A method for full orbit fitting of pipeline deviation of a strict regression orbit satellite

Abstract

A pipeline deviation full orbit fitting method of a rigorous regression orbit satellite can determine single-point pipeline deviation based on reference trajectory coordinates and cutting track plane alignment according to the characteristics of the rigorous regression orbit, can calculate and curve fit data of at least one track, and use the maximum deviation after the fitting as the pipeline deviation of the satellite, so as to comprehensively analyze the rigorous regression accuracy of the satellite, effectively overcome the limitations of single-point pipeline deviation calculation, and suppress the influence of single-point error data on pipeline deviation calculation by using the curve fitting method, so that the calculation result is more accurate and reliable.

Description

Technical Field

[0001] This invention relates to a method for full-orbit fitting of pipeline deviation for strictly regressive orbit satellites, belonging to the field of high-precision satellite orbit determination and control technology. Background Technology

[0002] With the increasing demands of in-orbit applications for satellite formation, traditional orbit design and maintenance control methods are no longer sufficient to meet the higher requirements for orbit control accuracy and autonomy in highly complex applications. Strictly regressive orbits are a new orbit design and control concept proposed for Earth observation missions with multiple orbits in recent years. The key feature of a strictly regressive orbit is that within a single regression cycle, the satellite's spatial trajectory is completely consistent between its initial and final states, thus achieving strict regression. The deviation of the satellite from the origin of the trajectory coordinate system when it crosses the tangent plane of the strictly regressive reference orbit is the pipe deviation at the current reference point. Previous methods using the six orbital roots to determine satellite orbits are no longer suitable for pipe deviation analysis, necessitating an accurate and reliable method for calculating the pipe deviation of strictly regressive orbits. Summary of the Invention

[0003] The technical problem solved by this invention is that the existing method of determining satellite orbits using the six orbital elements is no longer applicable to pipeline deviation analysis. Therefore, this invention proposes a full-orbit fitting method for pipeline deviation of satellites with strict regression orbits.

[0004] The present invention solves the above-mentioned technical problem through the following technical solution:

[0005] A method for full-orbit fitting of pipeline deviation for strictly regressive orbit satellites includes:

[0006] Collect measured satellite orbit state sequence information and reference orbit state sequence information;

[0007] By regressing the reference orbit sequence time of the current reference orbit point, the reference orbit point closest to the pre-selected time point of the satellite's measured orbit state sequence information is found.

[0008] Using the reference trajectory point as the origin, establish a formation coordinate system and calculate the relative position vector of the satellite in the formation coordinate system at the pre-selected time point;

[0009] The recursive time required for the satellite to travel from the position at the pre-selected time point to the reference orbit point in the measured orbit is calculated based on the relative position vector. The relative position vector of the orbit point in the trajectory coordinate system with the reference trajectory point as the origin is calculated by using the orbit state sequence information corresponding to the recursive orbit point.

[0010] Traverse all satellite measured orbit state sequence information under the measured orbit and select the pre-selected time points to obtain the relative position vector of the orbit point after the operation recursion at each pre-selected time point in the trajectory coordinate system with the reference trajectory point as the origin.

[0011] The two-dimensional vector sequence is formed by obtaining the relative position vectors of all orbit points after recursion in the trajectory coordinate system with the reference trajectory point as the origin. After ellipse fitting, the minimum circumscribed circle radius is obtained as the satellite's pipeline deviation.

[0012] The satellite's measured orbital state sequence information includes time t. i 3D position [x] i ,y i z i ], three-dimensional velocity [vx i ,vy i ,vz i Reference orbital state sequence information includes time t. ci 3D position [x ci ,y ci ,z ci ], three-dimensional velocity [vx ci ,vy ci ,vz ci i = 1, 2, 3…N; The measured orbital state sequence information and the reference orbital state sequence information are both parameter information within a regression period;

[0013] When the pre-selected time point is determined, select the reference orbit point P that is closest to the pre-selected time point on the satellite's actual measured orbit. c Determine the reference orbit point P c The corresponding reference orbit time t on the reference orbit cj .

[0014] Based on reference orbit point P c Reference orbit time t cj Pre-selected time point t i The comparison results show that the reference orbit point P is under the condition of insufficient time. c Reference orbit time t cj By recursively calculating backwards according to the integer regression period, the number of regression periods N to be recursively calculated is determined as follows:

[0015] N = fix((t) i -t cj ) / T)

[0016] In the formula, T is the regression period, N is the number of regression periods to be recursively applied, and the fix() operation represents rounding the calculated numerical result.

[0017] After determining the number of regression periods N that need to be recursively calculated, select the reference orbital point to be targeted from the reference orbital point sequence, as follows:

[0018] M = fix(((t) i -t cj )-N*T) / Ts)+1

[0019] In the formula, Ts is the time interval between adjacent strict regression orbit reference points, and M represents the Mth point in the reference orbit point sequence, i.e., the reference orbit point to be targeted.

[0020] The formation coordinate system OXYZ uses the vector direction from the Earth's center E to the origin as the OX axis, and sets the OY axis in the main star's orbital plane, with the direction of flight as the OX axis. The OZ axis satisfies the right-hand rule with the OX and OY axes. A pre-selected time point t... i At any given moment, the relative position vector of the satellite in the formation coordinate system is denoted as R1(R Hx1 R Hy1 R Hz1 ).

[0021] The relative position vector R1 is calculated as follows:

[0022]

[0023] In the formula, the reference orbit point For P c The position vector of a point in an inertial coordinate system. For P c The velocity vector of a point in the inertial coordinate system. For P s The position vector of a point in an inertial coordinate system. For P s The velocity vector of a point in the inertial coordinate system, A i2b This is the transformation matrix from the inertial frame to the formation coordinate system.

[0024] The track point P after operation s The corresponding orbital state sequence information includes time t k 3D position [x k ,y k ,z k ], three-dimensional velocity [vx k ,vy k ,vz k ]; Track point P after operation s The relative position vector in the trajectory coordinate system with Pc as the origin is R. i (R gjxi R gjyi R gjzi );

[0025] The method for calculating the travel time Δt required for a satellite to travel from a pre-selected time point to a reference orbit point in its measured orbit is as follows:

[0026]

[0027] In the formula, the molecule is the projection R of its relative position in the Hy direction. Hy1 The denominator is the magnitude of the velocity vector.

[0028] Based on the track point P after operation s The moment t i The satellite orbital elements at time +Δt [a,e,i,Ω,ω,M+n*Δt] are converted to obtain the orbital point P after operation. s orbital state sequence information [x si ,y si ,z si ] and [vx si ,vy si ,vz si ],calculate In The relative position vector in the trajectory coordinate system of the origin The method is as follows:

[0029]

[0030] In the formula, For P c The position vector of a point in the Earth-fixed coordinate system. For P c The velocity vector of a point in the Earth-fixed coordinate system. For P s The position vector of a point in the Earth-fixed coordinate system. For P s The velocity vector of a point in the Earth-fixed coordinate system.

[0031] The calculation method for the relative position vector of the orbit point corresponding to the pre-selected time point in the orbital state sequence information of all satellites is the same in the orbital coordinate system with the reference trajectory point as the origin. The reference orbit time interval is considered when selecting each pre-selected time point. In the case of no orbit control, the measured orbit is the same as the reference orbit. In the case of orbit control, the measured orbit is smaller than the reference orbit.

[0032] The X of N relative position vectors gj and Z gj The coordinates form a two-dimensional vector sequence. This two-dimensional sequence is fitted to an ellipse, and the general equation of the ellipse is obtained by numerical fitting using the method of undetermined coefficients.

[0033] ax 2 +bxy+cy 2 +dx+ey+f=0

[0034] Let α = [a, b, c, d, e, f] T , x = [x 2 ,xy,y 2 [x,y,1] T The elliptic least squares fitting method is used to solve for α = [a, b, c, d, e, f]. T ;

[0035] After solving, plot the elliptic curve and place it on the X-axis. gj O gj Z gj Within the coordinate system, draw the circumcircle of the elliptic curve with the origin as the center, and use the minimum radius of the circumcircle as the satellite's pipeline deviation.

[0036] The advantages of this invention compared to the prior art are:

[0037] (1) This invention provides a full-track fitting method for pipeline deviation of strictly regressing orbit satellites. Based on the characteristics of strictly regressing orbits, it determines single-point pipeline deviation by aligning the reference trajectory coordinate system and the tangent plane. It also calculates and curve-fits data from at least one orbit, using the maximum deviation after fitting as the satellite's pipeline deviation, thereby performing a comprehensive analysis of the satellite's strictly regressing accuracy. This method effectively overcomes the limitations of single-point pipeline deviation calculation. Furthermore, the use of curve fitting suppresses the influence of single-point erroneous data on pipeline deviation calculation, resulting in more accurate and reliable calculation results.

[0038] (2) The process of this invention is clear and the engineering feasibility is strong: combined with the actual situation of orbit changes, the orbit recursive calculation of the orbit alignment process is avoided, which has good engineering feasibility. At the same time, the method has strong anti-interference ability and the determination results are accurate and reliable: the curve fitting process avoids the possible errors and data disturbances in single or partial orbit measurement data. It can process orbit data of different scales as needed, and can be realized both on the satellite and on the ground. Attached Figure Description

[0039] Figure 1 A flowchart for determining the full-track pipeline deviation of the strict regression trajectory provided for the invention;

[0040] Figure 2 A schematic diagram of the pipeline deviation curve in the trajectory coordinate system within one orbital period of a satellite, provided for the invention; Detailed Implementation

[0041] A full-track fitting method for pipeline deviation of strictly regressing orbit satellites is proposed. Based on the characteristics of strictly regressing orbits, it can determine single-point pipeline deviation by aligning the reference trajectory coordinate system and the tangent plane. It can also calculate and curve fit data for at least one orbit, and use the maximum deviation after fitting as the satellite's pipeline deviation. This allows for a comprehensive analysis of the satellite's strictly regressing accuracy and effectively overcomes the limitations of single-point pipeline deviation calculation. Furthermore, the use of curve fitting can suppress the influence of single-point erroneous data on pipeline deviation calculation, making the calculation results more accurate and reliable.

[0042] The method for full-orbit fitting of pipeline deviation for strictly regressive orbit satellites consists of the following steps:

[0043] Collect measured satellite orbit state sequence information and reference orbit state sequence information;

[0044] By regressing the reference orbit sequence time of the current reference orbit point, the reference orbit point closest to the pre-selected time point of the satellite's measured orbit state sequence information is found.

[0045] The specific meaning of regression period recursion is that for a specific set of strict regression trajectory parameters, the regression period is determined (e.g., 3 days or 8 days, and there can only be one start time). Therefore, for actual tasks, it is necessary to map the start time of the reference trajectory to the vicinity of the actual task time before it can be used.

[0046] Using the reference trajectory point as the origin, establish a formation coordinate system and calculate the relative position vector of the satellite in the formation coordinate system at the pre-selected time point;

[0047] The recursive time required for the satellite to travel from the position at the pre-selected time point to the reference orbit point in the measured orbit is calculated based on the relative position vector. The relative position vector of the orbit point in the trajectory coordinate system with the reference trajectory point as the origin is calculated by using the orbit state sequence information corresponding to the recursive orbit point.

[0048] Traverse all satellite measured orbit state sequence information under the measured orbit and select the pre-selected time points to obtain the relative position vector of the orbit point after the operation recursion at each pre-selected time point in the trajectory coordinate system with the reference trajectory point as the origin.

[0049] The two-dimensional vector sequence is formed by obtaining the relative position vectors of all orbit points after recursion in the trajectory coordinate system with the reference trajectory point as the origin. After ellipse fitting, the minimum circumscribed circle radius is obtained as the satellite's pipeline deviation.

[0050] Satellite measured orbital state sequence information includes time t i 3D position [x i ,yi z i ], three-dimensional velocity [vx i ,vy i ,vz i Reference orbital state sequence information includes time t. ci 3D position [x ci ,y ci ,z ci ], three-dimensional velocity [vx ci ,vy ci ,vz ci i = 1, 2, 3…N; The measured orbital state sequence information and the reference orbital state sequence information are both parameter information within a regression period;

[0051] When the pre-selected time point is determined, select the reference orbit point P that is closest to the pre-selected time point on the satellite's actual measured orbit. c Determine the reference orbit point P c The corresponding reference orbit time t on the reference orbit cj .

[0052] Based on reference orbit point P c Reference orbit time t cj Pre-selected time point t i The comparison results show that the reference orbit point P is under the condition of insufficient time. c Reference orbit time t cj By recursively calculating backwards according to the integer regression period, the number of regression periods N to be recursively calculated is determined as follows:

[0053] N = fix((t) i -t cj ) / T)

[0054] In the formula, T is the regression period, N is the number of regression periods to be recursively applied, and the fix() operation represents rounding the calculated numerical result.

[0055] After determining the number of regression periods N that need to be recursively calculated, select the reference orbital point to be targeted from the reference orbital point sequence, as follows:

[0056] M = fix(((t) i -t cj )-N*T) / Ts)+1

[0057] In the formula, Ts is the time interval between adjacent strict regression orbit reference points, and M represents the Mth point in the reference orbit point sequence, i.e., the reference orbit point to be targeted.

[0058] The formation coordinate system is OXYZ, with the vector direction from the Earth's center E to the origin as the OX axis. The OY axis is set in the orbital plane of the primary star, and the direction of flight is the OX axis. The OZ axis satisfies the right-hand rule with the OX and OY axes. The pre-selected time point t i At any given moment, the relative position vector of the satellite in the formation coordinate system is denoted as R1(R Hx1 R Hy1 R Hz1 ).

[0059] The formation coordinate system is OXYZ, with the vector direction from the Earth's center E to the origin as the OX axis. The OY axis is set in the orbital plane of the primary star, and the direction of flight is the OX axis. The OZ axis satisfies the right-hand rule with the OX and OY axes. The pre-selected time point t i At any given moment, the relative position vector of the satellite in the formation coordinate system is denoted as R1(R Hx1 R Hy1 R Hz1 ).

[0060] Track point P after running s The corresponding orbital state sequence information includes time t k 3D position [x k ,y k ,z k ], three-dimensional velocity [vx k ,vy k ,vz k ]; Track point P after operation s The relative position vector in the trajectory coordinate system with Pc as the origin is R. i (R gjxi R gjyi R gjzi );

[0061] The method for calculating the travel time Δt required for a satellite to travel from a pre-selected time point to a reference orbit point in its measured orbit is as follows:

[0062]

[0063] In the formula, the molecule is the projection R of its relative position in the Hy direction. Hy1 The denominator is the magnitude of the velocity vector.

[0064] Based on the track point P after operation s The moment t i The satellite orbital elements at time +Δt [a,e,i,Ω,ω,M+n*Δt] are converted to obtain the orbital point P after operation. s orbital state sequence information [x si ,y si ,z si ] and [vxsi ,vy si ,vz si ],calculate In The relative position vector in the trajectory coordinate system of the origin The method is as follows:

[0065]

[0066] In the formula, For P c The position vector of a point in the Earth-fixed coordinate system. For P c The velocity vector of a point in the Earth-fixed coordinate system. For P s The position vector of a point in the Earth-fixed coordinate system. For P s The velocity vector of a point in the Earth-fixed coordinate system.

[0067] The calculation method for the relative position vector of the orbit point corresponding to the pre-selected time point in the satellite measured orbit state sequence information in the trajectory coordinate system with the reference trajectory point as the origin is the same. When selecting each pre-selected time point, the reference orbit time interval is taken into account. In the case of no orbit control, the measured orbit is the same as the reference orbit. In the case of orbit control, the measured orbit is smaller than the reference orbit.

[0068] X of N relative position vectors gj and Z gj The coordinates form a two-dimensional vector sequence. This two-dimensional sequence is fitted to an ellipse, and the general equation of the ellipse is obtained by numerical fitting using the method of undetermined coefficients.

[0069] ax 2 +bxy+cy 2 +dx+ey+f=0

[0070] Let α = [a, b, c, d, e, f] T , x = [x 2 ,xy,y 2 [x,y,1] T The elliptic least squares fitting method is used to solve for α = [a, b, c, d, e, f]. T ;

[0071] After solving, plot the elliptic curve and place it on the X-axis. gj O gj Z gj Within the coordinate system, draw the circumcircle of the elliptic curve with the origin as the center, and use the minimum radius of the circumcircle as the satellite's pipeline deviation.

[0072] The following description, in conjunction with the accompanying drawings and preferred embodiments, provides further details:

[0073] In the current embodiment, such as Figure 1 As shown, the algorithm for determining the pipe deviation of a strictly regressive orbit satellite through full-orbit fitting includes the following steps:

[0074] Step 1: Prepare the orbital state sequence (including time t) obtained from at least one actual orbital measurement of the satellite. i 3D position [x i ,y i z i ], three-dimensional velocity [vx i ,vy i ,vz i The state sequence (including time t) within a regression period of the reference orbit. c0 3D position [x ci ,y ci ,z ci ], three-dimensional velocity [vx ci ,vy ci ,vz ci ]), where i = 1, 2, 3…N;

[0075] Step 2: Find the time distance t i The nearest reference orbit point P c (The corresponding time is t) cj When the reference orbital sequence time is insufficient, the regression period is recursively pushed forward by t. cj =N*T+t c0 , where N is the number of regression periods in the forward recursion, and T is the regression period;

[0076] Take N = fix((t) i -t cj ) / T), M=fix(((t) i -t cj )-N*T) / Ts)+1

[0077] in:

[0078] Ts is the time interval between adjacent strict regression orbit reference points;

[0079] T is the regression period of the strict regression orbit;

[0080] N is the number of regression periods that need to be recursively applied forward;

[0081] The fix() operation rounds the calculated numerical result to the nearest integer.

[0082] M indicates that the Mth point in the reference orbit point sequence is the corresponding reference point that needs to be aimed at.

[0083] Step 3 uses reference orbit point P c Establish a formation coordinate system with the origin as the origin, and calculate the satellite t. i The relative position vector R1(R) in this coordinate system Hx1 R Hy1 R Hz1 );

[0084] The formation coordinate system OXYZ is defined as follows: OX is the vector direction from the Earth's center E to the origin; OY is in the plane of the main star's orbit, perpendicular to OX and pointing in the direction of flight; OZ, together with OX and OY, forms a right-handed coordinate system.

[0085]

[0086] in: For P c The position vector of a point in an inertial coordinate system. For P c The velocity vector of a point in the inertial coordinate system. For P s The position vector of a point in an inertial coordinate system. For P s The velocity vector of a point in the inertial coordinate system, A i2b The transformation matrix from the inertial frame to the formation coordinate system is given below, and the specific algorithm for this transformation is as follows:

[0087] in

[0088] Step 4: Based on R1, the satellite's trajectory from t can be quickly calculated. i Run to P c The required time Δt will be obtained by recursively calculating t using the orbital path. i The orbital state P at time +Δt s (time t) k 3D position [x k ,y k ,z k ], three-dimensional velocity [vx k ,vy k ,vz k ]); and calculate the relative position vector R of Ps in the trajectory coordinate system with Pc as the origin. i (R gjxi R gjyi R gjzi The specific algorithm is as follows:

[0089] By [x i ,y i z i] and [vx i ,vy i ,vz i The orbital elements [a,e,i,Ω,ω,M] are obtained through conversion. Due to the short recursion time, except for the mean anterior angle M, which is calculated based on time and the average angular velocity of the orbit, the other orbital elements are slow-varying terms and are taken with the same values ​​as before the recursion. Thus, with this simplified orbital recursion, the orbital elements [a,e,i,Ω,ω,M+n*Δt] after Δt can be quickly obtained, and then the orbital state P can be obtained. s [x si ,y si ,z si ] and [vx si ,vy si ,vz si ].calculate In The relative position vector in the trajectory coordinate system of the origin The specific process is as follows:

[0090] Calculate the transformation matrix from the Earth-fixed coordinate system to the trajectory coordinate system:

[0091] A c2g =[x g ,y g ,z g ] T ,in

[0092]

[0093] in: For P c The position vector of a point in the Earth-fixed coordinate system. For P c The velocity vector of a point in the Earth-fixed coordinate system. For P s The position vector of a point in the Earth-fixed coordinate system. For P s The velocity vector of a point in the Earth-fixed coordinate system.

[0094] Step 5: Repeat the above steps to obtain the relative position vector R corresponding to all measured orbital state sequences within one orbit. i (i = 1, 2, 3… N), the processing method for each measured point is the same. Considering the time interval of the reference track, the time interval of the measured points should be comparable to that of the reference track in the absence of control. However, if track control is carried out in a certain period of time, the time interval of the measured points in that period of time can be smaller, so as to better reflect the actual situation of pipeline deviation during track control.

[0095] Step 6: Convert the X values ​​of the N relative position vectors. gj and Z gj The coordinates form a two-dimensional vector sequence. By fitting this two-dimensional sequence to an ellipse, the minimum circumcircle radius of the resulting curve is the satellite's pipeline deviation.

[0096] Obtaining the general equation of an ellipse using numerical fitting with the method of undetermined coefficients.

[0097] ax 2 +bxy+cy 2 +dx+ey+f=0

[0098] Let α = [a, b, c, d, e, f] T , x = [x 2 ,xy,y 2 [x,y,1] T The elliptic least squares fitting method is used to solve for α = [a, b, c, d, e, f]. T Once completed, draw the elliptic curve and place it at the X-axis. gj O gj Z gj Within the coordinate system, draw the circumcircle of the elliptic curve with the origin as the center. The radius of this circle represents the satellite's total orbital deviation. For example... Figure 2 The figure shows a schematic diagram of the pipeline deviation curve in the trajectory coordinate system during one orbital period of the satellite.

[0099] The method proposed in this embodiment has a clear process and strong engineering feasibility: it avoids the recursive calculation of orbit in the orbit alignment process by combining the actual situation of orbit changes, and has good engineering feasibility. At the same time, the method has strong anti-interference ability and the determination results are accurate and reliable: the curve fitting process avoids the errors and data disturbances that may exist in single or partial orbit measurement data, and can process orbit data of different scales as needed. It can be implemented both on-board and on the ground.

[0100] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0101] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for full-orbit fitting of pipeline deviation for strictly regressive orbit satellites, characterized in that... include: Collect measured satellite orbit state sequence information and reference orbit state sequence information; By regressing the reference orbit sequence time of the current reference orbit point in the reference orbit state sequence information, the reference orbit point closest to the pre-selected time point of the satellite's measured orbit state sequence information is determined; Using the reference trajectory point as the origin, establish a formation coordinate system and calculate the relative position vector of the satellite in the formation coordinate system at the pre-selected time point; The recursive time required for the satellite to travel from the position at the pre-selected time point to the reference orbit point in the measured orbit is calculated based on the relative position vector and the satellite's measured orbit state sequence information. The relative position vector of the orbit point after the recursive operation is calculated in the trajectory coordinate system with the reference trajectory point as the origin, based on the orbit state sequence information corresponding to the recursive operation. Traverse all satellite measured orbit state sequence information under the measured orbit and select the pre-selected time points to obtain the relative position vector of the orbit point after the operation recursion at each pre-selected time point in the trajectory coordinate system with the reference trajectory point as the origin. The two-dimensional vector sequence is formed by obtaining the relative position vectors of all orbit points after recursion in the trajectory coordinate system with the reference trajectory point as the origin. After ellipse fitting, the minimum circumscribed circle radius is obtained as the satellite's pipeline deviation.

2. The method for full-orbit fitting of pipeline deviation for a strictly regressive orbit satellite according to claim 1, characterized in that: The satellite's measured orbital state sequence information includes time t. i 3D position [x] i , y i ,z i ], three-dimensional velocity [vx i ,vy i ,vz i The reference orbital state sequence information includes time t. ci 3D position [x] ci ,y ci ,z ci ], three-dimensional velocity [vx ci ,vy ci ,vz ci ] ; i=1,2,3…N; both the measured orbital state sequence information and the reference orbital state sequence information are parameter information within one regression period; N is the number of regression periods for forward recursion; When the pre-selected time point is determined, the reference orbit point P closest to the pre-selected time point is selected on the satellite's measured orbit. c Determine the reference orbit point P c The corresponding reference orbit time t on the reference orbit cj .

3. The method for full-orbit fitting of pipeline deviation for strictly regressive orbit satellites according to claim 2, characterized in that: Based on reference orbit point P c Reference orbit time t cj Pre-selected time point t i The comparison results show that the reference orbit point P is under the condition of insufficient time. c Reference orbit time t cj By recursively calculating backwards according to the integer regression period, the number of regression periods N to be recursively calculated is determined as follows: N=fix((t i -t cj ) / T) In the formula, T is the regression period, N is the number of regression periods to be recursively applied, and the fix() operation represents rounding the calculated numerical result.

4. The method for full-orbit fitting of pipeline deviation for strictly regressive orbit satellites according to claim 3, characterized in that: After determining the number of regression periods N that need to be recursively calculated, select the reference orbital point to be targeted from the reference orbital point sequence, as follows: M=fix(((t i -t cj )-N T) / Ts)+1 In the formula, Ts is the time interval between adjacent strict regression orbit reference points, and M represents the Mth point in the reference orbit point sequence, i.e., the reference orbit point to be targeted.

5. The method for full-orbit fitting of pipeline deviation for strictly regressive orbit satellites according to claim 1, characterized in that: The formation coordinate system OXYZ uses the vector direction from the Earth's center E to the origin as the OX axis, and sets the OY axis in the main star's orbital plane, pointing perpendicularly to the OX axis in the flight direction. The OZ axis satisfies the right-hand rule with the OX and OY axes. A pre-selected time point t... i At any given moment, the relative position vector of the satellite in the formation coordinate system is denoted as R1 (R Hx1 R Hy1 R Hz1 ).

6. The method for full-orbit fitting of pipeline deviation for a strictly regressive orbit satellite according to claim 5, characterized in that: The relative position vector R1 is calculated as follows: In the formula, the reference orbit point P c , For P c The position vector of a point in an inertial coordinate system. For P c The velocity vector of a point in the inertial coordinate system. For P s The position vector of a point in an inertial coordinate system. For P s The velocity vector of a point in the inertial coordinate system. This is the transformation matrix from the inertial frame to the formation coordinate system.

7. The method for full-orbit fitting of pipeline deviation for a strictly regressive orbit satellite according to claim 6, characterized in that: Track point P after running s The corresponding orbital state sequence information includes time t k 3D position [x] k ,y k ,z k ], three-dimensional velocity [vx k ,vy k ,vz k ]; Track point P after operation s The relative position vector in the trajectory coordinate system with Pc as the origin is R. i (R) gjxi R gjyi R gjzi ); The method for calculating the travel time Δt required for a satellite to travel from a pre-selected time point to a reference orbit point in its measured orbit is as follows: In the formula, the molecule is the projection of its relative position along the Hy direction. The denominator is the magnitude of the velocity vector. .

8. The method for full-orbit fitting of pipeline deviation for strictly regressive orbit satellites according to claim 7, characterized in that: Based on the track point P after operation s The moment t i Satellite orbital elements at time +Δt [a,e,i, Ω,ω,M+n] ], convert and obtain the track point P after running. s orbital state sequence information [x si , y si , z si ] and [vx si ,vy si ,vz si ], calculate P s In P c The relative position vector in the trajectory coordinate system of the origin (R) gjxi R gjyi R gjzi The method is as follows: In the formula, P c , For P c The position vector of a point in the Earth-fixed coordinate system. For P c The velocity vector of a point in the Earth-fixed coordinate system. For P s The position vector of a point in the Earth-fixed coordinate system. For P s The velocity vector of a point in the Earth-fixed coordinate system.

9. The method for full-orbit fitting of pipeline deviation for a strictly regressive orbit satellite according to claim 1, characterized in that: The calculation method for the relative position vector of the orbit point corresponding to the pre-selected time point in the orbital state sequence information of all satellites is the same in the orbital coordinate system with the reference trajectory point as the origin. The reference orbit time interval is considered when selecting each pre-selected time point. In the case of no orbit control, the measured orbit is the same as the reference orbit. In the case of orbit control, the measured orbit is smaller than the reference orbit.

10. The method for full-orbit fitting of pipeline deviation for a strictly regressive orbit satellite according to claim 2, characterized in that: X of N relative position vectors gj and Z gj The coordinates form a two-dimensional vector sequence. This two-dimensional sequence is fitted to an ellipse, and the general equation of the ellipse is obtained by numerical fitting using the method of undetermined coefficients. remember , The elliptic least squares fitting method is used to solve the problem. ; After solving, plot the elliptic curve and place it on the X-axis. gj O gj Z gj Within the trajectory coordinate system, draw the circumcircle of the elliptic curve with the origin as the center, and use the minimum radius of the circumcircle as the satellite's pipeline deviation.

Images