CN113607188B - Theodolite cross-hair imaging-based multi-view-field star sensor calibration system and method - Google Patents

Theodolite cross-hair imaging-based multi-view-field star sensor calibration system and method Download PDF

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CN113607188B
CN113607188B CN202110883235.XA CN202110883235A CN113607188B CN 113607188 B CN113607188 B CN 113607188B CN 202110883235 A CN202110883235 A CN 202110883235A CN 113607188 B CN113607188 B CN 113607188B
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江洁
田凌峰
杨季三
张广军
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Beihang University
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Abstract

A theodolite cross-hair imaging-based multi-view-field star sensor calibration system and method comprises the following steps: modeling the process of imaging a cross hair of the theodolite on the star sensor image surface through a telescope objective lens and a star sensor lens; establishing a calibration track according to the field parameters, and acquiring cross images shot by the star sensor at different calibration positions and theodolite measurement angles; extracting a cross image into a cross point image coordinate, taking the cross point coordinate and a theodolite angle as input data, and constructing an optimization problem according to a cross imaging model to solve the rotation relation between a theodolite coordinate system and a view field coordinate system; establishing a rotation relation between theodolite coordinate systems through theodolite cross sight; and fusing the step-by-step results to obtain a multi-view-field star sensor structure parameter calibration result. The method keeps high calibration precision, uses a plurality of electronic theodolites to construct a calibration system, has free system configuration, and is applied to a multi-view-field star sensor system with large size, large weight and any view-field distribution structure.

Description

Theodolite cross-hair imaging-based multi-view-field star sensor calibration system and method
Technical Field
The invention belongs to the technical field of astronomical navigation, and provides a calibration system and method of a multi-view-field star sensor based on theodolite cross hair imaging.
Background
The measurement precision and the dynamic performance are two important performance indexes of the star sensor. The single-view field star sensor is limited by the size of a view field, the attitude measurement error of the single-view field star sensor around the direction of an optical axis is one order of magnitude higher than that of the other two axes, and the multi-view field star sensor can compensate the low-precision measurement axes of other view fields by using the measurement result of the high-precision measurement axes of one view field, so that the three-axis equal-precision attitude measurement is realized; because the field range of the multi-field star sensor is far larger than that of a single-field star sensor with the same specification, the number of observation stars of the multi-field star sensor is larger than that of the single-field star sensor, and the multi-field star sensor has higher integral attitude measurement precision; in addition, when the angular speed of the star sensor is increased, the detection sensitivity of stars and the like of each field of view is reduced differently, the number of observed stars is reduced, and the multi-field star sensor can realize the information fusion of star points of each field of view, and can still output effective postures as long as the total number of observed stars is more than three, so that the multi-field star sensor has higher dynamic performance than a single-field star sensor.
The key step of measuring the attitude of the multi-view-field star sensor system is to fuse star vectors in different view fields into a unified coordinate system. Due to the existence of processing and adjusting errors, the rotation relation between the coordinate systems of the fields of view of the multi-field-of-view star sensor, namely the structural parameters, deviates from the design values, and therefore the attitude measurement is inaccurate. Therefore, the accurate calibration of the structural parameters has important significance for ensuring the attitude measurement accuracy of the multi-view-field star sensor.
At present, three methods are commonly used for calibrating the structural parameters of the multi-field star sensor. The first method is an external field calibration method, namely, different fields of view of the multi-field-of-view star sensor are controlled to be exposed simultaneously, the rotation relation of each field of view coordinate system relative to a celestial coordinate system is respectively calculated, and the structural parameters of each field of view are obtained by using the celestial coordinate system as a middle coordinate system. The method is easily influenced by atmospheric refraction, so that the calibration result precision is poor, and the measurement precision requirement of the multi-view-field star sensor cannot be met. The second method is to calibrate the structural parameters by combining an electronic theodolite with a reference cube mirror, and is disclosed as a method for calibrating the optical axis pointing direction of a star sensor probe assembly (application No. CN2011104609570, published No. CN 102538825A). The method is characterized in that the reference cube mirror is fixedly connected to each field of view of a multi-field star sensor, the rotating relation between a field of view coordinate system and a prism coordinate system can be established when the square elements inside and outside the star sensor of each field of view are calibrated, the rotating relation between each prism coordinate system and a theodolite coordinate system can be established by using a plurality of theodolite sighting prisms, the rotating relation between each theodolite coordinate system can be established by the mutual sighting of the theodolite, and finally, the field of view structural parameters are obtained by fusion. The calibration precision of the method is limited by the processing precision of the reference cube mirror to a great extent, the processing precision of the reference cube mirror can only reach the angle classification level, and the calibration precision can not meet the use requirement of the multi-field star sensor when the structural parameter precision is higher. The third method uses a three-axis turntable to calibrate the structural parameters, and is disclosed in the patent of ' a calibration system and a calibration method of a multi-view field star sensor based on a three-axis turntable ' (application number CN2018113663006, publication number CN109459059A) '. However, the mounting size and the load capacity of a three-axis turntable are limited, the method is only suitable for calibrating a light and small multi-view-field star sensor system, the visual axis distribution of the multi-view-field star sensor also needs to have symmetry, and the method cannot be applied to the multi-view-field star sensor system with large volume, large weight or asymmetric visual axis distribution. Furthermore, applications such as patent application, application No. CN2010101884887, publication No.: CN 101858755A discloses a calibration method of a star sensor; application No.: CN2010105127866, publication No.: the three-probe star sensor pointing calibration method disclosed in CN 102032918A; application No.: CN2014102253866, publication no: CN104154928A discloses a method for calibrating installation errors of a built-in star sensor suitable for an inertial platform; application No.: CN2014103608057, publication no: CN105318891B discloses a calibration device for the installation error of a star sensor reference cube mirror; application No.: CN2018115226969, publication No.: CN 109506645A discloses a star sensor mounting matrix ground precision measurement method; application No.: CN2019107203476, publication No.: CN 110345970A discloses a method and a device for calibrating an optical navigation sensor; application No.: CN2019113583595, publication No.: the calibration method between the star sensor measurement coordinate system and the reference cubic mirror coordinate system disclosed in CN 111044077A, and the like, all use theodolite to calibrate the conversion relationship between the star sensor relevant parameters and the relevant coordinate system, but these methods all need to be used in combination with the reference cubic mirror, some methods also need to add additional reference sources, such as collimator tubes, high-precision rotating tables or calibration fields formed by calibration points, and the like, the calibration system is complicated to build, and the reference cubic mirror needs to be used to build the intermediate conversion coordinate system, the related coordinate systems are numerous, calibration errors are difficult to control in multiple times of coordinate system conversion, and the insufficient processing precision of the reference cubic mirror can also cause the precision reduction of the calibration result.
Disclosure of Invention
The invention aims to: in the existing multi-view field star sensor structure parameter calibration method, both the external field calibration method and the theodolite combined prism calibration method cannot provide a calibration result with high enough precision, and the calibration method based on the three-axis turntable can provide a high-precision calibration result but has strict requirements on the overall dimension, the overall weight and the visual axis structure of the multi-view field star sensor.
Aiming at the problems, the method provides a multi-view field star sensor structure parameter calibration method based on electronic theodolite cross hair imaging, the method uses a plurality of electronic theodolites to respectively correspond to each view field of the multi-view field star sensor, a luminous cross hair in each theodolite can be imaged on an image surface of the corresponding view field through an optical system, the rotation relation between a theodolite coordinate system and a view field coordinate system can be calibrated by establishing an imaging model and collecting images, the rotation relation between the theodolite coordinate systems is established by mutually aiming through the theodolites, and finally, the view field structure parameters are obtained through fusion. The calibration process is mainly based on the optical imaging principle, higher calibration precision is guaranteed, meanwhile, the used electronic theodolite is free in installation mode, and the size, the weight and the configuration of the multi-view-field star sensor are not limited.
The technical scheme of the invention is as follows:
the invention discloses a calibration system of a multi-view-field star sensor based on theodolite cross hair imaging, which comprises a marble platform (1), a multi-view-field star sensor (2), an electronic theodolite (3) and data acquisition equipment (4); the marble platform (1) is used for bearing all other equipment; the multi-view-field star sensor (2) is arranged on the marble platform (1), and the visual axis of each view field is parallel to the plane of the marble platform; the electronic theodolite (3) is placed in front of each view field of the multi-view-field star sensor, the optical axis of a telescope of the electronic theodolite is superposed with the view axes of the view fields, and the base of the electronic theodolite is fixed and then the support foot leveling theodolite is adjusted; the data acquisition equipment (4) is connected with the multi-view-field star sensor (2) and the theodolite (3) and is used for acquiring images of the multi-view-field star sensor (2) and measurement data of the theodolite (3).
The invention discloses a calibration method of a multi-view-field star sensor based on theodolite cross hair imaging, which adopts the calibration system and comprises the following steps:
firstly, modeling a theodolite cross hair in the imaging process of a star sensor image surface through a telescope objective and a star sensor lens;
establishing a calibration track, and collecting cross images shot by the star sensor at different calibration positions and theodolite measurement angles;
extracting a cross image into a cross point image coordinate by using an image processing method, preprocessing the acquired data, and constructing an optimization problem according to a cross imaging model to solve the rotation relation between a theodolite coordinate system and a view field coordinate system;
establishing a rotation relation between theodolite coordinate systems through theodolite mutual aiming;
and step five, fusing the step results to obtain a multi-view field star sensor structure parameter calibration result.
Further, the step one further comprises the following steps: when the theodolite telescope is stable at a certain position, the luminous cross hairs clearly image on an image surface through the telescope objective lens and the star sensor lens; the telescope optical axis direction vector under the view field coordinate system is determined by the horizontal angle and the vertical angle of the theodolite and the installation angle of the theodolite coordinate system and the view field coordinate system; the vector of the principal ray direction of the cross-hair cross point under the field-of-view coordinate system is determined by the image coordinate of the cross point and the star sensor imaging model; the two vectors are parallel to each other and in opposite directions.
Further, the second step further includes the following steps: firstly, adjusting the brightness of cross hairs and the focusing position of a telescope, and establishing a calibration track according to the field condition of a star sensor; and sequentially rotating the theodolite to each calibration position in the calibration track, collecting the star sensor images for multiple times and measuring the horizontal angle and the vertical angle of the theodolite for multiple times.
Further, the third step is furtherThe method comprises the following steps: averaging the horizontal angle and the vertical angle of the theodolite collected at each calibration position to obtain the accurate theodolite angle of the calibration position; extracting sub-pixel level coordinates of the intersection points of the collected star sensor images by using an image processing method, and averaging the coordinates of the intersection points belonging to the same calibration position to obtain accurate image coordinates of the intersection points of the calibration position; according to a theodolite cross hair imaging model, using a telescope optical axis direction vector vSAnd cross point chief ray direction vector wSThe difference is a residual function, and a minimum optimization problem is constructed for the rotational Euler angle theta of the theodolite coordinate system and the single-view field coordinate system1,θ2,θ3Solving, and constructing a minimal value optimization problem as follows:
Figure BDA0003193003300000041
where m is the total number of calibration positions, /)i＝(Hzi,Vi)TTheodolite angle, x, for the ith calibration positioni＝(xp,i,yp,i)TFor the coordinates of the intersection image at the ith calibration position, p ═ f, xc,yc,p1,p2,q1,q2)TIs the internal parameter of the star sensor, including the focal length f and the principal point (x)c,yc) Radial distortion factor (p)1,p2) And tangential distortion coefficient (q)1,q2) The residual function is expressed as
Figure BDA0003193003300000042
Wherein the content of the first and second substances,
Figure BDA0003193003300000043
and
Figure BDA0003193003300000044
the vectors v of the optical axis directions of the telescopes respectively corresponding to the ith calibration positionS,iAnd the ith labelPosition cross point chief ray direction vector wS,iScaling to z is a vector after 1 plane. Solving the obtained rotation Euler angle theta1,θ2,θ3Converted into a direction cosine matrix form and recorded as a view field number k
Figure BDA0003193003300000051
Further, the fourth step further includes the following steps: aiming cross hairs of the two theodolites at each other and recording the measurement angle to obtain the rotation relation of the coordinate systems of the two theodolites; mutually aiming all the theodolites in pairs to obtain the rotation relation between coordinate systems of all the theodolites, and recording the direction cosine matrix from the coordinate system of the theodolite No. k to the coordinate system of the theodolite No. l as
Figure BDA0003193003300000052
Further, the fifth step further includes the following steps: and fusing all the obtained rotation relations to obtain a multi-view-field star sensor structure parameter calibration result, wherein a direction cosine matrix from a k view field coordinate system to a l view field coordinate system is as follows:
Figure BDA0003193003300000053
the invention also applies the calibration method of the multi-view field star sensor based on the cross-hair imaging of the theodolite to the astronomical navigation device.
The technical scheme of the invention can realize the following beneficial technical effects:
the calibration method calibrates the rotation relation between the theodolite coordinate system and the view field coordinate system by using a cross-hair imaging mode, and the calibration precision of the optical imaging method is usually in the order of angular seconds and is far higher than that of a reference cube mirror method.
The calibration method is characterized in that the multi-view-field star sensor to be calibrated is arranged on a stable base, a calibration system is constructed by a plurality of electronic theodolites around the multi-view-field star sensor, a high-precision rotary table is not needed, the limitation of the high-precision rotary table on the size and the weight of a bearing object is removed, and the method can be applied to the multi-view-field star sensor system with large size and large weight.
The calibration method uses the electronic theodolite and a single star sensor to form the sub-calibration systems, the sub-calibration systems are independent from each other, the special properties such as symmetry and the like of the field distribution of the multi-field star sensor are not required, and the method can be applied to the multi-field star sensor system with any structure and any number of fields.
Drawings
FIG. 1 is a schematic structural diagram of a calibration system of a multi-field-of-view star sensor based on cross hair imaging of an electronic theodolite according to the present invention;
FIG. 2 is a theodolite telescope optical axis direction vector model;
FIG. 3 is an imaging model of a star sensor;
FIG. 4 is a cross hair image real shot local picture;
fig. 5 shows calibration trajectories of the theodolite-single-view sub-calibration system.
Detailed Description
As shown in fig. 1, a calibration system of a theodolite cross-hair imaging-based multi-view-field star sensor comprises a marble platform 1 for providing stable support, a multi-view-field star sensor 2 to be calibrated, a plurality of electronic theodolites 3 with auto-collimation function and data acquisition equipment 4. Marble platform 1 be used for bearing all the other all equipment, isolated external vibrations, marble platform 1 is arranged in to multi-view star sensor 2, each view field visual axis is parallel with the platform plane, theodolite 3 places before each view field of multi-view star sensor, its telescope optical axis and each view field visual axis coincidence, base position fixed back adjustment stabilizer blade flattening theodolite, data acquisition equipment 4 link to each other with multi-view star sensor 2 and theodolite 3 for gather multi-view star sensor 2's image and theodolite 3's measured data.
The invention uses the self luminous cross-hair of the theodolite as the reference source, combines the reference source and the measuring device into a whole, reduces the complexity of the construction of the calibration system, adopts a cross-hair imaging method in the calibration process, does not need to use a reference cube mirror to establish a middle conversion coordinate system, simplifies the coordinate system conversion process, and simultaneously reduces the large-scale leveling work of the equipment placed on the marble platform in the practical application because the marble platform has high flatness.
The invention discloses a calibration method of a multi-view-field star sensor based on theodolite cross hair imaging, which uses the system of the invention and comprises the following steps:
step one, modeling is carried out on the process that the cross hairs of the theodolite are imaged on the star sensor image surface through the telescope objective lens and the star sensor lens.
In the system, each theodolite and one of the fields of view of the multi-field star sensor form a sub-calibration system, and the sub-system is used for calibrating the rotation relationship between the theodolite and the corresponding field of view. When the telescope of the theodolite is stabilized at a certain position, the cross-hair lighted by the auto-collimation function is imaged on the star sensor image surface through the telescope objective lens and the star sensor lens, and the direction of the principal ray of the cross-hair cross point is coincided with the direction of the optical axis of the telescope. The horizontal angle, the vertical angle and the installation angle of the theodolite are combined, and the direction vector of the optical axis of the telescope can be calculated. And combining the image coordinates of the cross-hair cross point and the internal parameters of the star sensor to calculate the direction vector of the main ray of the cross point. The two vectors are parallel to each other and opposite in direction, and the two vectors are used as a central pivot to establish a cross hair imaging model.
Star sensor single view field coordinate system OS-XSYSZSAt the optical center of the lens corresponding to the field of view, XSAxis and YSThe axes being parallel to the grid direction of the image sensor, X, respectivelySThe axis pointing to the right of the image, YSThe axis pointing above the image, ZSThe axis points to the front of the lens along the direction of the optical axis of the lens. During the calibration process, all vectors are converted into the coordinate system for calculation.
As shown in FIG. 2, the vector v of the theodolite telescope in the direction of the optical axisTDirectly under the zero coordinate system of the theodolite. Zero coordinate systemOT-XTYTZTSecured to the base, Z thereofTOTXTThe plane being parallel to the local horizontal plane, YTThe axis extending in the local vertical direction downwards, ZTThe axis direction coincides with the telescope pointing direction when the horizontal angle is 0 degrees and the vertical angle is 90 degrees, XTThe axial direction is determined by the right hand rule. When the horizontal angle of the theodolite is Hz and the vertical angle is V, the zero coordinate system OT-XTYTZTDirection vector v of lower telescope optical axisTThe expression of (a) is:
Figure BDA0003193003300000071
suppose that three-axis Euler angles (YXZ rotation order) from the theodolite zero coordinate system to the star sensor single-view field measurement coordinate system are respectively theta1,θ2,θ3Then the direction cosine matrix corresponding to the conversion relation
Figure BDA0003193003300000072
The expression of (a) is:
Figure BDA0003193003300000073
according to the direction cosine matrix, the star sensor view field coordinate system OS-XSYSZSDirection vector v of lower telescope optical axisSThe expression of (a) is:
Figure BDA0003193003300000074
since the length of the direction vector is fixed to 1 and has substantially only 2 degrees of freedom, v is set for convenience of useSScaling to the plane of z ═ 1, the expression:
Figure BDA0003193003300000075
as shown in fig. 3, the relationship between the image coordinates of the cross-hair intersection and the direction vector of the principal ray of the intersection can be established according to the star sensor imaging model. The internal parameters of the star sensor used by the model comprise a focal length f and a principal point (x)c，yc) Coefficient of radial distortion p1，p2And tangential distortion coefficient q1，q2The calibration of the parameters is completed before the calibration of the structural parameters of the multi-view-field star sensor.
Cross point image coordinates (x)p，yp) The image coordinate system is established under an image coordinate system, the origin of the image coordinate system is positioned in the center of a pixel at the lower left corner of an image, the X axis and the Y axis are parallel to the grid direction of the image, the X axis points to the right of the image, and the Y axis points to the upper part of the image. Coordinate (x) of image plane coordinate system for correcting image distortion with origin located under image coordinate systemc，yc) Here, the X-axis and Y-axis directions are the same as the image coordinate system, and a length unit is used. Thus, the image plane coordinate (x) of the intersectionp1，yp1) Comprises the following steps:
xp1＝DX·(xp-xc)
yp1＝DY·(yp-yc)
where DX and DY are pixel lengths in X-axis and Y-axis directions, respectively.
From the image distortion model, the coordinates (x) on the actual image planep1，yp1) The corresponding distortion amounts (Δ x, Δ y) are:
Figure BDA0003193003300000083
Figure BDA0003193003300000084
wherein p is1，p2Is the radial distortion coefficient, q1，q2Is the tangential distortion coefficient. Then the undistorted image plane coordinate (x) of the intersection pointp2，yp2) Comprises the following steps:
xp2＝xp1-Δx
yp2＝yp2-Δy
constructing a direction vector w of a main ray of a cross point according to a small hole imaging model of a star sensorSComprises the following steps:
Figure BDA0003193003300000081
for convenient use, w isSAlso scaled to the z-1 plane, the expression:
Figure BDA0003193003300000082
and step two, establishing a calibration track, and collecting cross images shot by the star sensor at different calibration positions and theodolite measurement angles.
The auto-collimation cross hair on the theodolite reticle is lightened, the telescope is focused to infinity, and the brightness of the cross hair is adjusted, so that the brightest part of the cross hair image shot by the star sensor just cannot cause gray saturation, as shown in fig. 4. Manually adjusting the horizontal angle and the vertical angle of the theodolite to make the image coordinate of the cross point approximately coincide with the coordinate of the principal point, and recording the horizontal angle and the vertical angle (Hz) at the moment0,V0)。
Horizontal and vertical angles (Hz) recorded as described above0,V0) Centered, calibration trajectories spaced 1 ° apart within a 14 ° field of view were constructed, as shown in fig. 5. And adjusting the angle of the theodolite to a first calibration position, keeping the angle of the theodolite unchanged, controlling the star sensor to shoot 100 images, and simultaneously recording the horizontal angle and the vertical angle of the theodolite for 100 times. And after the images and the angles are recorded, controlling the theodolite to move to the next calibration position, and repeating the recording process until the data recording at the last calibration position is finished.
And step three, extracting the cross image into a cross point image coordinate by using an image processing method, preprocessing the acquired data, and constructing an optimization problem according to a cross imaging model to solve the rotation relation between the theodolite coordinate system and the view field coordinate system.
And (3) eliminating coarse measurement results by using a 3 sigma criterion for 100 groups of horizontal angles and vertical angles collected from each calibration position, and respectively averaging the rest horizontal angles and the rest vertical angles to obtain actual horizontal angles and actual vertical angles of the corresponding calibration positions. For the ith calibration position, note as (Hz)i,Vi)。
And processing images shot by all the star sensors by using a quadric surface fitting method to obtain the sub-pixel image coordinates of the cross-hair cross points. The method comprises traversing the whole image, searching pixel point with maximum gray value, and recording the coordinate (x) of the pixel0,y0) As pixel level coordinates of the intersection. Further, the gradient and Hessian matrix at the intersection pixel level coordinates are calculated using a first order differential operator and a second order differential operator. The first order differential operator and the second order differential operator are constructed according to the following formulas:
Figure BDA0003193003300000091
Figure BDA0003193003300000092
Figure BDA0003193003300000093
Figure BDA0003193003300000094
Figure BDA0003193003300000095
convolving the image f (x, y) by using the operator to obtain the first-order partial derivative g of the imagex(x,y),gy(x, y) and second partial derivative Hxx(x,y),Hxy(x,y),Hyy(x, y), the expression is:
Figure BDA0003193003300000101
Figure BDA0003193003300000102
Figure BDA0003193003300000103
Figure BDA0003193003300000104
Figure BDA0003193003300000105
further, an image gradient g and a Hessian matrix H at the pixel level coordinate of the cross point can be obtained, and the expression is as follows:
Figure BDA0003193003300000106
fitting the gray scale change condition in the cross point neighborhood into a quadric according to the gradient g and the Hessian matrix H, and calculating the deviation s between the maximum point of the quadric and the current point, wherein the calculation formula is as follows:
Figure BDA0003193003300000107
the maximum point of the quadric surface is (x)0+s1,y0+s2) Is denoted as (x)p,yp) This coordinate corresponds to the sub-pixel level coordinate of the cross-hair like intersection.
100 images shot at each calibration position are extractedAnd (4) eliminating coarse measurement results by using a 3 sigma criterion, and averaging the coordinates of all the rest cross points to obtain the accurate cross point coordinates of the corresponding calibration positions. For the ith calibration position, note (x)p,i,yp,i)。
According to the model in the step one, the vectors of the directions of the optical axes of the telescope corresponding to the horizontal angle and the vertical angle
Figure BDA0003193003300000108
Cross point chief ray direction vector corresponding to cross point coordinate
Figure BDA0003193003300000109
Are substantially the same vector. To be provided with
Figure BDA00031930033000001010
And
Figure BDA00031930033000001011
the difference is a residual function, and a minimum optimization problem is constructed for the rotational Euler angle theta of the theodolite coordinate system and the single-view field coordinate system1,θ2,θ3Solving, and constructing a minimal value optimization problem as follows:
Figure BDA00031930033000001012
where m is the total number of calibration positions, #i＝(Hzi,Vi)TTheodolite angle, x, for the ith calibration positioni＝(xp,i,yp,i)TFor the coordinates of the intersection image at the ith calibration position, p ═ f, xc,yc,p1,p2,q1,q2)TIs the internal parameter of the star sensor, including the focal length f and the principal point (x)c,yc) Radial distortion factor (p)1,p2) And tangential distortion coefficient (q)1,q2) The residual function expression is:
Figure BDA00031930033000001013
Figure BDA00031930033000001014
wherein the content of the first and second substances,
Figure BDA0003193003300000111
and
Figure BDA0003193003300000112
the vectors v of the optical axis directions of the telescopes respectively corresponding to the ith calibration positionS,iAnd ith calibration position cross point chief ray direction vector wS,iScaling to z is a vector after 1 plane.
And solving the optimization problem by using a Levenberg-Marquardt nonlinear least square method to obtain a rotation Euler angle between a theodolite coordinate system and a single-view field coordinate system. For convenient use, the Euler angle theta is rotated1,θ2,θ3Conversion into a directional cosine matrix
Figure BDA0003193003300000113
The expression is as follows:
Figure BDA0003193003300000114
the calibration process is carried out on each theodolite-single-view sub-calibration system, and the obtained direction cosine matrix is recorded as the field number k
Figure BDA0003193003300000115
And step four, establishing a rotation relation between theodolite coordinate systems through theodolite mutual aiming.
And (3) lightening the auto-collimation cross-shaped wires on the theodolite reticle, and focusing the telescopes to an infinite distance to enable the telescopes of the two theodolites to be approximately in opposite positions. Observing from the telescope of one theodolite, manually adjusting the horizontal angle and the vertical angle of the theodolite to align the cross image formed by the other theodolite with the center of a cross reticle on a reticle of the telescope of the theodolite. The same alignment is performed for viewing from the other theodolite telescope and the operation is repeated a number of times.
Keeping the angles of the theodolites unchanged, and measuring the horizontal angle and the vertical angle of the two theodolites by data acquisition equipment for 100 times respectively.
Two groups of data collected during the cross-sighting of the theodolite are subjected to 3 sigma criterion to eliminate coarse measurement results, the rest data are averaged, and the results are respectively recorded as (Hz)A,VA) And (Hz)B,VB). The angle which needs to rotate around the Y axis is converted from the coordinate system of the theodolite A to the coordinate system of the theodolite B
Figure BDA0003193003300000116
Comprises the following steps:
Figure BDA0003193003300000117
for convenience of use, directional cosine matrices are used
Figure BDA0003193003300000118
Expressing the conversion relation, the expression is:
Figure BDA0003193003300000119
mutually aiming all the theodolites in pairs to obtain the rotation relation between coordinate systems of all the theodolites, and recording the direction cosine matrix from the coordinate system of the theodolite No. k to the coordinate system of the theodolite No. l as
Figure BDA00031930033000001110
And step five, fusing the stepping results to obtain a multi-view-field star sensor structure parameter calibration result.
And fusing all the obtained rotation relations to obtain a multi-view-field star sensor structure parameter calibration result, wherein a direction cosine matrix from a k view field coordinate system to a l view field coordinate system is as follows:
Figure BDA0003193003300000121
effects of the invention
In order to show the calibration effect of the method, the method is applied to calibrate the structural parameters of the airborne high-dynamic star sensor system with three view fields. The system takes a central No. 1 view field as a main view field, and the finally obtained structural parameter form is a direction cosine matrix converted from a No. 1 view field coordinate system to other view field coordinate systems.
The calibration process of the theodolite-single-view sub-calibration system is shown below by taking the view field No. 1 as an example. The internal parameters of the star sensor of the view field are as follows:
Figure BDA0003193003300000122
the star sensor images and theodolite angles at 145 calibration positions are collected by a sub-calibration system consisting of a No. 1 view field and a corresponding theodolite, and the data after pretreatment are shown in the following table:
Figure BDA0003193003300000131
obtaining a direction cosine matrix from a theodolite coordinate system to a view field coordinate system in the sub-calibration system through optimization solution
Figure BDA0003193003300000132
Comprises the following steps:
Figure BDA0003193003300000133
the coordinate system and the corresponding of No. 2 field of view can be obtained by the same methodCalibration result of theodolite coordinate system
Figure BDA0003193003300000134
Comprises the following steps:
Figure BDA0003193003300000135
through 1 theodolite and 2 theodolite cross sights, it is:
Figure BDA0003193003300000136
calculating to obtain a direction cosine matrix from the coordinate system of the theodolite No. 1 to the coordinate system of the theodolite No. 2
Figure BDA0003193003300000137
Comprises the following steps:
Figure BDA0003193003300000138
furthermore, the direction cosine matrix from the No. 1 view field coordinate system to the No. 2 view field coordinate system
Figure BDA0003193003300000141
Comprises the following steps:
Figure BDA0003193003300000142
the same method can be used for solving the direction cosine matrix from the No. 1 view field coordinate system to the No. 3 view field coordinate system
Figure BDA0003193003300000143
Comprises the following steps:
Figure BDA0003193003300000144
and completing the calibration of the multi-view-field structure parameters of the airborne high-dynamic star sensor system.
Compared with the existing calibration method adopting the theodolite, the method does not need to use an additional reference source coordinate system and a reference cube mirror coordinate system, eliminates errors caused by multiple times of conversion of the coordinate system and errors caused by processing deviation of the reference cube mirror, and can ensure higher calibration precision. Compared with another common multi-view-field star sensor calibration method based on a three-axis turntable, the method adopts the theodolite which can be placed at will to construct the calibration system, removes the requirements of the high-precision three-axis turntable on the overall dimension, the whole weight and the view field distribution structure of the multi-view-field star sensor system when the calibration system is constructed, and can be applied to the multi-view-field star sensor system with large dimension, large weight and any view field distribution structure.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are merely illustrative of the principles of the invention, but that various changes and modifications may be made without departing from the spirit and scope of the invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (4)

1. A calibration method of a multi-view field star sensor based on theodolite cross hair imaging comprises a calibration system of the multi-view field star sensor based on theodolite cross hair imaging, wherein the system comprises a marble platform, the multi-view field star sensor, an electronic theodolite and data acquisition equipment; the marble platform is used for bearing all other equipment; the multi-view-field star sensor is arranged on the marble platform, and the visual axis of each view field is parallel to the plane of the marble platform; the electronic theodolite is placed in front of each view field of the multi-view-field star sensor, the optical axis of a telescope of the electronic theodolite is superposed with the view axis of each view field, and the base of the electronic theodolite is fixed and then the support foot leveling theodolite is adjusted; the data acquisition equipment is connected with the multi-view-field star sensor and the theodolite and used for acquiring images of the multi-view-field star sensor and measurement data of the theodolite, and the data acquisition equipment is characterized in that: the method comprises the following steps:
step one, modeling the process of imaging a cross hair of a theodolite on a star sensor image surface through a telescope objective and a star sensor lens:
star sensor single view field coordinate system OS-XSYSZSAt the optical center of the lens corresponding to the field of view, XSAxis and YSThe axes being parallel to the grid direction of the image sensor, X, respectivelySThe axis pointing to the right of the image, YSThe axis pointing above the image, ZSThe axis points to the front of the lens along the direction of the optical axis of the lens; in the calibration process, all vectors are converted into the coordinate system for calculation;
theodolite telescope optical axis direction vector vTDirectly establishing the coordinate system under a theodolite zero coordinate system; zero coordinate system OT-XTYTZTFixedly connected to the base, Z thereofTOTXTThe plane being parallel to the local horizontal plane, YTThe axis extending in the local vertical direction downwards, ZTThe axis direction coincides with the telescope pointing direction when the horizontal angle is 0 degrees and the vertical angle is 90 degrees, XTThe axial direction is determined by the right-hand rule; when the horizontal angle of the theodolite is Hz and the vertical angle is V, the zero coordinate system OT-XTYTZTDirection vector v of lower telescope optical axisTThe expression of (a) is:
Figure 39235DEST_PATH_IMAGE001
suppose that the three-axis Euler angles from the zero coordinate system of the theodolite to the single-view field measurement coordinate system of the star sensor are rotated, namely YXZ rotation sequences are respectively theta1,θ2,θ3Then the direction cosine matrix corresponding to the conversion relation is converted
Figure 350262DEST_PATH_IMAGE002
The expression of (a) is:
Figure 918647DEST_PATH_IMAGE003
according to the direction cosine matrix, a star sensor view field coordinate system OS-XSYSZSDirection vector v of lower telescope optical axisSThe expression of (c) is:
Figure 977607DEST_PATH_IMAGE004
since the length of the direction vector is fixed to 1 and has substantially only 2 degrees of freedom, v is set for convenience of useSScaling to the plane where z is 1, the expression is:
Figure 125692DEST_PATH_IMAGE005
establishing a relation between the image coordinates of the cross point of the cross hair and the direction vector of the principal ray of the cross point according to the star sensor imaging model; the internal parameters of the star sensor used by the model comprise a focal length f and a principal point (x)c，yc) Coefficient of radial distortion p1，p2And tangential distortion coefficient q1，q2The calibration of the parameters is completed before the calibration of the structural parameters of the multi-view-field star sensor is carried out;
cross point image coordinates (x)p，yp) The image coordinate system is established under an image coordinate system, the origin of the image coordinate system is positioned in the center of a pixel at the lower left corner of an image, an X axis and a Y axis are parallel to the grid direction of the image, the X axis points to the right of the image, and the Y axis points to the upper part of the image; coordinate (x) of image plane coordinate system for correcting image distortion with origin located under image coordinate systemc，yc) The X-axis and Y-axis directions are the same as the image coordinate system, and length units are used; thus, the image plane coordinate (x) of the intersectionp1，yp1) Comprises the following steps:
xp1＝DX·(xp-xc)
yp1＝DY·(yp-yc)
wherein DX and DY are pixel lengths in the X-axis and Y-axis directions, respectively;
image plane coordinates (x) of the intersection point according to the image distortion modelp1，yp1) The corresponding distortion amounts (Δ x, Δ y) are:
Figure 87963DEST_PATH_IMAGE006
wherein p is1，p2Is the radial distortion coefficient, q1，q2Is the tangential distortion coefficient; then the undistorted image plane coordinate (x) of the intersection pointp2，yp2) Comprises the following steps:
xp2＝xp1-Δx
yp2＝yp2-Δy
constructing a direction vector w of a principal ray of a cross point according to a small hole imaging model of a star sensorSComprises the following steps:
Figure 827249DEST_PATH_IMAGE007
will wSAlso scaled to the z-1 plane, the expression:
Figure 999604DEST_PATH_IMAGE008
establishing a calibration track, and collecting cross images shot by the star sensor at different calibration positions and theodolite measurement angles;
extracting the cross image into a cross point image coordinate by using an image processing method, preprocessing the acquired data, constructing an optimization problem according to a cross imaging model, and solving the rotation relation between a theodolite coordinate system and a view field coordinate system, wherein the step further comprises the following steps of:
removing coarse measurement results from the horizontal angle and the vertical angle collected at each calibration position by using a 3 sigma criterion, and respectively averaging the rest horizontal angle and the rest vertical angle to obtain actual horizontal angle and actual vertical angle of the corresponding calibration position; for the ith calibration position, note as (Hz)i,Vi)；
Processing images shot by all star sensors by using a quadric surface fitting method to obtain sub-pixel image coordinates of cross hair intersection points; the method first traverses the whole image, searches the pixel point with the maximum gray value, records the coordinate (x) of the pixel0,y0) Pixel-level coordinates as intersections; calculating the gradient and the Hessian matrix at the pixel-level coordinate of the intersection point by using a first order differential operator and a second order differential operator; the first order differential operator and the second order differential operator are constructed according to the following formulas:
Figure 466226DEST_PATH_IMAGE009
convolving the image f (x, y) by using the operator to obtain the first-order partial derivative g of the imagex(x,y),gy(x, y) and second partial derivative Hxx(x,y),Hxy(x,y),Hyy(x, y), the expression is:
Figure 797851DEST_PATH_IMAGE010
and further obtaining an image gradient g and a Hessian matrix H at the coordinate of the cross point pixel level, wherein the expression is as follows:
Figure 458770DEST_PATH_IMAGE011
fitting the gray scale change condition in the cross point neighborhood into a quadric according to the gradient g and the Hessian matrix H, and calculating the deviation s between the maximum point of the quadric and the current point, wherein the calculation formula is as follows:
Figure 118422DEST_PATH_IMAGE012
the maximum point of the quadric surface is (x)0+s1,y0+s2) Is denoted as (x)p,yp) The coordinates corresponding to sub-pixel level coordinates of the cross-hair like intersections;
for the cross point coordinates extracted from the image shot at each calibration position, eliminating the coarse measurement results by using a 3 sigma criterion, and averaging the coordinates of all the rest cross points to obtain the accurate cross point coordinates of the corresponding calibration position; for the ith calibration position, note as (x)p,i,yp,i)；
According to the model in the step one, the vectors of the directions of the optical axes of the telescope corresponding to the horizontal angle and the vertical angle
Figure 139467DEST_PATH_IMAGE013
Cross point chief ray direction vector corresponding to cross point coordinate
Figure 309286DEST_PATH_IMAGE014
Substantially the same vector; to be provided with
Figure 390375DEST_PATH_IMAGE015
And
Figure 537322DEST_PATH_IMAGE016
the difference is a residual function, and a minimum optimization problem is constructed for the rotational Euler angle theta of the theodolite coordinate system and the single-view field coordinate system1,θ2,θ3Solving, and constructing a minimal value optimization problem as follows:
Figure 378371DEST_PATH_IMAGE017
where m is the total number of calibration positions, #i＝(Hzi,Vi)TTheodolite angle, x, for the ith calibration positioni＝(xp,i,yp,i)TFor the coordinates of the intersection image of the i-th nominal position, p ═ f, xc,yc,p1,p2,q1,q2)TIs the internal parameter of the star sensor, including the focal length f and the principal point (x)c,yc) The residual function expression is:
Figure 153428DEST_PATH_IMAGE018
wherein the content of the first and second substances,
Figure 400825DEST_PATH_IMAGE019
and
Figure 362965DEST_PATH_IMAGE020
the vectors v of the optical axis directions of the telescopes respectively corresponding to the ith calibration positionS,iAnd ith calibration position cross point chief ray direction vector wS,iScaling to a vector after the z is 1 plane;
solving the optimization problem by using a Levenberg-Marquardt nonlinear least square method to obtain a rotation Euler angle between a theodolite coordinate system and a single-view field coordinate system; will rotate by an Euler angle theta1,θ2,θ3Conversion into a directional cosine matrix
Figure 663496DEST_PATH_IMAGE021
The expression is as follows:
Figure 512635DEST_PATH_IMAGE022
the calibration process is carried out on each theodolite-single-view sub-calibration system, and the obtained direction cosine matrix is recorded as the view field number k
Figure 935526DEST_PATH_IMAGE023
；
Step four, establishing a rotation relation between theodolite coordinate systems through theodolite cross sight: aiming cross hairs of the two theodolites at each other and recording the measurement angle to obtain the rotation relation of the coordinate systems of the two theodolites; mutually aiming all the theodolites in pairs to obtain the rotation relation between coordinate systems of all the theodolites, and recording the coordinate system of the theodolite with the number k to
Figure 165388DEST_PATH_IMAGE024
The direction cosine matrix of the theodolite coordinate system is
Figure 269610DEST_PATH_IMAGE025
；
And step five, fusing the stepping results to obtain a multi-view-field star sensor structure parameter calibration result.
2. The method for calibrating the multi-view-field star sensor based on the theodolite cross hair imaging as claimed in claim 1, wherein the method comprises the following steps: the second step further comprises the following steps: firstly, adjusting the brightness of cross hairs and the focusing position of a telescope, and establishing a calibration track according to the field condition of a star sensor; and sequentially rotating the theodolite to each calibration position in the calibration track, collecting the star sensor images for multiple times and measuring the horizontal angle and the vertical angle of the theodolite for multiple times.
3. The method for calibrating the multi-view-field star sensor based on the theodolite cross hair imaging as claimed in claim 1, wherein the method comprises the following steps: the fifth step further comprises the following steps: fusing all the obtained rotation relations to obtain a multi-view-field star sensor structure parameter calibration result from a k view field coordinate system to
Figure 956943DEST_PATH_IMAGE024
The direction cosine matrix of the field coordinate system is:
Figure DEST_PATH_IMAGE026
。
4. the calibration method for the multi-view-field star sensor based on theodolite cross hair imaging as claimed in any one of claims 1 to 3, the method is applied to astronomical navigation devices.
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