, does not use observation data, so new TLE must be obtained to detect the orbit transfer event, so the orbit transfer detection is highly lagging; at the same time, the orbit transfer detection only depends on TLE data, and there is a large error in the calculation of the orbit transfer time and the orbit transfer quantity. SUMMARY

[0010] To solve the problems in the above background art, the present application provides a satellite pulse orbit transfer quantity calculation method based on phase difference, which calculates Δv by detecting the phase difference change of the target, and then calculates the orbit transfer quantity and the orbit transfer time.

[0011] The present application provides the following technical solutions:

[0012] The present application mainly aims at researching chemical fuel reverse thrust maneuvering orbit transfer situation. The impulse orbit transfer can be approximately considered as that the target generates an impulse in an instant It can be decomposed in three directions: the tangential direction of the original velocity, the main normal direction (the orbit normal direction in the orbit plane), and the normal direction (the orbit plane normal direction), which are recorded as U, N, and W in sequence. In terms of the efficiency of orbit transfer, the tangential orbit transfer is the most economical. The orbit transfer efficiency in the other two directions is extremely low. Therefore, in the actual orbit transfer operation process, the tangential orbit transfer is generally used to realize the change of the orbit, that is, an impulse is generated in the forward or reverse direction of the velocity of the satellite, so that the satellite generates an increment of .

[0013] Considering that the velocity of the space target is generally 7 km / s, and the value of Δv is generally not more than 10 m / s, Δv << v, the small quantity can be considered. Therefore, it is difficult to find the orbit maneuver of the target in a short time. Meanwhile, after a long time of accumulation, the orbit maneuver increases, and the difficulty of identifying and matching the target increases, which is not conducive to identifying the target.

[0014] After the satellite changes the velocity, the orbit elements will change. The most concerned change of the orbit is the change of the semi-major axis Δa and the time of orbit transfer.

[0015] The present application calculates Δv by detecting the change of the phase difference of the target, and then calculates the orbit transfer amount and the orbit transfer time.

[0016] The present application calculates Δv by detecting the change of the phase difference of the target, and then calculates the orbit transfer amount and the orbit transfer time.

[0017] S1, derivation of the relationship between the orbit transfer amount and the impulse Δv and the phase difference Δu;

[0018] S2, calculation of the phase difference;

[0019] S3, target maneuvering orbit transfer event detection and orbit transfer amount calculation;

[0020] S4, orbit maneuver detection and calculation steps.

[0021] S1, derivation of the relationship between the orbit transfer amount and the impulse Δv and the phase difference Δu

[0022] The main parameter for measuring the orbit maneuver amount of the space target is the change of the semi-major axis Δa, and Δa has a linear relationship with Δv and Δu,

[0023] According to the Gauss-type perturbation equation, the relationship between the orbit transfer amount and the velocity impulse can be calculated, and the Gauss-type perturbation equation is as follows

[0024]

[0025] where a, e, f, a U are semi-major axis, eccentricity, true anomaly and tangential acceleration respectively, since most of the orbits are near-circular orbits, for near-circular orbits, generally e≈0, ignoring small quantities:

[0026]

[0027] Let the impulse orbit transfer duration be Δt, multiply both sides of the formula by Δt to get:

[0028]

[0029] Since the orbit transfer time interval Δt≈0, it can be considered that in the Δt time period and a U do not change, then in the Δt time period the orbit change and the velocity change are

[0030]

[0031] Δv=a U Δt (5)

[0032] Bring (4-5) into (3) to get

[0033]

[0034] From this it can be concluded that the semi-major axis change is proportional to Δv

[0035] According to the formula n=a -1.5 , it can be obtained that

[0036]

[0037] Let there be an impulse Δv at t=t0, and the phase u is u0, then at t time the phase is

[0038] u t =u0+n(t-t0) (8)

[0039] According to formula (8-9), the phase difference at t time can be obtained as

[0040]

[0041] From this it can be seen that when the target performs orbit transfer, its phase difference will change linearly with time, and the slope of the change is

[0042] S2, calculation of phase difference

[0043] The unit vector of the theoretical orbit plane normal direction of the target at time t is

[0044]

[0045] The projection of the observation vector on W is r w

[0046]

[0047] Let the projection vector of the observation vector be r o

[0048]

[0049] In the STW (radial, lateral, and orbit plane normal) coordinate system, the components of r o o o

[0050]

[0051] T = W x S (14)

[0052] The phase difference is

[0053]

[0054] S3, Target maneuvering orbit transfer event detection and orbit transfer quantity calculation

[0055] Let the derivatives of the phase difference with respect to time before and after the orbit maneuver be k1 and k2, respectively. According to equation (9), we have

[0056]

[0057] According to equation (6), we have

[0058]

[0059] The orbit maneuver time is the intersection of the two phase difference straight lines, i.e.

[0060]

[0061] where b1 and b2 are the y-axis intercepts of the phase difference straight lines before and after the orbit maneuver, respectively.

[0062] S4, Orbit maneuver detection and calculation steps

[0063] Step 1: Preprocess the observation data, including removing outliers, refraction correction, removing data with pitch angles greater than 80° and less than 3°.​​​​​

[0064] Step 2: Coordinate conversion is carried out on the observation data to obtain an observation vector r in TEME coordinate system o ;

[0065] Step 3: A theoretical vector r at the same moment is calculated through the TLE of the target c and v c ;

[0066] Step 4: The phase difference Δu at the moment is calculated through formula (11)-formula (17);

[0067] Step 5: Steps (1)-(4) are repeated, all the phase differences corresponding to the observation data of all the arc segments are calculated, and a plot is drawn with time as the horizontal coordinate and the phase difference as the vertical coordinate, that is, a data set D{t, Δu} is formed;

[0068] Step 6: The gradient k of the phase difference with respect to time is detected, and when the change amount of the gradient k is greater than 0.002 radian / day, it is determined that the target has carried out an orbit maneuver, and the orbit change amount and the orbit change moment can be calculated according to steps 7-8, if the change amount of the gradient does not exceed 0.002 radian / day, it is considered that the target has not changed orbit;

[0069] Step 7: The orbit change amount is calculated according to formula ;

[0070] Step 8: The orbit change moment is calculated according to formula .

[0071] Compared with the prior art, the beneficial effects of the present application are:

[0072] For the orbit-changing target, the orbit maneuver event of the target can be detected by single measurement and control station data, but in order to suppress the occurrence of false alarm, the orbit maneuver is more reliable when detected by two stations at the same time. Considering the distribution of the measurement and control stations, the time difference of the space target passing through two measurement and control stations can be calculated as 5-20 minutes. Therefore, the orbit maneuver event can be detected by using the data of two stations separated by 20 minutes, considering that there are many space targets and it is impossible to observe them immediately after the orbit maneuver, therefore, the detection time of the orbit maneuver can be controlled within 1 hour. For the calculation of the orbit change amount, it mainly depends on the change amount of the phase difference and the time difference between the observation data, and after accumulating 1-3 hours of data, the calculation accuracy can be controlled near 4%. BRIEF DESCRIPTION OF DRAWINGS

[0073] Figure 1 It is a phase difference diagram of the present application.

[0074] Figure 2 It is a diagram for calculating the orbit change moment according to the phase difference of the present application.

[0075] Figure 3 A schematic diagram for calculating the orbit change amount according to the phase difference of the present application.

[0076] Figure 4 A schematic diagram of the phase difference targeted by the present application.

[0077] Figure 5 A flow chart for the entire space object orbit change detection and orbit change amount calculation of the present application. Embodiment

[0078] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0079] The satellite impulse orbit change amount calculation method based on the phase difference of the present application calculates the Δv by detecting the phase difference change of the target, and then calculates the orbit change amount and the orbit change time, including the following steps:

[0080] S1, derivation of the relationship between the orbit change amount and the impulse Δv and the phase difference Δu

[0081] The main parameter for measuring the orbit maneuver amount of the space target is the semi-major axis change amount Δa, and Δa has a linear relationship with Δv and Δu,

[0082] The relationship between the orbit change amount and the velocity impulse can be calculated according to the Gauss-type perturbation equation, and the Gauss-type perturbation equation is as follows

[0083]

[0084] Wherein a, e, f, a U are the semi-major axis, eccentricity, true anomaly and tangential acceleration, respectively. Since most orbits are near-circular orbits, for near-circular orbits, generally e≈0, and by neglecting small quantities:

[0085]

[0086] Suppose the impulse orbit change duration is Δt, and multiply Δt on both sides of the formula to get:

[0087]

[0088] Since the orbit change time interval Δt≈0, it can be considered that in the Δt time period and a U do not change, so in the Δt time period, the orbit change amount and the velocity change amount are

[0089]

[0090] Δv = a U Δt (5)

[0091] Substitute (4-5) into (3), we get

[0092]

[0093] Thus, we can conclude that the semi-major axis change is proportional to Δv

[0094] According to the formula n = a -1.5 , we can get

[0095]

[0096] Suppose at t = t0, there is an impulse Δv, and the phase u is u0, then at t, the phase is

[0097] u t = u0 + n(t - t0) (8)

[0098] According to formula (8-9), we can get the phase difference at t

[0099]

[0100] Figure 1 As shown in the figure, we can see that when the target is in orbit, its phase difference will change linearly with time, and the slope of the change is

[0101] S2, calculation of phase difference

[0102] For non-orbit-changing targets, the difference between the observation calculated by TLE and the actual observation is very small, but for orbit-changing targets, the difference between the observation calculated by TLE and the actual observation will increase with time after the target changes orbit. Let the subscript of the observation calculated by TLE be c (theoretical value): the subscript of the observation obtained by observation be o (observation value), then the phase difference is the difference between the observation phase and the theoretical phase, which is also equal to the angle difference between the projection of the observed vector on the orbital plane and the theoretical vector. As shown in Figure 2 and Figure 3 .

[0103] The unit vector of the theoretical orbital plane of the target at t is

[0104]

[0105] Thus, the projection of the observed vector on W is r w

[0106] ​

[0107] Let the projection vector of the observation vector be r. o ',but

[0108]

[0109] In the STW (radial, lateral, and orbital plane normal) coordinate system, r o The radial and lateral components are r respectively. o '·S and r o '·T, where S and T are the radial and lateral unit vectors, respectively, are calculated as follows:

[0110]

[0111] T = W × S (14)

[0112] Therefore, the phase difference is

[0113]

[0114] S3. Target maneuvering trajectory change event detection and trajectory change calculation

[0115] Orbital maneuver detection requires rapidly determining the target's maneuver time from acquired observation data, while simultaneously calculating the target's maneuver magnitude and timing. The advantage of using phase difference for maneuver detection is that the curve has a large linear range, and the sign of the orbital change can be determined based on the direction of abrupt changes in phase difference.

[0116] Ground-based observation equipment can track and detect space targets in real time, acquiring segmented observation data. A point can be selected from each data segment to calculate the phase difference between the observed data and the TLE extrapolated observations. Following the time sequence, a phase difference diagram of the target can be obtained, such as... Figure 4 As shown.

[0117] For the arc segment before the orbital change of the target, its characteristic is that the phase difference fluctuates around 0, such as... Figure 4 As shown by the blue dots, the phase difference increases linearly with time after the target changes its orbit, as shown by the red dots in the figure. Simultaneously, some space targets may cluster together, resulting in interference data from other targets mixed in with the observation data, as shown by the black dots in the figure.

[0118] Since the phase difference is a linear function of the orbital change, before the target orbit maneuvers, its phase difference changes linearly with time. After the target orbit maneuvers, its phase difference changes linearly again. Therefore, a threshold for the phase difference deviating from the linear path can be used to check whether the target has undergone a maneuver or orbital change. Orbital maneuvering events can be detected by the fluctuations in the phase difference. When the observed and predicted phase difference values ​​reach a certain threshold, it can be determined that the target has undergone a maneuver or orbital change.

[0119] After detecting the target's maneuver, the accuracy of the orbit maneuver is difficult to guarantee due to less data. The next observation data can be accumulated to calculate the maneuver and the time of the maneuver.

[0120] Let the derivatives of the phase difference with respect to time before and after the orbit maneuver be k1 and k2, respectively. According to equation (9), we have

[0121]

[0122] According to equation (6), we have

[0123]

[0124] The time of the orbit maneuver is the intersection of the two phase difference straight lines, i.e.

[0125]

[0126] where b1 and b2 are the y-axis intercepts of the phase difference straight lines before and after the orbit maneuver, respectively.

[0127] S4, Orbit maneuver detection and calculation steps

[0128] The flow chart is shown in Figure 5 .

[0129] Step 1: Preprocess the observation data, including removing outliers, refraction correction, removing data with a pitch angle greater than 80° and less than 3°;

[0130] Step 2: Convert the observation data to the TEME coordinate system to obtain the observation vector r o .

[0131] Step 3: Calculate the theoretical vector r c and v c at the same time through the target's TLE;

[0132] Step 4: Calculate the phase difference Δu at this time through equations (11)-(17);

[0133] Step 5: Repeat steps (1)-(4) to calculate the phase difference corresponding to all the observation data of the arc segment, plot the time as the horizontal coordinate and the phase difference as the vertical coordinate (as shown in Figure 4 ), i.e., form the data set D{t, Δu};

[0134] Step 6: Detect the gradient k of the phase difference with respect to time. When the change of the gradient k is greater than 0.002 rad / day, it is determined that the target has performed an orbit maneuver. The orbit change and the time of the orbit change can be calculated according to steps 7-8. If the change of the gradient does not exceed 0.002 rad / day, it is considered that the target has not changed the orbit.

[0135] Step 7: Calculate the amount of orbit change according to the formula

[0136] Step 8: Calculate the time of orbit change according to the formula

[0137] S5, Error Analysis

[0138] When analyzing the amount of orbit change, e = 0 is used for processing. In practice, e is a small amount, and the relative error amount brought by e is

[0139]

[0140] Sometimes the direction of the thrust is not strictly according to the direction of the speed, which will also bring some error. Generally, the amount of orbit change has an error of 1-4%, and the error is related to the quality of the observation data and the accuracy of the TLE. For the time of orbit change, the error is generally controlled within 20 minutes.

[0141] Simulation Calculation:

[0142] Python is used for simulation. First, five target initial orbits with different inclination and altitude are selected, and the time of orbit change and the amount of orbit change are set. High-precision predictors are used to obtain the position and velocity data before and after the orbit change. At the same time, two observation stations are set, the observation data is calculated and random error is added to obtain the observation data. Then the method of maneuver detection is used to accumulate the observation data. At the same time, the method of precise orbit determination is used to calculate the time of maneuver and the amount of maneuver. The final results are shown in Table 1

[0143] Table 1 shows the amount of orbit change obtained by the analytical method, the amount of orbit change and the time of orbit change set by simulation, and the error situation

[0144] Table 1 Comparison of analytical method and true value

[0145]

[0146] From Table 1, it can be seen that the amount of orbit change and the time of orbit change obtained by the analytical method have high precision, which can help to subdivide the pre-orbit and post-orbit segments of the maneuvering target, and further realize the detection of the orbit change of the maneuvering target.

[0147] ​​For orbit changing target, single TT&C station data can detect the orbit maneuver event of the target, but in order to suppress the occurrence of false alarm, two stations need to detect the orbit maneuver simultaneously. Considering the distribution of TT&C stations, the time difference of the space target passing through two TT&C stations can be calculated as 5-20 minutes. Therefore, the data of two stations separated by 20 minutes can be used to detect the orbit maneuver event. Considering that there are more space targets and it is impossible to observe them immediately after the orbit maneuver, the detection time of the orbit maneuver can be controlled within 1 hour. For the calculation of the orbit changing amount, the phase difference change amount and the time difference between the observation data are mainly relied on, and after accumulating 1-3 hours of data, the calculation accuracy can be controlled near 4%.

[0148] The satellite pulse orbit changing amount calculation method based on phase difference provided by the application mainly calculates the phase difference between the target theoretical value and the observation value, uses the phase difference as the basis for judging the orbit changing event, and calculates the orbit changing amount and the orbit changing time through the phase difference. Through the above method, the initial TLE number and the observation data can be used to find that the space target has changed orbit within 1 hour, and the orbit changing amount and the orbit changing time can be given within 3 hours.

[0149] Although the embodiments of the application have been shown and described, it can be understood by those skilled in the art that various changes, modifications, replacements and variations can be made to the embodiments without departing from the principles and spirits of the application, and the scope of the application is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the impulse orbit change of a satellite based on phase difference, characterized in that: calculating by detecting a phase difference change of the target and then calculating the amount of orbit change and the time of orbit change, including the steps of: S1, Relationship between the amount of orbit transfer and impulse and phase difference derivation; S2, calculation of phase difference; S3, target maneuvering orbit transfer event detection and calculation of orbit transfer amount; S4, orbit maneuver detection and calculation steps; S1, Relationship between the amount of orbit transfer and impulse and phase difference relationship derivation The main parameter of the space target orbit maneuver is the change of semi-major axis , With And There is a linear relationship, According to the Gaussian perturbation equation, the relationship between the orbit transfer amount and the velocity impulse can be calculated, and the Gaussian perturbation equation is as follows （1） where , , , are semi-major axis, eccentricity, true anomaly and tangential acceleration, respectively, and since most orbits are near-circular, for near-circular orbits, one generally has , neglecting small quantities. （2） Let the impulse orbit transfer duration be , multiply both sides of the equation by : （3） Due to the time interval of the track change It can be considered that in Within the time period and If nothing changes, then... The changes in orbit and velocity over the time period are （4） （5） Put (4-5) into (3) to get （6） It is concluded that the semi-major axis change is proportional to According to the formula one obtains （7） Let the impulse at t = t0be The phase at t = t0is​​ （8） According to formula (8-9), the phase difference at time t is （9） It can be seen that the phase difference of the target will change linearly with time after the target is transferred, and the slope of the change is ; S2, calculation of phase difference The unit vector of the target's theoretical orbit plane at time t is （10） Thus, the projection of the observation vector on is​ （11） Let the projection vector of the observation vector be then （12） In the STW (radial, tangential, normal to the orbital plane) coordinate system, The radial and tangential components are respectively and where and are the radial and tangential unit vectors respectively, and are calculated as follows （13） （14） The phase difference is （15） S3, target maneuvering orbit transfer event detection and calculation of orbit transfer amount Let the derivative of the phase difference before and after the orbit maneuver with respect to time be , , then according to formula (9) （16） According to formula (6), we get （17） The orbit maneuvering time is the intersection position of the two phase difference straight lines, that is （18） wherein , are the y-intercepts of the straight lines before and after the orbit maneuver, respectively. S4, orbit maneuver detection and calculation steps Step 1: Preprocess the observation data, including removing outliers, refraction correction, removing data with pitch angle greater than 80° and less than 3°; Step 2: Coordinate transformation of the observation data into the TEME coordinate system to obtain the observation vector ; Step 3: Calculate the theoretical vector at the same time by the TLE of the target and ; Step 4: Calculate the phase difference at this moment by formula (11) - formula (17) ; Step 5: Repeat steps (1) - (4) to calculate the phase difference of all the observation data of the arc segment, and plot the time as the horizontal coordinate and the phase difference as the vertical coordinate to form a data set D{t, } Step 6: Detect the gradient k of the phase difference with respect to time, when the change of the gradient k is greater than 0.002 radian / day, it is determined that the target has performed orbit maneuvering, and the orbit transfer amount and orbit transfer time can be calculated according to steps 7-8, if the change of the gradient does not exceed 0.002 radian / day, it is considered that the target has not performed orbit transfer; Step 7: Calculate the amount of orbit change according to the formula M = 2.5 * (1 - e) * (1 + e) Step 8: Calculate the time of orbit change according to the formula t = t0 + Δt.

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