CN112329202A - Method for optimizing direction algorithm of Mars vehicle to antenna of surround device - Google Patents

Method for optimizing direction algorithm of Mars vehicle to antenna of surround device Download PDF

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CN112329202A
CN112329202A CN202011066257.9A CN202011066257A CN112329202A CN 112329202 A CN112329202 A CN 112329202A CN 202011066257 A CN202011066257 A CN 202011066257A CN 112329202 A CN112329202 A CN 112329202A
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mars
coordinate system
antenna
calculating
angle
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CN112329202B (en
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郭坚
朱剑冰
彭松
张红军
赵蕾
朱玛
兰天
韦涌泉
杨小瑞
王翠莲
周东
张建利
温博
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Beijing Institute of Spacecraft System Engineering
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Beijing Institute of Spacecraft System Engineering
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/20—Design optimisation, verification or simulation
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Abstract

The invention discloses an optimization realization method of a Mars vehicle to a surround antenna pointing algorithm, wherein when the antenna pointing is calculated in the same wheel antenna control process, the longitude and latitude heights and the attitude angles of the Mars vehicle in the two calculation processes are all completely the same, so that a plurality of intermediate variables exist, and after the first calculation, the first calculation result can be directly used in the rest control process; in addition, because the mars antenna installation deviation matrix is completely fixed in the whole satellite life cycle, the method utilizes the characteristic, the conversion matrix from the antenna system to the satellite system is calculated in advance, the calculation result is stored in the satellite-borne memory, and the calculation is not needed when the calculation step of the conversion matrix from the antenna system to the satellite system is met in the antenna pointing calculation process, but the matrix data in the memory is directly read, so that the calculation amount of the satellite-borne processor is effectively reduced.

Description

Method for optimizing direction algorithm of Mars vehicle to antenna of surround device
Technical Field
The invention belongs to the technical field of satellite-borne antennas, and particularly relates to an optimization implementation method of a Mars vehicle to a direction algorithm of a circulator antenna.
Background
China launched a mars vehicle to perform mars surface inspection tour in 2020, and the mars vehicle is provided with a high-gain and narrow-beam directional antenna to perform data communication with a mars surround device. The autonomous pointing of the directional antenna to the surround is a key process, and directly influences the reliability and accuracy of data transmission. The process needs to consider the influence of multiple factors such as time, ephemeris, fire surface position, mars vehicle attitude, antenna installation error and the like. In the moon exploration task of Chang E III in China, engineers propose a method for planning the orientation of a directional antenna of a lunar Mars vehicle to a lunar circulator, and send an instruction to control a mechanism to move after ground planning is completed. Compared with a lunar Mars vehicle, the communication delay between the Mars vehicle and the earth is about 3-23 min, and quasi-real-time ground teleoperation control cannot be executed like the lunar Mars vehicle, so that the directional antenna of the Mars vehicle needs to be automatically implemented on a surrounding device for pointing, on one hand, planning algorithms such as ephemeris calculation and mechanism pointing calculation need to be operated on the device, and on the other hand, a motion instruction needs to be automatically generated on the device according to a planning result. Aiming at the requirement of autonomous orientation of the surrounding device, if a calculation method of a ground computer is directly adopted, as the capacity of an on-board computer is weak, long calculation time needs to be consumed, and the real-time requirement cannot be met, an on-board optimization calculation method for autonomous execution of the antenna of the surrounding device by a mars and mars vehicle needs to be provided.
Disclosure of Invention
In view of this, the present invention provides an optimized implementation method for independent pointing of a mars and mars vehicle to an antenna of a mars surround device, which can meet the requirement of real-time pointing of the antenna under a very limited space-borne calculation condition, and provide reliable guarantee for data communication between a directional antenna of the mars and the mars surround device.
A method for optimizing the orientation of a surrounding device antenna on a planet by a Mars vehicle comprises the following steps:
step 1, calculating the position of the surrounding device under a Mars inertial coordinate system:
for the orbit Mars surrounding device with large inclination angle and large eccentricity, the ground fits the extrapolation root number to obtain the epoch time t0Average number of a0、e0、i0、Ω0、ω0、M0Rate of change of mean radical
Figure BDA0002713836090000011
And second order rate of change of mean anomaly
Figure BDA0002713836090000012
The extrapolation formula for the Kepler root at time t is as follows:
ΔT＝t-t0 (1)
a＝a0 (2)
e＝e0 (3)
i＝i0 (4)
Figure BDA0002713836090000021
Figure BDA0002713836090000022
Figure BDA0002713836090000023
wherein ：
Figure BDA0002713836090000024
Figure BDA0002713836090000025
Figure BDA0002713836090000026
Figure BDA0002713836090000027
Figure BDA0002713836090000028
p＝a0(1-e0 2) (13)
c＝cosi0 (14)
wherein ,J2Representing the second order coefficient of the orbit; rmRepresents the Mars radius; mu.smRepresents the Mars constant;
the method for calculating the position of the surround device in the Mars inertial coordinate system according to the Kepler root number comprises the following steps:
s11, calculating delta T:
for time T, the time difference Δ T (in the Julian century) is found relative to time J2000.0:
ΔT＝(T0-TJ2000.0+t/86400)/Tcy (15)
in the formula ：T0Carrying a julian calendar day corresponding to the zero time of the computer; t isJ2000.0The julian calendar day corresponding to the moment J2000.0; t iscyThe number of days corresponding to one julian century;
s12, calculating a deviation angle:
E＝M+ee1×sinM+ee2×sin2M+ee3×sin3M (16)
s13, calculating a true proximal angle:
Figure BDA0002713836090000029
s14, calculating the track wheelbase:
Figure BDA00027138360900000210
s15, calculating the position coordinates of the surrounding device under the plane coordinate system of the orbit of the surrounding device:
Figure BDA0002713836090000031
s16, calculating the position coordinates of the surrounding device under the Mars inertial coordinate system as follows:
Figure BDA0002713836090000032
wherein ,
Figure BDA0002713836090000033
a transformation matrix representing rotation about the x-axis;
Figure BDA0002713836090000034
a transformation matrix representing rotation about the y-axis;
Figure BDA0002713836090000035
a transformation matrix representing rotation about the z-axis;
step 2, calculating Mars orientation parameters:
solving celestial body directional output parameters according to the time (t) and celestial body directional input parameters (A, B, C, D, E and F); wherein alpha is0Right ascension in ICRF for celestial arctic; delta0Declination in ICRF for celestial North; w is the distance from the 0 DEG meridian to the ascending intersection point of the celestial body equator:
for time T, the time difference Δ T from time J2000.0 is determined by referring to equation (1)1Then, there are:
α0＝A-B×ΔT1
δ0＝C-D×ΔT1 (21)
W＝E+F×ΔT1×Tcy
at a given time t, the directional input parameters (A, B, C, D, E, F) of the mars in the table are substituted into an equation (21) to calculate the directional parameter alpha of the mars0_mars，δ0_mars，Wmars；
Step 3, changing the position coordinate of the circulator from a Mars inertial coordinate system to a Mars astronomical reference coordinate system:
Figure BDA0002713836090000036
wherein ,RR1＝Rz(-θ3)·Ry(-θ2)·Rx(-θ1)；
And 4, transforming the position coordinates of the circulator from the Mars astronomical reference coordinate system to a Mars fixed connection coordinate system:
Figure BDA0002713836090000041
under the fixed coordinate system of the mars, the position of the mars car is as follows:
Figure BDA0002713836090000042
wherein H represents the height of the position of the Mars train; thetalatLatitude, theta, indicating the location of the Mars vehiclelonA longitude indicating the location of the Mars vehicle;
and 5, under the condition that the mars is fixedly connected with a coordinate system, the position of the surrounding device relative to the mars vehicle is as follows:
Figure BDA0002713836090000043
to rdPerforming orthogonalization to obtain a unit vector from the mars to the surround device as follows:
Figure BDA0002713836090000044
step 6, mixing rd_NThe Mars solid connection system is converted into a Mars surface under a coordinate system of the northeast of the sky:
rd_N1＝RR2·rd_N (28)
wherein ,RR2＝Ry(-θlat)·Rz(θlon)；
Step 7, mixing rd_N1The coordinate system of the Mars surface in the north-east direction is converted into the coordinate system of the Mars surface in the north-east direction:
rd_N2＝RR3·rd_N1 (29)
wherein ,RR3＝Ry(-90)；
Mars surface lower surround altitude in North east Earth coordinate:
ho＝-arcsin[rd_N2(3)] (30)
wherein ,rd_N2(3) Representing a vector rd_N2The third element of (C);
mars surface North east coordinate System lower surround azimuth:
Figure BDA0002713836090000051
step 8, mixing rd_N2The coordinate system of the North east of the Mars surface is converted to the position under the Mars vehicle control body:
reb＝RR4·rd_N2 (32)
wherein ,RR4＝Rx(θroll)·Ry(θpitch)·Rz(θyaw)；
θroll，θpitch，θyawRespectively representing the rolling angle, the pitch angle and the yaw angle of the mars vehicle;
step 9, controlling the height angle of the surrounding device under the coordinate system of the body by the train:
hob＝-arcsin[reb(3)] (33)
wherein ,reb(3) Representing a vector rebThe third element of (C);
the azimuth angle of the surrounding device under the coordinate system of the train control body is as follows:
Figure BDA0002713836090000052
step 10, calculating a pointing angle:
converting a pointing target from a train control body coordinate system to a directional antenna biaxial zero position coordinate system:
reb1＝Raz·reb (35)
wherein RazControlling a rotation matrix from a body coordinate system to a directional antenna biaxial zero position coordinate system for the train;
when the directional antenna is at a null position, the direction vector of the beam center line of the directional antenna is expressed in a biaxial null coordinate system of the directional antenna as follows:
Figure BDA0002713836090000053
the directional antenna has 2 pivots: firstly rotating around the B axis and then rotating around the A axis; rotation of directional antenna about axis BBAbout axis A by aAThen, the direction vector of the beam center line is expressed in a biaxial null coordinate system as:
Figure BDA0002713836090000061
rotation of directional antenna about axis AAAbout axis BBShould then be pointing to ground, so r1＝reb1Comparing equation (37) with reb1Comprises the following steps:
-sinθB＝reb1(1)
Figure BDA0002713836090000062
and (3) analyzing by combining with actual conditions:
θB＝-arcsin(reb1(1)) (38)
Figure BDA0002713836090000063
preferably, the sine and cosine calculations of the attitude angle and the track angle used in the single-time antenna pointing calculation are pre-calculated and stored in the corresponding attitude data structure and track data structure, and the pre-calculated results are directly used in the subsequent use.
Preferably, all values of angles in degrees are converted to radians.
Preferably, in the process of calculating the single antenna pointing, the function call of the matrix multiplication operation is converted into the assignment operation.
Preferably, when the antenna pointing direction is calculated in the same round of antenna control process, the intermediate result stored in the previous calculation is utilized:
Figure BDA0002713836090000064
Figure BDA0002713836090000065
ee1、ee2、ee3、ee4 and RR1Calculating the position of the surrounding device; intermediate results saved with the last calculation:
Figure BDA0002713836090000066
calculating the position of the Mars vehicle; intermediate results saved with the last calculation: RR2、RR3 and RR4Calculating a vector of the surrounding device to the inspection device; and finally, calculating the antenna direction of the time.
The invention has the following beneficial effects:
when the antenna pointing direction is calculated in the same wheel antenna control process, the longitude and latitude height and the attitude angle of the Mars train are completely the same in the two calculation processes, so that a plurality of intermediate variables exist, and after the calculation for the first time, the calculation result for the first time can be directly used in the rest control processes.
In addition, because the mars antenna installation deviation matrix is completely fixed in the whole satellite life cycle, the method utilizes the characteristic, the conversion matrix from the antenna system to the satellite system is calculated in advance, the calculation result is stored in the satellite-borne memory, and the calculation is not needed when the calculation step of the conversion matrix from the antenna system to the satellite system is met in the antenna pointing calculation process, but the matrix data in the memory is directly read, so that the calculation amount of the satellite-borne processor is effectively reduced.
Drawings
FIG. 1 is a coordinate system definition and directional antenna for a train control body;
FIG. 2 is a flow chart of single antenna pointing calculation;
FIG. 3 is a flow chart of an adjacent antenna pointing optimization calculation;
FIG. 4 is a model of the orientation of celestial bodies within a solar system.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
For convenience of the following description, the relevant convention of the mars and directional antennas will be explained.
As shown in fig. 1, a train control body coordinate system OB-XBYBZB is defined: the origin OB is at the geometrical center of the bottom plate of the Mars vehicle structure, the OBXB shaft points to the direction of the vehicle head, the OBZB shaft is perpendicular to the fire surface pointed by the bottom plate, the OBYB shaft is perpendicular to the OBXB shaft and the OBZB shaft, and the three shafts form a right-hand rectangular coordinate system.
The directional antenna is installed at the tail of the Mars vehicle and is driven by a double-shaft mechanism: the rotating shaft A and the rotating shaft B are perpendicular to each other, the shaft A drives the shaft B to rotate when rotating, and the shaft B does not influence the shaft A when rotating. Defining a biaxial zero coordinate system OS-XSYSZS of the directional antenna, namely when the directional antenna is in a zero position, pointing an OSXS axis to a rotating shaft A, pointing an OSYS axis to a rotating shaft B, and determining the OSZS according to a right-hand rule; under the ideal installation condition, the three-axis direction of the biaxial zero position coordinate system is correspondingly parallel to the three-axis direction of the train control body system.
It is to be noted that: the directional antenna points forward, the solar wing is in a flattening state, and the mast tilts forward so as to avoid the shielding of a self-moving mechanism of the vehicle body on the directional antenna.
The optimization calculation process comprises optimization of single antenna pointing calculation and optimization of adjacent satellite antenna pointing calculation.
A single antenna pointing calculation optimization method comprises the following steps:
the flow of single antenna pointing calculation is shown in fig. 2, and this process adopts three optimization methods to improve single calculation efficiency, which are respectively as follows:
a) angular sine and cosine pre-calculation method
The calculation process involves sine and cosine calculations of a large number of attitude angles and track angles, the calculations need to call sin and cos functions in a bottom mathematical library in a program, the calling process of the functions is time-consuming, the method pre-calculates the attitude angle and track angle sine and cosine calculations used in the antenna pointing calculation and stores the calculated attitude angle and track angle sine and cosine calculations in a corresponding attitude data structure and track data structure, the pre-calculated results are directly used in subsequent use, and the repeated calculation process is effectively reduced. Since the attitude angle and the orbit angle of the mars are not changed in the single antenna pointing calculation process, the pre-calculation method is completely applicable.
b) Dimension normalization method
The method converts all the angle values with the degrees as the unit into the radian, and the calculation processes are all unified into the radian. The method can reduce the calculation of dimension conversion when sine and cosine calls are carried out each time, and simultaneously improve the precision of the calculation result by reducing the calculation times of floating point numbers
c) Matrix multiplication expanding method
The method converts the function call of the matrix multiplication operation into the assignment operation, thereby effectively reducing the calculation amount.
The process of single antenna pointing is shown in fig. 2, and the specific steps include:
step 1, calculating the position of the surrounding device under a Mars inertial coordinate system:
for the orbit Mars surrounding device with large inclination angle and large eccentricity, the ground fits the extrapolation root number to obtain the epoch time t0Average number of a0、e0、i0、Ω0、ω0、M0Rate of change of mean radical
Figure BDA0002713836090000081
And second order rate of change of mean anomaly
Figure BDA0002713836090000082
The extrapolation formula for the keplerian root number at time t is as follows (the angles use radians):
ΔT＝t-t0 (1)
a＝a0 (2)
e＝e0 (3)
i＝i0 (4)
Figure BDA0002713836090000083
Figure BDA0002713836090000084
Figure BDA0002713836090000085
wherein ：
Figure BDA0002713836090000086
Figure BDA0002713836090000087
Figure BDA0002713836090000088
Figure BDA0002713836090000089
Figure BDA00027138360900000810
p＝a0(1-e0 2) (13)
c＝cosi0 (14)
wherein ,J2Representing the second order coefficient of the orbit; rmRepresents the Mars radius; mu.smRepresents the Mars constant;
the method for calculating the position of the surround device in the Mars inertial coordinate system according to Kepler root numbers a, e, i, omega and M is as follows:
s11, calculating delta T:
for time T (expressed in seconds relative to the zero time of the on-board computer, the same applies below), its time difference Δ T (in julian century) relative to time J2000.0 is found:
ΔT＝(T0-TJ2000.0+t/86400)/Tcy (15)
in the formula ：T0Carrying a julian calendar day corresponding to the zero time of the computer; t isJ2000.0The julian calendar day corresponding to the moment J2000.0; t iscyThe number of days corresponding to one julian century.
S12, calculating a deviation angle:
E＝M+ee1×sinM+ee2×sin2M+ee3×sin3M (16)
wherein ,
Figure BDA0002713836090000091
s13, calculating a true proximal angle:
Figure BDA0002713836090000092
wherein ,
Figure BDA0002713836090000093
s14, calculating the track wheelbase:
Figure BDA0002713836090000094
s15, calculating the position coordinates of the surrounding device under the plane coordinate system of the orbit of the surrounding device:
Figure BDA0002713836090000095
s16, calculating the position coordinates of the surrounding device under the Mars inertial coordinate system as follows:
Figure BDA0002713836090000096
wherein ,
Figure BDA0002713836090000097
a transformation matrix representing rotation about the x-axis;
Figure BDA0002713836090000098
a transformation matrix representing rotation about the y-axis;
Figure BDA0002713836090000099
a transformation matrix representing rotation about the z-axis;
step 2, calculating Mars orientation parameters:
according to the time (t) and the celestial body orientation input parameters (A, B, C, D, E, F), solving a celestial body orientation output parameter (alpha)0,δ0,W)。
As shown in fig. 4, α0Right ascension in ICRF for celestial arctic; delta0Declination in ICRF for celestial North; w is the distance from the meridian of 0 degree to the rising intersection point of the equator of the celestial body.
For time T, the time difference Δ T from time J2000.0 can be determined by referring to equation (1)1Then, there are:
Figure BDA0002713836090000101
in the formula: relevant input parameters for Mars are shown in the following table.
Serial number Name definition Value of
1) Parameter of the right ascension of the heaven 317.68143
2) Parameter B of the right ascension of the heaven 0.1061
3) Declination parameter C of celestial body 52.88650
4) Declination parameter D of celestial body 0.0609
5) 0 degree meridian distance parameter E of celestial body 176.630
6) 0 degree meridian distance parameter F of celestial body 350.89198226
At a given time t, the directional input parameters (A, B, C, D, E, F) of the mars in the table are substituted into an equation (21) to calculate the directional parameter alpha of the mars0_mars，δ0_mars，Wmars。
Step 3, changing the position coordinate of the circulator from a Mars inertial coordinate system to a Mars astronomical reference coordinate system:
Figure BDA0002713836090000102
wherein ,RR1＝Rz(-θ3)·Ry(-θ2)·Rx(-θ1)；
θ1，θ2，θ3Respectively representing the rotation angle of an X axis from an ICRF coordinate system to a Mars inertial coordinate system, wherein the rotation angle is 37.1135 degrees, and the rotation angle of a Y axis from the ICRF coordinate system to the Mars inertial coordinate system is 0 degree; the Z-axis rotation angle from the ICRF coordinate system to the Mars inertial coordinate system is 47.6814 degrees;
and 4, transforming the position coordinates of the circulator from the Mars astronomical reference coordinate system to a Mars fixed connection coordinate system:
Figure BDA0002713836090000103
α in the formula (23)0_mars，δ0_mars，WmarsThis is obtained from equation (21).
Under the fixed coordinate system of the mars, the position of the mars car is as follows:
Figure BDA0002713836090000111
wherein H represents the height of the position of the Mars train; thetalatLatitude, theta, indicating the location of the Mars vehiclelonIndicating the longitude of the location of the mars vehicle.
And 5, under the condition that the mars is fixedly connected with a coordinate system, the position of the surrounding device relative to the mars vehicle is as follows:
Figure BDA0002713836090000112
the distance of the surround from the mars train is:
Figure BDA0002713836090000113
the communication code rate can be determined based on the distance.
To rdPerforming orthogonalization to obtain a unit vector from the mars to the surround device as follows:
Figure BDA0002713836090000114
step 6, mixing rd_NThe Mars solid connection system is converted into a Mars surface under a coordinate system of the northeast of the sky:
rd_N1＝RR2·rd_N (28)
wherein ,RR2＝Ry(-θlat)·Rz(θlon)；
Step 7, mixing rd_N1The coordinate system of the Mars surface in the north-east direction is converted into the coordinate system of the Mars surface in the north-east direction:
rd_N2＝RR3·rd_N1 (29)
wherein ,RR3＝Ry(-90)；
Height angle (-90 deg.) of surrounding device under coordinate system of north east of Mars surface<ho<90°)：
ho＝-arcsin[rd_N2(3)] (30)
wherein ,rd_N2(3) Representing a vector rd_N2The third element of (C);
azimuth angle of lower surrounding device of coordinate system of north east of Mars surface
Figure BDA0002713836090000115
Figure BDA0002713836090000121
Step 8, mixing rd_N2The coordinate system of the North east of the Mars surface is converted to the position under the Mars vehicle control body:
reb＝RR4·rd_N2 (32)
wherein ,RR4＝Rx(θroll)·Ry(θpitch)·Rz(θyaw)；
θroll，θpitch，θyawRespectively representing the rolling angle, the pitch angle and the yaw angle of the mars vehicle;
step 9, controlling the height angle of the surround device (the height angle of the surround device relative to the top surface of the train body) (-90 DEG) under the train control body coordinate system<hob<90°)：
hob＝-arcsin[reb(3)] (33)
wherein ,reb(3) Representing a vector rebThe third element of (C);
azimuth angle of the surrounding device (azimuth angle of the surrounding device relative to the direction of the head) under the coordinate system of the train control body
Figure BDA0002713836090000123
Figure BDA0002713836090000124
Figure BDA0002713836090000122
Step 10, calculating a pointing angle:
according to the representation r of the pointing target under the coordinate system of the train control bodyebSolving for two rotation angles (theta) of the directional antennaA,θB)。
Converting a pointing target from a train control body coordinate system to a directional antenna biaxial zero position coordinate system:
reb1＝Raz·reb (35)
wherein RazRotation matrix for controlling a body coordinate system to a directional antenna two-axis zero coordinate system for a train
When the directional antenna is in a null position, the direction vector of the beam center line (electric axis) of the directional antenna is expressed in a two-axis null coordinate system of the directional antenna as follows:
Figure BDA0002713836090000131
the directional antenna has 2 pivots: the rotating shaft rotates around the B shaft (the zero position refers to a double-shaft zero position coordinate system and the Y shaft, and the B shaft cannot drive the A shaft to rotate when rotating), and then rotates around the A shaft (the rotating shaft points to the double-shaft zero position coordinate system and the X shaft, and the B shaft can be driven to rotate when rotating the A shaft).
Rotation of directional antenna about axis BBAbout axis A by aAThen, the direction vector of the beam center line is expressed in a biaxial null coordinate system as:
Figure BDA0002713836090000132
rotation of directional antenna about axis AAAbout axis BBShould then be pointing to ground, so r1＝reb1Comparing equation (37) with reb1Comprises the following steps:
-sinθB＝reb1(1)(r1(1)＝reb1(1))
Figure BDA0002713836090000133
and (3) analyzing by combining with actual conditions:
θB＝-arcsin(reb1(1)) (38)
Figure BDA0002713836090000134
after the solution is completed, theta is judgedAWhether or not [ theta ] is presentA_min,θA_max]In range of thetaBWhether or not [ theta ] is presentB_min,θB_max]Within the range:
if the 2 angles are all in the specified range, the solution is regarded as an effective solution;
if any one of the rotation angles is not within the specified range, the rotation angle is regarded as no solution.
Secondly, optimizing the antenna pointing calculation in the same round of antenna control process:
the longitude and latitude height and the attitude angle of the mars are completely the same in the two calculation processes when the antenna pointing direction is calculated in the same wheel of antenna control process, so that a plurality of intermediate variables exist, and after the calculation for the first time, the calculation result for the first time can be directly used in the rest control process.
In addition, because the mars antenna installation deviation matrix is completely fixed in the whole satellite life cycle, the method utilizes the characteristic, the conversion matrix from the antenna system to the satellite system is calculated in advance, the calculation result is stored in the satellite-borne memory, and the calculation is not needed when the calculation step of the conversion matrix from the antenna system to the satellite system is met in the antenna pointing calculation process, but the matrix data in the memory is directly read, so that the calculation amount of the satellite-borne processor is effectively reduced.
In the process, the characteristic that a plurality of same intermediate quantities exist in the direction calculation of adjacent antennas is utilized, the intermediate quantities calculated in the direction calculation of the first antenna are stored, the intermediate quantities are used for all the directions of other antennas in the same round of antenna control process to accelerate the calculation process, and the calculation flow is shown in fig. 3.
1. Calculate the intermediate results available for the surround position:
Figure BDA0002713836090000141
2. intermediate results available for the train position calculation:
Figure BDA0002713836090000142
3. available intermediate results in the course of the surround to mars vector calculation:
intermediate results available Storing procedure
Ry(-θlat)·Rz(θlon) RR2＝Ry(-θlat)·Rz(θlon)
Ry(-90) RR3＝Ry(-90)
Rx(θroll)·Ry(θpitch)·Rz(θyaw) RR4＝Rx(θroll)·Ry(θpitch)·Rz(θyaw)
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (5)

1. A method for optimizing the orientation of a surrounding device antenna on a planet by a mars car is characterized in that the method for optimizing the orientation of a single time comprises the following steps:
step 1, calculating the position of the surrounding device under a Mars inertial coordinate system:
for the orbit Mars surrounding device with large inclination angle and large eccentricity, the ground fits the extrapolation root number to obtain the epoch time t0Average number of a0、e0、i0、Ω0、ω0、M0Rate of change of mean radical
Figure FDA0002713836080000011
And second order rate of change of mean anomaly
Figure FDA0002713836080000012
The extrapolation formula for the Kepler root at time t is as follows:
ΔT＝t-t0 (1)
a＝a0 (2)
e＝e0 (3)
i＝i0 (4)
Figure FDA0002713836080000013
Figure FDA0002713836080000014
Figure FDA0002713836080000015
wherein ：
Figure FDA0002713836080000016
Figure FDA0002713836080000017
Figure FDA0002713836080000018
Figure FDA0002713836080000019
Figure FDA00027138360800000110
p＝a0(1-e0 2) (13)
c＝cosi0 (14)
wherein ,J2Representing the second order coefficient of the orbit; rmRepresents the Mars radius; mu.smRepresents the Mars constant;
the method for calculating the position of the surround device in the Mars inertial coordinate system according to the Kepler root number comprises the following steps:
s11, calculating delta T:
for time T, the time difference Δ T (in the Julian century) is found relative to time J2000.0:
ΔT＝(T0-TJ2000.0+t/86400)/Tcy (15)
in the formula ：T0Carrying a julian calendar day corresponding to the zero time of the computer; t isJ2000.0The julian calendar day corresponding to the moment J2000.0; t iscyThe number of days corresponding to one julian century;
s12, calculating a deviation angle:
E＝M+ee1×sinM+ee2×sin2M+ee3×sin3M (16)
s13, calculating a true proximal angle:
Figure FDA0002713836080000021
s14, calculating the track wheelbase:
Figure FDA0002713836080000022
s15, calculating the position coordinates of the surrounding device under the plane coordinate system of the orbit of the surrounding device:
Figure FDA0002713836080000023
s16, calculating the position coordinates of the surrounding device under the Mars inertial coordinate system as follows:
Figure FDA0002713836080000024
wherein ,
Figure FDA0002713836080000025
a transformation matrix representing rotation about the x-axis;
Figure FDA0002713836080000026
a transformation matrix representing rotation about the y-axis;
Figure FDA0002713836080000027
a transformation matrix representing rotation about the z-axis;
step 2, calculating Mars orientation parameters:
solving celestial body directional output parameters according to the time (t) and celestial body directional input parameters (A, B, C, D, E and F); wherein alpha is0Right ascension in ICRF for celestial arctic; delta0Declination in ICRF for celestial North; w is the distance from the 0 DEG meridian to the ascending intersection point of the celestial body equator:
for time T, the time difference Δ T from time J2000.0 is determined by referring to equation (1)1Then, there are:
Figure FDA0002713836080000028
given aAt time t, the directional input parameters (A, B, C, D, E, F) of the mars in the table are substituted into formula (21) to calculate the directional parameter alpha of the mars0_mars，δ0_mars，Wmars；
Step 3, changing the position coordinate of the circulator from a Mars inertial coordinate system to a Mars astronomical reference coordinate system:
Figure FDA0002713836080000031
wherein ,RR1＝Rz(-θ3)·Ry(-θ2)·Rx(-θ1)；
θ1，θ2，θ3Respectively representing the X-axis rotation angle from the ICRF coordinate system to the Mars inertial coordinate system and the Y-axis rotation angle from the ICRF coordinate system to the Mars inertial coordinate system; the Z-axis rotation angle from the ICRF coordinate system to the Mars inertial coordinate system;
and 4, transforming the position coordinates of the circulator from the Mars astronomical reference coordinate system to a Mars fixed connection coordinate system:
Figure FDA0002713836080000032
under the fixed coordinate system of the mars, the position of the mars car is as follows:
Figure FDA0002713836080000033
wherein H represents the height of the position of the Mars train; thetalatLatitude, theta, indicating the location of the Mars vehiclelonA longitude indicating the location of the Mars vehicle;
and 5, under the condition that the mars is fixedly connected with a coordinate system, the position of the surrounding device relative to the mars vehicle is as follows:
Figure FDA0002713836080000034
to rdPerforming orthogonalization to obtain a unit vector from the mars to the surround device as follows:
Figure FDA0002713836080000035
step 6, mixing rd_NThe Mars solid connection system is converted into a Mars surface under a coordinate system of the northeast of the sky:
rd_N1＝RR2·rd_N (28)
wherein ,RR2＝Ry(-θlat)·Rz(θlon)；
Step 7, mixing rd_N1The coordinate system of the Mars surface in the north-east direction is converted into the coordinate system of the Mars surface in the north-east direction:
rd_N2＝RR3·rd_N1 (29)
wherein ,RR3＝Ry(-90)；
Mars surface lower surround altitude in North east Earth coordinate:
ho＝-arcsin[rd_N2(3)] (30)
wherein ,rd_N2(3) Representing a vector rd_N2The third element of (C);
mars surface North east coordinate System lower surround azimuth:
Figure FDA0002713836080000041
step 8, mixing rd_N2The coordinate system of the North east of the Mars surface is converted to the position under the Mars vehicle control body:
reb＝RR4·rd_N2 (32)
wherein ,RR4＝Rx(θroll)·Ry(θpitch)·Rz(θyaw)；
θroll，θpitch，θyawRespectively representing the rolling angle, the pitch angle and the yaw angle of the mars vehicle;
step 9, controlling the height angle of the surrounding device under the coordinate system of the body by the train:
hob＝-arcsin[reb(3)] (33)
wherein ,reb(3) Representing a vector rebThe third element of (C);
the azimuth angle of the surrounding device under the coordinate system of the train control body is as follows:
Figure FDA0002713836080000042
step 10, calculating a pointing angle:
converting a pointing target from a train control body coordinate system to a directional antenna biaxial zero position coordinate system:
reb1＝Raz·reb (35)
wherein RazControlling a rotation matrix from a body coordinate system to a directional antenna biaxial zero position coordinate system for the train;
when the directional antenna is at a null position, the direction vector of the beam center line of the directional antenna is expressed in a biaxial null coordinate system of the directional antenna as follows:
Figure FDA0002713836080000051
the directional antenna has 2 pivots: firstly rotating around the B axis and then rotating around the A axis; rotation of directional antenna about axis BBAbout axis A by aAThen, the direction vector of the beam center line is expressed in a biaxial null coordinate system as:
Figure FDA0002713836080000052
rotation of directional antenna about axis AAAbout axis BBShould then be pointing to ground, so r1＝reb1Comparing equation (37) with reb1Comprises the following steps:
-sinθB＝reb1(1)
Figure FDA0002713836080000053
and (3) analyzing by combining with actual conditions:
θB＝-arcsin(reb1(1)) (38)
Figure FDA0002713836080000054
2. the method as claimed in claim 1, wherein the sine and cosine calculations of the attitude angle and the orbit angle used in the calculation of the single antenna pointing direction are pre-calculated and stored in the corresponding attitude data structure and orbit data structure, and the pre-calculated results are directly used in the subsequent use.
3. The method of claim 1, wherein all angular values in degrees are converted to radians.
4. The method for on-board optimization of Mars train to surround machine antenna pointing, according to claim 1, characterized in that in calculating single antenna pointing, the function call of matrix multiplication operation is converted into assignment operation.
5. The method of any of claims 1-4, wherein the same round of antenna steering is used for on-board optimization of the orientation of the antenna of the surround unit by the Mars trainWhen the antenna pointing direction is calculated in the manufacturing process, the intermediate result stored by the last calculation is utilized:
Figure FDA0002713836080000055
Figure FDA0002713836080000056
ee1、ee2、ee3、ee4 and RR1Calculating the position of the surrounding device; intermediate results saved with the last calculation:
Figure FDA0002713836080000057
calculating the position of the Mars vehicle; intermediate results saved with the last calculation: RR2、RR3 and RR4Calculating a vector of the surrounding device to the inspection device; and finally, calculating the antenna direction of the time.
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