CN106017417A - Track irregularity-based large wheel track antenna pointing root mean square error calculating method - Google Patents

Abstract

The invention discloses a track irregularity-based large wheel track antenna pointing root mean square error calculating method. The method comprises the following steps: measuring the height value of a track sampling point in the service process of an antenna; determining the coordinate system of an antenna mount; carrying out coordinate transformation on the height values of all points of the track; fitting track irregularity; and calculating the antenna pointing root mean square error caused by track irregularity through adopting two processes: calculating the pointing root mean square errors under a single pitch angle and solving the root mean square of the errors under the pitch angle, and calculating the pointing error under one azimuth and pitch angle, and solving the root mean square of errors under all azimuths and pitch angles. The method truly reflects the antenna track surface, can accurately calculate the wave beam pointing root mean square errors caused by the track irregularity of the large wheel track antenna in a pointing domain, is used for quantitatively evaluating the influences of the track irregularity on the performances of the antenna, and has great science meaning and engineering application values.

Description

Large-scale wheel-track type antenna based on track unevenness points to the calculating of root-mean-square error Method

Technical field

The invention belongs to antenna technical field, a kind of large-scale wheel-track type antenna based on track unevenness points to all The computational methods of square error, can accurately calculate large-scale wheel-track type antenna and cause in sensing definition territory endogenous cause of ill track unevenness Beam position root-mean-square error, for the impact on antenna performance of the quantitative assessment track unevenness, thus instructs each point of the antenna to be The error distribution of system, has important academic significance and engineer applied is worth.

Background technology

Large-scale antenna is the precision instrument of primary recipient celestial radio wave radiation, is widely used in radio astronomy, radar, leads to The fields such as news and deep space probing.In order to meet the growth requirement of radio astronomy, antenna aperture is made bigger and bigger, structure is more and more multiple Miscellaneous.Along with the development of large-scale antenna proposes requirements at the higher level to antenna beam pointing accuracy, for preferably support low speed, heavy duty Large-scale antenna, and make it carry out predetermined azimuth pitch operating, wheel-track antenna mount is an inevitable choice.Wheel-track type sky Line mounting is usually truss structure, and antenna bearingt rotating part is supported by roller and track, so can omit gear wheel, turn greatly The components such as platform, have simple in construction, cost low, convenient to install and maintain, and have the advantages such as higher structure precision.In view of design, The aspects such as manufacture, transport, cost, current large-scale radio telescope many employings wheel-track type mounting both domestic and external designs, due to track Manufacture limited with installation accuracy, be in adverse circumstances the large-scale antenna being on active service and be also performed to rotary motion, propped up by wheel track Support such huge monster, it is to avoid can not cause the unevenness of raceway surface, this will drastically influence antenna beam pointing capability.

Along with increasing of Antenna Operation frequency range, even small track unevenness, antenna beam pointing accuracy also becomes Sensitivity, the antenna beam that usual track unevenness causes points to deviation and is up to 2 rads, and this antenna that high accuracy is pointed to requirement is Very important.In more existing correlational study based on track unevenness, the document of such as Jiang Zhengyang etc. " considers track The radio telescope of unevenness points to modification method " in, give the most conventional large-scale antenna and point to correction mathematical model, But this method uses simple trigonometric function to represent raceway surface, and the most coarse, the residual error after matching is excessive, and causing cannot The beam position deviation of the large-scale high pointing accuracy antenna of accurate evaluation；Document " the Antenna Orbit deformation accurate measurement of Li Yongjiang etc. With point to buggy model research " in, it is indicated that the unevenness of raceway surface may cause antenna tilt and flexible deformation, thus drops Low antenna-point accuracy, but in its sensing buggy model set up, point to deviation by four fixed-directions of azimuth axis Heeling error matching, error of fitting is relatively big, and result of calculation can not accurately reflect the impact on antenna performance of the track unevenness.

It is therefore desirable to track unevenness to be carried out higher-dimension matching, and set up antenna beam sensing all based on track unevenness The mathematical model of square error, accurately calculates large-scale wheel-track type antenna at the ripple pointing to definition territory endogenous cause of ill track unevenness and cause Shu Zhixiang root-mean-square error, with the impact on antenna performance of the quantitative assessment track unevenness, thus instructs each subsystem of antenna Error distribution.This process is large-scale wheel-track type antenna based on track unevenness and points to the computational methods of root-mean-square error.

Summary of the invention

For being previously calculated the deficiency that method exists, invent a kind of large-scale wheel-track type sky based on track unevenness herein Line points to the computational methods of root-mean-square error, and the method, for large-scale wheel-track type antenna, by best fit track unevenness, is built Vertical track unevenness and antenna beam point to the mathematical model of root-mean-square error, and the quantitatively track unevenness shadow to antenna performance Ring, to instruct the error distribution of each subsystem of antenna.

To achieve these goals, the computational methods that the present invention provides comprise the steps:

(1) according to the track size of large-scale wheel-track type antenna, determine the sampled point quantity of Antenna Orbit, and utilize high accuracy Measuring instrument measures the height value of the track each point after large-scale wheel-track type antenna a period of time under arms；

(2) determine antenna mount coordinate system, track each point height value is carried out coordinate transform；

(3) based on the principle of least square, determine the best fit function of track unevenness, and judge track each point height value Average whether be 0, if it is, go to step (4), if it does not, go to step (7)；

(4) according to best fit function, calculate raceway surface height value a little and root-mean-square error thereof；

(5) antenna a certain angle of pitch El is determined_j, set up track unevenness root-mean-square and point to root-mean-square error with antenna beam Mathematical model, and calculate antenna beam under this angle of pitch and point to root-mean-square error, it may be judged whether the ripple under all angles of pitch Shu Zhixiang root-mean-square error all calculates complete, if it is, go to step (6), if it does not, make j=j+1, repeats step (5), meter The antenna beam calculating the next angle of pitch points to root-mean-square error；

(6) calculate antenna and point to the beam position root-mean-square error in definition territory, go to step (10)；

(7) antenna one party parallactic angle Az is determined_i, angle of pitch El_j, optimal according to the azimuth of antenna and track unevenness Fitting function, calculates the orbit altitude value that all pairs of rollers of antenna are answered；

(8) set up the mathematical model of track unevenness and antenna beam error in pointing, answer according to the angle of pitch and pair of rollers Orbit altitude value, calculates antenna beam error in pointing, it may be judged whether the Beam steering error under all azimuths, the angle of pitch is all counted Complete, if it is, go to step (9), if it does not, make i=i+1, j=j+1, go to step (7), calculate next orientation Antenna beam error in pointing under angle, the angle of pitch；

(9) calculate antenna and point to the beam position root-mean-square error in definition territory, go to step (10)；

(10) antenna beam obtaining being caused by track unevenness points to root-mean-square error, quantitative assessment track unevenness pair The impact of antenna performance.

The determination of described antenna mount coordinate system, is with the orbit centre of large-scale antenna as initial point, Z axis and azimuth axis weight Closing, be perpendicular to ground and point into the sky, Y-axis points to direction, due south.

Described step (3) determines the best fit function of track unevenness, including following process:

(3a) the best fit function of hypothesis track unevenness is:

H (x)=a₀+a₁x+a₂x²+...+a_kx^k

Wherein x represents that orbital position, h (x) represent corresponding orbit altitude value, and k is high reps, a of fitting function₀, a₁,a₂...a_kFor the undetermined coefficient in fitting function；

(3b) according to the height value of track each point, it is (x respectively₁,h₁)…(x_i,h_i)…(x_C,h_C), calculate track each point side The fitting coefficient matrix X and the fitting coefficient vector H of track each point height of position coordinate:

(3c) according to the principle of least square, equationof structure group XA=H, it may be assumed that

Wherein, C is sampled point number；

(3d) according to the fitting coefficient matrix X and the fitting coefficient vector H of track each point height of track each point azimuthal coordinates, Can calculate matrix A is:

A=(X^TX)^-1X^TH

Wherein, X^TTransposition for fitting coefficient matrix；

So that it is determined that the numerical value of each parameter in track unevenness best fit function, i.e. calculate these parameters (a₀, a₁,…,a_k)。

Described step (4) calculate raceway surface height value a little and root-mean-square error thereof, including following process:

(4a) according to the best fit function of track unevenness, calculate raceway surface height value Δ h a little_i；

(4b) according to raceway surface height value Δ h a little_i, root-mean-square error σ of calculating track unevenness:

$\mathrm{\σ}=\sqrt{\frac{\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{\left({\mathrm{\Δh}}_i\right)}^2}{M}}$

Isodisperse in wherein M represents antenna bearingt operating definition territory.

Described step (5) calculates the antenna beam under a certain angle of pitch and points to root-mean-square error, including following process:

(5a) antenna a certain angle of pitch El is determined_j；

(5b) set up the mathematical model of track unevenness root-mean-square and antenna beam sensing root-mean-square error, calculate this pitching Antenna beam under angle points to root-mean-square error σ_j:

${\mathrm{\σ}}_j=\frac{u}{\sqrt{2}r}\left(\sqrt{{\tan }^2{\mathrm{El}}_j+\frac{2}{r^2}+1}\right)\mathrm{\σ}$

Wherein r is orbit radius, and m, u are conversion coefficient.

In described step (6), point to root-mean-square error according to the antenna beam under each angle of pitch, calculate antenna and point to definition Beam position root-mean-square error RMS in territory_BS:

${\mathrm{RMS}}_{BS}=\sqrt{\frac{\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\left({\mathrm{\σ}}_j\right)}^2}{N}}$

Isodisperse in wherein N represents antenna pitching operating definition territory.

Described step (7) calculates the orbit altitude value that all pairs of rollers of antenna are answered, including following process:

(7a) antenna one party parallactic angle Az is determined_i, angle of pitch El_j；

(7b) combining the distribution of antenna bearingt mounting and roller, the track each point azimuth x corresponding according to four rolling divides It is not WithAzimuth according to antenna and the best fit of track unevenness Function h (x)=a₀+a₁x+a₂x²+...+a_kx^k, calculate the orbit altitude value answered of antenna pair of rollers:

$h({\mathrm{Az}}_i+\frac{\mathrm{\π}}{4}),h({\mathrm{Az}}_i-\frac{\mathrm{\π}}{4}),h({\mathrm{Az}}_i-\frac{3\mathrm{\π}}{4}),h({\mathrm{Az}}_i+\frac{3\mathrm{\π}}{4}).$

Described step (8) calculates antenna beam error in pointing, including following process:

(8a) the orbit altitude value answered according to the angle of pitch and the pair of rollers of antenna, sets up track unevenness and refers to antenna beam To the mathematical model of error, calculate antenna azimuth error in pointing Δ Az_iWith angle of pitch error in pointing Δ El_j:

$\left[\begin{array}{c}{\mathrm{\ΔAz}}_i\\ {\mathrm{\ΔEl}}_j\end{array}\right]=\left[\begin{array}{ccc}0& \tan {\mathrm{El}}_j& -1\\ -1& 0& 0\end{array}\right]\left[\begin{array}{cccc}\frac{1}{2\sqrt{2}r}& -\frac{1}{2\sqrt{2}r}& -\frac{1}{2\sqrt{2}r}& \frac{1}{2\sqrt{2}r}\\ -\frac{1}{2\sqrt{2}r}& -\frac{1}{2\sqrt{2}r}& \frac{1}{2\sqrt{2}r}& \frac{1}{2\sqrt{2}r}\\ -\frac{s}{2r^2}& \frac{s}{2r^2}& -\frac{s}{2r^2}& \frac{s}{2r^2}\end{array}\right]\left[\begin{array}{c}h({\mathrm{Az}}_i+\frac{\mathrm{\π}}{4})\\ h({\mathrm{Az}}_i-\frac{\mathrm{\π}}{4})\\ h({\mathrm{Az}}_i-\frac{3\mathrm{\π}}{4})\\ h({\mathrm{Az}}_i+\frac{3\mathrm{\π}}{4})\end{array}\right]$

Wherein s is pitch axis height in antenna mount coordinate system；

(8b) according to antenna azimuth error in pointing Δ Az_iWith angle of pitch error in pointing Δ El_j, calculate antenna in this orientation Beam steering error when angle, the angle of pitch

In described step (9), according to the Beam steering error under all azimuths, the angle of pitch, calculate antenna and point to definition Beam position root-mean-square error RMS in territory_BS:

Isodisperse in wherein M, N represent antenna bearingt, pitching operating definition territory respectively.

The invention have the characteristics that:

(1) the raceway surface each point height value that the present invention obtains based on measurement, can quickly give the optimal of errant unevenness Fitting function, uses two kinds of methods to calculate the antenna beam caused by track unevenness and points to root-mean-square error, describe well The TP of track unevenness.

(2) present invention establishes track unevenness antenna beam and points to the mathematical model of root-mean-square error, can accurately calculate Going out large-scale wheel-track type antenna and pointing to the beam position root-mean-square error defining territory endogenous cause of ill track unevenness and cause, it is fixed to can be used for Amount is evaluated track unevenness and on the impact of antenna performance thus is instructed antenna respectively to analyze the error distribution of system, has higher work Journey practical value.

Accompanying drawing explanation

Fig. 1 is the flow chart of the present invention；

Fig. 2 is large-scale wheel-track type antenna overall schematic；

Fig. 3 is antenna mount coordinate system and antenna roller, orientation frame schematic diagram；

Fig. 4 is that track unevenness affects schematic diagram to antenna bearingt frame；

Fig. 5 is track non-planeness measurement value and optimum fit curve figure.

Detailed description of the invention

Below in conjunction with the accompanying drawings and embodiment the invention will be further described.

As it is shown in figure 1, a kind of large-scale wheel-track type antenna based on track unevenness points to the computational methods of root-mean-square error, Specifically comprise the following steps that

Step 1, determines the sampled point quantity of Antenna Orbit, measures the height value of track each point when antenna is on active service

According to the track size of large-scale wheel-track type antenna, determine the sampled point quantity of Antenna Orbit, and utilization comes card numeral Level gauge or other high precision measuring instruments, measure the height of the track each point after large-scale wheel-track type antenna a period of time under arms Value.

Step 2, determines antenna mount coordinate system, and track each point height value is carried out coordinate transform

With the orbit centre of large-scale antenna as initial point, Z axis overlaps with azimuth axis, is perpendicular to ground and points into the sky, and Y-axis is pointed to Direction, due south, determines antenna mount coordinate system, and based on step 1 is measured the height of track each point when the antenna obtained is on active service Value, carries out coordinate transform to it.

Step 3, determines the best fit function of track unevenness

3.1 assume that the best fit function of track unevenness is:

H (x)=a₀+a₁x+a₂x²+...+a_kx^k

Wherein x represents that orbital position, h (x) represent corresponding orbit altitude value, and k is high reps, a of fitting function₀, a₁,a₂...a_kFor the undetermined coefficient in fitting function；

3.2 height values based on the track each point obtained in step 2, are (x respectively₁,h₁)…(x_i,h_i)…(x_C,h_C), meter The fitting coefficient matrix X and the fitting coefficient vector H of track each point height of calculation track each point azimuthal coordinates:

3.3 according to the principle of least square, equationof structure group XA=H, it may be assumed that

Wherein, C is sampled point number；

3.4 according to the fitting coefficient matrix X and the fitting coefficient vector H of track each point height of track each point azimuthal coordinates, Can calculate matrix A is:

A=(X^TX)^-1X^TH

Wherein, X^TTransposition for fitting coefficient matrix；

So that it is determined that the numerical value of each parameter in track unevenness best fit function, i.e. calculate these parameters (a₀, a₁,…,a_k)。

Step 4, calculate raceway surface height value a little and root-mean-square error thereof

4.1 best fit functions based on the track unevenness obtained in step 3, calculate raceway surface height a little Value Δ h_i；

4.2 according to raceway surface height value Δ h a little_i, root-mean-square error σ of calculating track unevenness:

$\mathrm{\σ}=\sqrt{\frac{\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{\left({\mathrm{\Δh}}_i\right)}^2}{M}}$

Isodisperse in wherein M represents antenna bearingt operating definition territory.

Step 5, calculates the antenna beam under a certain angle of pitch and points to root-mean-square error

5.1 determine antenna a certain angle of pitch El_j；

5.2 mathematical modeies setting up track unevenness root-mean-square and antenna beam sensing root-mean-square error, calculate this pitching Antenna beam under angle points to root-mean-square error σ_j:

${\mathrm{\σ}}_j=\frac{u}{\sqrt{2}r}\left(\sqrt{{\tan }^2{\mathrm{El}}_j+\frac{2}{r^2}+1}\right)\mathrm{\σ}$

Wherein r is orbit radius (unit: rice), and u is conversion coefficient,

Step 6, calculates antenna and points to the beam position root-mean-square error in definition territory

Point to root-mean-square error based on the antenna beam under each angle of pitch obtained in step 5, calculate antenna and point to definition Beam position root-mean-square error RMS in territory_BS:

${\mathrm{RMS}}_{BS}=\sqrt{\frac{\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\left({\mathrm{\σ}}_j\right)}^2}{N}}$

Isodisperse in wherein N represents antenna pitching operating definition territory.

Step 7, calculates the orbit altitude value that all pairs of rollers of antenna are answered

7.1 determine antenna one party parallactic angle Az_i, angle of pitch El_j；

7.2 is four for the roller of most large-scale wheel-track type antennas, in conjunction with the distribution of antenna bearingt mounting Yu roller, this In take track each point azimuth x corresponding to four rolling be respectively WithAccording to The azimuth of antenna and best fit function h (the x)=a of track unevenness₀+a₁x+a₂x²+...+a_kx^k, calculate antenna pair of rollers The orbit altitude value answered:

$h({\mathrm{Az}}_i+\frac{\mathrm{\π}}{4}),h({\mathrm{Az}}_i-\frac{\mathrm{\π}}{4}),h({\mathrm{Az}}_i-\frac{3\mathrm{\π}}{4}),h({\mathrm{Az}}_i+\frac{3\mathrm{\π}}{4}).$

Step 8, calculates antenna beam error in pointing

8.1 answer orbit altitude value based on the antenna elevation angle obtained in step 7 and pair of rollers, set up track unevenness and sky The mathematical model of line Beam steering error, calculates antenna azimuth error in pointing Δ Az_iWith angle of pitch error in pointing Δ El_j:

$\left[\begin{array}{c}{\mathrm{\ΔAz}}_i\\ {\mathrm{\ΔEl}}_j\end{array}\right]=\left[\begin{array}{ccc}0& \tan {\mathrm{El}}_j& -1\\ -1& 0& 0\end{array}\right]\left[\begin{array}{cccc}\frac{1}{2\sqrt{2}r}& -\frac{1}{2\sqrt{2}r}& -\frac{1}{2\sqrt{2}r}& \frac{1}{2\sqrt{2}r}\\ -\frac{1}{2\sqrt{2}r}& -\frac{1}{2\sqrt{2}r}& \frac{1}{2\sqrt{2}r}& \frac{1}{2\sqrt{2}r}\\ -\frac{s}{2r^2}& \frac{s}{2r^2}& -\frac{s}{2r^2}& \frac{s}{2r^2}\end{array}\right]\left[\begin{array}{c}h({\mathrm{Az}}_i+\frac{\mathrm{\π}}{4})\\ h({\mathrm{Az}}_i-\frac{\mathrm{\π}}{4})\\ h({\mathrm{Az}}_i-\frac{3\mathrm{\π}}{4})\\ h({\mathrm{Az}}_i+\frac{3\mathrm{\π}}{4})\end{array}\right]$

Wherein s is pitch axis height in antenna mount coordinate system；

8.2 according to antenna azimuth error in pointing Δ Az_iWith angle of pitch error in pointing Δ El_j, calculate antenna in this orientation Beam steering error when angle, the angle of pitch

Step 9, calculates antenna and points to the beam position root-mean-square error in definition territory

Based on the Beam steering error under all azimuths obtained in step 8, the angle of pitch, calculate antenna and point to definition territory Interior beam position root-mean-square error RMS_BS:

Isodisperse in wherein M, N represent antenna bearingt, pitching operating definition territory respectively.

Step 10, the antenna beam that output is caused by track unevenness points to root-mean-square error

Beam position root-mean-square error RMS in definition territory is pointed to based on the antenna obtained in step 6 or 9_BS, output is by rail The antenna beam that road unevenness causes points to root-mean-square error, with the impact on antenna performance of the quantitative assessment track unevenness.

Advantages of the present invention can be further illustrated by emulation once:

1. determine the sampled point quantity of Antenna Orbit, measure the height value of track each point when antenna is on active service

In the present embodiment, it is analyzed with the large-scale wheel-track type antenna of certain 50 meters of bore for case, as shown in Figure 2, its side The position a diameter of 32.5m of track B, four antenna roller A are arranged along orientation track, and track unevenness is better than 0.8mm.Track orientation frame C entirety is spliced by 21 sections, and rail contact angle is 45 °, and joint arranges large-scale backing plate to ensure seaming position two ends rail Road is contour, arranges small raft in the middle part of every section of track, and thickness of slab is 30mm.Track orientation frame C is provided with pitching gear D, reflector E It is erected on track orientation frame C；Track uses foundation bolt and pressing plate to fix, in inverted T shape structure.Rail superior portion uses 42CrMo Forging processes, and after surface tempering processes, hardness can reach HRC22～HRC26, has the contact strength of excellence and resists Curved intensity.

In the present embodiment, the measurement of track unevenness has been selected and has been come card NI007 type high-precision level, and sampled point is the closeest Collection, more can reflect the verity of track pattern.According to measurement requirement, full track sets 120 measuring points, i.e. sampled point number C=altogether 120, after the stable reading of position to be initiated, record numerical value, then antenna is rotated 3 ° every time and arrive next measuring point.

2. determine antenna mount coordinate system, track each point height value is carried out coordinate transform

With the orbit centre of large-scale antenna as initial point, Z axis overlaps with azimuth axis, is perpendicular to ground and points into the sky, and Y-axis is pointed to Direction, due south, determines antenna mount coordinate system, as it is shown on figure 3, be antenna mount coordinate system and antenna roller, the signal of orientation frame Figure.When track exists error, inclination and the distortion of orientation frame can be caused, be illustrated in figure 4 track unevenness to antenna bearingt Frame affect schematic diagram.And according to previous step is measured the height value of track each point when the antenna obtained is on active service, it is carried out Coordinate transform.Measurement result and the optimum fit curve of track unevenness are shown in Fig. 5.

3. determine the best fit function of track unevenness

In the present embodiment, multinomial high math power k=20, based on the antenna after coordinate transform obtained in step 2 The height value of track each point during military service, is (x respectively₁,h₁)…(x_i,h_i)…(x_C,h_C), track each point orientation can be calculated and sit Target fitting coefficient matrix X and the fitting coefficient vector H of track each point height, then calculated by software programming, utilize formula A= (X^TX)^-1X^TH, can calculate the numerical value of each parameter, i.e. matrix in track unevenness best fit function

A=[0 ... 0-0.0001-0.0004 0.0098-0.0678 4.5806], the optimal plan of track unevenness Conjunction function:

H (x)=-0.0001x¹⁶-0.0004x¹⁷+0.0098x¹⁸-0.0678x¹⁹+4.5806x²⁰。

4. calculate raceway surface height value a little and root-mean-square error thereof

In the present embodiment, the average of track each point height value is 0 as shown in Figure 5, takes M=360, can be calculated track not Root-mean-square error σ of Pingdu is:

$\mathrm{\σ}=\sqrt{\frac{\underset{i=1}{\overset{360}{\mathrm{\Σ}}}{\left({\mathrm{\Δh}}_i\right)}^2}{360}}=\mathrm{0.2724.}$

5. the antenna beam calculated under a certain angle of pitch points to root-mean-square error

In the present embodiment, orbit radius r=16.25m, antenna pitching transmission range is 5 ° to 89 °.Determine that antenna is a certain to bow Elevation angle El_j, calculate the antenna beam under this angle of pitch and point to root-mean-square error σ_j:

${\mathrm{\σ}}_j=\frac{u}{\sqrt{2}r}\left(\sqrt{{\tan }^2{\mathrm{El}}_j+\frac{2}{r^2}+1}\right)\mathrm{\σ}$

Wherein u is conversion coefficient,

6. calculate antenna and point to the beam position root-mean-square error in definition territory

Point to root-mean-square error based on the antenna beam under each angle of pitch obtained in step 5, take N=85, calculate this 50m mouth Large-scale wheel-track type antenna beam position root-mean-square error in pointing to definition territory in footpath is Finally export the beam position root-mean-square error that the sensing caused by track unevenness defines in territory, uneven with quantitative assessment track The degree impact on antenna performance.

By above-mentioned emulation it can be seen that use the present invention method track unevenness can be carried out quick, accurately retouch State, to the best fit function of errant unevenness, and set up antenna beam based on track unevenness sensing root-mean-square error Mathematical model, accurately calculate large-scale wheel-track type antenna equal at the beam position pointing to definition territory endogenous cause of ill track unevenness and cause Square error, can be used for instructing the error distribution of each subsystem of antenna, thus ensures the high pointing accuracy during antenna military service Requirement.

Claims (9)

1. the computational methods of large-scale wheel-track type antenna based on a track unevenness sensing root-mean-square error, it is characterised in that Including following process:

(1) according to the track size of large-scale wheel-track type antenna, determine the sampled point quantity of Antenna Orbit, and utilize high-acruracy survey The height value of the track each point after apparatus measures large-scale wheel-track type antenna a period of time under arms；

(2) determine antenna mount coordinate system, track each point height value is carried out coordinate transform；

(3) based on the principle of least square, determine the best fit function of track unevenness, and judge the equal of track each point height value Whether value is 0, if it is, go to step (4), if it does not, go to step (7)；

(4) according to best fit function, calculate raceway surface height value a little and root-mean-square error thereof；

(5) antenna a certain angle of pitch El is determined_j, set up the number of track unevenness root-mean-square and antenna beam sensing root-mean-square error Learn model, and calculate the antenna beam sensing root-mean-square error under this angle of pitch, it may be judged whether the wave beam under all angles of pitch refers to All calculate to root-mean-square error complete, if it is, go to step (6), if it does not, make j=j+1, repeat step (5), under calculating The antenna beam of one angle of pitch points to root-mean-square error；

(6) calculate antenna and point to the beam position root-mean-square error in definition territory, go to step (10)；

(7) antenna one party parallactic angle Az is determined_i, angle of pitch El_j, according to azimuth and the best fit of track unevenness of antenna Function, calculates the orbit altitude value that all pairs of rollers of antenna are answered；

(8) mathematical model of track unevenness and antenna beam error in pointing is set up, the track answered according to the angle of pitch and pair of rollers Height value, calculates antenna beam error in pointing, it may be judged whether the Beam steering error under all azimuths, the angle of pitch has all calculated Finish, if it is, go to step (9), if it does not, make i=i+1, j=j+1, go to step (7), calculate next azimuth, bow Antenna beam error in pointing under the elevation angle；

(9) calculate antenna and point to the beam position root-mean-square error in definition territory, go to step (10)；

(10) antenna beam obtaining being caused by track unevenness points to root-mean-square error, and quantitative assessment track unevenness is to antenna The impact of performance.

A kind of large-scale wheel-track type antenna based on track unevenness the most according to claim 1 points to the meter of root-mean-square error Calculation method, it is characterised in that in step (2), the determination of described antenna mount coordinate system, is to be with the orbit centre of large-scale antenna Initial point, Z axis overlaps with azimuth axis, is perpendicular to ground and points into the sky, and Y-axis points to direction, due south.

A kind of large-scale wheel-track type antenna based on track unevenness the most according to claim 1 points to the meter of root-mean-square error Calculation method, it is characterised in that step (3) is carried out according to the following procedure:

(3a) the best fit function of hypothesis track unevenness is:

H (x)=a₀+a₁x+a₂x²+...+a_kx^k

Wherein x represents that orbital position, h (x) represent corresponding orbit altitude value, and k is high reps, a of fitting function₀,a₁, a₂…a_kFor the undetermined coefficient in fitting function；

(3b) according to the height value of track each point, it is (x respectively₁,h₁)…(x_i,h_i)…(x_C,h_C), calculate track each point orientation and sit Target fitting coefficient matrix X and the fitting coefficient vector H of track each point height:

(3c) according to the principle of least square, equationof structure group XA=H, it may be assumed that

Wherein, C is sampled point number；

(3d) according to the fitting coefficient matrix X and the fitting coefficient vector H of track each point height of track each point azimuthal coordinates, permissible Calculating matrix A is:

A=(X^TX)^-1X^TH

Wherein, X^TTransposition for fitting coefficient matrix；

So that it is determined that the numerical value of each parameter in track unevenness best fit function, i.e. calculate these parameters (a₀,a₁,…, a_k)。

A kind of large-scale wheel-track type antenna based on track unevenness the most according to claim 1 points to the meter of root-mean-square error Calculation method, it is characterised in that step (4) is carried out according to the following procedure:

(4a) according to the best fit function of track unevenness, calculate raceway surface height value Δ h a little_i；

(4b) according to raceway surface height value Δ h a little_i, root-mean-square error σ of calculating track unevenness:

$\mathrm{\σ}=\sqrt{\frac{\underset{i=1}{\overset{M}{\Σ}}{\left({\mathrm{\Δh}}_i\right)}^2}{M}}$

Isodisperse in wherein M represents antenna bearingt operating definition territory.

A kind of large-scale wheel-track type antenna based on track unevenness the most according to claim 1 points to the meter of root-mean-square error Calculation method, it is characterised in that step (5) is carried out according to the following procedure:

(5a) antenna a certain angle of pitch El is determined_j；

(5b) set up the mathematical model of track unevenness root-mean-square and antenna beam sensing root-mean-square error, calculate under this angle of pitch Antenna beam point to root-mean-square error σ_j:

${\mathrm{\σ}}_j=\frac{u}{\sqrt{2}r}\left(\sqrt{{\tan }^2{\mathrm{El}}_j+\frac{2}{r^2}+1}\right)\mathrm{\σ}$

Wherein r is orbit radius, and m, u are conversion coefficient.

A kind of large-scale wheel-track type antenna based on track unevenness the most according to claim 1 points to the meter of root-mean-square error Calculation method, it is characterised in that in step (6), points to root-mean-square error according to the antenna beam under each angle of pitch, calculates antenna and refers to Beam position root-mean-square error RMS in definition territory_BS:

${\mathrm{RMS}}_{BS}=\sqrt{\frac{\underset{j=1}{\overset{N}{\Σ}}{\left({\mathrm{\σ}}_j\right)}^2}{N}}$

Isodisperse in wherein N represents antenna pitching operating definition territory.

A kind of large-scale wheel-track type antenna based on track unevenness the most according to claim 1 points to the meter of root-mean-square error Calculation method, it is characterised in that step (7) is carried out according to the following procedure:

(7a) antenna one party parallactic angle Az is determined_i, angle of pitch El_j；

(7b) combining the distribution of antenna bearingt mounting and roller, the track each point azimuth x corresponding according to four rolling is respectivelyWithAzimuth according to antenna and the best fit letter of track unevenness Number h (x)=a₀+a₁x+a₂x²+...+a_kx^k, calculate the orbit altitude value answered of antenna pair of rollers:

$h({\mathrm{Az}}_i+\frac{\mathrm{\π}}{4}),h({\mathrm{Az}}_i-\frac{\mathrm{\π}}{4}),h({\mathrm{Az}}_i-\frac{3\mathrm{\π}}{4}),h({\mathrm{Az}}_i+\frac{3\mathrm{\π}}{4}).$

A kind of large-scale wheel-track type antenna based on track unevenness the most according to claim 1 points to the meter of root-mean-square error Calculation method, it is characterised in that step (8) is carried out according to the following procedure:

(8a) the orbit altitude value answered according to the angle of pitch and the pair of rollers of antenna, sets up track unevenness and points to by mistake with antenna beam The mathematical model of difference, calculates antenna azimuth error in pointing Δ Az_iWith angle of pitch error in pointing Δ El_j:

$\left[\begin{array}{c}{\mathrm{\ΔAz}}_i\\ {\mathrm{\ΔEl}}_j\end{array}\right]=\left[\begin{array}{ccc}0& \tan {\mathrm{El}}_j& -1\\ -1& 0& 0\end{array}\right]\left[\begin{array}{cccc}\frac{1}{2\sqrt{2r}}& -\frac{1}{2\sqrt{2r}}& -\frac{1}{2\sqrt{2r}}& \frac{1}{2\sqrt{2r}}\\ -\frac{1}{2\sqrt{2r}}& -\frac{1}{2\sqrt{2r}}& \frac{1}{2\sqrt{2r}}& \frac{1}{2\sqrt{2r}}\\ -\frac{s}{2r^2}& \frac{s}{2r^2}& -\frac{s}{2r^2}& \frac{s}{2r^2}\end{array}\right]\left[\begin{array}{c}h\left({\mathrm{Az}}_i+\frac{\mathrm{\π}}{4}\right)\\ h\left({\mathrm{Az}}_i-\frac{\mathrm{\π}}{4}\right)\\ h\left({\mathrm{Az}}_i-\frac{3\mathrm{\π}}{4}\right)\\ h\left({\mathrm{Az}}_i+\frac{3\mathrm{\π}}{4}\right)\end{array}\right]$

Wherein s is pitch axis height in antenna mount coordinate system；

(8b) according to antenna azimuth error in pointing Δ Az_iWith angle of pitch error in pointing Δ El_j, calculate antenna at this azimuth, bow The Beam steering error during elevation angle

A kind of large-scale wheel-track type antenna based on track unevenness the most according to claim 1 points to the meter of root-mean-square error Calculation method, it is characterised in that in step (9), according to the Beam steering error under all azimuths, the angle of pitch, calculates antenna and refers to Beam position root-mean-square error RMS in definition territory_BS:

Isodisperse in wherein M, N represent antenna bearingt, pitching operating definition territory respectively.