CN114509066A - High-speed target astronomical positioning method - Google Patents

High-speed target astronomical positioning method Download PDF

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CN114509066A
CN114509066A CN202210109594.4A CN202210109594A CN114509066A CN 114509066 A CN114509066 A CN 114509066A CN 202210109594 A CN202210109594 A CN 202210109594A CN 114509066 A CN114509066 A CN 114509066A
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target
observation camera
astronomical positioning
observation
attitude
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CN114509066B (en
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李强
韩维强
傅景能
邓超
张辉
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Institute of Optics and Electronics of CAS
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/02—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by astronomical means
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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Abstract

The invention discloses a high-speed target astronomical positioning method, which comprises the steps of shooting a series of star maps by an observation camera in a staring imaging mode, calculating an attitude matrix of the camera through star point extraction and star map matching, and calculating celestial coordinates of a target by combining the coordinate position of the target on a camera detector plane. Calibrating before a task, and calibrating distortion, luminosity and an installation matrix of an optical system of an observation camera; detecting a high-speed target by adopting a full-area exposure mode; adjusting the posture of an observation camera to ensure that the high-speed target is in the central area of the view field; the zonal exposure setting ensures that fixed stars and targets have high-center extraction precision; observing astronomical attitude determination of the camera; and finally, resolving the celestial coordinates of the observation target by adopting an astronomical positioning basic equation. The invention avoids the lineation and dispersion of fixed stars and high-speed targets in different motion modes on the image surface, and the observation camera can realize the functions of monitoring the high-speed targets, fixing the attitude of astronomy and positioning the astronomy of the high-speed targets at the same time.

Description

High-speed target astronomical positioning method
Technical Field
The invention belongs to the field of space precision measurement, relates to image data processing and astronomical positioning of a high-speed moving target under a fixed star background, and particularly relates to an astronomical positioning method of the high-speed target.
Background
The astronomical observation can realize the positioning of the target by using two modes of shafting positioning and astronomical positioning. The astronomical positioning method comprises the steps of shooting a series of star maps by an observation camera in a staring imaging mode, carrying out star point extraction and star map matching, calculating to obtain a posture matrix of the camera, and then combining a coordinate position of a target on a camera detector plane to obtain position information of the target relative to a fixed star. Compared with a shafting positioning method, the astronomical positioning has relatively low requirements on platform attitude control and visual axis pointing accuracy, and the attitude of the observation camera can be obtained in real time by utilizing fixed star matching and attitude calculation, so that the target is ensured to have higher positioning accuracy. The orbit parameters of the target can be determined by utilizing the astronomical positioning sequence information of the target and solving by a least square method. The positioning accuracy of the target directly affects the orbit determination accuracy, so that it is necessary to optimize the detection system of the target to realize high-accuracy astronomical positioning.
The centroid extraction errors of the target and the fixed stars determine the target astronomical positioning accuracy, but for a high-speed target, such as an angular speed of the target 10 degrees/s relative to the background of the fixed stars, due to different movement modes of the fixed stars and the high-speed target on an image surface, when the target is tracked and observed, the fixed stars scribe and disperse on the image surface, the star centroid extraction accuracy is seriously reduced, and the astronomical positioning accuracy is influenced. Especially, in the case that the size of an observation target is smaller and smaller, the relative speed is larger and larger, and the target needs to be exposed for a long time, if the same exposure time is adopted in the whole image, the marking of the fixed star cannot be avoided.
Due to the large difference between the high-speed target and the star motion mode, the problem cannot be solved by optimizing the whole-area exposure time. The existing method comprises the steps of adopting an alternate image frame long-short exposure mode for a target and a fixed star, avoiding the fixed star from marking lines and dispersing and observing a high-speed target at the same time, but because the observation data of the fixed star and the high-speed target are not at the same moment, even though motion compensation is carried out, the influence on the astronomical positioning precision is inevitable. In addition, the target observation camera and the star sensor are adopted for combined observation, so that firstly, the complexity of design is increased, and the principle of design reliability of an electronic system is violated; and secondly, calibrating the installation relation of the observation camera and the star sensor.
Disclosure of Invention
The purpose of the invention is: aiming at the problems of astronomical positioning of the high-speed target, the astronomical positioning method of the high-speed target with low cost, high reliability and minimized electronic system is provided. The observation camera can realize the astronomical positioning function of monitoring the target, positioning the attitude of the observation camera and positioning the high-speed target at the same time.
The technical scheme adopted by the invention is as follows: a high-speed target astronomical positioning method comprises the following steps:
step 1, modeling of target observation system
1.1 target measurement modeling
Basic equation of target astronomical positioning
H(X,Y)＝MICwT-vT (6)
Wherein, the influence factor X of the target astronomical positioning is (alpha, delta, phi, X)T,yT,xo,yo,f)TThe astronomical positioning result is that the right ascension and the declination under the target celestial coordinates are respectively Y ═ alpha (alpha)T,δT)T；
The attitude angles of the observation camera are (alpha, delta, phi), alpha, delta and phi are respectively visual axis pointing right ascension, visual axis pointing declination and roll angle, wherein the visual axis pointing right ascension alpha is OZCAxis in XIOZIProjection on plane and OXIAngle of axis according to OXIMetering in the counterclockwise direction from the axis; declination delta of visual axis orientation is OZCAxis in XIOZIThe included angle of the projection on the plane is measured in the counterclockwise direction from the projection; the roll angle phi being OZIAxis in XCOZCProjection on plane and OYCThe included angle of the axes; measuring clockwise from projection, and obtaining the coordinate system (namely C system) of the observation camera through three times of conversion of the equatorial inertial system (namely I system) according to the definition of the attitude angle, wherein the coordinate system is firstly measured around OZIRotation of the shaft
Figure BDA0003494714230000021
Make OXCThe axis is vertical to the meridian plane; second, re-rotation of OXCRotating shaft
Figure BDA0003494714230000022
So that OZCAnd OZIOverlapping; third, OZ after two previous rotationsCWhen the axis is rotated phi, the system I is overlapped with the system C, and the attitude transformation matrix from the system C to the system I can be obtained:
Figure BDA0003494714230000023
wherein the content of the first and second substances,
Figure BDA0003494714230000024
and
Figure BDA0003494714230000025
basic transformation matrices representing rotation by theta around the OZ axis and OX axis, respectively, the transformation matrix row elements:
Figure BDA0003494714230000026
the coordinate of the target on the image surface is obtained by shooting through the observation camera and is (x)T,yT) The coordinate under the corresponding celestial coordinates, right ascension and declination are respectively (alpha)T,δT)，
Unit direction vector of target under equatorial inertial system of geocentric:
vT＝[cosαTcosδT sinαTcosδT sinδT]T
unit direction vector of the target under the observation camera coordinate system:
Figure BDA0003494714230000027
normalization parameters
Figure BDA0003494714230000031
(xo,yo) And f are respectively observation camera lightThe principal point and focal length of the optical system;
1.2 target astronomical positioning error analysis modeling
The influencing factors X of the target astronomical positioning error are divided into two types of random errors and system errors which are respectively (alpha, delta, phi and X)T,yT)TAnd (x)o,yo,f)TThe systematic error can be eliminated by the calibration before the task, the random error can not be eliminated, only the random error is considered, and then the influence factor X of the target astronomical positioning error is (alpha, delta, phi, X)T,yT)TThe optical system parameter is a known quantity;
to obtain the target astronomical positioning error, equation (6) is fully-differentially expanded with respect to (X, Y):
Figure BDA0003494714230000032
δX1,δX2and δ Y are with respect to X respectively1＝(α,δ,φ)T,X2＝(xT,yT)TAnd Y ═ αT,δT)TA small amount of (a);
wherein
Figure BDA0003494714230000033
Is H for X1Sensitivity matrix of (2):
Figure BDA0003494714230000034
wherein the content of the first and second substances,
Figure BDA0003494714230000035
Figure BDA0003494714230000036
Figure BDA0003494714230000037
Figure BDA0003494714230000038
Figure BDA0003494714230000039
Figure BDA00034947142300000310
Figure BDA00034947142300000311
Figure BDA00034947142300000312
Figure BDA00034947142300000313
Figure BDA00034947142300000314
is H for X2Sensitivity matrix of (2):
Figure BDA00034947142300000315
wherein the content of the first and second substances,
Figure BDA0003494714230000041
Figure BDA0003494714230000042
Figure BDA0003494714230000043
is the sensitivity matrix of H with respect to Y:
Figure BDA0003494714230000044
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003494714230000045
shifting the terms of equation (9) and multiplying with the respective transpose matrices:
Figure BDA0003494714230000046
by finding the expectation and assigning (X, Y) to the estimated value
Figure BDA0003494714230000047
The astronomical positioning error transfer formula can be obtained by the following shorthand:
Figure BDA0003494714230000048
wherein
Figure BDA0003494714230000049
And
Figure BDA00034947142300000410
respectively function H about X1,X2And a sensitivity matrix with Y around the estimated value,
Figure BDA00034947142300000411
and UY＝E[(δY)(δY)T]Are each about X1,X2And a small correlation matrix of Y,its diagonal elements reflect the level of noise;
then the transfer formula for the target astronomical positioning error:
Figure BDA00034947142300000412
the formula shows that the target astronomical positioning error mainly comes from two aspects, namely the attitude measurement error of an observation camera and the centroid extraction error of the target on an image surface;
the Abreu carries out qualitative analysis on an error source of the star sensor system, and generates a large amount of data through the orbit flight simulator to carry out numerical analysis, so that an empirical formula for evaluating the attitude measurement precision of the observation camera working in the star sensor mode is obtained:
the attitude errors of the visual axis pointing right ascension and the visual axis pointing declination are as follows:
Figure BDA00034947142300000413
the roll angle attitude error is expressed as:
Figure BDA00034947142300000414
wherein N is the number of stars used in the calculation; sigmaXYAngle measurement errors in the X and Y directions in image plane coordinates; thetasepIs the average angular distance of the stars involved in the calculation.
Under the condition of relevant parameter confirmation, the attitude measurement error of the observation camera depends on the star centroid extraction error, so that the centroid extraction errors of the target and the star on the image surface determine the target astronomical positioning accuracy;
step 2, camera exposure work modeling
2.1 full field Exposure mode
When the observation camera needs to be calibrated, or a 'stamping' working mode is adopted, or a target is guided to a field of view before astronomical positioning, a full-area exposure mode and Tb full-area exposure time are adopted;
2.2 divisional exposure mode
When the high-speed target is guided into a view field and astronomical positioning is carried out on the high-speed target, a subarea exposure mode is adopted, wherein Tb is background exposure time, T0-TN is target exposure time, and T0 is key observation target exposure time;
step 3, designing high-speed target astronomical positioning workflow
(a) Pre-mission calibration
Starting an observation camera, aligning the observation camera to a fixed star, starting a calibration mode before a task by adopting a full-area exposure mode, and calibrating the distortion, luminosity and an installation matrix of an optical system of the observation camera;
(b) target capture phase
Starting a target observation task, loading target characteristic parameters including track parameters, brightness, size and other information, calculating the target exposure time of an observation camera, enabling the observation camera to adopt a full-area exposure mode, and starting a high-speed target detection function;
(c) observation camera pose adjustment
After the high-speed target detection is finished, correcting the attitude offset of the observation camera to ensure that the key observation high-speed target is positioned near the central area of the field of view, and the observation camera still works in a guide mode;
(d) zoned exposure setting
Determining the distribution condition of the pointed fixed stars in the sky area and the rotation angular speed of the observation camera by the guidance information of the observation camera to the key targets, determining the exposure time and the size of a background area by an error analysis formula, determining a subarea exposure mode, and adaptively adjusting the exposure time and the exposure subareas along with the change of the targets and the background;
(e) astronomical attitude determination for observation camera
Extracting the coordinates on the background star pixel image surface, compensating the star position distortion, resolving the observation camera attitude angle (alpha, delta, phi) by local star map matching and adopting an astronomical positioning basic equationT；
(f) Target astronomical positioning
Extracting coordinates on the image plane of the high-speed target, compensating the position distortion of the target, and bringing the coordinates into the current frame to measure the attitude angle (alpha, delta, phi)TAnd calculating coordinates under the celestial coordinates by adopting an astronomical positioning basic equation.
Compared with the prior art, the invention has the advantages that:
(1) the observation camera can realize the functions of high-speed target monitoring, astronomical attitude determination and astronomical positioning of the high-speed target at the same moment;
(2) the invention overcomes the problem of marking caused by different motion modes of fixed stars and high-speed targets on the image surface, and gives consideration to the clear imaging of the high-speed targets and the fixed stars;
(3) the invention can automatically select the subarea exposure mode and the exposure parameters according to the target characteristics;
(4) the invention provides a high-dynamic high-speed target astronomical positioning method with low cost, high reliability and minimized electronic system.
Drawings
FIG. 1 shows the observation camera aperture imaging principle involved in the high-speed target astronomical localization method of the present invention.
FIG. 2 is a schematic diagram of a whole-area exposure working mode of an observation camera of the high-speed target astronomical positioning method of the present invention.
FIG. 3 is a schematic diagram of a local exposure operation mode of an observation camera of the high-speed target astronomical localization method of the present invention, wherein FIG. 3(a) is a single-target zonal exposure mode; FIG. 3(b) single target frame selection zone exposure mode; FIG. 3(c) multiple target banded segment exposure mode; FIG. 3(d) multiple target frame-selected partition exposure mode. Wherein Tb is the background exposure time, T0-TN is the target exposure time, and T0 is the focus observation target exposure time.
FIG. 4 is a high-speed target astronomical positioning work flow chart of a high-speed target astronomical positioning method of the present invention.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
The invention relates to a high-speed target astronomical positioning method, which comprises the steps of shooting a series of star maps by using an observation camera in a staring imaging mode, carrying out star point extraction and star map matching, calculating to obtain a posture matrix of the camera, and then combining a coordinate position of a target on a camera detector plane to obtain the position information of the target relative to a fixed star.
The invention relates to a high-speed target astronomical positioning method, which comprises the steps of calibrating before-task, calibrating distortion and luminosity of an optical system of an observation camera and an installation matrix; detecting the high-speed target in a full-view field by adopting a full-area exposure mode; correcting the posture of the observation camera to ensure that the high-speed target with key attention is in the central area of the field of view; the regional exposure setting ensures that fixed stars and targets have high center extraction precision; observing astronomical attitude determination of the camera; and finally, resolving the position under the coordinate system of the observation target celestial sphere by adopting an astronomical positioning basic equation, which specifically comprises the following steps:
step 1, modeling of target observation system
1.1 target measurement modeling
The attitude angle of the observation camera is (alpha, delta, phi), and alpha, delta and phi are respectively the visual axis pointing right ascension, the visual axis pointing declination and the roll angle. Wherein the right ascension α directed to the visual axis is OZCAxis in XIOZIProjection on plane and OXIAngle of axis according to OXIMetering in the counterclockwise direction from the axis; declination delta of visual axis orientation is OZCAxis in XIOZIThe included angle of the projection on the plane is measured in the counterclockwise direction from the projection; the roll angle phi being OZIAxis in XCOZCProjection on plane and OYCThe included angle of the axes is measured clockwise from the projection. And (4) obtaining an observation camera coordinate system (C system) by three times of conversion of the geocentric equatorial inertial system (I system) according to the definition of the attitude angle. First, winding around OZIRotation of the shaft
Figure BDA0003494714230000071
Make OXCThe axis is vertical to the meridian plane; second, re-rotation of OXCRotating shaft
Figure BDA0003494714230000072
So that OZCAnd OZIOverlapping; first, theThree times, OZ after two previous rotationsCWhen the shaft is rotated phi, I is coincident with C. Therefore, a posture conversion matrix from C-system to I-system can be obtained:
Figure BDA0003494714230000073
wherein the content of the first and second substances,
Figure BDA0003494714230000074
and
Figure BDA0003494714230000075
representing the basic transformation matrices for rotation by theta around the OZ axis and OX axis, respectively. Converting matrix row elements:
Figure BDA0003494714230000076
the coordinate of the target on the image surface is obtained by shooting through the observation camera and is (x)T,yT) The coordinate under the corresponding celestial coordinates, right ascension and declination are respectively (alpha)T,δT). According to the pinhole imaging principle (see fig. 1), ideally, the following calculation formula is satisfied:
vT＝MICwT (3)
wherein, the unit direction vector of the target under the geocentric equator inertia system is as follows:
vT＝[cosαTcosδT sinαTcosδT sinδT]T (4)
unit direction vector of the target under the observation camera coordinate system:
Figure BDA0003494714230000077
normalization parameters
Figure BDA0003494714230000078
(xo,yo) And f are the principal point and focal length of the observation camera optical system, respectively.
Finally, the basic equation for target astronomical localization can be expressed as:
H(X,Y)＝MICwT-vT (6)
wherein, the influence factor X of the target astronomical positioning is (alpha, delta, phi, X)T,yT,xo,yo,f)TThe astronomical positioning result is that the right ascension and the declination under the target celestial coordinates are respectively Y ═ alpha (alpha)T,δT)T。
1.2 target astronomical positioning error analysis modeling
The influencing factors X of the target astronomical positioning are divided into two types of random errors and system errors which are respectively (alpha, delta, phi and X)T,yT)TAnd (x)o,yo,f)TThe systematic error can be eliminated by the calibration before the task, and the random error can not be eliminated, so the invention only considers the random error, and then the influence factor X of the target astronomical positioning is (alpha, delta, phi, X)T,yT)TOptical system parameters are considered known quantities herein.
To obtain the target astronomical positioning error, equation (6) is fully-differentially expanded with respect to (X, Y):
Figure BDA0003494714230000081
δX1,δX2and δ Y are with respect to X respectively1＝(α,δ,φ)T,X2＝(xT,yT)TAnd Y ═ αT,δT)TA small amount of (a).
Wherein
Figure BDA0003494714230000082
Is H for X1Sensitivity matrix of (2):
Figure BDA0003494714230000083
wherein the content of the first and second substances,
Figure BDA0003494714230000084
Figure BDA0003494714230000085
Figure BDA0003494714230000086
Figure BDA0003494714230000087
Figure BDA0003494714230000088
Figure BDA0003494714230000089
Figure BDA00034947142300000810
Figure BDA00034947142300000811
Figure BDA00034947142300000812
Figure BDA00034947142300000813
is H for X2Sensitivity matrix of (2):
Figure BDA00034947142300000814
wherein the content of the first and second substances,
Figure BDA00034947142300000815
Figure BDA0003494714230000091
Figure BDA0003494714230000092
is the sensitivity matrix of H with respect to Y:
Figure BDA0003494714230000093
wherein the content of the first and second substances,
Figure BDA0003494714230000094
transpose equation (9) and multiply by the respective transpose matrices:
Figure BDA0003494714230000095
by finding the expectation and assigning (X, Y) to the estimated value
Figure BDA0003494714230000096
The astronomical positioning error transfer formula can be obtained by the following shorthand:
Figure BDA0003494714230000097
wherein
Figure BDA0003494714230000098
And
Figure BDA0003494714230000099
respectively function H about X1,X2And a sensitivity matrix with Y around the estimated value,
Figure BDA00034947142300000910
and UY＝E[(δY)(δY)T]Are each about X1,X2And Y, whose diagonal elements reflect the level of noise.
Then the transfer formula for the target astronomical positioning error:
Figure BDA00034947142300000911
the above formula shows that the target astronomical positioning error mainly comes from two aspects, namely the attitude measurement error of the observation camera and the centroid extraction error of the target on the image surface.
Abreu qualitatively analyzes an error source of the star sensor system, and generates a large amount of data through the orbit flight simulator to perform numerical analysis, so that an empirical formula for evaluating the attitude measurement precision of the observation camera working in the star sensor mode is obtained
The errors of the right ascension and declination of the visual axis direction are as follows:
Figure BDA00034947142300000912
the roll angle attitude error is expressed as:
Figure BDA00034947142300000913
wherein N is the number of stars used in the calculation; sigmaXYAngle measurement errors in the X and Y directions in image plane coordinates; thetasepIs the average angular distance of the stars involved in the calculation.
In the case of relevant parameter confirmation, the attitude measurement error of the observation camera depends on the star centroid extraction error, so that the centroid extraction errors of the target and the star on the image surface determine the target astronomical positioning accuracy.
Step 2, camera exposure work modeling
2.1 full field Exposure mode
When in-orbit calibration of the observation camera is needed, or a 'stamping' working mode is adopted, or a target is guided to the front of the field of view astronomical positioning, a full-area exposure mode is adopted (see figure 2). Tb full field exposure time.
2.2 divisional exposure mode
When the high-speed target is guided into the view field and astronomical positioning is carried out on the high-speed target, a subarea exposure mode (see figure 3) is adopted, wherein Tb is background exposure time, T0-TN are target exposure time, and T0 is important observation target exposure time.
Step 3, designing high-speed target astronomical positioning workflow
(a) Pre-mission calibration
Starting an observation camera, aligning the observation camera to a fixed star, starting a calibration mode before a task by adopting a full-area exposure mode, and calibrating the distortion, luminosity and an installation matrix of an optical system of the observation camera;
(b) target capture
Starting a target observation task, loading target characteristic parameters including track parameters, brightness, size and other information, calculating the target exposure time of an observation camera, enabling the observation camera to adopt a full-area exposure mode, and starting a high-speed target detection function;
(c) observation camera pose adjustment
After the target detection is finished, correcting the attitude offset of the observation camera to ensure that the key observation high-speed target is positioned near the central area of the field of view, and the observation camera still works in a guide mode;
(d) zoned exposure setting
Determining the distribution situation of a sky region pointing to a fixed star and the rotation angular speed of an observation camera by the guidance information of the observation camera to a key target, determining the exposure time and the size of a background region by an error analysis formula (14), determining a subarea exposure mode (see figure 3), and adaptively adjusting the exposure time and the exposure subareas along with the change of the target and the background;
(e) astronomical attitude determination for observation camera
Extracting the coordinates on the background star pixel image surface, compensating the star position distortion, adopting an astronomical positioning basic equation (6) to solve the attitude angles (alpha, delta, phi) of the observation camera through local star map matchingT；
(f) High speed target astronomical positioning
Extracting coordinates on the image plane of the high-speed target, compensating the position distortion of the target, and bringing the coordinates into the current frame to measure the attitude angle (alpha, delta, phi)TAnd calculating coordinates under the celestial coordinates by adopting an astronomical positioning basic equation (6).

Claims (1)

1. A high-speed target astronomical positioning method is characterized by comprising the following steps:
step 1, modeling of target observation system
1.1 target measurement modeling
Basic equation of target astronomical positioning
H(X,Y)＝MICwT-vT (6)
Wherein, the influence factor X of the target astronomical positioning is (alpha, delta, phi, X)T,yT,xo,yo,f)TThe astronomical positioning result is that the right ascension and the declination under the target celestial coordinates are respectively Y ═ alpha (alpha)T,δT)T；
The attitude angles of the observation camera are (alpha, delta, phi), alpha, delta and phi are respectively visual axis pointing right ascension, visual axis pointing declination and roll angle, wherein the visual axis pointing right ascension alpha is OZCAxis in XIOZIProjection on plane and OXIAngle of axis according to OXIMetering in the counterclockwise direction from the axis; declination delta of visual axis orientation is OZCAxis in XIOZIThe included angle of the projection on the plane is measured in the counterclockwise direction from the projection; the roll angle phi being OZIAxis in XCOZCOn a planeProjection and OYCThe included angle of the axes; measuring clockwise from projection, and obtaining the coordinate system (namely C system) of the observation camera through three times of conversion of the equatorial inertial system (namely I system) according to the definition of the attitude angle, wherein the coordinate system is firstly measured around OZIRotation of the shaft
Figure FDA0003494714220000011
Make OXCThe axis is vertical to the meridian plane; second, re-rotation of OXCRotating shaft
Figure FDA0003494714220000012
So that OZCAnd OZIOverlapping; third, OZ after two previous rotationsCWhen the axis is rotated phi, the system I is overlapped with the system C, and the attitude transformation matrix from the system C to the system I can be obtained:
Figure FDA0003494714220000013
wherein the content of the first and second substances,
Figure FDA0003494714220000014
and
Figure FDA0003494714220000015
basic transformation matrices representing rotation by theta around the OZ axis and OX axis, respectively, the transformation matrix row elements:
Figure FDA0003494714220000016
the coordinate of the target on the image surface is obtained by shooting through the observation camera and is (x)T,yT) The coordinate under the corresponding celestial coordinates, right ascension and declination are respectively (alpha)T,δT)，
Unit direction vector of target under equatorial inertial system of geocentric:
vT＝[cosαTcosδT sinαTcosδT sinδT]T
unit direction vector of the target under the observation camera coordinate system:
Figure FDA0003494714220000021
normalization parameters
Figure FDA0003494714220000022
(xo,yo) And f is the principal point and focal length of the observation camera optical system, respectively;
1.2 target astronomical positioning error analysis modeling
The influencing factors X of the target astronomical positioning are divided into two types of random errors and system errors which are respectively (alpha, delta, phi and X)T,yT)TAnd (x)o,yo,f)TThe systematic error can be eliminated by pre-task calibration, the random error cannot be eliminated, only the random error is considered, and then the influence factor X of the target astronomical positioning is (alpha, delta, phi, X)T,yT)TThe optical system parameter is a known quantity;
to obtain the target astronomical positioning error, equation (6) is fully-differentially expanded with respect to (X, Y):
Figure FDA0003494714220000023
δX1,δX2and δ Y are with respect to X respectively1＝(α,δ,φ)T,X2＝(xT,yT)TAnd Y ═ αT,δT)TA small amount of (a);
wherein
Figure FDA0003494714220000024
Is H for X1Sensitivity matrix of (2):
Figure FDA0003494714220000025
wherein the content of the first and second substances,
Figure FDA0003494714220000026
Figure FDA0003494714220000027
Figure FDA0003494714220000028
Figure FDA0003494714220000029
Figure FDA00034947142200000210
Figure FDA00034947142200000211
Figure FDA00034947142200000212
Figure FDA00034947142200000213
Figure FDA00034947142200000214
Figure FDA00034947142200000215
is H for X2Sensitivity matrix of (2):
Figure FDA0003494714220000031
wherein the content of the first and second substances,
Figure FDA0003494714220000032
Figure FDA0003494714220000033
Figure FDA0003494714220000034
is the sensitivity matrix of H with respect to Y:
Figure FDA0003494714220000035
wherein the content of the first and second substances,
Figure FDA0003494714220000036
transpose equation (9) and multiply by the respective transpose matrices:
Figure FDA0003494714220000037
by finding the expectation and assigning (X, Y) to the estimated value
Figure FDA0003494714220000038
The astronomical positioning error transfer formula can be obtained by the following shorthand:
Figure FDA0003494714220000039
wherein
Figure FDA00034947142200000310
And
Figure FDA00034947142200000311
respectively function H about X1,X2And a sensitivity matrix with Y around the estimated value,
Figure FDA00034947142200000312
and UY＝E[(δY)(δY)T]Are each about X1,X2And a small correlation matrix of Y whose diagonal elements reflect the level of noise;
then the transfer formula for the target astronomical positioning error:
Figure FDA00034947142200000313
the formula shows that the target astronomical positioning error mainly comes from two aspects, namely the attitude measurement error of an observation camera and the centroid extraction error of the target on an image surface;
the Abreu carries out qualitative analysis on an error source of the star sensor system, and generates a large amount of data through the orbit flight simulator to carry out numerical analysis, so that an empirical formula for evaluating the attitude measurement precision of the observation camera working in the star sensor mode is obtained:
the attitude errors of the visual axis pointing right ascension and the visual axis pointing declination are as follows:
Figure FDA00034947142200000314
the roll angle attitude error is expressed as:
Figure FDA0003494714220000041
wherein N is the number of stars used in the calculation; sigmaXYAngle measurement errors in the X and Y directions in image plane coordinates; thetasepIs the average angular distance of the stars involved in the calculation;
under the condition of relevant parameter confirmation, the attitude measurement error of the observation camera depends on the star centroid extraction error, so that the centroid extraction errors of the target and the star on the image surface determine the target astronomical positioning accuracy;
step 2, camera exposure work modeling
2.1 full field Exposure mode
When the observation camera needs to be calibrated, or a 'stamping' working mode is adopted, or a target is guided to a field of view before astronomical positioning, a full-area exposure mode and Tb full-area exposure time are adopted;
2.2 divisional exposure mode
When the high-speed target is guided into a view field and astronomical positioning is carried out on the high-speed target, a subarea exposure mode is adopted, wherein Tb is background exposure time, T0-TN is target exposure time, and T0 is key observation target exposure time;
step 3, designing high-speed target astronomical positioning workflow
(a) Pre-mission calibration
Starting an observation camera, aligning the observation camera to a fixed star, starting a calibration mode before a task by adopting a full-area exposure mode, and calibrating the distortion, luminosity and an installation matrix of an optical system of the observation camera;
(b) target capture phase
Starting a target observation task, loading target characteristic parameters including track parameters, brightness, size and other information, calculating the target exposure time of an observation camera, enabling the observation camera to adopt a full-area exposure mode, and starting a high-speed target detection function;
(c) observation camera pose adjustment
After the high-speed target detection is finished, correcting the attitude offset of the observation camera to ensure that the key observation high-speed target is positioned near the central area of the field of view, and the observation camera still works in a guide mode;
(d) zoned exposure setting
Determining the distribution condition of the pointed fixed stars in the sky area and the rotation angular speed of the observation camera by the guidance information of the observation camera to the key targets, determining the exposure time and the size of a background area by an error analysis formula, determining a subarea exposure mode, and adaptively adjusting the exposure time and the exposure subareas along with the change of the targets and the background;
(e) astronomical attitude determination for observation camera
Extracting the coordinates on the background star pixel image surface, compensating the star position distortion, resolving the observation camera attitude angle (alpha, delta, phi) by local star map matching and adopting an astronomical positioning basic equationT；
(f) Target astronomical positioning
Extracting coordinates on the image plane of the high-speed target, compensating the position distortion of the target, and bringing the coordinates into the current frame to measure the attitude angle (alpha, delta, phi)TAnd calculating coordinates under the celestial coordinates by adopting an astronomical positioning basic equation.
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