CN102879179B - Pointing correction method of biased three-axis telescope - Google Patents

Pointing correction method of biased three-axis telescope Download PDF

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CN102879179B
CN102879179B CN201210338770.8A CN201210338770A CN102879179B CN 102879179 B CN102879179 B CN 102879179B CN 201210338770 A CN201210338770 A CN 201210338770A CN 102879179 B CN102879179 B CN 102879179B
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pointing
error
telescope shafts
telescope
axis
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CN102879179A (en
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钟代均
唐涛
王强
刘兴法
柳万胜
任戈
包启亮
刘儒贞
陈科
黄永梅
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Institute of Optics and Electronics of CAS
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Institute of Optics and Electronics of CAS
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Abstract

The invention relates to a pointing correction method, which is mainly used for eliminating the system pointing error of a biased three-axis telescope to improve the pointing accuracy of the biased three-axis telescope. The pointing error correction method is characterized in that the method comprises picking up images of a plurality of fixed stars in the biased three-axis telescope system under the condition of locked azimuth axis; respectively calculating the pointing error of each fixed star; constructing pointing error model equation set according to a pointing error model provided by the invention; solving the equation set to obtain the model parameters and to obtain a pointing error model formula; and correcting the pointing of the biased three-axis telescope by removing the pointing error of the system. The pointing correction method provided by the invention is easy in engineering realization, and has high practicability.

Description

A kind of sensing modification method of inclined three telescope shafts
Technical field
The present invention relates to a kind of sensing modification method of inclined three telescope shafts, be mainly used in the systematic error eliminating inclined three telescope shafts, improve the pointing accuracy of inclined three telescope shafts.
Background technology
Astronomical telescope is generally altitude azimuth form rack construction, and its mechanical property is good, and volume is little, lightweight, but there is zenith tracking blind area.Adopt inclined three telescope shafts can realize following the tracks of without sky-earth integration.Document is (based on three axle photoelectric follow-up error correcting methods of spheric harmonic function, photoelectric project, Vol.34, No.12, Dec, 2007) altitude azimuth form rack construction error in pointing method is proposed, under can constraint condition being applied to, the altitude azimuth form of three axle photoelectric follow-up equivalences or X-Y formula photoelectric follow-up.Altitude azimuth form rack construction, conventional error in pointing model has spheric harmonic function model, basic parameter model, frame model etc.In the inclined three telescope shaft system application of reality, these point to modification method and are difficult to obtain high pointing accuracy.The concrete deficiency of these methods is: (1) spheric harmonic function model carries out matching to the error taking sphere as reference field, and the every of its expression formula does not have physical significance, and precision is higher, poor stability; (2) model parameter of basic parameter model has actual physics meaning, and Measures compare is stablized, and precision is not high; (3) frame model is the expansion to basic parameter model, and precision is higher, but poor stability, and complete inclined three axle frame models are difficult to set up.
Summary of the invention
The technical problem to be solved in the present invention is: for the deficiency of the precision and stability of existing error in pointing modification method, a kind of high-precision sensing modification method of high stability that can realize inclined three telescope shafts is provided, improves the pointing accuracy of inclined three telescope shafts.
Technical solution of the present invention: a kind of sensing modification method of inclined three telescope shafts, its feature is that step is as follows:
(1) the pitch axis error in pointing model of inclined three telescope shafts is calculated:
ΔE＝a 0+a 1cosEtanG-a 2sinEtanG+a 3tanG+a 4secG+a 5E+a 6E×G ①
Wherein:
A 0, a 1, a 2, a 3, a 4, a 5, a 6for treating rational method;
Δ E is the pitch axis error in pointing of inclined three telescope shafts;
E, G represent the angle of pitch of inclined three telescope shafts and the roll angle of inclined three telescope shafts;
(2) axis of rolling error in pointing model of inclined three telescope shafts is calculated:
ΔG＝b 0-b 1sinE-b 2cosE+b 3cos G+b 4G+b 5E ×G ②
Wherein:
B 0, b 1, b 2, b 3, b 4, b 5for treating rational method;
Δ G is the axis of rolling error in pointing of inclined three telescope shafts;
E, G represent the angle of pitch of inclined three telescope shafts and the roll angle of inclined three telescope shafts;
(3), under the condition locked at azimuth axis by inclined three telescope shafts, take some fixed stars, obtain one group of true place data (A under inclined three telescope shafts 0, E 0i, G 0i) and measuring position data (A 0, E i, G i), and calculate error in pointing (the Δ E at each fixed star place i, Δ G i);
Wherein:
A 0represent the position angle of the azimuth axis latched position of inclined three telescope shafts;
E 0i, G 0ibe the true place angle of pitch and roll angle, the wherein i=1 of i-th fixed star, 2 ..., n;
E i, G ibe the measuring position angle of pitch and roll angle, the wherein i=1 of i-th fixed star, 2 ..., n;
Δ E i=E i-E 0ibe the pitch axis error of i-th fixed star, wherein i=1,2 ..., n;
Δ G i=G i-G 0ibe the axis of rolling error of i-th fixed star, wherein i=1,2 ..., n;
(4) utilize formula 1. to set up Simultaneous Equations 3., calculate the parameter of the pitch axis error in pointing model formation of inclined three telescope shafts:
M EX E＝L E ③
Wherein:
M E = 1 cos E 1 tan G 1 - sin E 1 tan G 1 tan G 1 sec G 1 E 1 E 1 × G 1 1 cos E 2 tan G 2 - sin E 2 tan G 2 tan G 2 sec G 2 E 2 E 2 × G 2 . . . . . . . . . . . . . . . . . . . . . 1 cos E n tan G n - sin E n tan G n tan G n sec G n E n E n × G n , Represent the pitch axis error in pointing model matrix of inclined three telescope shafts;
X E = a 0 a 1 . . . a 6 , Represent the pitch axis error model parameters matrix of inclined three telescope shafts;
L E = Δ E 1 ΔE 2 . . . ΔE n , Represent the pitch axis error in pointing matrix of inclined three telescope shafts;
E 1..., E n, G 1..., G nrepresent the true place angle of pitch under inclined three telescope shafts of n fixed star and roll angle respectively;
Δ E 1..., Δ E nrepresent the pitch axis error in pointing of n fixed star under inclined three telescope shafts respectively;
Ask system of equations least square solution 3., obtain a 0, a 1, a 2, a 3, a 4, a 5, a 6treat the value of rational method;
(5) utilize formula 2. to set up Simultaneous Equations 4., calculate the parameter of the axis of rolling error in pointing model formation of inclined three telescope shafts:
M GX G＝L G ④
Wherein:
M G = 1 - sin E 1 - cos E 1 cos G 1 G 1 E 1 × G 1 1 - sin E 2 - cos E 2 cos G 2 G 2 E 2 × G 2 . . . . . . . . . . . . . . . . . . 1 - sin E n - cos E n cos G n G n E n × G n , Represent the axis of rolling error in pointing model matrix of inclined three telescope shafts;
X G = b 0 b 1 . . . b 5 , Represent the axis of rolling error model parameters matrix of inclined three telescope shafts;
L G = Δ G 1 Δ G 2 . . . Δ G n , Represent the axis of rolling error in pointing matrix of inclined three telescope shafts;
E 1..., E n, G 1..., G nrepresent the true place angle of pitch of n fixed star under inclined three telescope shafts and roll angle;
Δ G 1..., Δ G nrepresent the axis of rolling error in pointing of n fixed star under inclined three telescope shafts;
Ask system of equations least square solution 4., obtain b 0, b 1, b 2, b 3, b 4, b 5treat the value of rational method;
(6) utilize formula 1. and 2. and parameter inclined three telescope shafts pointed to implement to revise:
If the true place of target is (A 0, E 0, G 0), inclined three telescope shafts will point to target accurately, then the actual sensing position of inclined three telescope shafts should be (A 0, E 0+ Δ E, G 0+ Δ G);
Wherein:
A 0represent the position angle of the azimuth axis latched position of inclined three telescope shafts;
E 0, G 0for the angle of pitch of inclined three telescope shafts and the roll angle of inclined three telescope shafts;
Δ E, Δ G are the pitch axis error in pointing of inclined three telescope shafts and the axis of rolling error in pointing of inclined three telescope shafts, and 1., 2. calculate by the error in pointing model formation of inclined three telescope shafts respectively and try to achieve, computing method are as follows:
ΔE＝a 0+a 1cosE 0tan G 0-a 2sinE 0tan G 0+a 3tan G 0+a 4sec G 0+a 5E 0+a 6E0×G 0⑤
Wherein: a 0, a 1, a 2, a 3, a 4, a 5, a 6for step (4) calculates the error in pointing model parameter of gained;
ΔG＝b 0-b 1sinE 0-b 2cosE 0+b 3cosG 0+b 4G 0+b 5E 0×G 0 ⑥
Wherein: b 0, b 1, b 2,b 3, b 4, b 5for step (5) calculates the error in pointing model parameter of gained.
The present invention's advantage is compared with prior art:
(1) application of the present invention is conducive to eliminating the systematic error of inclined three telescope shafts to the impact of pointing of the telescope, improves telescopical pointing accuracy.
(2) be that the present invention has the high-precision feature of high stability compared to the advantage of prior art.
Accompanying drawing explanation
Fig. 1 is the structural representation of inclined three telescope shafts of the present invention;
Fig. 2 is the coordinate system definition of inclined three telescope shafts.
Wherein, symbol is defined as follows:
1 represents imageing sensor;
X, Y, Z represent telescope three rotation, and wherein X-axis is pitch axis, and angle of rotation is angle of pitch E; Y-axis is the axis of rolling, and angle of rotation is roll angle G; Z axis is azimuth axis, and angle of rotation is position angle A.
Embodiment
As shown in Figure 1, inclined three telescope shafts are made up of the mutually orthogonal vertical axle system of X, Y, Z tri-, and each axle is installed servomotor, angular transducer (scrambler), rotation direction is as shown in Figure 1.Inclined three telescope shaft lens barrels are arranged in Y-axis, and can rotate with it.Wherein, the rotary scope of X, Y, Z is respectively 90 °, 180 °, 360 ° × N.
As shown in Figure 2, the coordinate system definition of inclined three telescope shafts, when setting inclined three telescope shaft lens barrels just to zenith, the output of X-axis angular transducer is 90 °, and the output of Y-axis angular transducer is 0 °.Therefore X-axis angular range is (0 ° ~ 90 °), and Y-axis angular range is (-90 ° ~+90 °).When Z axis locking, inclined three telescope shafts can realize the covering observation in district's half a day by the rotation of X-axis and Y-axis.
The step that inclined three telescope shafts of the present invention point to modification method is as follows:
(1) the pitch axis error in pointing model of inclined three telescope shafts is calculated:
ΔE＝a 0+a 1cosEtan G-a 2sinEtan G+a 3tan G+a 4sec G+a 5E+a 6E×G ①
Wherein:
A 0, a 1, a 2, a 3, a 4, a 5, a 6for treating rational method;
Δ E is the pitch axis error in pointing of inclined three telescope shafts;
E, G represent the angle of pitch of inclined three telescope shafts and the roll angle of inclined three telescope shafts;
(2) axis of rolling error in pointing model of inclined three telescope shafts is calculated:
ΔG＝b 0-b 1sinE-b 2cosE+b 3cos G+b 4G+b 5E×G ②
Wherein:
B 0, b 1, b 2, b 3, b 4, b 5for treating rational method;
Δ G is the axis of rolling error in pointing of inclined three telescope shafts;
E, G represent the angle of pitch of inclined three telescope shafts and the roll angle of inclined three telescope shafts;
(3), under the condition locked at azimuth axis by inclined three telescope shafts, take some fixed stars, obtain one group of true place data (A under inclined three telescope shafts 0, E 0i, G 0i) and measuring position data (A 0, E i, G i), and calculate error in pointing (the Δ E at each fixed star place i, Δ G i);
Wherein:
A 0represent the position angle of the azimuth axis latched position of inclined three telescope shafts;
E 0i, G 0ibe the true place angle of pitch and roll angle, the wherein i=1 of i-th fixed star, 2 ..., n;
E i, G ibe the measuring position angle of pitch and roll angle, the wherein i=1 of i-th fixed star, 2 ..., n;
Δ E i=E i-E 0ibe the pitch axis error of i-th fixed star, wherein i=1,2 ..., n;
Δ G i=G i-G 0ibe the axis of rolling error of i-th fixed star, wherein i=1,2 ..., n;
(4) utilize formula 1. to set up Simultaneous Equations 3., calculate the parameter of the pitch axis error in pointing model formation of inclined three telescope shafts:
M EX E＝L E ③
Wherein:
M E = 1 cos E 1 tan G 1 - sin E 1 tan G 1 tan G 1 sec G 1 E 1 E 1 × G 1 1 cos E 2 tan G 2 - sin E 2 tan G 2 tan G 2 sec G 2 E 2 E 2 × G 2 . . . . . . . . . . . . . . . . . . . . . 1 cos E n tan G n - sin E n tan G n tan G n sec G n E n E n × G n , Represent the pitch axis error in pointing model matrix of inclined three telescope shafts;
X E = a 0 a 1 . . . a 6 , Represent the pitch axis error model parameters matrix of inclined three telescope shafts;
L E = Δ E 1 ΔE 2 . . . ΔE n , Represent the pitch axis error in pointing matrix of inclined three telescope shafts;
E 1..., E n, G 1..., G nrepresent the true place angle of pitch under inclined three telescope shafts of n fixed star and roll angle respectively;
Δ E 1..., Δ E nrepresent the pitch axis error in pointing of n fixed star under inclined three telescope shafts respectively;
Ask system of equations least square solution 3., obtain a 0, a 1, a 2, a 3, a 4, a 5, a 6treat the value of rational method;
(5) utilize formula 2. to set up Simultaneous Equations 4., calculate the parameter of the axis of rolling error in pointing model formation of inclined three telescope shafts:
M GX G＝L G ④
Wherein:
M G = 1 - sin E 1 - cos E 1 cos G 1 G 1 E 1 × G 1 1 - sin E 2 - cos E 2 cos G 2 G 2 E 2 × G 2 . . . . . . . . . . . . . . . . . . 1 - sin E n - cos E n cos G n G n E n × G n , Represent the axis of rolling error in pointing model matrix of inclined three telescope shafts;
X G = b 0 b 1 . . . b 5 , Represent the axis of rolling error model parameters matrix of inclined three telescope shafts;
L G = Δ G 1 Δ G 2 . . . Δ G n , Represent the axis of rolling error in pointing matrix of inclined three telescope shafts;
E 1..., E n, G 1..., G nrepresent the true place angle of pitch of n fixed star under inclined three telescope shafts and roll angle;
Δ G 1..., Δ G nrepresent the axis of rolling error in pointing of n fixed star under inclined three telescope shafts;
Ask system of equations least square solution 4., obtain b 0, b 1, b 2, b 3, b 4, b 5treat the value of rational method;
(6) utilize formula 1. and 2. and parameter inclined three telescope shafts pointed to implement to revise:
If the true place of target is (A 0, E 0, G 0), inclined three telescope shafts will point to target accurately, then the actual sensing position of inclined three telescope shafts should be (A 0, E 0+ Δ E, G 0+ Δ G);
Wherein:
A 0represent the position angle of the azimuth axis latched position of inclined three telescope shafts;
E 0, G 0for the angle of pitch of inclined three telescope shafts and the roll angle of inclined three telescope shafts;
Δ E, Δ G are the pitch axis error in pointing of inclined three telescope shafts and the axis of rolling error in pointing of inclined three telescope shafts, and 1., 2. calculate by the error in pointing model formation of inclined three telescope shafts respectively and try to achieve, computing method are as follows:
ΔE＝a 0+a 1cosE 0tan G 0-a 2sinE 0tan G 0+a 3tan G 0+a 4sec G 0+a 5E 0+a 6E 0×G 0⑤
Wherein: a 0, a 1, a 2, a 3, a 4, a 5, a 6for step (4) calculates the error in pointing model parameter of gained;
ΔG＝b 0-b 1sinE 0-b 2cosE 0+b 3cosG 0+b 4G 0+b 5E 0×G 0 ⑥
Wherein: b 0, b 1, b 2, b 3, b 4, b 5for step (5) calculates the error in pointing model parameter of gained.
The present invention is further illustrated below by concrete utilization example.
Point to the precision revised and be usually divided into precision of inner coincidence and precision of exterior coincidence, and the quality of precision of exterior coincidence weighs the key of the quality pointing to correction effect.Provided below is the example that certain inclined three telescope shafts point to modification method application.
Data acquisition process: make telescopical orientation be locked in 0 °, 90 °, 180 °, 270 ° positions respectively, each position of orientation is taken one group respectively and is clapped star error information, data acquisition.Then use method provided by the invention and existing sensing modification method to carry out calculating respectively to compare.
Precision of inner coincidence: data are respectively hung oneself and pointed to the medial error of revised residual error,
Precision of exterior coincidence: use odd row data (even number of lines certificate) to calculate corrected parameter, remove according to the parameter obtained the medial error revising the residual error that even number of lines produces according to (odd row data).
Table 1 lists four groups of actual measurements respectively to table 4 and claps sing data.
Table 5 lists the correction accuracy comparison of the present invention and existing modification method to table 7.
Existing modification method illustrates:
(1) basic parameter model
Pitch axis error model:
ΔE＝a 0+a 1cosEtan G-a 2sinEtan G+a 3tan G+a 4sec G
Wherein a i, (i=0,1 ..., 4) and be undetermined coefficient, Δ E is pitch axis error in pointing, and E, G represent the angle of pitch and roll angle.
Axis of rolling error model:
ΔG＝b 0-b 1sinE-b 2cosE+b 3cosG
Wherein b i, (i=0,1 ..., 3) and be undetermined coefficient, Δ G is axis of rolling error in pointing, and E, G represent the angle of pitch and roll angle.
(2) frame model
Pitch axis error model:
ΔE＝a 0-a 1cosEtan G-a 2sinEtan G+a 3sec G-a 4tan G+a 5sinE+
a 6cosE+a 7(E/2π)+a 8sin 2E+a 9cos 2E+a 10sin 2Esec G+a 11cos 2Esec G
Wherein a i, (i=0,1 ..., 11) and be undetermined coefficient, Δ E is pitch axis error in pointing, and E, G represent the angle of pitch and roll angle.
Axis of rolling error model:
ΔG＝b 0+b 1sinE-b 2cosE+b 3sin G+b 4cos G+b 5cot G+b 6(G/2π)
+b 7sinE+b 8cosE+b 9RsinE+b 10GcosE+b 11sin2E+b 12cos2E
Wherein b i, (i=0,1 ..., 12) and be undetermined coefficient, Δ G is axis of rolling error in pointing, and E, G represent the angle of pitch and roll angle.
(3) spheric harmonic function model
Pitch axis error model:
ΔEcos G＝a 0+a 1sin G+a 2cosEcos G+a 3sinEcos G+a 4sin 2G
+a 5cosEsin G cos G+a 6sinEsin G cos G+a 7cos 2Esin G+a 8sin 2Ecos 2G
+a 9sin 3G+a 10cosEsin 2G sinG+a 11sinEsin 2GcosG+a1 2cos2Ecos 2G sinG
Wherein a i, (i=0,1 ..., 12) and be undetermined coefficient, Δ E is pitch axis error in pointing, and E, G represent the angle of pitch and roll angle.
Axis of rolling error model:
ΔG＝b 0+b 1sin G+b 2cosEcos G+b 3sinEcos G+b 4sin 2G
+b 5cosEsin G cos G+b 6sinEsin G cos G+b 7cos 2Esin G+b 8sin 2Ecos 2G
+b 9sin 3G+b 10cosEsin 2Gsin G+b 11sinEsin 2G cos G+b 12cos 2Ecos 2Gsin G
Wherein b i, (i=0,1 ..., 12) and be undetermined coefficient, Δ G is axis of rolling error in pointing, and E, G represent the angle of pitch and roll angle.
Table 1, sing data one (unit: degree) is clapped in actual measurement
Table 2, sing data two (unit: degree) is clapped in actual measurement
Table 3. is surveyed and is clapped sing data three (unit: degree)
Table 4. is surveyed and is clapped sing data four (unit: degree)
Table 5. the inventive method compares (unit: rad) with basic parameter model method
Table 6. the inventive method compares (unit: rad) with frame model method
Table 7. the inventive method compares (unit: rad) with spheric harmonic function method
From table 5 to table 7:
(1) the inventive method methodically meets that to revise precision high outward than existing.
(2) the inventive method stability compared with spheric harmonic function method, frame model method is higher:
Pitch axis correction precision:
Precision ratio is met for (1.449/1.852=78.2%) inside and outside the inventive method;
Precision ratio is met for (1.122/3.031=37.0%) inside and outside frame model method;
Precision ratio is met for (1.188/3.096=38.4%) inside and outside spheric harmonic function method;
Axis of rolling correction precision:
Precision ratio is met for (0.929/1.204=77.2%) inside and outside the inventive method;
Precision ratio is met for (1.112/2.028=54.8%) inside and outside frame model method;
Precision ratio is met for (0.781/1.864=41.9%) inside and outside spheric harmonic function method.
Conclusion: the inventive method has the advantage of high precision, high stability compared with the conventional method.
Correction effect of the present invention is see above-mentioned concrete utilization example, the pitch axis original pointing accuracy medial error average out to 66.8 rad of inclined three telescope shafts in 4 orientation in instances, uses the revised pointing accuracy of the present invention to bring up to medial error average out to 1.85 rads; The axis of rolling original pointing accuracy medial error average out to 28.1 rad of inclined three telescope shafts in 4 orientation, uses the revised pointing accuracy of the present invention to bring up to medial error average out to 1.2 rads.
The part that the present invention does not elaborate belongs to techniques well known.

Claims (1)

1. a sensing modification method for inclined three telescope shafts, is characterized in that performing step is as follows:
(1) the pitch axis error in pointing model of inclined three telescope shafts is calculated:
ΔE＝a 0+a 1cosEtanG-a 2sinEtanG+a 3tanG+a 4secG+a 5E+a 6E×G ①
Wherein:
A 0, a 1, a 2, a 3, a 4, a 5, a 6for treating rational method;
Δ E is the pitch axis error in pointing of inclined three telescope shafts;
E, G represent the angle of pitch of inclined three telescope shafts and the roll angle of inclined three telescope shafts;
(2) axis of rolling error in pointing model of inclined three telescope shafts is calculated:
ΔG＝b 0-b 1sinE-b 2cosE+b 3cosG+b 4G+b 5E×G ②
Wherein:
B 0, b 1, b 2, b 3, b 4, b 5for treating rational method;
Δ G is the axis of rolling error in pointing of inclined three telescope shafts;
E, G represent the angle of pitch of inclined three telescope shafts and the roll angle of inclined three telescope shafts;
(3), under the condition locked at azimuth axis by inclined three telescope shafts, take some fixed stars, obtain one group of true place data (A under inclined three telescope shafts 0, E 0i, G 0i) and measuring position data (A 0, E i, G i), and calculate error in pointing (the Δ E at each fixed star place i, Δ G i);
Wherein:
A 0represent the position angle of the azimuth axis latched position of inclined three telescope shafts;
E 0i, G 0ibe the true place angle of pitch and roll angle, the wherein i=1 of i-th fixed star, 2 ..., n;
E i, G ibe the measuring position angle of pitch and roll angle, the wherein i=1 of i-th fixed star, 2 ..., n;
Δ E i=E i-E 0ibe the pitch axis error of i-th fixed star, wherein i=1,2 ..., n;
Δ G i=G i-G 0ibe the axis of rolling error of i-th fixed star, wherein i=1,2 ..., n;
(4) utilize formula 1. to set up Simultaneous Equations 3., calculate the parameter of the pitch axis error in pointing model formation of inclined three telescope shafts:
M EX E＝L E ③
Wherein:
M E = 1 cos E 01 tan G 01 - sin E 01 tan G 01 tan G 01 sec G 01 E 01 E 01 × G 01 1 cos E 02 tan G 02 - sin E 02 tan G 02 tan G 02 sec G 02 E 02 E 02 × G 02 . . . . . . . . . . . . . . . . . . . . . 1 cos E 0 n E 0 n tan G 0 n - sin E 0 n tan G 0 n tan G 0 n sec G 0 n E 0 n E 0 n × G 0 n , Represent the pitch axis error in pointing model matrix of inclined three telescope shafts;
X E = a 0 a 1 . . . a 6 , Represent the pitch axis error model parameters matrix of inclined three telescope shafts;
L E = Δ E 1 Δ E 2 . . . Δ E n , Represent the pitch axis error in pointing matrix of inclined three telescope shafts;
E 01..., E 0nrepresent n the true place angle of pitch E of fixed star under inclined three telescope shafts respectively 0i, wherein i=1,2 ..., n;
G 01..., G 0nrepresent n the true place roll angle G of fixed star under inclined three telescope shafts respectively 0i, wherein i=1,2 ..., n;
Δ E 1..., Δ E nrepresent n the pitch axis error in pointing Δ E of fixed star under inclined three telescope shafts respectively i, wherein i=1,2 ..., n;
Ask system of equations least square solution 3., obtain a 0, a 1, a 2, a 3, a 4, a 5, a 6treat the value of rational method;
(5) utilize formula 2. to set up Simultaneous Equations 4., calculate the parameter of the axis of rolling error in pointing model formation of inclined three telescope shafts:
M GX G＝L G ④
Wherein:
M G = 1 - sin E 01 - cos E 01 cos G 01 G 01 E 01 × G 01 1 - sin E 02 - cos E 02 cos G 02 G 02 E 02 × G 02 . . . . . . . . . . . . . . . . . . 1 - sin E 0 n - cos E 0 n cos G 0 n G 0 n E 0 n × G 0 n , Represent the axis of rolling error in pointing model matrix of inclined three telescope shafts;
X G = b 0 b 1 . . . b 5 , Represent the axis of rolling error model parameters matrix of inclined three telescope shafts;
L G = Δ G 1 Δ G 2 . . . Δ G n , Represent the axis of rolling error in pointing matrix of inclined three telescope shafts;
E 01..., E 0nrepresent n the true place angle of pitch E of fixed star under inclined three telescope shafts respectively 0i, wherein i=1,2 ..., n;
G 01..., G 0nrepresent n the true place roll angle G of fixed star under inclined three telescope shafts respectively 0i, wherein i=1,2 ..., n;
Δ G 1..., Δ G nrepresent n the axis of rolling error in pointing Δ G of fixed star under inclined three telescope shafts respectively i, wherein i=1,2 ..., n;
Ask system of equations least square solution 4., obtain b 0, b 1, b 2, b 3, b 4, b 5treat the value of rational method;
(6) utilize formula 1. and 2. and parameter inclined three telescope shafts pointed to implement to revise:
If the true place of target is (A 0, E 0, G 0), inclined three telescope shafts will point to target accurately, then the actual sensing position of inclined three telescope shafts should be (A 0, E 0+ Δ E, G 0+ Δ G);
Wherein:
A 0represent the position angle of the azimuth axis latched position of inclined three telescope shafts;
E 0, G 0for the angle of pitch of inclined three telescope shafts and the roll angle of inclined three telescope shafts;
Δ E, Δ G are the pitch axis error in pointing of inclined three telescope shafts and the axis of rolling error in pointing of inclined three telescope shafts, and 1., 2. calculate by the error in pointing model formation of inclined three telescope shafts respectively and try to achieve, computing method are as follows:
ΔE＝a 0+a 1cosE 0tanG 0-a 2sinE 0tanG 0+a 3tanG 0+a 4secG 0+a 5E 0+a 6E 0×G 0 ⑤
Wherein: a 0, a 1, a 2, a 3, a 4, a 5, a 6for step (4) calculates the error in pointing model parameter of gained;
ΔG＝b 0-b 1sinE 0-b 2cosE 0+b 3cosG 0+b 4G 0+b 5E 0×G 0 ⑥
Wherein: b 0, b 1, b 2, b 3, b 4, b 5for step (5) calculates the error in pointing model parameter of gained.
CN201210338770.8A 2012-09-13 2012-09-13 Pointing correction method of biased three-axis telescope Active CN102879179B (en)

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