A satellite formation baseline control method based on inter-satellite ranging information

Abstract

The present invention provides a method for controlling the satellite formation baseline based on inter-satellite ranging information. For a satellite formation without a GNSS system, it can achieve precise control of the baseline without relying on real-time navigation information and by relying on inter-satellite ranging information. This baseline control method mainly includes three parts: the establishment of the state transition matrix, the establishment of the ranging measurement equation, and the solution of the correction control pulse. Compared with the acquisition of navigation data, the acquisition of ranging data is more convenient, and the ranging accuracy of the low-gain link between satellites reaches 1 m. This method can achieve precise control of the baseline without relying on real-time navigation information and by making full use of inter-satellite ranging information.

Description

Technical Field

[0001] The invention relates to the field of aerospace, and in particular to a satellite formation baseline control method based on inter-satellite ranging information. Background Art

[0002] Satellite formation technology has extremely critical application value in many important fields such as earth remote sensing, space science exploration and space operations. During the mission execution phase, in order to meet the specific requirements of different tasks, the satellite formation needs to stably maintain the established configuration or flexibly realize the configuration conversion, which makes the precise control of the satellite formation a core research topic in this field.

[0003] At present, the Global Navigation Satellite System (GNSS) can provide high-precision orbit determination services for low-Earth orbit satellites. Based on this, in the process of low-Earth orbit satellite formation control, the navigation information provided by GNSS can be fully utilized to achieve effective control of the satellite formation. There are many related research results. For example, in the article "High-precision Micro-Nano Satellite Formation Maintenance Based on SiC MEMS Array", the technical solution of achieving high-precision micro-nano satellite formation maintenance with the help of instantaneous pulse control strategy was deeply studied; and "Satellite Formation Pulse Maneuvering Maintenance Control and Strategy" focuses on the problem of low-Earth circular orbit satellite formation maintenance, and conducts a systematic study on the pulse control scheme and maintenance control strategy.

[0004] However, when the research scope is expanded to lunar orbit satellite formations and other satellite formations that cannot obtain GNSS system support due to the environment, the traditional control method that relies on real-time navigation status information is difficult to meet actual needs. Therefore, it is urgent to develop an innovative control method that does not rely on navigation status information to fill the technical gap in this field and promote the application and development of satellite formation technology in a wider range of space scenarios. Summary of the invention

[0005] The present invention proposes a satellite formation baseline control method based on inter-satellite ranging information for a satellite formation without a GNSS system, which is characterized by comprising:

[0006] Obtain the analytical solution based on the CW equation and establish the state transfer matrix;

[0007] According to the state transfer matrix, the terminal position state reached from the expected initial state and the actual initial state is obtained;

[0008] Subtract the terminal position states to obtain a relationship equation between the initial state deviation of the satellite motion and the terminal moment position deviation;

[0009] Subtracting the expected baseline distance from the actual baseline distance to obtain the baseline distance deviation;

[0010] According to the relationship between the expected baseline distance and the initial state of satellite motion, the relationship equation between the baseline distance deviation and the initial state deviation of satellite motion is obtained;

[0011] Perform N distance measurements, and establish a distance measurement equation group of six past moments according to a relationship equation between the baseline distance deviation and the initial state deviation of the satellite motion, where N is a positive integer greater than or equal to six;

[0012] According to the distance measurement equation group, an inverse solution is performed to obtain the initial state deviation of the satellite motion;

[0013] The terminal moment position deviation is obtained by the relationship equation between the initial state deviation of the satellite motion and the terminal moment position deviation; and

[0014] A corrected control pulse is obtained according to the position deviation at the end moment.

[0015] In one embodiment of the present invention, obtaining an analytical solution according to the CW equation includes: establishing the following CW equation:

[0016]

[0017] in is the x-acceleration of the satellite relative to the main star in the LVLH coordinate system of the main star;

[0018] is the y-acceleration of the satellite relative to the main star in the LVLH coordinate system of the main star;

[0019] is the z-acceleration of the satellite relative to the main star in the LVLH coordinate system of the main star;

[0020] is the y-speed of the satellite relative to the main star in the LVLH coordinate system of the main star;

[0021] is the x-speed of the satellite relative to the primary star in the primary star LVLH coordinate system;

[0022] n is the orbital angular velocity of the primary star;

[0023] (x, y, z) is the motion position of the satellite relative to the main star in the LVLH coordinate system of the main star.

[0024] In one embodiment of the present invention, obtaining an analytical solution according to the CW equation further includes: obtaining an analytical solution as:

[0025]

[0026] Where (x 0 ,y 0 , z 0) is the initial position state of the satellite relative to the main star;

[0027] , , , is the initial velocity state of the satellite relative to the main star at time t0;

[0028] , , is the velocity state of the satellite relative to the main star at time t;

[0029] t is the movement time.

[0030] In one embodiment of the present invention, the equation for obtaining the relationship between the initial state deviation of the satellite motion and the terminal time position deviation includes: obtaining the terminal time The satellite's y-direction deviation is:

[0031]

[0032] in A The matrix is ​​represented as

[0033] ,

[0034] ;

[0035] ;

[0036] is the initial state deviation;

[0037] , , is the initial position state deviation of the satellite relative to the primary satellite;

[0038] , , is the initial velocity state deviation of the satellite relative to the primary satellite.

[0039] In one embodiment of the present invention, obtaining a corrected control pulse according to the terminal moment position deviation includes:

[0040] Solve the terminal moment Satellite y deviation The relationship equation with the modified control pulse is:

[0041]

[0042] In the formula, ;

[0043] ;

[0044] Solve to get the corrected control pulse: ;

[0045] in The correction control pulse required for the correction time;

[0046] , , They are Components in the x, y, and z directions.

[0047] In one embodiment of the present invention, the correction control pulse is the control of the distance in the y direction in the relative motion coordinate system, and its expression is:

[0048] .

[0049] In one embodiment of the present invention, the relationship equation between the baseline distance deviation and the satellite motion initial state deviation comprises:

[0050] Get the baseline distance deviation expression ;

[0051] Provide the relationship between the expected baseline distance and the initial state of the initial state satellite motion; ;

[0052] By taking the total differential of the expected baseline distance expression, the relationship equation between the baseline distance deviation and the initial state deviation of the satellite motion is obtained;

[0053] in represents the expected baseline distance of the slave star relative to the master star;

[0054] Indicates the actual baseline distance of the slave star relative to the master star.

[0055] In one embodiment of the present invention, the establishing of the distance measurement equation group of six past moments includes: obtaining the distance measurement equation group:

[0056]

[0057] in is the initial state deviation;

[0058] , , is the initial velocity state of the satellite relative to the main star at time t0;

[0059] (x 0 ,y 0 , z 0 ) is the initial position state of the satellite relative to the main star;

[0060] l 1 , l 2 , l 3 , l 4 , l 5 , l 6 Measure the baseline distance of the neutron star relative to the primary star for six past times

[0061] Δl 1 , Δl 2 , Δl 3 , Δl 4 , Δl 5 , Δl 6 is the baseline distance deviation in the six past distance measurements.

[0062] Based on the lunar orbit satellite formation without GNSS system, the present invention takes advantage of the convenient acquisition of inter-satellite ranging data and the high ranging accuracy of inter-satellite low-gain link, and proposes a baseline control method based on inter-satellite ranging information, which can achieve accurate baseline control. It has the following beneficial effects:

[0063] (1) This method gets rid of the dependence on accurate real-time navigation information, greatly reduces the difficulty and cost of engineering implementation, and has extremely high practical value and promotion potential in actual engineering applications.

[0064] (2) Compared with traditional navigation data acquisition methods, the ranging data acquisition process is simpler and faster. At the same time, it demonstrates excellent ranging performance in the intersatellite low-gain link, with a stable ranging accuracy of 1m, providing a solid and reliable data foundation for achieving high-precision baseline control. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 A flowchart of satellite formation baseline control based on inter-satellite ranging information in one embodiment of the present invention is shown;

[0066] Figure 2 A baseline control flow chart based on inter-satellite ranging information in one embodiment of the present invention is shown;

[0067] Figure 3 A diagram showing the effect of baseline control based on inter-satellite ranging information in one embodiment of the present invention is shown;

[0068] Figure 4 A comparison diagram of baseline control effects based on inter-satellite ranging information and based on past navigation information in one embodiment of the present invention is shown;

[0069] Figure 5 A diagram showing the effect of baseline control based on inter-satellite ranging information in another embodiment of the present invention is shown; and

[0070] Figure 6 A diagram showing the effect of baseline control based on inter-satellite ranging information in another embodiment of the present invention is shown. DETAILED DESCRIPTION

[0071] In the following description, the present invention is described with reference to various embodiments. However, those skilled in the art will recognize that various embodiments may be implemented without one or more specific details or with other replacement and / or additional methods, materials or components. In other cases, well-known structures, materials or operations are not shown or described in detail to avoid obscuring the inventive point of the present invention. Similarly, for the purpose of explanation, specific quantities, materials and configurations are set forth to provide a comprehensive understanding of embodiments of the present invention. However, the present invention is not limited to these specific details.

[0072] In the present invention, each embodiment is only intended to illustrate the aspects of the present invention and should not be construed as limiting.

[0073] In this specification, reference to "one embodiment" or "the embodiment" means that a particular feature, structure, or characteristic described in conjunction with the embodiment is included in at least one embodiment of the present invention. The phrase "in one embodiment" appearing in various places in this specification does not necessarily all refer to the same embodiment.

[0074] In addition, the numbering of the steps of the methods of the present invention does not limit the execution order of the method steps. Unless otherwise specified, the method steps can be executed in different orders.

[0075] The present invention will be further described below in conjunction with specific embodiments with reference to the accompanying drawings.

[0076] Figure 1 A flowchart of satellite formation baseline control based on inter-satellite ranging information in one embodiment of the present invention is shown.

[0077] In the present invention, the satellite formation baseline control based on inter-satellite ranging information is mainly divided into the following processes:

[0078] (1) Establish the state transfer matrix 10:

[0079] The analytical solution is obtained according to the CW equation, and the state transfer matrix is ​​established. The CW equation is the linear differential relative motion dynamics equations of the satellite formation in the circular reference orbit when the two satellites are in two-body motion and the distance between the master and slave satellites is relatively close:

[0080]

[0081] in is the x-acceleration of the satellite relative to the main star in the LVLH coordinate system of the main star;

[0082] is the y-acceleration of the satellite relative to the main star in the LVLH coordinate system of the main star;

[0083] is the z-acceleration of the satellite relative to the main star in the LVLH coordinate system of the main star;

[0084] is the y-speed of the satellite relative to the main star in the LVLH coordinate system of the main star;

[0085] is the x-speed of the satellite relative to the primary star in the primary star LVLH coordinate system;

[0086] n is the orbital angular velocity of the primary star;

[0087] (x, y, z) is the motion position of the satellite relative to the main star in the LVLH coordinate system of the main star.

[0088] The analytical solution of the CW equation is:

[0089]

[0090] Where (x 0 ,y 0 , z 0 ) is the initial position state of the satellite relative to the main star;

[0091] , , , is the initial velocity state of the satellite relative to the main star at time t0;

[0092] , , is the velocity state of the satellite relative to the main star at time t;

[0093] t is the movement time.

[0094] (2) The relationship between the initial state deviation and the terminal position deviation is obtained as equation 20:

[0095] According to the state transfer matrix, the terminal position state reached from the expected initial state and the actual initial state is obtained. Subtracting them to obtain the relationship equation between the initial state deviation of the satellite motion and the terminal moment position deviation, the terminal moment From the Stars y The deviation to

[0096] (1-3)

[0097] in A The matrix is ​​represented as

[0098] ;

[0099] , ;

[0100] is the initial state deviation.

[0101] (3) The relationship between the baseline distance deviation and the initial state deviation is obtained as equation 30:

[0102] make Indicates the expected baseline distance of the slave star relative to the master star Distance from actual baseline The difference between According to the relationship between the expected baseline distance and the initial state of satellite motion, By taking the total differential, we can obtain the relationship between the baseline distance deviation and the initial state deviation.

[0103] (4) Establish the distance measurement equation group 40:

[0104] Perform N distance measurements, and establish a distance measurement equation group for six past moments according to the relationship equation between the baseline distance deviation and the initial state deviation of the satellite motion, where N is a positive integer greater than or equal to six, to obtain the distance measurement equation for six past moments:

[0105] ;

[0106] , , is the initial velocity state of the satellite relative to the main star at time t0;

[0107] (x 0 ,y 0 , z 0 ) is the initial position state of the satellite relative to the main star;

[0108] l 1 , l 2 , l 3 , l 4 , l 5 , l 6 Measure the baseline distance of the neutron star relative to the primary star for six past times

[0109] is the baseline distance deviation in the six past distance measurements.

[0110] (5) Calculate the initial state deviation of the satellite motion 50:

[0111] According to the distance measurement equation group, the initial state deviation of the satellite motion is obtained by inverse solution. .

[0112] , , is the initial position state deviation of the satellite relative to the primary satellite;

[0113] , , is the initial velocity state deviation of the satellite relative to the primary satellite.

[0114] (6) Calculate the terminal position deviation 60:

[0115] Substitute the initial state deviation of the satellite motion into the relationship equation between the initial state deviation of the satellite motion and the position deviation at the terminal moment to obtain the terminal moment Deviation from star y direction:

[0116]

[0117] in A The matrix is ​​represented as

[0118] ,

[0119] ;

[0120] .

[0121] (7) Obtain the corrected control pulse 70

[0122] Because in When the correction control pulse is applied at any time, the position state remains unchanged, so there is . Further considering the baseline direction of the serial formation and the relative coordinate system y The directions coincide, so , and the corrected control pulse is obtained, and its expression is:

[0123] .

[0124] in The correction control pulse required for the correction time;

[0125] , , They are Components in the x, y, and z directions.

[0126] Figure 2 A baseline control flow chart based on inter-satellite ranging information in one embodiment of the present invention is shown.

[0127] The present invention proposes a baseline control method for a satellite formation without a GNSS system, which can achieve accurate baseline control by relying on inter-satellite ranging information without relying on real-time navigation information. In one embodiment of the present invention, the specific process is as follows:

[0128] (1) Establishment of state transfer matrix 101

[0129] When the two satellites are in two-body motion and the distance between the master and slave satellites is relatively close, the linear differential relative motion dynamics equations of the satellite formation in the circular reference orbit are:

[0130] (1-1)

[0131] The above equation is the Clohessy-Whiltshire equation (CW equation for short), where (x, y, z) are the relative coordinates of the satellite formation.

[0132] Solving the equation group (1-1), we obtain the analytical solution of the CW equation:

[0133] (1-2)

[0134] Where (x0, y0, z0) are the initial coordinates of the satellite formation in the circular reference orbit, and t is the current time.

[0135] Baseline control is the control of the distance in the y direction in the relative motion coordinate system, which is the control of the end deviation in the present invention. Calculate the corrected control pulse .

[0136] According to the analytical solution of the CW equation, the terminal time can be obtained From the Stars y The deviation to

[0137] (1-3)

[0138] in A The matrix is ​​represented as

[0139] ,

[0140] ;

[0141] ;

[0142] is the initial state deviation.

[0143] If the correction time is According to the CW equation, we can further establish With modified control pulse The relationship between:

[0144] (1-4)

[0145] In formula (1-4), , .

[0146] From (1-4), we can see that the control quantity required is , first of all, we need to solve the initial state deviation.

[0147] (2) Establishment of distance measurement equation 102

[0148] The present invention proposes a formation satellite baseline control method based on inter-satellite ranging information. Indicates the expected baseline distance of the slave star relative to the master star Distance from actual baseline The difference between

[0149] (1-5)

[0150] in represents the expected baseline distance of the slave star relative to the master star;

[0151] Indicates the actual baseline distance of the slave star relative to the master star.

[0152] Through The total differential gives the relationship between the baseline distance deviation and the initial state deviation. For six-dimensional unknown variables, at least six distance measurements are required, and then the distance measurement equation for six past moments can be established:

[0153] (1-6)

[0154] (3) Correction control pulse solution 103

[0155] According to (1-6), the initial state deviation is obtained .

[0156] Substituting it into formula (1-5) we can obtain .

[0157] Because in When the correction control pulse is applied at any time, the position state remains unchanged, so there is . Further considering the baseline direction of the serial formation and the relative coordinate system y The directions coincide, so , so according to formula (1-6) we can get the corrected control pulse

[0158] .

[0159] The present invention will be described below with reference to specific embodiments.

[0160] In one embodiment of the present invention, taking the serial formation near the lunar orbit as an example, the initial state of the slave star is selected as , , the target state of the star is , the position error of autonomous navigation is 0.5e - 3 km, speed error is 0.3e -6 km / s, orbit control error is 0.05, mission duration is 7 days, correction time is the 3rd day, and the control effect of 1km baseline is as follows Figure 3 and Figure 4 shown.

[0161] like Figure 4 As shown, the purple track represents the result of correction based on past navigation information, with a baseline deviation of 0.5m, and the green track represents the result of correction based on intersatellite measurement, with a baseline deviation of 8.6m. The control effect accuracy of the two methods is comparable.

[0162] In another embodiment of the present invention, Figure 5 FIG. 1 shows the effect of baseline control based on inter-satellite ranging information in another embodiment of the present invention. In this embodiment, the control effect of the 10 km baseline is as follows: Figure 5 As shown, the baseline deviation of the control result in the figure is 12m.

[0163] In another embodiment of the present invention, Figure 6 FIG. 1 shows the effect of baseline control based on inter-satellite ranging information in another embodiment of the present invention. In this embodiment, the control effect of the 100 km baseline is as follows: Figure 6 As shown, the baseline deviation of the control result in the figure is 211m.

[0164] In summary, the present invention performs baseline control based on inter-satellite ranging information. Compared with the traditional navigation data acquisition method, the ranging data acquisition process is simpler and faster. At the same time, it shows excellent ranging performance in the inter-satellite low-gain link, providing a solid and reliable data foundation for achieving high-precision baseline control. It can be seen from the above embodiments that the present invention has high-precision control effects at 1km, 10km, and 100km.

[0165] Although various embodiments of the present invention are described above, it should be understood that they are presented as examples only and not as limitations. It is obvious to those skilled in the relevant art that various combinations, deformations and changes can be made thereto without departing from the spirit and scope of the present invention. Therefore, the breadth and scope of the present invention disclosed herein should not be limited by the exemplary embodiments disclosed above, but should only be defined according to the attached claims and their equivalents.

Claims

1. A satellite formation baseline control method based on inter-satellite ranging information, characterized in that: include: Obtain the analytical solution based on the CW equation and establish the state transfer matrix; According to the state transfer matrix, the terminal position state reached from the expected initial state and the actual initial state is obtained; Subtract the terminal position states to obtain a relationship equation between the initial state deviation of the satellite motion and the terminal moment position deviation; Subtracting the expected baseline distance from the actual baseline distance to obtain the baseline distance deviation; According to the relationship between the expected baseline distance and the initial state of satellite motion, the relationship equation between the baseline distance deviation and the initial state deviation of satellite motion is obtained; Perform N distance measurements, and establish a distance measurement equation group of six past moments according to a relationship equation between the baseline distance deviation and the satellite motion initial state deviation, where N is a positive integer greater than or equal to six; According to the distance measurement equation group, an inverse solution is performed to obtain the initial state deviation of the satellite motion; The terminal moment position deviation is obtained through the relationship equation between the initial state deviation of the satellite motion and the terminal moment position deviation; as well as A corrected control pulse is obtained according to the position deviation at the end moment.

2. The satellite formation baseline control method according to claim 1, characterized in that: The obtaining of the analytical solution according to the CW equation includes: establishing the following CW equation: in is the x-axis acceleration of the satellite relative to the main star in the LVLH coordinate system of the main star; is the y-acceleration of the satellite relative to the main star in the LVLH coordinate system of the main star; is the z-acceleration of the satellite relative to the main star in the LVLH coordinate system of the main star; is the y-speed of the satellite relative to the main star in the LVLH coordinate system of the main star; is the x-speed of the satellite relative to the main star in the LVLH coordinate system of the main star; n is the orbital angular velocity of the primary star; (x, y, z) is the motion position of the satellite relative to the main star in the LVLH coordinate system of the main star.

3. The satellite formation baseline control method according to claim 2, characterized in that: The step of obtaining an analytical solution according to the CW equation further includes: obtaining an analytical solution as: Among them, (x0, y0, z0) is the initial position state of the satellite relative to the main star; , , , is the initial velocity state of the satellite relative to the main star at time t0; , , is the velocity state of the satellite relative to the main star at time t; t is the movement time.

4. The satellite formation baseline control method according to claim 1, characterized in that: The equation for obtaining the relationship between the initial state deviation of the satellite motion and the position deviation at the terminal moment includes: obtaining the terminal moment The satellite's y-direction deviation is: in A The matrix is ​​represented as ， ； ； is the initial state deviation; , , is the initial position state deviation of the satellite relative to the primary satellite; , , is the initial velocity state deviation of the satellite relative to the primary satellite.

5. The satellite formation baseline control method according to claim 1, characterized in that: The corrected control pulses obtained according to the terminal moment position deviation include: Solve the terminal moment Satellite y deviation The relationship equation with the modified control pulse is: In the formula, ; ； Solve to get the corrected control pulse: ; in The correction control pulse required for the correction time; , , They are Components in the x, y, and z directions.

6. The satellite formation baseline control method according to claim 5, characterized in that: The correction control pulse is the control of the distance in the y direction in the relative motion coordinate system, and its expression is: 。 7. The satellite formation baseline control method according to claim 1, characterized in that: The relationship equation between the baseline distance deviation and the initial state deviation of the satellite motion includes: Get the baseline distance deviation expression ; Provide the relationship between the expected baseline distance and the initial state of the initial state satellite motion; ; By taking the total differential of the expected baseline distance expression, the relationship equation between the baseline distance deviation and the initial state deviation of the satellite motion is obtained; in represents the expected baseline distance of the slave star relative to the master star; Indicates the actual baseline distance of the slave star relative to the master star.

8. The satellite formation baseline control method according to claim 1, characterized in that: The establishing of the distance measurement equation group of six past moments includes: obtaining the distance measurement equation group: in is the initial state deviation; , , is the initial velocity state of the satellite relative to the main star at time t0; (x0, y0, z0) is the initial position state of the satellite relative to the main satellite; l1, l2, l3, l4, l5, l6 are the baseline distances of the neutron star relative to the primary star measured at six past moments Δl1, Δl2, Δl3, Δl4, Δl5, Δl6 are the baseline distance deviations in the six past distance measurements.

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