CN104931008A - Method for determining wheel-track type reflector antenna pointing error - Google Patents

Abstract

The invention discloses a method for determining a wheel-track type reflector antenna pointing error. The problems that an existing analysis method cannot give complete consideration to factors of out-of-level tracks, non-plumb azimuth axes, non-vertical pitch axes, non-vertical pitch azimuth axes and non-vertical mechanical axes and pitch axes, and the relationship between a comprehensive axial system error and the antenna pointing error cannot be built are solved. The method includes the implementation steps that according to wheel-track type reflector antenna model parameters, a conversion matrix of a geodetic coordinate system to a reflector coordinate system under the ideal condition, namely the axial-system-error-free condition is built, and the pointing vector quantity under the ideal condition is obtained; then according to the axial system error distribution condition, a conversion matrix under the condition that the error exists is built, and the pointing vector quantity at the time is obtained; the azimuth and pitching pointing errors are accordingly obtained. According to the method, the influences of the comprehensive axial system error on the antenna pointing error are systematically considered, a foundation is laid to designing a follow-up high-pointing-accuracy antenna, and the development period is shortened.

Description

The defining method of wheel-track type reflector antenna error in pointing

Technical field

The invention belongs to antenna technical field, be specifically related to the defining method of wheel-track type reflector antenna error in pointing, be used to guide the design of large-scale wheel track reflector antenna.

Background technology

In order to detect more, more weak celestial body, require that reflector antenna has higher angular resolution and sensitivity, this makes antenna towards high band, heavy caliber future development.In succession establish the Radio Telescope Antenna of many bores up to hundred meter levels both at home and abroad.Pointing accuracy is the extremely important performance index of radio telescope, reflects the ability that antenna system accurately points to target azimuth.Its height not only affects the operational paradigm of the handling capacity of telescope communication system, the system accuracy of laser ranging and tracker, also can affect the ability of its observation and discovery specific objective.Because the strong radio source of radio telescope is few, visual field is limited (comprising diffracted beam), it is made to be difficult near object of observation, find suitable radio source carry out sensing inspection.Thus, cause the absolute sensing requirement higher to radio telescope.

The factor affecting antenna-point accuracy can be divided into structural factor and controlling factor two parts.Structural factor refers to that antenna mount and reflecting body are due to the axial system error etc. manufacturing, install and malformation causes under extraneous environmental load effect; It is delayed that controlling factor comprises Velocity-acceleration, amplifier zero point drift and servo noise etc.As above in influence factor, axial system error refers to the angular error of the axle system of antenna mount and reflector structure, comprise orientation track inclination degree error, azimuth axis verticality error, pitch axis and the azimuth axis error of perpendicularity and mechanical axis deviation etc. are class errors larger on the pointing accuracy impact of antenna.

At present, Chinese scholars has carried out much work for this part research.Document Gawronski W.Modeling and control of antennas and telescopes [M] .Germany:Springer, 2008:211-222. measuring certain orientation track unevenness is by experiment the antenna of 0.5mm, corresponding produce 72 " error in pointing, and established by the data that inclinator records and search table of corrections; Document rice month English .65m Radio Telescope Antenna structure pointing accuracy design and study [J]. electromagnetic field and microwave, 2014,44 (5): 60-63. is maximum for current domestic bore, 65 meters of bore full movable wheel rail antennas that precision is the highest, analysis meter is let it pass its structure error in pointing, describe track combination, the careful design process of the critical component such as pivot assemblies and angle-measuring equipment, and the structural failure caused by gravity and environmental factor is on the impact of error in pointing; Document Zheng Yuan roc. surface antenna structure dynamic error is on the impact [J] of pointing accuracy. radio communication technology, 2002,28 (6): 37-39. analyze in conjunction with 50 meters of aperture antennas the structural factor affecting antenna-point accuracy, the perfect computing method of antenna-point accuracy; The complete movable antenna axial system error of document Yu Meng month .110 rice bore ultra-large type is on the impact [D] of pointing accuracy. China: Xian Electronics Science and Technology University's master thesis, 2014. give and consider azimuth axis simultaneously, when pitch axis and mechanical axis deviation, the axial system error of antenna is to the interact relation model of error in pointing.By the research to said method, summarize its weak point to be: (1) most of document is all after antenna builds up, consider based on the methods analyst axial system error of experiment measuring the impact of error in pointing, the method is only applicable to specific antenna, do not have generality, the design for other antennas does not have directive significance; (2) although part document establishes the interact relation of axial system error to error in pointing, the impact of track unevenness is not considered.And orientation track is as the support section of whole antenna, its error in pointing impact of unevenness on antenna be can not ignore.

In sum, there is no a kind of orbit error and the comprehensive axial system error such as azimuth axis, pitch axis, mechanical axis of considering antenna at present simultaneously, study the analytical approach that it affects antenna pointing error.

Summary of the invention

For the deficiencies in the prior art, the present invention aims to provide a kind of defining method of wheel-track type reflector antenna error in pointing, to realize the Accurate Prediction to large-scale wheel track reflector antenna error in pointing, for the design of large-scale wheel-track type reflector antenna lays the foundation.

To achieve these goals, the present invention adopts following technical scheme:

First under setting up the free from error situation of ideal situation and axle system, terrestrial coordinate is tied to the transition matrix of reflecting body coordinate system, obtains sensing vector ideally; Then according to axial system error distribution situation, set up error there is situation under transition matrix, obtain now sensing vector; Thus obtain orientation and pitching error in pointing respectively.

The defining method of this wheel-track type reflector antenna error in pointing specifically comprises the steps:

S1, if the orientation orbit radius of wheel-track type reflector antenna be r, orientation mounting height is h, pitch axis central point distance reflector vertex is h ₁; Then when the position angle of wheel-track type reflector antenna and the angle of pitch are respectively A, during E, from earth coordinates OXYZ to reflecting body coordinate system O _rx _ry _rz _rtransition matrix Z _lfor:

Z _L＝Z _EJ·Z _AE·Z _φA·Z _Oφ；

Wherein, Z _{o φ}for from earth coordinates OXYZ to orientation orbital coordinate system O _ax _φy _φz _φtransition matrix, Z _{φ A}for from orbital coordinate system O _ax _φy _φz _φto azimuth axis coordinate system O _ax _ay _az _atransition matrix, Z _aEfor from azimuth axis coordinate system O _ax _ay _az _ato pitch axis coordinate system O _ex _ey _ez _etransition matrix, Z _eJfor from pitch axis coordinate system O _ex _ey _ez _eto reflecting body coordinate system O _rx _ry _rz _rtransition matrix;

S2, (present patent application in full indication ideal situation refers to: track level, azimuth axis vertical in the ideal case, pitch axis is vertical with azimuth axis, mechanical axis is vertical with pitch axis), when namely there is not error in the orientation track of antenna and each axle system, then reflecting body coordinate system mid point Q ₌( _{x y z}) ^tcoordinate corresponding in earth coordinates ( _x' _y' _z') ^tmeet following formula:

${\left(\begin{array}{cccc}{x}^{\′}& y^{\′}& z^{\′}& 1\end{array}\right)}^T=Z_L^{-1}{\left(\begin{array}{cccc}x& y& z& 1\end{array}\right)}^T;$

S3, supposes that, under reflecting body coordinate system, the coordinate pointing to vectorial two-end-point is respectively O _r=(x ₀y ₀z ₀) ^t, P _r=(x ₀y ₀z ₀+ z ₁) ^t, then can draw ideally, in earth coordinates, desirable sensing vector for:

S4, supposes only there is orbit error, then from earth coordinates OXYZ to reflecting body coordinate system O _rx _ry _rz _rtransition matrix Z _l1' be:

Z _L1′＝Z _EJ·Z _AE·Z _φA·Z _Oφ′；

S5, supposes only there is azimuth axis error, then from earth coordinates OXYZ to reflecting body coordinate system O _rx _ry _rz _rtransition matrix Z _l2' be:

Z _L2′＝Z _EJ·Z _AE·Z _φA′·Z _Oφ；

S6, when supposing only there is pitch axis error, then from earth coordinates OXYZ to reflecting body coordinate system O _rx _ry _rz _rtransition matrix Z _l3' be:

Z _L3′＝Z _EJ·Z _AE′·Z _φA·Z _Oφ；

S7, when supposing only there is mechanical axis error, then from earth coordinates OXYZ to reflecting body coordinate system O _rx _ry _rz _rtransition matrix Z _l4' be:

Z _L4′＝Z _EJ′·Z _AE·Z _φA·Z _Oφ；

S8, when supposing to there is orbit error, azimuth axis error, pitch axis error and mechanical axis error, then from earth coordinates OXYZ to reflecting body coordinate system O simultaneously _rx _ry _rz _rtransition matrix Z _l' be:

Z _L′＝Z _EJ′·Z _AE′·Z _φA′·Z _Oφ′；

S9, when to there is orbit error, azimuth axis error, pitch axis error and mechanical axis error simultaneously, then in earth coordinates, corresponding actual sensings is vectorial

S10, the ideal according to S3 gained points to vector with the actual sensing vector of S9 gained can respectively bearing sense error alpha and pitching error in pointing β as follows:

Preferred technical scheme, the transition matrix Z described in step S1 _lin concrete every as follows,

$Z_{\mathrm{EJ}}=T(\mathrm{0,0},h_1),Z_{\mathrm{AE}}=R_x(E-\frac{\mathrm{\π}}{2})T(\mathrm{0,0},h),Z_{\mathrm{\φA}}=R_z\left(A\right),Z_{\mathrm{O\φ}}=I;$

R in formula _x(θ), R _y(φ), represent respectively around x-axis, y-axis, the z-axis anglec of rotation is time transition matrix, T (x _s, y _s, z _s) represent along x-axis, y-axis, the translation unit of z-axis is x _s, y _s, z _stime translation matrix, concrete form is as follows:

$R_x\left(\mathrm{\θ}\right)=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos \mathrm{\θ}& -\sin \mathrm{\θ}& 0\\ 0& \sin \mathrm{\θ}& \cos \mathrm{\θ}& 0\\ 0& 0& 0& 1\end{array}\right]$

$R_y\left(\mathrm{\φ}\right)=\left[\begin{array}{cccc}\cos \mathrm{\φ}& 0& \sin \mathrm{\φ}& 0\\ 0& 1& 0& 0\\ -\sin \mathrm{\φ}& 0& \cos \mathrm{\φ}& 0\\ 0& 0& 0& 1\end{array}\right]$

$T(x_s,y_s,z_s)=\left[\begin{array}{cccc}1& 0& 0& x_s\\ 0& 1& 0& y_s\\ 0& 0& 1& z_s\\ 0& 0& 0& 1\end{array}\right].$

Preferred technical scheme further, the transition matrix Z described in step S4 _{o φ}' be:

Z _Oφ'＝R _x(γ _φx)R _y(γ _φy)T(0,0,δ _φz)；

γ _{φ x}, γ _{φ y}be respectively the uneven track caused of orientation track around the angle of inclination of x-axis, y-axis, δ _{φ z}for track injustice cause along z-axis to displacement, specifically determined by following steps;

1) suppose that ideal track is surface level, radius is r, because the z of the track track that causes of injustice and roller contact point is to being highly respectively Δ (A), Δ (A+ π), matching gained actual track plane can be obtained:

z＝ax+by+c；

$a=\frac{(\mathrm{\Δ}\left(A\right)-\mathrm{\Δ}(A+\mathrm{\π}))\cos A+(\mathrm{\Δ}(A+\frac{3\mathrm{\π}}{2})-\mathrm{\Δ}(A+\frac{\mathrm{\π}}{2}))\sin A}{2r};$

$b=\frac{(\mathrm{\Δ}\left(A\right)-\mathrm{\Δ}(A+\mathrm{\π}))\sin A+(\mathrm{\Δ}(A+\frac{3\mathrm{\π}}{2})-\mathrm{\Δ}(A+\frac{\mathrm{\π}}{2}))\cos A}{2r};$

$c=\frac{\mathrm{\Δ}\left(A\right)+\mathrm{\Δ}(A+\frac{\mathrm{\π}}{2})+\mathrm{\Δ}(A+\mathrm{\π})+\mathrm{\Δ}(A-\frac{\mathrm{\π}}{2})}{4};$

2) error of matching gained actual track and ideal track plane is respectively:

γ _φx＝-arctan(-b)， ${\mathrm{\γ}}_{\mathrm{\φy}}=\arctan (-\frac{a}{\sqrt{b^2+1}});$

δ _φx＝δ _φy＝0，δ _φz＝c。

Further preferred technical scheme, the transition matrix Z described in step S5 _{φ A}' be:

Z _φA'＝R _y(φ _ay)R _x(φ _ax)T(δ _ax,δ _ay,δ _az)R _z(A)；

φ _ax, φ _ayrepresent that azimuth axis is around x-axis respectively, the angular error of y-axis, δ _ax, δ _ay, δ _azrepresent azimuthal coordinates system initial point respectively along x-axis in earth coordinates, y-axis, z-axis is to displacement.

Further preferred technical scheme again, the transition matrix Z described in step S6 _aE' be:

represent the angular error of pitch axis around y-axis, z-axis respectively, δ _ex, δ _ey, δ _ezrepresent pitching coordinate origin respectively along x-axis in earth coordinates, y-axis, z-axis is to displacement.

Transition matrix Z described in step S7 _eJ' be:

Z _EJ'＝R _y(ψ _jy)R _x(ψ _jx)T(δ _jx,δ _jy,δ _jz)T(0,0,h ₁)；

ψ _jx, ψ _jyrepresent that mechanical axis is around x-axis respectively, the angular error of y-axis, δ _jx, δ _jy, δ _jzrepresent mechanical coordinate system initial point respectively along x-axis in earth coordinates, y-axis, z-axis is to displacement.

Beneficial effect of the present invention is:

1, the present invention considers the comprehensive axial system error of large-scale wheel track reflector antenna, specifically consider factors such as comprising orientation track unevenness, azimuth axis degree of tilt, pitch axis and azimuth axis non-perpendicularity, mechanical axis and pitch axis non-perpendicularity, establish the impact of comprehensive axial system error on antenna pointing error, determine the error in pointing of wheel-track type reflector antenna further accurately, solid foundation has been established in the design for subsequent antenna system.

2, shown by simulation result, point to requirement relative to the high precision of antenna, the unevenness of orientation track is very large on the impact pointed to, and can not ignore.The present invention considers each axial system error simultaneously, finally determines wheel-track type reflector antenna error in pointing, for the correction work of follow-up error in pointing lays the first stone, thus improves pointing accuracy and the work efficiency of antenna, shortens its lead time.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is antenna and coordinate system schematic diagram in emulation experiment of the present invention.

Embodiment

Below with reference to accompanying drawing, the invention will be further described, it should be noted that, the present embodiment, premised on the technical program, give detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to the present embodiment.

As shown in Figure 1, the defining method of wheel-track type reflector antenna error in pointing, comprises the steps:

S1 is for wheel-track type reflector antenna, and orientation orbit radius is r, and orientation mounting height is h, and pitch axis central point distance reflector vertex is h ₁, when the position angle of antenna and the angle of pitch are respectively A, during E, calculate from earth coordinates OXYZ to reflecting body coordinate system O _rx _ry _rz _rtransition matrix be Z _l:

Z _L＝Z _EJ·Z _AE·Z _φA·Z _Oφ；

Z _{o φ}for from earth coordinates OXYZ to orientation orbital coordinate system O _ax _φy _φz _φtransition matrix, Z _{φ A}for from orbital coordinate system O _ax _φy _φz _φto azimuth axis coordinate system O _ax _ay _az _atransition matrix, Z _aEfor from azimuth axis coordinate system O _ax _ay _az _ato pitch axis coordinate system O _ex _ey _ez _etransition matrix, Z _eJfor from pitch axis coordinate system O _ex _ey _ez _eto reflecting body coordinate system O _rx _ry _rz _rtransition matrix.

S2 is (track level in the ideal case, azimuth axis vertical, pitch axis is vertical with azimuth axis, and mechanical axis is vertical with pitch axis), namely when the orientation track of antenna and each axle system do not exist error, according to S1 computational reflect body coordinate system mid point Q=(x y z) ^tcoordinate corresponding in earth coordinates ( _x' _y' _z') ^tmeet following formula:

${\left(\begin{array}{cccc}{x}^{\′}& y^{\′}& z^{\′}& 1\end{array}\right)}^T=Z_L^{-1}{\left(\begin{array}{cccc}x& y& z& 1\end{array}\right)}^T;$

S3 points to vectorial two-end-point coordinate under supposing reflecting body coordinate system is respectively O _r=(x ₀y ₀z ₀) ^t, P _r=(x ₀y ₀z ₀+ z ₁) ^t, calculate ideally at the corresponding vector of earth coordinates

When S4 supposes individualism orbit error, from earth coordinates OXYZ to reflecting body coordinate system O _rx _ry _rz _rtransition matrix Z _l1' be:

Z _L1′＝Z _EJ·Z _AE·Z _φA·Z _Oφ′；

When S5 supposes individualism azimuth axis error, from earth coordinates OXYZ to reflecting body coordinate system O _rx _ry _rz _rtransition matrix Z _l2' be:

Z _L2′＝Z _EJ·Z _AE·Z _φA′·Z _Oφ；

When S6 supposes individualism pitch axis error, from earth coordinates OXYZ to reflecting body coordinate system O _rx _ry _rz _rtransition matrix Z _l3' be:

Z _L3′＝Z _EJ·Z _AE′·Z _φA·Z _Oφ；

When S7 supposes individualism mechanical axis error, from earth coordinates OXYZ to reflecting body coordinate system O _rx _ry _rz _rtransition matrix Z _l4' be:

Z _L4′＝Z _EJ′·Z _AE·Z _φA·Z _Oφ；

When S8 considers to there is comprehensive axial system error, from earth coordinates OXYZ to reflecting body coordinate system O _rx _ry _rz _rtransition matrix Z _l' be:

Z _L′＝Z _EJ′·Z _AE′·Z _φA′·Z _Oφ′；

When S9 considers to there is comprehensive axial system error, point to vector corresponding in earth coordinates

S10 ideally points to vector according to S3 gained and S9 when considering to there is comprehensive axial system error gained point to vector bearing sense error alpha and pitching error in pointing β can be obtained respectively:

Advantage of the present invention further illustrates by following emulation:

By a kind of wheel track reflector antenna axle system of the present invention composition error to the impact analysis method of error in pointing, the simulation analysis of axial system error to error in pointing is carried out in certain Antenna Design stage, this Antenna Design bore is 110 meters, pointing accuracy requirement is 2.5 "; adopt coordinate system as shown in Figure 2, wherein:

OXYZ is earth coordinates, and initial point is in orientation orbit centre, and Z axis is perpendicular to ground, and Y-axis negative sense points to direct north;

O _ax _φy _φz _φfor being fixed on the coordinate system of orientation track, initial point in orientation orbit centre, Z _φaxle is perpendicular to orbit plane, and global coordinate system follows orientation orbit rotation, deflection and moving; As the completely desirable and position angle A=0 ° of track, it overlaps with earth coordinates;

O _ax _ay _az _afor being fixed on the coordinate system of azimuth axis, initial point in orientation orbit centre, Z _aaxle overlaps with azimuth axis, and global coordinate system is followed azimuth axis and rotated, offset and move;

O _ex _ey _ez _efor being fixed on the coordinate system of pitch axis, initial point at pitch axis mid point, X _eaxle overlaps with pitch axis, and global coordinate system is followed pitch axis and rotated, offset and move; When antenna there is not axial system error and angle of pitch E=90 ° time, itself and earth coordinates OXYZ only differ the height value h of orientation mounting in Z-direction;

O _rx _ry _rz _rfor being fixed on the coordinate system of reflecting body, during angle of pitch E=90 °, itself and pitching coordinate system O _ex _ey _ez _eat Z-direction difference height h ₁;

Gravity load is a basic load in structure analysis, and under gravity, entire physical can produce distortion, thus causes each axle to produce angular error, finally affects sensing.This sentences gravity load is example, analyzes and to refer under flat operating mode that its corresponding axial system error of producing of being out of shape is on the impact of antenna pointing error.Result is had in conjunction with document, the complete movable antenna axial system error of Yu Meng month .110 rice bore ultra-large type is on the impact [D] of pointing accuracy. China: Xian Electronics Science and Technology University's master thesis, 2014, when not considering the affecting of track unevenness, the orientation caused by gravity under referring to flat operating mode and pitching error in pointing are:

$\left(\begin{array}{c}\mathrm{\α}\\ \mathrm{\β}\end{array}\right)=\left(\begin{array}{c}{-0.5465}^{\′\′}\\ {-88.6629}^{\′\′}\end{array}\right);$

Absolute error in pointing is δ=88.6648 ".

Be more than, in ideal track situation, do not consider the impact of track unevenness; Suppose because on the track that making and installation causes, each point height value meets normal distribution herein, i.e. Δ N (0, σ ²), in conjunction with current domestic manufacturing process, get σ=0.25mm, one group of random series can be obtained.When position angle A fixed value, respective carter height value can be found out in this random series, suppose A=0, can obtain:

$\mathrm{\Δ}\left(A\right)=0.114,\mathrm{\Δ}(A+\frac{\mathrm{\π}}{2})=-0.098,\mathrm{\Δ}(A+\mathrm{\π})=0.175,\mathrm{\Δ}(A-\frac{\mathrm{\π}}{2})=-0.206;$

Corresponding orbit error is:

γ _φx＝-0.0943°，γ _φy＝0.0855°，δ _φz＝-0.038；

In conjunction with the inventive method, when can consider the comprehensive axial system error such as the impact of track unevenness, under the flat operating mode of finger, antenna due to orientation corresponding to the axial system error that gravity deformation causes and pitching error in pointing is:

$\left(\begin{array}{c}\mathrm{\α}\\ \mathrm{\β}\end{array}\right)=\left(\begin{array}{c}{-0.7523}^{\′\′}\\ {-95.3478}^{\′\′}\end{array}\right);$

Absolute error in pointing is: δ=95.3508 ", as seen relative to this antenna 2.5 " pointing accuracy requirement, orientation track unevenness is comparatively large on the impact of error in pointing, can not ignore.

For a person skilled in the art, according to above technical scheme and design, various corresponding change and distortion can be made, and all these change and distortion all should be included within the protection domain of the claims in the present invention.

Claims (7)

1. the defining method of wheel-track type reflector antenna error in pointing, is characterized in that, it comprises the steps:

First, under setting up the free from error situation of ideal situation and axle system, terrestrial coordinate is tied to the transition matrix of reflecting body coordinate system, and the ideal obtained ideally points to vector;

Then, according to axial system error distribution situation, set up error there is situation under transition matrix, obtain actual sensing vector now;

Finally, point to according to ideal bearing sense error and the pitching error in pointing that vector sum actual sensing vector calculation goes out wheel-track type reflector antenna.

2. the defining method of wheel-track type reflector antenna error in pointing according to claim 1, it is characterized in that, it specifically comprises the steps:

S1, if the orientation orbit radius of wheel-track type reflector antenna be r, orientation mounting height is h, pitch axis central point distance reflector vertex is h ₁; Then when the position angle of wheel-track type reflector antenna and the angle of pitch are respectively A, during E, from earth coordinates OXYZ to reflecting body coordinate system O _rx _ry _rz _rtransition matrix Z _lfor:

Z _L＝Z _EJ·Z _AE·Z _φA·Z _Oφ；

Wherein, Z _{o φ}for from earth coordinates OXYZ to orientation orbital coordinate system O _ax _φy _φz _φtransition matrix, Z _{φ A}for from orbital coordinate system O _ax _φy _φz _φto azimuth axis coordinate system O _ax _ay _az _atransition matrix, Z _aEfor from azimuth axis coordinate system O _ax _ay _az _ato pitch axis coordinate system O _ex _ey _ez _etransition matrix, Z _eJfor from pitch axis coordinate system O _ex _ey _ez _eto reflecting body coordinate system O _rx _ry _rz _rtransition matrix;

S2, in the ideal case, when namely all there is not the situation of error in the orientation track of antenna and each axle system, then reflecting body coordinate system mid point Q=(x y z) ^tcoordinate (x'y'z') corresponding in earth coordinates ^tmeet following formula:

S3, supposes that, under reflecting body coordinate system, the coordinate pointing to vectorial two-end-point is respectively O _r=(x ₀y ₀z ₀) ^t, P _r=(x ₀y ₀z ₀+ z ₁) ^t, then can draw ideally, in earth coordinates, desirable sensing vector for:

S4, supposes only there is orbit error, then from earth coordinates OXYZ to reflecting body coordinate system O _rx _ry _rz _rtransition matrix Z _l1' be:

Z _L1′＝Z _EJ·Z _AE·Z _φA·Z _Oφ′；

S5, supposes only there is azimuth axis error, then from earth coordinates OXYZ to reflecting body coordinate system O _rx _ry _rz _rtransition matrix Z _l2' be:

Z _L2′＝Z _EJ·Z _AE·Z _φA′·Z _Oφ；

S6, when supposing only there is pitch axis error, then from earth coordinates OXYZ to reflecting body coordinate system O _rx _ry _rz _rtransition matrix Z _l3' be:

Z _L3′＝Z _EJ·Z _AE′·Z _φA·Z _Oφ；

S7, when supposing only there is mechanical axis error, then from earth coordinates OXYZ to reflecting body coordinate system O _rx _ry _rz _rtransition matrix Z _l4' be:

Z _L4′＝Z _EJ′·Z _AE·Z _φA·Z _Oφ；

S8, when supposing to there is orbit error, azimuth axis error, pitch axis error and mechanical axis error, then from earth coordinates OXYZ to reflecting body coordinate system O simultaneously _rx _ry _rz _rtransition matrix Z _l' be:

Z _L′＝Z _EJ′·Z _AE′·Z _φA′·Z _Oφ′；

S9, when to there is orbit error, azimuth axis error, pitch axis error and mechanical axis error simultaneously, then in earth coordinates, corresponding actual sensings is vectorial

S10, the ideal according to S3 gained points to vector with the actual sensing vector of S9 gained can respectively bearing sense error alpha and pitching error in pointing β as follows:

。

3. the defining method of wheel-track type reflector antenna error in pointing according to claim 2, is characterized in that: the transition matrix Z described in step S1 _lin every design parameter as follows:

In formula represent respectively around x-axis, y-axis, the z-axis anglec of rotation is time transition matrix, T (x _s, y _s, z _s) represent along x-axis, y-axis, the translation unit of z-axis is x _s, y _s, z _stime translation matrix, concrete form is as follows:

4. the defining method of wheel-track type reflector antenna error in pointing according to claim 2, is characterized in that: the transition matrix Z described in step S4 _{o φ}' be:

Z _Oφ'＝R _x(γ _φx)R _y(γ _φy)T(0,0,δ _φz)；

γ _{φ x}, γ _{φ y}be respectively the uneven track caused of orientation track around the angle of inclination of x-axis, y-axis, δ _{φ z}for track injustice cause along z-axis to displacement, specifically determined by following steps;

1) suppose that ideal track is surface level, radius is r, because the z of the track track that causes of injustice and roller contact point is to being highly respectively Δ (A), Δ (A+ π), matching gained actual track plane can be obtained:

z＝ax+by+c；

2) error of matching gained actual track and ideal track plane is respectively:

δ _φx＝δ _φy＝0，δ _φz＝c。

5. the defining method of wheel-track type reflector antenna error in pointing according to claim 2, is characterized in that: the transition matrix Z described in step S5 _{φ A}' be:

Z _φA'＝R _y(φ _ay)R _x(φ _ax)T(δ _ax,δ _ay,δ _az)R _z(A)；

φ _ax, φ _ayrepresent that azimuth axis is around x-axis respectively, the angular error of y-axis, δ _ax, δ _ay, δ _azrepresent azimuthal coordinates system initial point respectively along x-axis in earth coordinates, y-axis, z-axis is to displacement.

6. the defining method of wheel-track type reflector antenna error in pointing according to claim 2, is characterized in that: the transition matrix Z described in step S6 _aE' be:

represent the angular error of pitch axis around y-axis, z-axis respectively, δ _ex, δ _ey, δ _ezrepresent pitching coordinate origin respectively along x-axis in earth coordinates, y-axis, z-axis is to displacement.

7. the defining method of wheel-track type reflector antenna error in pointing according to claim 2, is characterized in that: the transition matrix Z described in step S7 _eJ' be:

Z _EJ'＝R _y(ψ _jy)R _x(ψ _jx)T(δ _jx,δ _jy,δ _jz)T(0,0,h ₁)；

ψ _jx, ψ _jyrepresent that mechanical axis is around x-axis respectively, the angular error of y-axis, δ _jx, δ _jy, δ _jzrepresent mechanical coordinate system initial point respectively along x-axis in earth coordinates, y-axis, z-axis is to displacement.