CN104154928B - Installation error calibrating method applicable to built-in star sensor of inertial platform - Google Patents

Abstract

The invention discloses an installation error calibrating method applicable to a built-in star sensor of an inertial platform. The installation error calibrating method is used for calibrating an installation error of a measurement coordinate system of the star sensor. The method comprises the following steps: (1) imaging parallel light emitted from a star simulator in the center of a view field of the star sensor; (2) calculating unit vectors of the light emitted from the star simulator in a geographic coordinate system by utilizing an optical theodolite; (3) adjusting the attitude of the inertial platform, and calculating the unit vectors of the light emitted from the star simulator in a current star sensor measurement coordinate system; (4) measuring the current attitude of the inertial platform, and a transformation matrix of a hexahedron of the inertial platform and a local geographic coordinate system by using two optical theodolites; and (5) calculating the transformation matrix, namely the installation error of the star sensor, between the star sensor measurement coordinate system and an inertial platform coordinate system by utilizing a least square method. According to the method, an error link is reduced, a calibrating result directly reflects the installation error of the measurement coordinate system of the star sensor, and the calibration accuracy is high.

Description

A kind of mounting error calibration method being applied to the built-in star sensor of inertial platform

Technical field

The present invention relates to a kind of mounting error calibration method, more particularly, to one kind are applied to the built-in star of inertia inertial platform The mounting error calibration method of sensor.

Background technology

Inertial/stellar integrated navigation system is applied to long-range vehicle and can adopt inertia inertial platform+star sensor Compound mode, star sensor is built in Inertial Platform inside (connecting firmly with inertial platform coordinate system), is flown out using carrier The error of the starlight Information revision pure-inertial guidance system of observation after atmosphere, improves the precision of integrated navigation system.This group Conjunction mode utilizes the advantages of inertial platform internal temperature is constant, inertial attitude stabilization, dynamic environment are good to reduce the survey of star sensor Amount error, simultaneously because star sensor measurement coordinate system and navigational coordinate system connect firmly, it is to avoid attitude conversion and malformation etc. The loss of significance that error link causes.

The precision of inertial/stellar integrated navigation system is directly related with starlight certainty of measurement, and therefore research is applied to inertia The mounting error calibration method of the built-in star sensor of platform, significant to the precision of integrated navigation system.

It is not directed to the mounting error calibration method of the built-in star sensor of inertial platform at present both at home and abroad, factory is installing When measure generally by micrometer instrument (or autocollimator) and to install on inertial platform benchmark hexahedron and star sensor Little hexahedral method measures its alignment error.But it is true that due to the measurement coordinate system of star sensor, (i.e. optical axis is photosensitive with it The virtual optics coordinate system that face is constituted) there is deviation and its hexahedron between, and this deviation can in time and use environment temperature Change and there are minor variations.Therefore this method of testing is difficult to meet high-precision use requirement it is necessary to directly demarcate star Sensor measures the alignment error of coordinate.

Content of the invention

The technology solve problem of the present invention is: overcomes the deficiencies in the prior art it is proposed that a kind of profit is applied to inertial platform The mounting error calibration method of built-in star sensor, reduces error link, and calibration result directly reflects star sensor The alignment error of measurement coordinate system, stated accuracy is high.

The technical solution of the present invention:

A kind of mounting error calibration method being applied to the built-in star sensor of inertial platform, step is as follows:

(1) adjust inertial platform pedestal orientation and star simulator support makes the directional light of star simulator outgoing image in star Sensor field of view center, described inertial platform is a kind of common gimbaled inertial navigation system, and star simulator is used for indoors Simulation fixed star source of parallel light；

(2) utilize micrometer instrument demarcate star simulator outgoing directional light with respect to local geographic coordinate system the angle of site and Azimuth, calculates unit vector under geographic coordinate system for the star simulator emergent ray；

(3) keep star simulator position and attitude constant, the attitude of adjustment inertial platform, so that star simulator emergent ray is become As in star sensor difference coordinate points, recording each imager coordinate, calculating star simulator emergent ray sensitive in current star Unit vector under device measurement coordinate system；

(4) measure the current attitude of inertial platform with two micrometer instruments, and calculate inertial platform hexahedron and work as The transition matrix of ground geographic coordinate system, described two micrometer instruments are the first micrometer instrument and the second micrometer instrument；

(5) result of calculation according to step (2) and step (4), calculates the installation of star sensor using method of least square The alignment error of matrix, as star sensor.

Unit vector under geographic coordinate system for the star simulator emergent ray is calculated in described step (2), method particularly includes:

By formula

${\stackrel{\→}{a}}_e=\left(\begin{array}{c}{\cos e}_s{\cos \mathrm{\σ}}_s\\ {\sin e}_s\\ {\cos e}_s\sin {\mathrm{\σ}}_s\end{array}\right)$

Calculate unit vector under geographic coordinate system for the star simulator emergent rayWherein e_sAnd σ_sIt is respectively optics warp Latitude instrument measures star simulator outgoing directional light with respect to the angle of site of local geographic coordinate system and azimuth.

The transition matrix of inertial platform hexahedron and local geographic coordinate system in described step (4), method particularly includes:

By formula

$c_e^{\mathrm{pi}}=\left(\begin{array}{ccc}{c}_{11}& c_{12}& c_{13}\\ c_{21}& c_{22}& c_{23}\\ c_{31}& c_{32}& c_{33}\end{array}\right)$

Calculate the transition matrix of inertial platform hexahedron and local geographic coordinate systemWherein:

c₁₁=cose_i1cosσ_i1；

c₁₂=sine_i1；

c₁₃=cose_i1sinσ_i1；

c₂₁=cose_i1sine_i2sinσ_i1-sine_i1cose_i2sinσ_i2；

c₂₂=cose_i1cose_i2sin(σ_i2-σ_i1)；

c₂₃=sine_i1cose_i2cosσ_i1-cose_i1sine_i2cosσ_i2；

c₃₁=cose_i2cosσ_i2；

c₃₂=sine_i2；

c₃₃=cose_i2sinσ_i2；

e_i1And σ_i1It is respectively the first micrometer instrument measurement inertial platform hexahedron y_pioz_piPlane normal, i.e. x_piAxle phase The angle of site for geographic coordinate system and azimuth, e_i2And σ_i2It is respectively the second micrometer instrument measurement inertial platform hexahedron x_pioy_piPlane normal, i.e. z_piAxle is with respect to the angle of site of geographic coordinate system and azimuth.

The installation matrix of star sensor in described step (5), method particularly includes:

By formula

$c_p^s=a_s{a}_p^t{\left(a_p{a}_p^t\right)}^{-1}$

Calculate the transition matrix between star sensor measurement coordinate system and inertial platform coordinate systemWherein, a_sQuick for star The matrix of sensor measurement data construction, a_pFor the matrix of the projection construction in inertial platform coordinate system for the star simulator vector, construction Mode is as follows:

$a_s={\left[\begin{array}{cccc}{\stackrel{\→}{a}}_{s1}& {\stackrel{\→}{a}}_{s2}& ...& {\stackrel{\→}{a}}_{\mathrm{sn}}\end{array}\right]}_{3\×n},a_p={\left[\begin{array}{cccc}{\stackrel{\→}{a}}_{p1}& {\stackrel{\→}{a}}_{p2}& ...& {\stackrel{\→}{a}}_{\mathrm{pn}}\end{array}\right]}_{3\×n}$

Wherein,For list under current star sensor measurement coordinate system for the star simulator emergent ray Bit vector,For projection vector under inertial platform coordinate system for the star simulator vector.

The unit vector of described star sensor measured value particularly as follows:

${\stackrel{\→}{a}}_{\mathrm{si}}=\left(\begin{array}{c}\frac{-x_i}{\sqrt{x_i^2+y_i^2+f^2}}\\ \frac{-y_i}{\sqrt{x_i^2+y_i^2+f^2}}\\ \frac{f}{\sqrt{x_i^2+y_i^2+f^2}}\end{array}\right)$

Wherein, x_iAnd y_iIt is respectively the length away from star sensor zero for the punctate opacity of the cornea coordinate, f is star sensor focal length, i= 1,2,3…n.

Star simulator projection vector in described constructive formula particularly as follows:

${\stackrel{\→}{a}}_{\mathrm{pi}}=c_e^{\mathrm{pi}}\·{\stackrel{\→}{a}}_e$

Calculate projection vector under inertial platform coordinate system for the star simulator vectorIn formula,For the transition matrix of inertial platform hexahedron and geographic coordinate system,For star simulator emergent ray under geographic coordinate system Unit vector, i=1,2,3 ... n.

Compared with the prior art, the invention has the advantages that:

(1) directly test the alignment error of star sensor measurement coordinate system, rather than simply use star sensor hexahedron to sit Mark system substitutes, and demarcates object closer to application conditions.

(2) test under inertial platform and star sensor operating temperature and environmental condition, it is to avoid the factor such as temperature is to demarcation The impact of result.

(3) do not use star sensor hexahedron in test process, it is to avoid by star sensor hexahedron and measurement coordinate system it Between error and star sensor hexahedron and inertial platform hexahedron between error introduce final calibration result, reduce by mistake Difference ring section, improves process alignment error calibration precision.

Brief description

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

Fig. 2 is demarcation object and the test equipment schematic diagram of the present invention.

Fig. 3 is the definition in geographic coordinate system for the star simulator vector of the present invention.

Fig. 4 is the star sensor imaging schematic diagram of the present invention.

Fig. 5 is the inertial platform hexahedron attitude determination schematic diagram of the present invention.

Specific embodiment

Below in conjunction with the accompanying drawings the specific embodiment of the invention is described further.

The flow chart of the present invention as shown in figure 1, define mounting means on inertial platform for the star sensor as shown in Fig. 2 Star sensor is arranged on inertial platform, camera lens optical axis parallel to local level, towards star simulator optical axis direction.Implemented Journey is as follows:

(1) under inertial platform leveling state, made by the orientation and star simulator support adjusting inertial platform pedestal The directional light of star simulator outgoing images in star sensor field of view center.

(2) high-precision optical theodolite is utilized to demarcate star simulator outgoing directional lightWith respect to local geographic coordinate system Angle of site e_sWith azimuth σ_s, coordinate definition is as shown in Figure 3.In figure o-xyz represents geographic coordinate system, and x-axis positive direction is north, y Perpendicular to ground upwards, z-axis positive direction is east to axle positive direction, and o is zero.Angle of site e_sRepresent star simulator emergent rayAngle and horizontal plane between, azimuth σ_sRepresent the angle of its projection in the horizontal plane and x-axis.Star simulator emergent light LineCoordinatograph under geographic coordinate system is represented by for unit vector

${\stackrel{\→}{a}}_e=\left(\begin{array}{c}{\cos e}_s{\cos \mathrm{\σ}}_s\\ {\sin e}_s\\ {\cos e}_s\sin {\mathrm{\σ}}_s\end{array}\right)$

Wherein e_sAnd σ_sIt is respectively micrometer instrument measurement star simulator outgoing directional light with respect to local geographic coordinate system The angle of site and azimuth.

(3) star simulator position immobilizes.Inertial Platform is adjusted by the gentle indexing of inertial platform slop regulation Attitude, makes star simulator emergent ray image in the image plane of star sensor measurement coordinate system, but adjusting range must not exceed Star sensor visual field, after 3min is stablized in each position, records the coordinate (x of current punctate opacity of the cornea_i,y_i), wherein i=1,2,3 ... n, n are Inertial platform difference pose adjustment number of times, corresponding difference star sensor coordinate figure.

If fixed star imager coordinate in star sensor measurement coordinate system is (x, y), wherein x, y are that punctate opacity of the cornea coordinate is former away from coordinate The length of point, star sensor focal length is f, as shown in Figure 4.In figure o_s-x_sy_sz_sRepresent star sensor measurement coordinate system, it is photosensitive The horizontal stroke in face, vertical coordinate are respectively defined as x_sAxle and y_sAxle, z_sAxle points to optical axis direction and x_sAxle, y_sAxle constitutes right hand rectangular coordinate System, initial point o_sFor photosurface central point.Then the space vector of fixed star can be expressed as under star sensor measurement coordinate system (- x ,- y,f).Simulate fixed star light source, then punctate opacity of the cornea coordinate (x with star simulator_i,y_i) correspond to star simulator emergent ray in current star sensitivity Coordinatograph under device measurement coordinate system for unit vector is:

${\stackrel{\→}{a}}_{\mathrm{si}}=\left(\begin{array}{c}\frac{-x_i}{\sqrt{x_i^2+y_i^2+f^2}}\\ \frac{-y_i}{\sqrt{x_i^2+y_i^2+f^2}}\\ \frac{f}{\sqrt{x_i^2+y_i^2+f^2}}\end{array}\right)$

Wherein, x_iAnd y_iIt is respectively the length away from star sensor zero for the punctate opacity of the cornea coordinate, f is star sensor focal length, i= 1,2,3…n.

(4) measure the current attitude of Inertial Platform with micrometer instrument, and calculate inertial platform hexahedron and work as The transition matrix of ground geographic coordinate system.If inertial platform coordinate definition is as shown in figure 5, o-x_piy_piz_piRepresent inertial platform coordinate System, selected inertial platform hexahedron drift angle is as initial point o, x_piAxle is inertial platform roll axle, y_piAxle is azimuth axis, z_piAxle For pitch axis.Measure inertial platform hexahedron y with the first micrometer instrument_pioz_piPlane normal (i.e. x_piAxle) sit with respect to geographical The angle of site e of mark system_i1With azimuth σ_i1, measure inertial platform hexahedron x with the second micrometer instrument_pioy_piPlane normal is (i.e. z_piAxle) with respect to geographic coordinate system angle of site e_i2With azimuth σ_i2, the computational methods with reference to step (2) can draw two The unit vector of normal represents, that is,

${\stackrel{\→}{x}}_{\mathrm{pi}}=\left(\begin{array}{c}\cos e_{i1}\cos {\mathrm{\σ}}_{i1}\\ \sin e_{i1}\\ {\cos e}_{i1}\sin {\mathrm{\σ}}_{i1}\end{array}\right),{\stackrel{\→}{z}}_{\mathrm{pi}}=\left(\begin{array}{c}\cos e_{i2}\cos {\mathrm{\σ}}_{i2}\\ \sin e_{i2}\\ \cos e_{i2}\sin {\mathrm{\σ}}_{i2}\end{array}\right)$

In view of the hexahedral orthogonality of inertial platform, can obtain

${\stackrel{\→}{y}}_{\mathrm{pi}}={\stackrel{\→}{z}}_{\mathrm{pi}}\×{\stackrel{\→}{x}}_{\mathrm{pi}}$

Then inertial platform hexahedron and the transition matrix of local geographic coordinate system are

$c_e^{\mathrm{pi}}=\left(\begin{array}{ccc}{c}_{11}& c_{12}& c_{13}\\ c_{21}& c_{22}& c_{23}\\ c_{31}& c_{32}& c_{33}\end{array}\right)$

Wherein:

c₁₁=cose_i1cosσ_i1；

c₁₂=sine_i1；

c₁₃=cose_i1sinσ_i1；

c₂₁=cose_i1sine_i2sinσ_i1-sine_i1cose_i2sinσ_i2；

c₂₂=cose_i1cose_i2sin(σ_i2-σ_i1)；

c₂₃=sine_i1cose_i2cosσ_i1-cose_i1sine_i2cosσ_i2；

c₃₁=cose_i2cosσ_i2；

c₃₂=sine_i2；

c₃₃=cose_i2sinσ_i2；

Wherein, e_i1And σ_i1It is respectively the first micrometer instrument measurement inertial platform hexahedron y_pioz_piPlane normal (i.e. x_pi Axle) with respect to the angle of site of geographic coordinate system and azimuth, e_i2And σ_i2It is respectively the second micrometer instrument measurement inertial platform six Face body x_pioy_piPlane normal (i.e. z_piAxle) with respect to the angle of site of geographic coordinate system and azimuth.

(5) calculate the alignment error of star sensor measurement coordinate system

According to the result of calculation of step (2) and step (4), coordinate unit arrow under local geographic coordinate system for the star simulator Measure and beInertial platform hexahedron with the transition matrix of geographic coordinate system isThen star simulator vector is in inertial platform coordinate Projection vector under system is:

${\stackrel{\→}{a}}_{\mathrm{pi}}=c_e^{\mathrm{pi}}\·{\stackrel{\→}{a}}_e$

Wherein,For the transition matrix of inertial platform hexahedron and geographic coordinate system,For star simulator emergent ray Unit vector under geographic coordinate system, i=1,2,3 ... n.

If the alignment error matrix of star sensor measurement coordinate system isThen

${\stackrel{\→}{a}}_{\mathrm{si}}=c_s^p{\stackrel{\→}{a}}_{\mathrm{pi}}=c_p^s{c}_e^{\mathrm{pi}}{\stackrel{\→}{a}}_e$

Wherein i=1,2,3 ... n, i are each measurement position sequence number.

N measurement data is carried out least square process, because star sensor is solid with inertial platform hexahedron coordinate basis Connection, therefore no matter inertial platform is in which kind of attitude is constant value, so that

${\left[\begin{array}{cccc}{\stackrel{\→}{a}}_{s1}& {\stackrel{\→}{a}}_{s2}& ...& {\stackrel{\→}{a}}_{\mathrm{sn}}\end{array}\right]}_{3\×n}=c_p^s{\left[\begin{array}{cccc}{\stackrel{\→}{a}}_{p1}& {\stackrel{\→}{a}}_{p2}& ...& {\stackrel{\→}{a}}_{\mathrm{pn}}\end{array}\right]}_{3\×n}$

If ${\left[\begin{array}{cccc}{\stackrel{\→}{a}}_{s1}& {\stackrel{\→}{a}}_{s2}& ...& {\stackrel{\→}{a}}_{\mathrm{sn}}\end{array}\right]}_{3\×n}=a_s,{\left[\begin{array}{cccc}{\stackrel{\→}{a}}_{p1}& {\stackrel{\→}{a}}_{p2}& ...& {\stackrel{\→}{a}}_{\mathrm{pn}}\end{array}\right]}_{3\×n}=a_p,$ Then

$a_s=c_p^s{a}_p$

Therefore, can be drawn by method of least square, the alignment error matrix of star sensor is

$c_p^s=a_s{a}_p^t{\left(a_p{a}_p^t\right)}^{-1}$

Above formula is the calibration result of star sensor measurement coordinate system alignment error on inertial platform,It is and install The matrix of error represents.

Unspecified part of the present invention belongs to general knowledge as well known to those skilled in the art.

Claims (1)

1. a kind of mounting error calibration method being applied to the built-in star sensor of inertial platform is it is characterised in that step is as follows:

(1) adjust inertial platform pedestal orientation and star simulator support makes the directional light of star simulator outgoing image in star sensitivity Device field of view center, described star simulator is used for simulating fixed star source of parallel light indoors, method particularly includes:

By formula

${\stackrel{\→}{a}}_e=\left(\begin{array}{c}\cos e_{s}cos{\mathrm{\σ}}_s\\ {\mathrm{sine}}_s\\ {\mathrm{cose}}_s{\mathrm{sin\σ}}_s\end{array}\right)$

Calculate unit vector under local geographic coordinate system for the star simulator emergent rayWherein e_sAnd σ_sIt is respectively optics warp Latitude instrument measures star simulator outgoing directional light with respect to the angle of site of local geographic coordinate system and azimuth；

(2) micrometer instrument is utilized to demarcate star simulator outgoing directional light with respect to the angle of site of local geographic coordinate system and orientation Angle, calculates unit vector under local geographic coordinate system for the star simulator emergent ray；

(3) keep star simulator position and attitude constant, the attitude of adjustment inertial platform, so that star simulator emergent ray is imaged in Star sensor difference coordinate points, record each imager coordinate, calculate star simulator emergent ray and survey in current star sensor Unit vector under amount coordinate system, particularly as follows:

${\stackrel{\→}{a}}_{si}=\left(\begin{array}{c}\frac{-x_i}{\sqrt{x_i^2+y_i^2+f^2}}\\ \frac{-y_i}{\sqrt{x_i^2+y_i^2+f^2}}\\ \frac{f}{\sqrt{x_i^2+y_i^2+f^2}}\end{array}\right)$

Wherein, x_iAnd y_iIt is respectively the length away from star sensor zero for the punctate opacity of the cornea coordinate, f is star sensor focal length, i=1,2, 3…n；

(4) measure the current attitude of inertial platform with two micrometer instruments, and calculate inertial platform hexahedron and local ground The transition matrix of reason coordinate system, described two micrometer instruments are the first micrometer instrument and the second micrometer instrument；Described meter Calculate the transition matrix of inertial platform hexahedron and local geographic coordinate system, method particularly includes:

By formula

$c_e^{pi}=\left(\begin{array}{ccc}{c}_{11}& c_{12}& c_{13}\\ c_{21}& c_{22}& c_{23}\\ c_{31}& c_{32}& c_{33}\end{array}\right)$

Calculate the transition matrix of inertial platform hexahedron and local geographic coordinate systemWherein:

c₁₁=cose_i1cosσ_i1；

c₁₂=sine_i1；

c₁₃=cose_i1sinσ_i1；

c₂₁=cose_i1sine_i2sinσ_i1-sine_i1cose_i2sinσ_i2；

c₂₂=cose_i1cose_i2sin(σ_i2-σ_i1)；

c₂₃=sine_i1cose_i2cosσ_i1-cose_i1sine_i2cosσ_i2；

c₃₁=cose_i2cosσ_i2；

c₃₂=sine_i2；

c₃₃=cose_i2sinσ_i2；

e_i1And σ_i1It is respectively the first micrometer instrument measurement inertial platform hexahedron y_pioz_piPlane normal, i.e. x_piAxle with respect to work as The angle of site of ground geographic coordinate system and azimuth, e_i2And σ_i2It is respectively the second micrometer instrument measurement inertial platform hexahedron x_pioy_piPlane normal, i.e. z_piAxle is with respect to the angle of site of local geographic coordinate system and azimuth；

(5) result of calculation according to step (2)～step (4), calculates the installation matrix of star sensor using method of least square, It is the alignment error of star sensor, described calculate star sensor using method of least square matrix is installed method particularly includes:

By formula

$c_p^s=a_s{a}_p^t{\left(a_p{a}_p^t\right)}^{-1}$

Calculate the transition matrix between star sensor measurement coordinate system and inertial platform coordinate systemWherein, a_sFor star sensor The matrix of measurement data construction, a_pFor the matrix of the projection construction in inertial platform coordinate system for the star simulator vector, make As follows:

$a_s={\left[\begin{array}{cccc}{\stackrel{\→}{a}}_{s1}& {\stackrel{\→}{a}}_{s2}& ...& {\stackrel{\→}{a}}_{sn}\end{array}\right]}_{3\×n},a_p={\left[\begin{array}{cccc}{\stackrel{\→}{a}}_{p1}& {\stackrel{\→}{a}}_{p2}& ...& {\stackrel{\→}{a}}_{pn}\end{array}\right]}_{3\×n}$

Wherein,For Unit Vector under current star sensor measurement coordinate system for the star simulator emergent ray Amount,For projection vector under inertial platform coordinate system for the star simulator vector；

Projection vector under inertial platform coordinate system for the described star simulator vector particularly as follows:

${\stackrel{\→}{a}}_{pi}=c_e^{pi}\·{\stackrel{\→}{a}}_e$

In formula,For the transition matrix of inertial platform hexahedron and local geographic coordinate system,Exist for star simulator emergent ray Unit vector under local geographic coordinate system, i=1,2,3 ... n.