Joint orbit determination method based on slr and inter-satellite link

Abstract

The application relates to a combined orbit determination method based on SLR and intersatellite links, which comprises the following steps: S100, determining a nonlinearized intersatellite observation equation according to intersatellite observation data; S200, determining a nonlinearized SLR observation equation according to SLR observation data; S300, determining a state transition matrix and a linearized satellite orbit determination observation equation according to a satellite motion equation and the nonlinearized satellite orbit determination observation equation; S400, determining a linearized SLR observation equation according to the nonlinearized SLR observation equation, the state transition matrix and the linearized satellite orbit determination observation equation; S500, determining a linearized intersatellite observation equation according to the nonlinearized intersatellite observation equation, the state transition matrix and the linearized satellite orbit determination observation equation; and S600, performing satellite combined orbit determination according to the linearized intersatellite observation equation and the linearized SLR observation equation. The application can simultaneously exert the technical advantages of SLR and intersatellite links, and can obtain a high-precision satellite orbit.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of satellite technology, in particular to a joint orbit determination method based on SLR (satellite laser ranging) and inter-satellite link. BACKGROUND

[0002] The BDS-3 ground monitoring stations are mainly distributed in China, which has an impact on satellite orbit determination and global service. The BDS-3 satellites are equipped with inter-satellite link devices, which use inter-satellite ranging technology to make up for the lack of observation arcs, separate the satellite relative clock bias and relative geometric distance, decouple the satellite orbit and clock bias, and then use the satellite-ground distance as an observation combined with ground measurement data for joint satellite-ground-satellite orbit determination. However, due to the inter-satellite link measurement system, when only using satellite inter-satellite ranging data for satellite orbit determination processing, the navigation constellation has the problem of overall rotation.

[0003] Satellite laser ranging (SLR, Satellite Laser Ranging) technology measures the round-trip time interval of a laser pulse from a ground observation point to a satellite equipped with a reflector, thereby calculating the distance from the ground observation station to the satellite. SLR technology is not affected by carrier phase ambiguity, clock bias and ionosphere, and SLR satellites used in geodesy have a spherical shape and a small area mass ratio, which can reduce non-gravity-related orbital perturbations such as atmospheric resistance and solar radiation pressure. Based on its technical characteristics, SLR technology has unique advantages in the study of the Earth Reference Frame, scale, Earth's motion, Earth's rotation parameters and Earth's gravity field. The scale and the Earth's center of the International Terrestrial Reference Frame are mainly obtained from SLR observations of LAGEOS and other geodetic satellites. However, due to the small number of SLR ground tracking stations, uneven distribution and small amount of observation data, the orbit determination accuracy using single SLR observation data is poor.

[0004] Jointing satellite-ground pseudorange phase data and inter-satellite link can improve the orbit accuracy, but pseudorange phase observation data will be affected by factors such as antenna phase center, solar radiation pressure and ambiguity during data processing. The existing BDS satellite orbit determination method does not consider the joint precise orbit determination of SLR and inter-satellite link for BDS satellites. SUMMARY

[0005] Therefore, the present application aims to solve the above problems and proposes a joint orbit determination method based on SLR and inter-satellite link.

[0006] The present application provides a joint orbit determination method based on SLR and inter-satellite link, which comprises:

[0007] S100, determining a non-linearized inter-satellite observation equation according to inter-satellite observation data;

[0008] S200, determining a nonlinearized SLR observation equation according to SLR observation data;

[0009] S300, determining a state transition matrix and a linearized satellite orbit determination observation equation according to a satellite motion equation and the nonlinearized satellite orbit determination observation equation;

[0010] S400, determining a linearized SLR observation equation according to the nonlinearized SLR observation equation, the state transition matrix and the linearized satellite orbit determination observation equation;

[0011] S500, determining a linearized inter-satellite observation equation according to the nonlinearized inter-satellite observation equation, the state transition matrix and the linearized satellite orbit determination observation equation;

[0012] S600, performing satellite joint orbit determination according to the linearized inter-satellite observation equation and the linearized SLR observation equation.

[0013] In the preferred embodiment of the present application, step S100 comprises:

[0014] determining that the first satellite receives a ranging signal ρ BA (t1) transmitted by the second satellite at its own clock time t1, and determining that the second satellite receives a ranging signal ρ AB (t2) transmitted by the first satellite at its own clock time t2;

[0015]

[0016]

[0017] wherein r A and r B are three-dimensional positions of the first satellite and the second satellite respectively, c is the speed of light, clk A and clk B are satellite clock errors of the first satellite and the second satellite respectively, Δt1 and Δt2 are light travel times respectively, τ send and τ rcv are transmission time delay and reception time delay of the satellites respectively, Δδ BA and Δδ AB are error correction terms which can be accurately modeled in ranging;

[0018] ρ BA (t1) and ρ AB (t2) are reduced to an intermediate epoch t0 according to the following formula to obtain the nonlinearized inter-satellite observation equation:

[0019]

[0020]

[0021] wherein dρ BA and dρ AB are the correction values of satellite position and satellite clock bias.

[0022] The addition of the simultaneous two-way ranging can eliminate the satellite clock bias and only contain the satellite distance information. The subtraction of the simultaneous two-way ranging can eliminate the satellite orbit and only contain the satellite clock bias. The relative distance between the satellites is:

[0023]

[0024] The formula is the inter-satellite link observation equation for satellite orbit determination.

[0025] In the preferred embodiment of the present application, Δδ BA and Δδ AB include the satellite antenna phase center correction value and the relativistic effect correction value.

[0026] In the preferred embodiment of the present application, in step S200:

[0027] The non-linearized SLR observation equation is:

[0028] ρ0=ρ′-(Δρ TD +Δρ RF +Δρ REL +Δρ MC +Δρ RO );

[0029] wherein ρ0 is the SLR observation, ρ′ is the original observation distance of the SLR station, Δρ TD is the error of the tidal variation of the SLR station position, Δρ RF is the error of the refraction effect of the light in the atmosphere, Δρ REL is the deviation of the general relativity effect of the light in the gravitational field, Δρ MC is the deviation of the reflection point of the ranging laser on the satellite surface from the center of mass, Δρ Ro is the system deviation of the SLR station.

[0030] In the preferred embodiment of the present application, in step S300:

[0031] The satellite motion equation and the corresponding initial condition are respectively:

[0032]

[0033] X(t0)=X0.

[0034] In the preferred embodiment of the present application, the non-linearized satellite orbit determination observation equation is:

[0035] F = G(X, t) + ε.

[0036] Wherein, G(X, t) is the true value corresponding to the observation data Y, X is the state vector of the satellite at t moment, and ε is the random noise of the observation data Y.

[0037] In the preferred embodiment of the present application, step S300 comprises:

[0038] When the initial value X * of X is close to the actual orbit of the satellite within a predetermined range, the actual orbit of the satellite is Taylor expanded at the position X * , and x(t) = X(t) - X * (t), the nonlinear satellite orbit determination observation equation and the satellite motion equation are respectively:

[0039]

[0040]

[0041] After ignoring the high-order terms, the linearized satellite orbit determination observation equation and the linearized satellite motion equation are respectively:

[0042]

[0043]

[0044] Wherein:

[0045]

[0046]

[0047] The general solution of the linearized satellite motion equation is:

[0048] x = Φ(t, t0)x0;

[0049] Wherein, Φ(t, t0) is the state transition matrix.

[0050] Then the linearized satellite orbit determination observation equation is:

[0051]

[0052] Wherein,

[0053] In the preferred embodiment of the present application, step S400 comprises:

[0054] According to the nonlinear SLR observation equation and the state transition matrix, the linearized SLR observation equation is obtained according to the writing method of the linearized satellite orbit determination observation equation as follows:

[0055] y1 = Ax0 - l;

[0056] wherein:

[0057]

[0058]

[0059] In the preferred embodiment of the present application, step S500 comprises:

[0060] According to the nonlinear inter-satellite observation equation and the state transition matrix, the linearized inter-satellite observation equation is obtained according to the writing method of the linearized satellite orbit determination observation equation as follows:

[0061] y2 = Bx0 - l;

[0062] wherein:

[0063]

[0064]

[0065] In the preferred embodiment of the present application, step S600 comprises:

[0066] The satellite orbit determination is performed according to the joint solution of y1 and y2 by using the least square method.

[0067] The embodiment of the present application adopts the observation data of SLR ground station and the satellite inter-satellite link measurement data to jointly perform the satellite precise orbit determination, simultaneously plays the advantages of SLR technology and inter-satellite link technology, and can obtain the high-precision satellite orbit. BRIEF DESCRIPTION OF DRAWINGS

[0068] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort on the basis of these drawings.

[0069] Figure 1 FIG. 1 is a flowchart of the joint orbit determination method based on SLR and inter-satellite link according to the embodiment of the present application;

[0070] Figure 2 FIG. 2 is a satellite orbit overlap residual RMS diagram according to the embodiment of the present application;

[0071] Figure 3 Figure 6 is a plot of the RMS difference between predicted and precise orbits for satellites of embodiments of the application. DETAILED DESCRIPTION

[0072] The description of embodiments of the application in this specification should be understood as limited in scope by the appended claims, in which reference numerals are used in the claims section of this specification for consistency with the description and their application should not be limited by the description and drawings describing the embodiments.

[0073] Any reference in this specification to a direction or orientation should be interpreted as being only for convenience of description and not limiting on the scope of the application. The following description of preferred embodiments will be made with reference to the accompanying drawings, in which the features of the embodiments are not necessarily drawn to scale, and in which like numerals represent similar features in the various embodiments of the application. The description of preferred embodiments is not intended to limit the scope of the application, which is defined in the appended claims.

[0074] As shown in Figure 1 and Figure 2 Embodiments of the application provide a joint orbit determination method based on SLR and inter-satellite links, the method comprising:

[0075] S 100, determining a non-linearized inter-satellite observation equation according to inter-satellite observation data.

[0076] For example, the Beidou inter-satellite link adopts a time-sharing measurement system, and can obtain forward and reverse ranging observation values, including ranging information between satellites and relative clock differences. Let ρ BA (t1) be the ranging signal transmitted by satellite B received by satellite A at time t1 on its clock face, let ρ AB (t2) be the ranging signal transmitted by satellite A received by satellite B at time t2. Then:

[0077]

[0078]

[0079] wherein r A and r B are the three-dimensional positions of satellites A and B respectively, c is the speed of light, clk A and clk B are the satellite clock errors of satellites A and B respectively, Δt1 and Δt2 are the light travel times respectively, ε send and ε rcv are the transmission and reception delays of the satellites respectively, Δδ BA and Δδ ABrespectively, are error correction terms that can be accurately modeled in ranging BA and Δδ AB including satellite antenna phase center correction value, relativistic effect correction value, troposphere delay correction value, station eccentricity correction value and tidal effect correction value, etc., can be corrected by modeling.

[0080] The addition of two-way ranging at the same time can eliminate satellite clock error and only contain satellite distance information. The subtraction of two-way ranging at the same time can eliminate satellite orbit and only contain satellite clock error. Since the time of sending and receiving ranging is different, the single and double direction observation values need to be calculated to the middle epoch t0, and the formula is:

[0081]

[0082]

[0083] Where dρ BA and dρ AB are satellite position and satellite clock error correction values:

[0084] dρ BA = |r A (t0)-r B (t0)|-|r A (t1)-r B (t1-Δt)|+c·(clk A (t0)-clk B (t0))-c·(clk A (t1)-clk B (t1-Δt)); (5)

[0085] dρ AB = |r A (t0)-r B (t0)|-|r B (t2)-r A (t2-Δt)|+c·(clk B (t0)-clk A (t0))-c·(clk B (t2)-clk A (t2-Δt)); (6)

[0086] According to the addition of formula (3) and (4), the satellite clock error can be eliminated, and the relative distance between satellites is obtained:

[0087]

[0088] The nonlinearized inter-satellite observation equation of formula (7) can decouple the satellite orbit and clock error in the inter-satellite two-way pseudorange measurement, and the result can be directly used in subsequent orbit calculation.

[0089] S200, determining a nonlinearized SLR observation equation according to SLR observation data.

[0090] Supposing that the original observation distance is ρ', the SLR observation data is the distance from the SLR observation station to the satellite, and the nonlinearized SLR observation equation is:

[0091] ρ0=ρ'-(Δρ TD +Δρ RF +Δρ REL +Δρ MC +Δρ RO ); (8)

[0092] Wherein, Δρ TD is the error of the tidal variation of the SLR observation station position, Δρ RF is the error of the refraction effect of the light in the atmosphere, Δρ REL is the deviation of the general relativity effect of the light in the gravitational field, Δρ MC is the deviation of the reflection point of the ranging laser on the satellite surface to the center of mass, Δρ Ro is the system deviation of the SLR station.

[0093] S300, determining a state transition matrix and a linearized satellite orbit determination observation equation according to a satellite motion equation and the nonlinearized satellite orbit determination observation equation.

[0094] The satellite motion equation is:

[0095]

[0096] The initial condition is:

[0097] X(t0)=X0; (10)

[0098] The process of establishing the observation equation of the satellite orbit determination is the process of linearizing the nonlinearized orbit determination observation equation. Supposing that the nonlinearized satellite orbit determination observation equation is:

[0099] Y=G(X,t)+ε; (11)

[0100] Wherein, G(X,t) is the true value corresponding to the observation data Y, X is the state vector of the satellite at the time t, and ε is the random noise of the observation data Y;

[0101] When the initial value X * of X is close enough to the actual orbit of the satellite, the actual orbit of the satellite is close to the position X *The Taylor expansion is performed at the point, where

[0102] x(t) = X(t) - X * (t); (12)

[0103] Equations (9) and (11) can be written as

[0104]

[0105]

[0106] Neglecting the higher order terms, we have

[0107]

[0108]

[0109] where

[0110]

[0111]

[0112] The solution of equation (16) is

[0113] x = Φ(t, t0)x0; (17)

[0114] where Φ(t, t0) is the state transition matrix.

[0115] According to equation (17), equation (13) can be written as

[0116]

[0117] where

[0118]

[0119] Equation (18) is the final form of the linearized satellite orbit determination observation equation.

[0120] S400, determining a linearized SLR observation equation according to the nonlinear SLR observation equation, the state transition matrix and the linearized satellite orbit determination observation equation.

[0121] Taking the SLR ranging of a satellite by an SLR ground station as the observation (i.e., equation (8)), according to the form of the linearized satellite orbit determination observation equation (i.e., equation (18)), and according to the state transition matrix (i.e., equation (17)), the nonlinear SLR observation equation is linearized to obtain a linearized SLR observation equation:

[0122] yl = Ax0 - l; (19)

[0123] wherein:

[0124]

[0125]

[0126] S500, determining a linearized inter-satellite observation equation according to the non-linearized inter-satellite observation equation, the state transition matrix and the linearized satellite orbit determination observation equation.

[0127] The inter-satellite observation is inter-satellite ranging as an observation (i.e. equation (7)), and the non-linearized inter-satellite observation equation is linearized according to the linearized satellite orbit determination observation equation (i.e. equation (18)) to obtain a linearized inter-satellite observation equation according to a state transition matrix (i.e. equation (17)):

[0128] y2 = Bx0 - l; (22)

[0129] wherein:

[0130]

[0131]

[0132] S600, performing satellite joint orbit determination according to the linearized inter-satellite observation equation and the linearized SLR observation equation.

[0133] The observation equations of equations (19) to (24) are superimposed and jointly solved by a least square method to realize joint orbit determination of SLR and inter-satellite link.

[0134] The following takes the BDS-3 navigation system as an example to specifically illustrate the joint orbit determination method of the embodiment.

[0135] (1) Orbit overlap accuracy

[0136] The orbit overlap arc is one of the important internal consistency evaluation methods for satellite orbit determination accuracy. The orbit overlap accuracy of the 3d orbit determination arc segment is analyzed in the RTN direction and three-dimensional position RMS, and the results show that the radial, tangential and normal accuracy of 11 satellites is about 4.2 cm, 20.4 cm and 19.9 cm respectively, and the three-dimensional position accuracy is 30.2 cm. The radial accuracy of GEO satellites is 8.2 cm, and the three-dimensional position accuracy is about 39.1 cm. The radial accuracy of IGSO satellites is 4.1 cm, and the three-dimensional position accuracy is about 35.4 cm. The radial accuracy of MEO satellites is 3.7 cm, and the three-dimensional accuracy is 27.8 cm. It can be seen from the statistical results that the orbit accuracy of the three types of satellites is roughly equivalent.

[0137] (2) Orbit prediction accuracy

[0138] 11 satellites 3D orbit determination and 12h orbit prediction The orbit prediction accuracy is evaluated by comparing the 12h predicted orbit with the precise orbit. The RMS of the orbit difference between the predicted orbit and the precise orbit is calculated for each satellite. The results show that the orbit prediction accuracy of GEO and IGSO satellites is poor. Table 1 shows the RMS of the 12h and 24h orbit prediction for MEO, GEO and IGSO satellites. The results show that the orbit prediction accuracy of MEO satellites is the highest. The radial accuracy is better than 7.0cm and the 3D accuracy is about 40.0cm. The radial accuracy of GEO satellites is 17.0cm and 24.3cm for 12h and 24h orbit prediction respectively, and the 3D accuracy is about 100.0cm. The radial accuracy of IGSO satellites is about 10.0cm for 12h and 24h orbit prediction, and the 3D accuracy is better than 60.0cm.

[0139]

[0140] Table 1. Orbit prediction accuracy statistics of three types of satellites

[0141] In summary, the joint orbit determination method of the embodiment of the application realizes joint orbit determination based on SLR and inter-satellite link. The clock bias and distance information of two connected satellites can be decoupled by using two inter-satellite link ranging values, the inter-satellite relative distance is obtained, and the observation equation is established. The observation equation is established by using the observation of the SLR tracking station. The satellite is precisely determined by combining the two observation equations, and the satellite orbit is obtained, which provides technical support for realizing the autonomous and controllable Beidou navigation system space-time reference.

[0142] The above only describes the preferred embodiments of the application and should not be used to limit the application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the application should be included in the protection scope of the application.

Claims

1. A joint orbit determination method based on SLR and inter-satellite links, characterized in that, The method includes: S100, determines the nonlinear inter-satellite observation equations based on inter-satellite observation data; S200, based on SLR observation data, determines the nonlinearized SLR observation equations; In step S200: The nonlinearized SLR observation equation is: p0 = p' - (Ap TD + Ap RF + Ap REL + Ap MC + Ap RO ) wherein p0 is the SLR observation, p' is the original observation distance of the SLR station, Δρ TD is the error of the tidal variation of the SLR station position, Δρ RF is the error of the refraction effect of the light in the atmosphere, Δρ REL is the error of the general relativity effect of the light in the gravitational field, Δρ MC is the deviation of the reflection point of the ranging laser on the satellite surface to the center of mass, Δρ RO is the system deviation of the SLR station; S300 determines the state transition matrix and the linearized satellite orbit determination and observation equations based on the satellite motion equations and the nonlinearized satellite orbit determination and observation equations. S400, determine the linearized SLR observation equation based on the nonlinearized SLR observation equation, the state transition matrix, and the linearized satellite orbit determination observation equation; S500, determine the linearized inter-satellite observation equation based on the nonlinearized inter-satellite observation equation, the state transition matrix, and the linearized satellite orbit determination and observation equation; S600 performs joint satellite orbit determination based on the linearized inter-satellite observation equations and the linearized SLR observation equations.

2. The joint orbit determination method based on SLR and inter-satellite links according to claim 1, characterized in that, Step S100 includes: determining that the first satellite received a ranging signal p transmitted by the second satellite at a time t1 in its own clock BA (t1), and determining that the second satellite received a ranging signal p transmitted by the first satellite at a time t2 in its own clock AB (t2); wherein r A , r B are the three-dimensional positions of the first and second satellites, c is the speed of light, clk A , clk B are the satellite clock errors of the first and second satellites, Δt1 and Δt2 are the light times, τ send and τ rcv are the transmission and reception delays of the satellites, Δδ BA and Δδ AB are error correction terms that can be accurately modeled in the ranging. The ρ BA (t1) and ρ AB (t2) are reduced to an intermediate epoch t0 according to the following formulae to obtain the non-linearized inter-satellite observation equations: where dρ BA and dρ AB are the corrections for satellite position and satellite clock error.

3. The joint orbit determination method based on SLR and inter-satellite links according to claim 2, characterized in that, In step S300: The satellite's equations of motion and their corresponding initial conditions are as follows: X(t0)=X0.

4. The joint orbit determination method based on SLR and inter-satellite links according to claim 3, characterized in that, The nonlinearized satellite orbit determination and observation equation is as follows: Y = G(X, t) + ε Where G(X, t) is the true value corresponding to the observed data Y, X is the satellite's state vector at time t, and ε is the random noise of the observed data Y.

5. The joint orbit determination method based on SLR and inter-satellite links according to claim 4, characterized in that, Step S300 includes: When the initial value X of X is X * When the actual orbit of the satellite is close to a predetermined range, the actual orbit of the satellite is Taylor expanded at the position X * , and x(t) = X(t) - X * (t). The nonlinearized satellite orbit determination observation equation and the satellite motion equation are respectively After ignoring higher-order terms, the linearized satellite orbit determination and observation equations and the linearized satellite motion equations are obtained as follows: in: The general solution to the linearized satellite motion equations is: x = Φ(t, t0)x0; Wherein, Φ(t, t0) is the state transition matrix; The linearized satellite orbit determination and observation equations are then: in, 6. The joint orbit determination method based on SLR and inter-satellite links according to claim 5, characterized in that, Step S400 includes: Based on the nonlinearized SLR observation equations and the state transition matrix, and following the syntax of the linearized satellite orbit determination and observation equations, the linearized SLR observation equations are obtained as follows: y1 = Ax0 - l; in:

7. The joint orbit determination method based on SLR and inter-satellite links according to claim 6, characterized in that, Step S500 includes: Based on the nonlinear inter-satellite observation equations and the state transition matrix, and following the syntax of the linearized satellite orbit determination and observation equations, the linearized inter-satellite observation equations are obtained as follows: y2 = Bx0 - l; in:

8. The joint orbit determination method based on SLR and inter-satellite links according to claim 7, characterized in that, Step S600 includes: The least squares method is used to determine the satellite orbit based on the joint solution of y1 and y2.

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