Satellite attitude guiding method and system for same-view-angle observation with target satellite

Abstract

The invention provides a satellite attitude guiding method and system capable of observing at the same visual angle as a target satellite. The method comprises the following steps: calculating the position Rm0 and the speed Vm0 of the target satellite at an ephemeris data moment; s2, the position Rmt0 and the speed Vmt0 of the target satellite at the task starting moment are solved through numerical integration; according to the position Rmt0 and the speed Vmt0, the orbital mean element of the target satellite at the task starting moment is solved; solving the real-time position Rm and speed Vm of the target satellite based on the orbit mean element; and calculating the guiding attitude of the satellite according to the position Rm and the speed Vm. According to the method, through orbit information autonomous recursion, the same-view-angle observation tracking performance of the satellite and the target satellite can be improved, on-satellite computing resources are considered, and the method has practical significance on a dynamic target tracking imaging task of the satellite.

Description

Technical Field

[0001] The present invention belongs to the technical field of satellite attitude guidance, and in particular, relates to a satellite attitude guidance method and system for observing at the same viewing angle as a target star. Background Art

[0002] For some advanced optical imaging technologies suitable for medium and high orbit satellites, low-orbit demonstration and verification satellites are often used to verify the actual application of subsequent medium and high orbit satellites during on-orbit verification. This requires low-orbit satellites to obtain observation data from the same perspective as medium and high orbit satellites, which involves attitude guidance algorithms for satellites and other target stars to observe from the same perspective. Among them, low-orbit satellites have the characteristics of low launch cost, low launch difficulty, and high spatial resolution. Under the same angular resolution, medium and high orbit satellites have a wider field of view.

[0003] In some satellite cross-radiation calibration mission scenarios, two satellites need to observe the same target at the same time, and the satellite with better calibration results is used to accurately calibrate the sensor of the satellite to be calibrated. This process requires the intervention of high-precision attitude guidance algorithms in orbit.

[0004] When the satellite observes the target star from the same angle of view, it needs to obtain the target star's trajectory in advance. Since the mission has a certain degree of uncertainty, it is difficult to track the direction by looking up a table with a large amount of target star position data on the ground. Therefore, it is necessary for the satellite to complete the orbit information during the mission based on the orbit parameter information of the target star at a certain moment. The existing methods provide some orbit recursion calculation methods, but these methods are no longer applicable in the mission that requires real-time observation from the same angle of view as the target star on the satellite. The main reasons are as follows:

[0005] Patent document CN104459732A discloses a desingularization method suitable for recursive calculation of satellite orbit parameters. The solution adopts the GLONASS satellite position solution algorithm, but uses a numerical integration algorithm and relies on the GLONASS receiver.

[0006] Patent document CN103268407A discloses a method for orbit data interpolation based on Lagrange interpolation and Kalman filtering. The scheme introduces an orbit data interpolation algorithm. Due to the variability of the mission period, the orbit position deviation is small only within a limited period of time. When the mission changes beyond the original period, the orbit position deviation will increase rapidly if the interpolation data is extrapolated, affecting the tracking and pointing accuracy.

[0007] Patent document CN103995800A discloses an on-board autonomous orbit extrapolation method suitable for circular orbit satellites. The scheme introduces an orbit recursion algorithm for circular orbit satellites, but the recursion model of the algorithm is relatively simple and is not suitable for long-term high-precision orbit recursion.

[0008] Patent document CN114002713A discloses a satellite orbit parameter recursive processing prediction system. The scheme introduces a satellite orbit parameter prediction method. The use of normalization processing can reduce the amount of calculation. However, for the scenario where the on-board calculation method needs to calculate the guidance attitude in real time during the mission, the amount of calculation is still not enough.

[0009] "Optical Precision Engineering", 2016, Issue 10, published an algorithm for predicting low-orbit satellite orbits based on orbital elements. The scheme introduced an algorithm for predicting satellite orbits using elliptic curves, but the partial differentials of the coefficients need to be calculated during the solution process, which is not suitable for onboard computer operations.

[0010] When the satellite observes the target star from the same viewing angle, it needs to obtain the target star's trajectory in advance. Due to the uncertainty of the mission, it is difficult to track the direction by looking up a large amount of target star position data on the ground. The satellite needs to complete the orbit information during the mission based on the orbit parameter information of the target star at a certain moment.

[0011] As mentioned above, existing methods have given some orbital recursive calculation methods, but these methods are no longer applicable in tasks on the satellite that require real-time observation from the same perspective as the target star. This problem needs to be solved urgently. Summary of the invention

[0012] In view of the defects in the prior art, the object of the present invention is to provide a satellite attitude guidance method and system for observing at the same viewing angle as a target star.

[0013] A satellite attitude guidance method for observing a target satellite at the same viewing angle as the target satellite is provided according to the present invention, comprising:

[0014] Step S1: Calculate the position R of the target star at the time of the ephemeris data m0 and speed V m0 ;

[0015] Step S2: Numerical integration to solve the position R of the target star at the start of the mission mt0 and speed V mt0 ;

[0016] Step S3: According to the position R mt0 With speed V mt0 , find the mean orbital root number of the target star at the start of the mission;

[0017] Step S4: Based on the orbital mean root number, calculate the real-time position R of the target star m and speed V m ;

[0018] Step S5: According to the position R m With speed V m The guidance attitude of the satellite is calculated.

[0019] Preferably, in step S1, the position R m0 The mathematical expression is:

[0020] R m0 =Q·r p

[0021] Among them, r p represents the position vector in the near focus coordinate system, Q represents the transformation matrix from the near focus coordinate system to the inertial system;

[0022] The speed V m0 The mathematical expression is:

[0023] V m0 =Q·v p

[0024] The mathematical expression of Q is:

[0025]

[0026] Wherein, the superscript T is the symbol for matrix transposition; R X R is the X-axis rotation matrix function; Z is the Z-axis rotation matrix function; Ω ms represents the right ascension of the ascending node; i ms represents the orbital inclination; ω ms represents the argument of perigee;

[0027] The R X , that is, the mathematical expression of the X-axis rotation matrix function is:

[0028]

[0029] The R Z , that is, the mathematical expression of the Z-axis rotation matrix function is:

[0030]

[0031] Among them, α represents the angle;

[0032] The r p The mathematical expression is:

[0033]

[0034] Among them, f ms Indicates the true anomaly angle; e ms represents eccentricity; μ represents the earth's gravitational constant; h ms represents the target star angular momentum;

[0035] The v p The mathematical expression is:

[0036]

[0037] Among them, v p represents the velocity vector in the near focus coordinate system;

[0038] The h ms The mathematical expression is:

[0039]

[0040] Among them, a ms represents the semi-major axis of the orbit;

[0041] In step S2, the numerical integration solution method step includes:

[0042] Step A1: Calculate the integration step length from the task start time;

[0043] Step A2: Set the maximum integration step size h max , and then decompose the integral step;

[0044] Step A3: Recursively extrapolate the orbit of the target star from the ephemeris data time to the mission start time, and calculate the position R of the target star at the mission start time mt0 With speed V mt0 ;

[0045] In step A1, the mathematical expression of the integration step length is:

[0046] h=t0-t s

[0047] Where h is the integration step; t0 is the task start time; t s Indicates the time of ephemeris data;

[0048] In step A2, the mathematical expression of the decomposition process is:

[0049] h=N·h max +h0

[0050] Where N represents a natural number, and 0≤h0<h max ; h0 represents the initial integration step;

[0051] In step A3, the N+1 numerical calculation method is called to obtain the position R of the target star at the start time of the mission. mt0 With speed V mt0 ;

[0052] The numerical calculation method, the mathematical expression is:

[0053]

[0054] Where f represents the function; y0 represents the initial value of the integral; the symbol Δ represents the increment symbol; the differential equation system f(p) is a 6×1 column vector, p is the term in the brackets between k1 and k4, let

[0055] The mathematical expression of f(p) is:

[0056]

[0057] Among them, R e is the equatorial radius of the Earth, J2 is the second-order harmonic coefficient of the non-spherical gravitational perturbation term of the Earth;

[0058] In step A3, y0 is the initial value of the integration used for the first time, and its mathematical expression is:

[0059] y0=[R m0 ; V m0 ]

[0060] For the first N times, use the maximum integration step size h max , that is, let Δ=h max And use the output y1 of each time as the initial value y0 of the next integration; the last time let Δ=h0, calculate the output y1 to get the position R of the target star at the start time of the mission mt0 With speed V mt0 ;

[0061] The R mt0 The mathematical expression is:

[0062] R mt0 =[y1(1);y1(2);y1(3)]

[0063] The speed V mt0 The mathematical expression is:

[0064] V mt0 =[y1(4);y1(5);y1(6)]

[0065] Among them, y1(1), y1(2), y1(3), y1(4), y1(5) and y1(6) represent six components of the output y1.

[0066] Preferably, in step S3, according to the position R mt0 With speed V mt0 , find the orbital instantaneous root number and argument information; find the orbital mean root number of the target satellite at the start time of the mission based on the orbital instantaneous root number and the argument information;

[0067] The instantaneous orbital elements include: e′, a′, i′, Ω′ and ω′;

[0068] The mathematical expression of e′ is:

[0069] e′=‖E‖

[0070] Among them, e′ represents the eccentricity of the target star at the start of the mission, which is the instantaneous root of the orbit; E represents the eccentricity vector at the start of the target star mission;

[0071] The mathematical expression of E is:

[0072]

[0073] Where, E represents the eccentricity vector of the target star at the start of the mission; the symbol |||| represents the modulo operator; H represents the angular momentum vector of the target star at the start of the mission;

[0074] The mathematical expression of H is:

[0075] H=R mt0 ×V mt0

[0076] The mathematical expression of a′ is:

[0077]

[0078] Where a′ represents the semi-major axis of the orbit of the target star at the start of the mission;

[0079] The mathematical expression of i′ is:

[0080]

[0081] Where i′ represents the orbital inclination of the target satellite at the start of the mission;

[0082] The mathematical expression of Ω′ is:

[0083]

[0084] Among them, Ω′ represents the right ascension of the ascending node of the target star at the start time of the mission;

[0085] The mathematical expression of ω′ is:

[0086]

[0087] Among them, ω′ represents the argument of perigee at the start of the target satellite mission;

[0088] The argument information includes: u′, φ′ and λ′;

[0089]

[0090] Where u′ represents the true latitude argument of the target satellite at the start of the mission;

[0091]

[0092] Among them, φ′ represents the latitude argument of the target satellite at the start of the mission;

[0093] λ′=φ′-e′sin(φ′-ω′)

[0094] Among them, λ′ represents the mean latitude argument of the target satellite at the start time of the mission.

[0095] Preferably, in step S3, the track average root number includes: a mt0 、i mt0 ,Ω mt0 ,ω mt0 、e mt0 With M mt0 ;

[0096] The a mt0 The mathematical expression is:

[0097]

[0098] Among them, a mt0 represents the semi-major axis of the orbit of the target star at the start of the mission; x5 represents the intermediate variable five; x6 represents the intermediate variable six;

[0099] The i mt0 The mathematical expression is:

[0100] i mt0 =i′+(1 / 6)x2Ω1sin i′

[0101] Among them, i mt0 represents the orbital inclination of the target star at the start of the mission; x2 is the second intermediate variable:

[0102] The Ω mt0 The mathematical expression is:

[0103] Ω mt0 =Ω′-Ω1(x1-x3 / 6)

[0104] Among them, Ωmt0 represents the right ascension of the ascending node of the target star at the start of the mission; x1 is the intermediate variable one; x3 is the intermediate variable three;

[0105] The mathematical expression of Ω1 is:

[0106]

[0107] The ω mt0 The mathematical expression is:

[0108] ω mt0 =arctan(-η / ξ)

[0109] Among them, ω mt0 Indicates the argument of perigee at the start of the target star mission;

[0110] The mathematical expression of η is:

[0111] η=η′-(-x 10 -(x4+x7)ξ′+x8η′)

[0112] Among them, x 10 is the intermediate variable ten; x4 is the intermediate variable four; x7 is the intermediate variable seven; x8 is the intermediate variable eight;

[0113] The mt0 The mathematical expression is:

[0114]

[0115] Among them, e mt0 represents the eccentricity of the target star at the start of the mission;

[0116] The mathematical expression of ξ is:

[0117] ξ=ξ′-(x9+(x4+x7)η′+x8ξ′)

[0118] Among them, x8 is the intermediate variable eight; x9 is the intermediate variable nine;

[0119] The M mt0 The mathematical expression is:

[0120] M mt0 =λ-ω mt0

[0121] Among them, M mt0 Indicates the mean anomaly angle of the target star at the start of the mission;

[0122] The mathematical expression of λ is:

[0123] λ=λ′-(x4+ε(x7e′2 +x9η′+x 10 ξ′))

[0124] Among them, x9 is the intermediate variable nine.

[0125] Preferably, in step S4, the R m The mathematical expression is:

[0126]

[0127] Among them, E mt is the near point angle;

[0128] The V m The mathematical expression is:

[0129]

[0130] The P m The mathematical expression is:

[0131]

[0132] Among them, P m is an intermediate variable;

[0133] The Q m The mathematical expression is:

[0134]

[0135] Among them, Q m is an intermediate variable;

[0136] In step S5, the guidance attitude of the satellite, that is, the rolling angle of the satellite under inertia The mathematical expressions of pitch angle θ and yaw angle ψ are:

[0137]

[0138] θ=arcsin(i z (1))

[0139]

[0140] Among them, i x 、i y 、i z The mathematical expression is:

[0141]

[0142] i x =i y ×i z

[0143] Among them, i x 、i y 、i z Respectively represent the direction vectors of the three axes of the satellite body in the inertial system; R s With V s They are respectively the projections of the satellite’s position vector and velocity vector in the J2000 inertial coordinate system.

[0144] A satellite attitude guidance system for observing a target satellite at the same viewing angle as the target satellite is provided according to the present invention, comprising:

[0145] Module M1: Calculate the position R of the target star at the time of the ephemeris data m0 and speed V m0 ;

[0146] Module M2: Numerical integration to solve the position R of the target star at the start of the mission mt0 and speed V mt0 ;

[0147] Module M3: According to the position R mt0 With speed V mt0 , find the mean orbital root number of the target star at the start of the mission;

[0148] Module M4: Based on the orbital average root number, calculate the real-time position R of the target star m and speed V m ;

[0149] Module M5: According to the position R m With speed V m The guidance attitude of the satellite is calculated.

[0150] Preferably, in the module M1, the position R m0 The mathematical expression is:

[0151] R m0 =Q·r p

[0152] Among them, r p represents the position vector in the near focus coordinate system, Q represents the transformation matrix from the near focus coordinate system to the inertial system;

[0153] The speed V m0 The mathematical expression is:

[0154] V m0 =Q·v p

[0155] The mathematical expression of Q is:

[0156]

[0157] Wherein, the superscript T is the symbol for matrix transposition; R X R is the X-axis rotation matrix function; Z is the Z-axis rotation matrix function; Ω ms represents the right ascension of the ascending node; i ms represents the orbital inclination; ω ms represents the argument of perigee;

[0158] The R X , that is, the mathematical expression of the X-axis rotation matrix function is:

[0159]

[0160] The R Z , that is, the mathematical expression of the Z-axis rotation matrix function is:

[0161]

[0162] Among them, α represents the angle;

[0163] The r p The mathematical expression is:

[0164]

[0165] Among them, f ms Indicates the true anomaly angle; e ms represents eccentricity; μ represents the earth's gravitational constant; h ms represents the target star angular momentum;

[0166] The v p The mathematical expression is:

[0167]

[0168] Among them, v p represents the velocity vector in the near focus coordinate system;

[0169] The h ms The mathematical expression is:

[0170]

[0171] Among them, a ms represents the semi-major axis of the orbit;

[0172] In the module M2, the numerical integration solution step includes:

[0173] Module A1: Calculate the integration step length from the task start time;

[0174] Module A2: Setting the maximum integration step length h max , and then decompose the integral step;

[0175] Module A3: Recursively extrapolate the orbit of the target star from the ephemeris data time to the mission start time, and calculate the position R of the target star at the mission start time mt0 With speed V mt0 ;

[0176] In the module A1, the mathematical expression of the integration step is:

[0177] h=t0-t s

[0178] Where h is the integration step; t0 is the task start time; t s Indicates the time of ephemeris data;

[0179] In the module A2, the mathematical expression of the decomposition process is:

[0180] h=N·h max +h0

[0181] Where N represents a natural number, and 0≤h0<h max ; h0 represents the initial integration step;

[0182] In the module A3, the N+1 numerical calculation method is called to obtain the position R of the target star at the start time of the mission. mt0 With speed V mt0 ;

[0183] The numerical calculation method, the mathematical expression is:

[0184]

[0185] Where f represents the function; y0 represents the initial value of the integral; the symbol Δ represents the increment symbol; the differential equation system f(p) is a 6×1 column vector, p is the term in the brackets between k1 and k4, let

[0186] The mathematical expression of f(p) is:

[0187]

[0188] Among them, R e is the equatorial radius of the Earth, J2 is the second-order harmonic coefficient of the non-spherical gravitational perturbation term of the Earth;

[0189] In the module A3, y0 is the initial value of the integration used for the first time, and the mathematical expression is:

[0190] y0=[Rm0 ; V m0 ]

[0191] For the first N times, use the maximum integration step size h max , that is, let Δ=h max And use the output y1 of each time as the initial value y0 of the next integration; the last time let Δ=h0, calculate the output y1 to get the position R of the target star at the start time of the mission mt0 With speed V mt0 ;

[0192] The R mt0 The mathematical expression is:

[0193] R mt0 =[y1(1);y1(2);y1(3)]

[0194] The speed V mt0 The mathematical expression is:

[0195] V mt0 =[y1(4);y1(5);y1(6)]

[0196] Among them, y1(1), y1(2), y1(3), y1(4), y1(5) and y1(6) represent six components of the output y1.

[0197] Preferably, in the module M3, according to the position R mt0 With speed V mt0 , find the orbital instantaneous root number and argument information; find the orbital mean root number of the target satellite at the start time of the mission based on the orbital instantaneous root number and the argument information;

[0198] The instantaneous orbital elements include: e′, a′, i′, Ω′ and ω′;

[0199] The mathematical expression of e′ is:

[0200] e′=‖E‖

[0201] Among them, e′ represents the eccentricity of the target star at the start of the mission, which is the instantaneous root of the orbit; E represents the eccentricity vector at the start of the target star mission;

[0202] The mathematical expression of E is:

[0203]

[0204] Where, E represents the eccentricity vector of the target star at the start of the mission; the symbol |||| represents the modulo operator; H represents the angular momentum vector of the target star at the start of the mission;

[0205] The mathematical expression of H is:

[0206] H=R mt0 ×V mt0

[0207] The mathematical expression of a′ is:

[0208]

[0209] Where a′ represents the semi-major axis of the orbit of the target star at the start of the mission;

[0210] The mathematical expression of i′ is:

[0211]

[0212] Where i′ represents the orbital inclination of the target satellite at the start of the mission;

[0213] The mathematical expression of Ω′ is:

[0214]

[0215] Among them, Ω′ represents the right ascension of the ascending node of the target star at the start time of the mission;

[0216] The mathematical expression of ω′ is:

[0217]

[0218] Among them, ω′ represents the argument of perigee at the start of the target satellite mission;

[0219] The argument information includes: u′, φ′ and λ′;

[0220]

[0221] Where u′ represents the true latitude argument of the target satellite at the start of the mission;

[0222]

[0223] Among them, φ′ represents the latitude argument of the target satellite at the start of the mission;

[0224] λ′=φ′-e′sin(φ′-ω′)

[0225] Among them, λ′ represents the mean latitude argument of the target satellite at the start time of the mission.

[0226] Preferably, in the module M3, the track average root number includes: a mt0 、i mt0 ,Ω mt0 ,ω mt0 、e mt0 With Mmt0 ;

[0227] The a mt0 The mathematical expression is:

[0228]

[0229] Among them, a mt0 represents the semi-major axis of the orbit of the target star at the start of the mission; x5 represents the intermediate variable five; x6 represents the intermediate variable six;

[0230] The i mt0 The mathematical expression is:

[0231] i mt0 =i′+(1 / 6)x2Ω1sin i′

[0232] Among them, i mt0 represents the orbital inclination of the target star at the start of the mission; x2 is the second intermediate variable:

[0233] The Ω mt0 The mathematical expression is:

[0234] Ω mt0 =Ω′-Ω1(x1-x3 / 6)

[0235] Among them, Ω mt0 represents the right ascension of the ascending node of the target star at the start of the mission; x1 is the intermediate variable one; x3 is the intermediate variable three;

[0236] The mathematical expression of Ω1 is:

[0237]

[0238] The ω mt0 The mathematical expression is:

[0239] ω mt0 =arctan(-η / ξ)

[0240] Among them, ω mt0 Indicates the argument of perigee at the start of the target star mission;

[0241] The mathematical expression of η is:

[0242] η=η′-(-x 10 -(x4+x7)ξ′+x8η′)

[0243] Among them, x 10 is the intermediate variable ten; x4 is the intermediate variable four; x7 is the intermediate variable seven; x8 is the intermediate variable eight;

[0244] The mt0The mathematical expression is:

[0245]

[0246] Among them, e mt0 represents the eccentricity of the target star at the start of the mission;

[0247] The mathematical expression of ξ is:

[0248] ξ=ξ′-(x9+(x4+x7)η′+x8ξ′)

[0249] Among them, x8 is the intermediate variable eight; x9 is the intermediate variable nine;

[0250] The M mt0 The mathematical expression is:

[0251] M mt0 =λ-ω mt0

[0252] Among them, M mt0 Indicates the mean anomaly angle of the target star at the start of the mission;

[0253] The mathematical expression of λ is:

[0254] λ=λ′-(x4+ε(x7e′ 2 +x9η′+x 10 ξ′))

[0255] Among them, x9 is the intermediate variable nine.

[0256] Preferably, in the module M4, the R m The mathematical expression is:

[0257]

[0258] Among them, E mt is the near point angle;

[0259] The V m The mathematical expression is:

[0260]

[0261] The P m The mathematical expression is:

[0262]

[0263] Among them, P m is an intermediate variable;

[0264] The Q m The mathematical expression is:

[0265]

[0266] Among them, Q m is an intermediate variable;

[0267] In the module M5, the guidance attitude of the satellite, that is, the rolling angle of the satellite under inertia The mathematical expressions of pitch angle θ and yaw angle ψ are:

[0268]

[0269] θ=arcsin(i z (1))

[0270]

[0271] Among them, i x 、i y 、i z The mathematical expression is:

[0272]

[0273] i x =i y ×i z

[0274] Among them, i x 、i y 、i z Respectively represent the direction vectors of the three axes of the satellite body in the inertial system; R s With V s They are respectively the projections of the satellite’s position vector and velocity vector in the J2000 inertial coordinate system.

[0275] Compared with the prior art, the present invention has the following beneficial effects:

[0276] 1. The present invention uses a numerical integration method to recursively calculate the orbit of the target star to the starting time of the observation mission, and uses mean instantaneous root conversion to obtain the orbital mean root number.

[0277] 2. The present invention uses an analytical method to quickly calculate the position and velocity of the target star at the current moment, and finally combines the real-time orbit of the satellite to solve the three-axis guidance attitude observed from the same viewing angle of the satellite and the target star.

[0278] 3. The present invention can improve the same-angle observation and tracking performance of the satellite and the target star through autonomous recursion of orbital information, while taking into account the on-board computing resources, which has practical significance for the satellite's dynamic target tracking and imaging tasks. BRIEF DESCRIPTION OF THE DRAWINGS

[0279] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0280] Figure 1 A schematic diagram of the process provided by the present invention. DETAILED DESCRIPTION

[0281] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0282] The present invention provides a satellite attitude guidance method for observing from the same viewing angle as a target star. The orbit of the target star is recursively deduced to the start time of the observation task by a numerical integration method, and the mean instantaneous root conversion is used to obtain the mean root of the orbit. Then, the position and speed of the target star at the current moment are quickly calculated by an analytical method. Finally, the three-axis guidance attitude of the satellite and the target star observed from the same viewing angle is solved in combination with the real-time orbit of the satellite. The present invention can improve the same viewing angle observation and tracking performance of the satellite and the target star, and take into account the on-board computing resources, and has practical significance for the satellite's dynamic target tracking and imaging tasks.

[0283] In other words, when the satellite maintains the same viewing angle as the target star, the present invention can improve the same-viewing angle observation and tracking performance of the satellite and the target star, while taking into account the on-board computing resources, which has practical significance for the satellite's dynamic target tracking and imaging tasks.

[0284] As attached Figure 1 As shown, a method for attitude guidance for observing at the same viewing angle as a target star provided by the present invention comprises:

[0285] Step S1: Calculate the position R of the target star at the time of the ephemeris data m0 and speed V m0 ;

[0286] Step S2: Numerical integration to solve the position R of the target star at the start of the mission mt0 and speed V mt0 ;

[0287] Step S3: Calculate the mean orbital root number of the target star at the start time of the mission;

[0288] Step S4: Analytically solve the position R of the target star at the current time m and speed V m ;

[0289] Step S5: Calculate the three-axis guidance attitude of the satellite at the same viewing angle θ and ψ.

[0290] The present invention is based on the target star at the ephemeris data time t s The orbital instant root in the J2000.0 inertial system, the projection of the position vector and velocity vector of the satellite in the J2000 inertial coordinate system and other parameters are used to calculate the three-axis attitude of the satellite in the inertial system when observing from the same viewing angle as the target satellite. The orbital instant root includes: the semi-major axis a ms , eccentricity e ms , orbital inclination i ms , right ascension of ascending node Ω ms 、Arg of perigee ω ms 、True anomaly f ms .

[0291] First, it is necessary to use a numerical integration method to recursively calculate the orbit of the target star to the start time of the mission.

[0292] (1) Calculate the position R of the target star at the time of the ephemeris data m0 and speed V m0

[0293] The target star marked on the ground is at the time t of the ephemeris data s The instantaneous root of the orbit in the J2000.0 inertial system is used to calculate the position R in the inertial system. m0 and speed V m0 The formula is as follows:

[0294] Calculate the target star angular momentum h ms The transformation matrix Q from the near-focus coordinate system to the inertial system;

[0295]

[0296] Where μ represents the Earth's gravitational constant;

[0297]

[0298] The superscript T is the symbol for matrix transposition; the rotation matrix function R with α as the independent variable is X (α), R Z The expressions of (α) are:

[0299]

[0300] Then calculate the position vector r in the near focus coordinate system p , velocity vector v in the near-focus coordinate system p ; α represents the angle;

[0301]

[0302] The position R is obtained m0and speed V m0 ;

[0303] R m0 =Q·r p

[0304] V m0 =Q·v p

[0305] Numerical integration solves the position R of the target star at the start of the mission mt0 and speed V mt0 ; Symbol·Represents the multiplication symbol of matrix and vector.

[0306] The integral step length h is calculated from the task start time t0, according to the set single-step maximum integral step length h max Decompose the integral step length h = N·h max +h0, where N is a non-negative integer and 0≤h0<h max , the target star orbit is recursively deduced from the ephemeris data time to the mission start time. It is necessary to call the following numerical calculation method N+1 times. The initial value of the integral used in the first time is y0 = [R m0 ; V m0 ].

[0307] Specifically, the first N times use the maximum single-step integration step size, that is, let Δ = h max The output y1 of each time is used as the initial value y0 of the next integration. The last time, let Δ = h0, and use the calculated output y1 to obtain the position R of the target star at the start time of the mission. mt0 =[y1(1);y1(2);y1(3)] and velocity V mt0 =[y1(4); y1(5); y1(6)] y1(1), y1(2), y1(3), y1(4), y1(5), y1(6) respectively represent the six components of the output y1;

[0308] The mathematical expression of the integration step length h is:

[0309] h=t0-t s

[0310] Where h is the integration step; t0 is the task start time; t s Indicates the time of ephemeris data;

[0311] In step S2, the following numerical calculation method is used:

[0312]

[0313] f represents a function; y0 represents the initial value of the integral; the symbol Δ represents the increment symbol; the differential equation system f(p) is a 6×1 column vector, p is the term in the brackets between k1 and k4, let The simplified approximate expression of f(p) is

[0314]

[0315] Among them, R e is the equatorial radius of the Earth, and J2 is the second-order harmonic coefficient of the Earth's non-spherical gravitational perturbation term.

[0316] Secondly, the analytical method is used to solve the inertial position and velocity of the target star at the current moment.

[0317] In step S3, according to the position R of the target star at the start time of the mission mt0 and speed V mt0 , calculate the instantaneous orbital root number;

[0318] H=R mt0 ×V mt0

[0319] Where H represents the angular momentum vector of the target star at the start of the mission;

[0320]

[0321] Where E represents the eccentricity vector of the target star at the start of the mission; the symbol |||| represents the modulo operator;

[0322] e′=‖E‖

[0323] Among them, e′ represents the eccentricity of the target star at the start of the mission, which is the instantaneous root number;

[0324]

[0325] Where a′ represents the semi-major axis of the orbit of the target satellite at the start of the mission, which is the instantaneous root number;

[0326]

[0327] Among them, i′ represents the orbital inclination of the target satellite at the start of the mission, which is an instantaneous root number;

[0328]

[0329] Where, Ω′ represents the right ascension of the ascending node of the target star at the start of the mission (instantaneous root number);

[0330]

[0331] Where, ω′ represents the argument of perigee (instantaneous root number) of the target satellite at the start of the mission;

[0332]

[0333] Where u′ represents the true latitude argument of the target satellite at the start of the mission;

[0334]

[0335] Among them, φ′ represents the latitude argument of the target satellite at the start of the mission;

[0336] λ′=φ′-e′sin(φ′-ω′)

[0337] Among them, λ′ represents the mean latitude argument of the target satellite at the start time of the mission;

[0338] In step S3, (2) the orbital average root number is calculated from the orbital instantaneous root number, and the simplified algorithm is as follows:

[0339]

[0340] ξ′=e′cosω′

[0341] η′=-e′sinω′

[0342] δ=a′(1-e ′2 )

[0343] γ=a′(1-ξ′cosφ′+η′sinφ′)

[0344]

[0345] Specifically, in summary, ε, ξ′, η′, δ, γ, Ω1, and ω1 are all intermediate variables and have no real meaning;

[0346] x1=u′-λ′+ξ′sinu′+η′cosu′

[0347] x2=ξ′(3cos u′+cos3u′)+η′(3sin u′-sin3u′)+3cos2u′+ε(2-ε)(ξ′ 2 -η′ 2 )

[0348] x3=ξ′(3sin u′+sin3u′)-η′(3cos u′-cos3u′)+3sin2u′-2ε(2-ε)ξ′η′

[0349] x4=-(5 / 6)Ω1x3cos i′+ω1(x1-0.5x3)

[0350]

[0351] x7=-x5(ξ′sin u′+η′cosu′)-2x6ε(1-ε) 2 ξ′η′

[0352] x8=0.5x5(3-ε(2-ε)e′ 2 )+3x6(δ / γ)cos2u′

[0353]

[0354] Among them, x1~x 10 are intermediate variables and have no real meaning; specifically, x1~x 10 Corresponding to intermediate variable one to intermediate variable ten;

[0355]

[0356] Among them, a mt0 Indicates the orbital semi-major axis of the target star at the start of its mission; (square root);

[0357] i mt0 =i′+(1 / 6)x2Ω1sini′

[0358] Among them, i mt0 Indicates the orbital inclination of the target satellite at the start of the mission (square root);

[0359] Ω mt0 =Ω′-Ω1(x1-x3 / 6)

[0360] Among them, Ω mt0 Indicates the right ascension of the ascending node of the target star at the start of the mission (mean root);

[0361] ξ=ξ′-(x9+(x4+x7)η′+x8ξ′)

[0362] η=η′-(-x 10 -(x4+x7)ξ′+x8η′)

[0363] λ=λ′-(x4+ε(x7e′ 2 +x9η′+x 10 ξ′))

[0364] Among them, λ, ξ and η are all intermediate variables and have no real meaning;

[0365] ω mt0 =arctan(-η / ξ)

[0366] Among them, ω mt0 Indicates the argument of perigee (mean root) of the target star at the start of its mission;

[0367]

[0368] Among them, e mt0 Indicates the eccentricity of the target star at the start of the mission (square root);

[0369] M mt0 =λ-ω mt0

[0370] Among them, M mt0 Indicates the mean anomaly angle of the target star at the start of the mission (mean root);

[0371] (3) Analytical method to solve the position R of the target star at the current time m and speed V m

[0372] Calculate auxiliary vector

[0373]

[0374] Among them, P m It is an intermediate variable and has no real meaning;

[0375]

[0376] Among them, Q m It is an intermediate variable and has no real meaning;

[0377] At this point, the above steps only need to be calculated once in one observation task, and the calculation steps of each control cycle only need to perform the following steps, saving computing resources.

[0378] In step S4, the recursive time Δt is calculated from the current time t, and the mean anomaly angle is analytically recursive Then the mean anomaly angle M mt Convert to eccentric anomaly angle E mt The calculation method for converting the mean anomaly angle into the eccentric anomaly angle is a conventional algorithm, which will not be described in detail in the present invention.

[0379] The mathematical expression of the recursive time Δt is:

[0380] Δt=t-t0

[0381] Mean anomaly angle M mt The mathematical expression is:

[0382]

[0383] The position R of the target star at the current moment is calculated by using the orbital elements of the target star using an analytical algorithm. m and speed V m The formula is the current position R m and speed Vm The formula is as follows:

[0384]

[0385] Finally, the three-axis attitude of the satellite in the inertial system when observing the target star from the same viewing angle is calculated based on the position and velocity information of the target star and the local star.

[0386] (1) Calculate the expected attitude rotation matrix of the satellite and the target star under the same viewing angle, with the satellite camera's visual axis (+Z axis) pointing in the opposite direction to the target star and making the visual axis rotate parallel to the +Y axis during the mission as the constraint condition. The vector i x ,i y ,i z The calculation method is as follows:

[0387]

[0388] i x =i y ×i z

[0389] Among them, R s and V s They are respectively the projections of the satellite’s position vector and velocity vector in the J2000 inertial coordinate system.

[0390] In step S5, (2) the three-axis attitude in the inertial system is calculated. Here, the Euler angle of 1-2-3 is taken as an example. The satellite and the target star are observed from the same perspective, that is, the rolling angle of the satellite in the inertial system is The pitch angle θ and yaw angle ψ are calculated according to the following formula:

[0391]

[0392] θ=arcsin(i z (1))

[0393]

[0394] Among them, i x 、i y 、i z The mathematical expression is:

[0395]

[0396] i x =i y ×i z

[0397] Among them, i x 、i y 、i zRespectively represent the direction vectors of the three axes of the satellite body in the inertial system; R s With V s They are respectively the projections of the satellite’s position vector and velocity vector in the J2000 inertial coordinate system.

[0398] The present invention also provides a satellite attitude guidance system for observing at the same viewing angle as a target star. The satellite attitude guidance system for observing at the same viewing angle as a target star can be implemented by executing the process steps of the satellite attitude guidance method for observing at the same viewing angle as a target star, that is, those skilled in the art can understand the satellite attitude guidance method for observing at the same viewing angle as a preferred implementation mode of the satellite attitude guidance system for observing at the same viewing angle as a target star.

[0399] A satellite attitude guidance system for observing a target satellite at the same viewing angle as the target satellite is provided according to the present invention, comprising:

[0400] Module M1: Calculate the position R of the target star at the time of the ephemeris data m0 and speed V m0 ;

[0401] Module M2: Numerical integration to solve the position R of the target star at the start of the mission mt0 and speed V mt0 ;

[0402] Module M3: According to the position R mt0 With speed V mt0 , find the mean orbital root number of the target star at the start of the mission;

[0403] Module M4: Based on the orbital average root number, calculate the real-time position R of the target star m and speed V m ;

[0404] Module M5: According to the position R m With speed V m The guidance attitude of the satellite is calculated.

[0405] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0406] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A satellite attitude guidance method for observing from the same viewing angle as a target satellite, characterized in that: include: Step S1: Calculate the position R of the target star at the time of the ephemeris data m0 and speed V m0 ; Step S2: Numerical integration to solve the position R of the target star at the start of the mission mt0 and speed V mt0 ; Step S3: According to the position R mt0 With speed V mt0 , find the mean orbital root number of the target star at the start of the mission; Step S4: Based on the orbital mean root number, calculate the real-time position R of the target star m and speed V m ; Step S5: According to the position R m With speed V m The guidance attitude of the satellite is calculated.

2. The satellite attitude guidance method for observing at the same viewing angle as the target satellite according to claim 1, characterized in that: In step S1, the position R m0 The mathematical expression is: R m0 =Q·r p Among them, r p represents the position vector in the near focus coordinate system, Q represents the transformation matrix from the near focus coordinate system to the inertial system; The speed V m0 The mathematical expression is: V m0 =Q·v p The mathematical expression of Q is: Wherein, the superscript T is the symbol for matrix transposition; R X R is the X-axis rotation matrix function; Z is the Z-axis rotation matrix function; Ω ms represents the right ascension of the ascending node; i ms represents the orbital inclination; ω ms represents the argument of perigee; The R X , that is, the mathematical expression of the X-axis rotation matrix function is: The R Z , that is, the mathematical expression of the Z-axis rotation matrix function is: Among them, α represents the angle; The r p The mathematical expression is: Among them, f ms Indicates the true anomaly angle; e ms represents eccentricity; μ represents the earth's gravitational constant; h ms represents the target star angular momentum; The v p The mathematical expression is: Among them, v p represents the velocity vector in the near focus coordinate system; The h ms The mathematical expression is: Among them, a ms represents the semi-major axis of the orbit; In step S2, the numerical integration solution method step includes: Step A1: Calculate the integration step length from the task start time; Step A2: Set the maximum integration step size h max , and then decompose the integral step; Step A3: Recursively extrapolate the orbit of the target star from the ephemeris data time to the mission start time, and calculate the position R of the target star at the mission start time mt0 With speed V mt0 ; In step A1, the mathematical expression of the integration step length is: h=t0-t s Where h is the integration step; t0 is the task start time; t s Indicates the time of ephemeris data; In step A2, the mathematical expression of the decomposition process is: h=N·h max +g0 Where N represents a natural number, and 0≤h0<h max ; h0 represents the initial integration step; In step A3, the N+1 numerical calculation method is called to obtain the position R of the target star at the start time of the mission. mt0 With speed V mt0 ; The numerical calculation method, the mathematical expression is: Where f represents the function; y0 represents the initial value of the integral; the symbol Δ represents the increment symbol; the differential equation system f(p) is a 6×1 column vector, p is the term in the brackets between k1 and k4, let The mathematical expression of f(p) is: Among them, R e is the equatorial radius of the Earth, J2 is the second-order harmonic coefficient of the non-spherical gravitational perturbation term of the Earth; In step A3, y0 is the initial value of the integration used for the first time, and its mathematical expression is: y0=[R m0 ;V m0 ] For the first N times, use the maximum integration step size h max , that is, let Δ=h max And use the output y1 of each time as the initial value y0 of the next integration; the last time let Δ=h0, calculate the output y1 to get the position R of the target star at the start time of the mission mt0 With speed V mt0 ; The R mt0 The mathematical expression is: R mt0 =[y1(1);y1(2);y1(3)] The speed V mt0 The mathematical expression is: In mt0 =[y1(4);y1(5);y1(6)] Among them, y1(1), y1(2), y1(3), y1(4), y1(5) and y1(6) represent six components of the output y1.

3. The satellite attitude guidance method for observing at the same viewing angle as the target satellite according to claim 2, characterized in that: In step S3, according to the position R mt0 With speed V mt0 , find out the instantaneous orbital roots and argument information; According to the instantaneous orbital root number and the argument information, the mean orbital root number of the target star at the start time of the mission is calculated; The instantaneous orbital elements include: e′, a′, i′, Ω′ and ω′; The mathematical expression of e′ is: e′=‖E‖ Among them, e′ represents the eccentricity of the target star at the start of the mission, which is the instantaneous root of the orbit; E represents the eccentricity vector at the start of the target star mission; The mathematical expression of E is: Where, E represents the eccentricity vector of the target star at the start of the mission; the symbol |||| represents the modulo operator; H represents the angular momentum vector of the target star at the start of the mission; The mathematical expression of H is: H=R mt0 ×V mt0 The mathematical expression of a′ is: Where a′ represents the semi-major axis of the orbit of the target star at the start of the mission; The mathematical expression of i′ is: Where i′ represents the orbital inclination of the target satellite at the start of the mission; The mathematical expression of Ω′ is: Among them, Ω′ represents the right ascension of the ascending node of the target star at the start time of the mission; The mathematical expression of ω′ is: Among them, ω′ represents the argument of perigee at the start of the target satellite mission; The argument information includes: u′, φ′ and λ′; Where u′ represents the true latitude argument of the target satellite at the start of the mission; Among them, φ′ represents the latitude argument of the target satellite at the start of the mission; λ′=φ′-e′sin(φ′-ω′) Among them, λ′ represents the mean latitude argument of the target satellite at the start time of the mission.

4. The satellite attitude guidance method for observing at the same viewing angle as the target satellite according to claim 3, characterized in that: In step S3, the track average root number includes: a mt0 、i mt0 ,Ω mt0 ,ω mt0 、e mt0 With M mt0 ; The a mt0 The mathematical expression is: Among them, a mt0 represents the semi-major axis of the orbit of the target star at the start of the mission; x5 represents the intermediate variable five; x6 represents the intermediate variable six; The i mt0 The mathematical expression is: i mt0 =i′+(1 / 6)x2Ω1sin i′ Among them, i mt0 represents the orbital inclination of the target star at the start of the mission; x2 is the second intermediate variable: The Ω mt0 The mathematical expression is: Oh mt0 =Ω′-Ω1(x1-x3 / 6) Among them, Ω mt0 represents the right ascension of the ascending node of the target star at the start of the mission; x1 is the intermediate variable one; x3 is the intermediate variable three; The mathematical expression of Ω1 is: The ω mt0 The mathematical expression is: oh mt0 =arctan(-η / ξ) Among them, ω mt0 Indicates the argument of perigee at the start of the target star mission; The mathematical expression of η is: η=η′-(-x 10 -(x4+x7)ξ′+x8η′) Among them, x 10 is the intermediate variable ten; x4 is the intermediate variable four; x7 is the intermediate variable seven; x8 is the intermediate variable eight; The mt0 The mathematical expression is: Among them, e mt0 represents the eccentricity of the target star at the start of the mission; The mathematical expression of ξ is: ξ=ξ′-(x9+(x4+x7)η′+x8ξ′) Among them, x8 is the intermediate variable eight; x9 is the intermediate variable nine; The M mt0 The mathematical expression is: M mt0 =l-w mt0 Among them, M mt0 Indicates the mean anomaly angle of the target star at the start of the mission; The mathematical expression of λ is: λ=λ′-(x4+ε(x7e′ 2 +x9th′+x 10 ξ′)) Among them, x9 is the intermediate variable nine.

5. The satellite attitude guidance method for observing at the same viewing angle as the target satellite according to claim 4, characterized in that: In step S4, the R m The mathematical expression is: Among them, E mt is the near point angle; The V m The mathematical expression is: The P m The mathematical expression is: Among them, P m is an intermediate variable; The Q m The mathematical expression is: Among them, Q m is an intermediate variable; In step S5, the guidance attitude of the satellite, that is, the rolling angle of the satellite under inertia The mathematical expressions of pitch angle θ and yaw angle ψ are: θ=arcsin(i z (1)) Among them, i x 、i y 、i z The mathematical expression is: i x =i y ×i z Among them, i x 、i y 、i z Respectively represent the direction vectors of the three axes of the satellite body in the inertial system; R s With V s They are respectively the projections of the satellite’s position vector and velocity vector in the J2000 inertial coordinate system.

6. A satellite attitude guidance system for observing from the same viewing angle as a target satellite, characterized in that: include: Module M1: Calculate the position R of the target star at the time of the ephemeris data m0 and speed V m0 ; Module M2: Numerical integration to solve the position R of the target star at the start of the mission mt0 and speed V mt0 ; Module M3: According to the position R mt0 With speed V mt0 , find the mean orbital root number of the target star at the start of the mission; Module M4: Based on the orbital average root number, calculate the real-time position R of the target star m and speed V m ; Module M5: According to the position R m With speed V m The guidance attitude of the satellite is calculated.

7. The satellite attitude guidance system for observing at the same viewing angle as the target satellite according to claim 6, characterized in that: In the module M1, the position R m0 The mathematical expression is: R m0 =Q·r p Among them, r p represents the position vector in the near focus coordinate system, Q represents the transformation matrix from the near focus coordinate system to the inertial system; The speed V m0 The mathematical expression is: V m0 =Q·v p The mathematical expression of Q is: Wherein, the superscript T is the symbol for matrix transposition; R X R is the X-axis rotation matrix function; Z is the Z-axis rotation matrix function; Ω ms represents the right ascension of the ascending node; i ms represents the orbital inclination; ω ms represents the argument of perigee; The R X , that is, the mathematical expression of the X-axis rotation matrix function is: The R z , that is, the mathematical expression of the Z-axis rotation matrix function is: Among them, α represents the angle; The r p The mathematical expression is: Among them, f ms Indicates the true anomaly angle; e ms represents eccentricity; μ represents the earth's gravitational constant; h ms represents the target star angular momentum; The v p The mathematical expression is: Among them, v p represents the velocity vector in the near focus coordinate system; The h ms The mathematical expression is: Among them, a ms represents the semi-major axis of the orbit; In the module M2, the numerical integration solution step includes: Module A1: Calculate the integration step length from the task start time; Module A2: Setting the maximum integration step length h max , and then decompose the integral step; Module A3: Recursively extrapolate the orbit of the target star from the ephemeris data time to the mission start time, and calculate the position R of the target star at the mission start time mt0 With speed V mt0 ; In the module A1, the mathematical expression of the integration step is: h=t0-t s Where h is the integration step; t0 is the task start time; t s Indicates the time of ephemeris data; In the module A2, the mathematical expression of the decomposition process is: h=N·h max +h0 Where N represents a natural number, and 0≤h0<h max ; h0 represents the initial integration step; In the module A3, the N+1 numerical calculation method is called to obtain the position R of the target star at the start time of the mission. mt0 With speed V mt0 ; The numerical calculation method, the mathematical expression is: Where f represents the function; y0 represents the initial value of the integral; the symbol Δ represents the increment symbol; the differential equation system f(p) is a 6×1 column vector, p is the term in the brackets between k1 and k4, let The mathematical expression of f(p) is: Among them, R e is the equatorial radius of the Earth, J2 is the second-order harmonic coefficient of the non-spherical gravitational perturbation term of the Earth; In the module A3, y0 is the initial value of the integration used for the first time, and the mathematical expression is: y0=[R m0 ;V m0 ] For the first N times, use the maximum integration step size h max , that is, let Δ=h max And use the output y1 of each time as the initial value y0 of the next integration; the last time let Δ=h0, calculate the output y1 to get the position R of the target star at the start time of the mission mt0 With speed V mt0 ; The R mt0 The mathematical expression is: R mt0 =[y1(1);y1(2);y1(3)] The speed V mt0 The mathematical expression is: In mt0 =[y1(4);y1(5);y1(6)] Among them, y1(1), y1(2), y1(3), y1(4), y1(5) and y1(6) represent six components of the output y1.

8. The satellite attitude guidance system for observing at the same viewing angle as the target satellite according to claim 7, characterized in that: In the module M3, according to the position R mt0 With speed V mt0 , find out the instantaneous orbital roots and argument information; According to the instantaneous orbital root number and the argument information, the mean orbital root number of the target star at the start time of the mission is calculated; The instantaneous orbital elements include: e′, a′, i′, Ω′ and ω′; The mathematical expression of e′ is: e′=‖E‖ Among them, e′ represents the eccentricity of the target star at the start of the mission, which is the instantaneous root of the orbit; E represents the eccentricity vector at the start of the target star mission; The mathematical expression of E is: Where, E represents the eccentricity vector of the target star at the start of the mission; the symbol |||| represents the modulo operator; H represents the angular momentum vector of the target star at the start of the mission; The mathematical expression of H is: H=R mt0 ×V mt0 The mathematical expression of a′ is: Where a′ represents the semi-major axis of the orbit of the target star at the start of the mission; The mathematical expression of i′ is: Where i′ represents the orbital inclination of the target satellite at the start of the mission; The mathematical expression of Ω′ is: Among them, Ω′ represents the right ascension of the ascending node of the target star at the start time of the mission; The mathematical expression of ω′ is: Among them, ω′ represents the argument of perigee at the start of the target satellite mission; The argument information includes: u′, φ′ and λ′; Where u′ represents the true latitude argument of the target satellite at the start of the mission; Among them, φ′ represents the latitude argument of the target satellite at the start of the mission; λ′=φ′-e′sin(φ′-ω′) Among them, λ′ represents the mean latitude argument of the target satellite at the start time of the mission.

9. The satellite attitude guidance system for observing at the same viewing angle as the target satellite according to claim 8, characterized in that: In the module M3, the track average root number includes: a mt0 、i mt0 ,Ω mt0 ,ω mt0 、e mt0 With M mt0 ; The a mt0 The mathematical expression is: Among them, a mt0 represents the semi-major axis of the orbit of the target star at the start of the mission; x5 represents the intermediate variable five; x6 represents the intermediate variable six; The i mt0 The mathematical expression is: i mt0 =i′+(1 / 6)x2Ω1sin i′ Among them, i mt0 represents the orbital inclination of the target star at the start of the mission; x2 is the second intermediate variable: The Ω mt0 The mathematical expression is: Oh mt0 =Ω′-Ω1(x1-x3 / 6) Among them, Ω mt0 represents the right ascension of the ascending node of the target star at the start of the mission; x1 is the intermediate variable one; x3 is the intermediate variable three; The mathematical expression of Ω1 is: The ω mt0 The mathematical expression is: oh mt0 =arctan(-η / ξ) Among them, ω mt0 Indicates the argument of perigee at the start of the target star mission; The mathematical expression of η is: η=η′-(-x 10 -(x4+x7)ξ′+x8η′) Among them, x 10 is the intermediate variable ten; x4 is the intermediate variable four; x7 is the intermediate variable seven; x8 is the intermediate variable eight; The mt0 The mathematical expression is: Among them, e mt0 represents the eccentricity of the target star at the start of the mission; The mathematical expression of ξ is: ξ=ξ′-(x9+(x4+x7)η′+x8ξ′) Among them, x8 is the intermediate variable eight; x9 is the intermediate variable nine; The M mt0 The mathematical expression is: M mt0 =l-w mt0 Among them, M mt0 Indicates the mean anomaly angle of the target star at the start of the mission; The mathematical expression of λ is: λ=λ′-(x4+ε(x7e′ 2 +x9th′+x 10 ξ′)) Among them, x9 is the intermediate variable nine.

10. The satellite attitude guidance system for observing at the same viewing angle as the target satellite according to claim 9, characterized in that: In the module M4, the R m The mathematical expression is: Among them, E mt is the near point angle; The V m The mathematical expression is: The P m The mathematical expression is: Among them, P m is an intermediate variable; The Q m The mathematical expression is: Among them, Q m is an intermediate variable; In the module M5, the guidance attitude of the satellite, that is, the rolling angle of the satellite under inertia The mathematical expressions of pitch angle θ and yaw angle ψ are: θ=arcsin(i z (1)) Among them, i x 、i y 、i z The mathematical expression is: i x =i y ×i z Among them, i x 、i y 、i z Respectively represent the direction vectors of the three axes of the satellite body in the inertial system; R s With V s They are respectively the projections of the satellite’s position vector and velocity vector in the J2000 inertial coordinate system.

Images